Modulated InGaAs/GaAs Quantum Dot Lasers · Modulated InGaAs/GaAs Quantum Dot Lasers vorgelegt von Diplom-Physiker Matthias Kuntz aus Berlin von der Fakultät II – Mathematik und

Modulated InGaAs/GaAs Quantum Dot Lasers

vorgelegt von

Diplom-Physiker

Matthias Kuntz aus Berlin

von der Fakultät II – Mathematik und Naturwissenschaften der Technischen Universität Berlin

zur Erlangung des akademischen Grades

Doktor der Naturwissenschaften - Dr. rer. nat. –

genehmigte Dissertation

Promotionsausschuss: Vorsitzender: Prof. Dr. E. Schöll Berichter / Gutachter: Prof. Dr. D. Bimberg Berichter / Gutachter: Prof. Dr. N. N. Ledentsov Tag der wissenschaftlichen Aussprache: 9.11.2005

Berlin 2006

D 83

Zusammenfassung In dieser Arbeit wurden die dynamischen Eigenschaften von InGaAs-Quantenpunkt-Lasern in drei verschiedenen Bauformen untersucht: als kantenemittierende Laserdioden, oberflächenemittierende Laserdioden sowie Zwei-Sektions-Kantenemitter für Modenkopplung. Kantenemittierende Quantenpunktlaser mit Emissionswellenlängen zwischen 1,1 und 1,3 µm wurden bezüglich ihrer epitaktischen Struktur und ihrer Prozessierung verbessert. Optimierte Laserdioden mit 15 Quantenpunktschichten, durchgeätzten Rippenwellenleiter und Oberseiten-Kontakten für schnelle Tastkopf-Kontaktierung und Bonding wurden hergestellt. Eine entsprechende Modellierung von Quantenpunkt-Kantenemittern wurde entwickelt, die eine Ersatzschaltkreis-Modellierung des Laserchips und des Submounts, eine quasi-statische Modellierung der aktiven Zone sowie eine dynamische Modellierung der aktiven Zone bei Laseroperation umfasst. Ein Relaxationszeit-Modell basierend auf gekoppelten Ratengleichungen sowie ein Mikrozustands-Modell wurden implementiert und für die Simulation der dynamischen Eigenschaften von Quantenpunktlasern verwendet. Simulationen mit Hilfe eines umfassenden Mikrozustandsmodells waren durch die zur Verfügung stehende Rechnerleistung begrenzt. Kleinsignalmessungen, spektral und zeitlich aufgelöste Messungen sowie digitale Modulation von Quantenpunkt-Lasern wurden durchgeführt, um die physikalischen Grundlagen der dynamischen Eigenschaften wie Modulationsbandbreite, Dämpfung, Einschaltverzögerung sowie spektraler Veränderungen zu beleuchten. Besonderes Augenmerk lag auf der Unterscheidung von intrinsischen, Quantenpunkt-inhärenten Effekten und Eigenschaften der die aktive Zone umgebenden Laserstruktur. Eines der Ziele meiner Arbeit war die Identifikation dieser intrinsischen Limitierungen des Quantenpunkt-Gewinnmediums. Der Vergleich von experimentellen Resultaten und entsprechenden Simulationen zeigt, dass die entscheidenden Mechanismen zur Limitierung des dynamischen Verhaltens zum einen die Reduktion des differentiellen Gewinns durch Auffüllung der Zustände der aktiven Zone und zum anderen die relativ langsame Transport- , Relaxations- und Einfangzeit von Ladungsträgern in der Barriereschicht, den Quantenfilmen und den Quantenpunkten sind. Modulationsbandbreiten bis zu 7 GHz wurden erreicht, welche nur schwach von der Zahl der Quantenpunktschichten abhingen. Augendiagrammmessungen mit Datenraten zwischen 2.5 GHz und 12 GHz wurden durchgeführt und zeigten symmetrische und offene Augenmessungen. Bitfehlerraten-Messungen mit 8 und 10 Gb/s Datenrate ergaben fehlerfreie Übertragung (Fehlerrate < 10-12) bei einer Empfängerleistung von 2 dBm und einer Wellenlänge von 1,3 µm. Um den Bereich der fehlerfreien Übertragung digital modulierter Quantenpunktlaser bei 10 Gb/s zu vergrössern (kleinere Empfängerleistung, kleinere elektrische Eingangsleistung), bedarf es einer Anhebung der Modulationsbandbreite auf 12 bis 15 GHz. Keine signifikante Verbesserung der Bandbreite durch p-Dotierung und Tunnelinjektion konnte von uns gefunden werden. Andere Wege zur Erhöhung der Bandbreite liegen in der vertikalen Kopplung von Quantenpunkten, der Verringerung der inhomogenen Verbreiterung, der Erhöhung der Quantenpunktdichte sowie der strukturellen Anpassung des die Quantenpunkte umgebenden Quantenfilms.

Quantenpunkt-Oberflächenemitter mit 1,1 µm Emissionswellenlänge wurden bezüglich ihrer Modulationsbandbreite in Abhängigkeit vom Kontakt-Layout und Aperturdurchmesser charakterisiert. Die aus Klein- und Grosssignalmessungen bestimmte Modulationsbandbreite lag zwischen 1 und 2 GHz. Die wesentlichen Begrenzungen für die Bandbreite sind der niedrige modale Gewinn und differentielle Gewinn des QP-Gewinnmediums, die grosse Ladungsträgerkapazität der QP-Region und die thermische Limitierung der Ausgangsleistung und Bandbreite. Zudem unterliegen (einmodige) Oberflächenemitter im verstärkten Maße den begrenzenden Effekten der Gewinnkompression. Quantenpunkt-Oberflächenemitter mit kleinen Aperturen sind aufgrund ihrer monomodigen Emission für die Datenübertragung sehr geeignet. Allerdings zeigen diese Bauelemente aufgrund der verstärkten Strompfad-Aufweitung eine kleinere RC-Bandbreite und Modulationsbandbreite. Basierend auf dem Design der kantenemittierenden Quantenpunkt-Laserdioden wurden Bauelemente für passive und hybride Modenkopplung prozessiert. Eine Gegenspannungs-Absorbersektion wurde durch ein Zwei-Kontakt-Layout realisiert. Die elektrische Isolierung zwischen Absorber- und Gewinnsektion wurde durch Durchätzen bzw. Ionenimplantation gewährleistet. Die Einbringung eines sättigbaren Absorbers mit Hilfe von Ionenimplantation durch die Facette bzw. Oberseite des Bauelements war nicht erfolgreich, da die Ionendosis nur unzureichend kontrolliert werden konnte. Bauelemente mit Längen zwischen 0,8 und 8 mm und entsprechenden Wiederholraten zwischen 5 und 50 GHz wurden mit verschiedenen Absorber-/Gewinnsektions-Verhältnissen realisiert und charakterisiert. Stabile passive Modenkopplung mit Fourier-limitierten Pulsen mit typischem Pulsbreite/Periodendauer-Verhältnis von 10-20 % wurde für Absorberspannungen zwischen -2 und -6 V gefunden. Hybride Modenkopplung wurde bei 20 GHz Wiederholrate realisiert und ergab eine Locking-Bandbreite von 100 MHz bei einer elektrischen Modulationsleistung von 25 dBm. Die Pulsbreite der passiven und hybriden Modenkopplung war durch die maximale angelegte Absorber-Gegenspannung, Gewinn- und Absorbersättigung begrenzt. Kürzere Pulse sollten durch eine Vergrösserung der QP-Schicht-Anzahl, höhere Absorberspannungen sowie eine Abstimmung der Absorberlänge möglich sein. Die Weiterentwicklung modulierter Quantenpunktlaser hängt von der wesentlichen Verbesserung der intrinsischen Quantenpunkt-Modulationseigenschaften ab. Die Entwicklung neuer Epitaxie-Konzepte für schnellere Quantenpunkt-Strukturen kann nur mit dem umfassenden Verständnis und der Modellierung der kompletten Quantenpunkt-Struktur einhergehen. Obwohl die notwendigen Elemente für die Modellierung von Quantenpunkt-Lasern in den letzten Jahren zusammengetragen wurden, existiert bisher kein vollständiges dynamisches und rechnertaugliches Modell, welches alle wesentlichen spektralen und elektronischen Eigenschaften von Quantenpunkten berücksichtigt. Daher werden Modellierung und Simulation zukünftig stärker in den Vordergrund rücken. Gleichzeitig müssen bekannte Sachverhalte wie die starke inhomogene Verbreiterung selbstorganisierter Quantenpunkte verstärkt angegangen werden, um das Potential null-dimensionalen Ladungsträger-Confinements voll auszuschöpfen.

Parts of this work have been published: 1 M. Kuntz, N.N. Ledentsov, D. Bimberg, A.R. Kovsh, V.M. Ustinov, A.E.

Zhukov, Yu.M. Shernyakov Spectrotemporal response of 1.3 µm quantum-dot lasers

Appl. Phys. Lett. 81, p. 3846 (2002)

2 M.G. Thompson, K.T. Tan, C. Marinelli, K.A. Williams, R.V. Penty, I. H. White, M. Kuntz, D. Ouyang, I.N. Kaiander, R.L. Sellin, N. Ledentsov, D. Bimberg, A.E. Zhukov, D. Kang, M.G. Blamire, F. Visinka, S. Jochum, S. Hansmann

18 GHz mode-locking of InGaAs quantum dot lasers at 1.3 µm Proc. of SPIE, Photonics Europe 5452, p. (2004)

3 M. Kuntz, G. Fiol, M. Laemmlin, N.N. Ledentsov, D. Bimberg, M.G.

Thompson, K.T. Tan, C. Marinelli, R.V. Penty, I.H. White, V.M. Ustinov, A.E. Zhukov, Yu.M. Shernyakov, A.R. Kovsh,

35 GHz mode-locking of 1.3 µm quantum dot lasers Appl. Phys. Lett. 85, p. 843 (2004)

4 M. Kuntz, G. Fiol, M. Laemmlin, N.N. Ledentsov, D. Bimberg, M.G. Thompson, K.T. Tan, C. Marinelli, R.V. Penty, I.H. White, M. van der Poel, D. Birkedal, J. Hvam, A.R. Kovsh, V.M. Ustinov

35 GHz passive mode-locking of InGaAs/GaAs quantum dot lasers at 1.3 µm with Fourier-limited pulses CLEO/IQEC and PhAST Technical Digest (OSA), C. G. Durfee and J. A. Squier (eds.) , p. CTuP21 (2004)

5 K.T. Tan, C. Marinelli, M.G. Thompson, A. Wonfor, R.L. Sellin, R.V. Penty,

Ian H. White, M. Kuntz, M. Lämmlin, N.N. Ledentsov, D. Bimberg, V.M. Ustinov, A.E. Zhukov, A.R. Kovsh

5 Gb/s elevated temperature data transmission using quantum dot lasers CLEO/IQEC and PhAST Technical Digest (OSA), C. G. Durfee and J. A. Squier (eds.) , p. CThB4 (2004)

6 M. Kuntz, G. Fiol, M. Lämmlin, D. Bimberg, M.G. Thompson, K.T. Tan, C. Marinelli, A. Wonfor, R. Sellin, R.V. Penty, I.H. White, V.M. Ustinov, A.E. Zhukov, Yu.M. Shernyakov, A.R. Kovsh, N.N. Ledentsov, C. Schubert, V. Marembert

Direct modulation and mode locking of 1.3 µm quantum dot lasers NJP (New Journal of Physics) 6, p. 181 (2004)

7 K.T. Tan, C. Marinelli, M.G. Thompson, A. Wonfor, M. Silver, R.L. Sellin, R.V. Penty, Ian H. White, M. Kuntz, M. Lämmlin, N.N. Ledentsov, D. Bimberg, A.E. Zhukov, V.M. Ustinov, A.R. Kovsh

High bit rate and elevated temperature data transmission using InGaAs quantum dot lasers IEEE Photonics Techn. Lett. 16, p. 1415 (2004)

8 M. Kuntz, D. Bimberg High Speed quantum dot lasers for novel photonic systems

Ext. Abstract Book on Taiwan Intern. Conf. on Nano Science and Technology, TICON , p. 38 (2004)

9 R.L. Sellin, D. Bimberg, V. Ustinov, N.N. Ledentsov, I. Kaiander, M. Kuntz, M. Lämmlin, K.T. Tan, C. Marinelli, M.G. Thompson, A. Wonfor, R.V. Penty, I.H. White, D. O'Brien, S.P. Hegarty, G. Huyet, J.G. McInerney, J.K. White

High-power ultra-fast single- and multi-mode quantum-dot lasers with superior beam profile Semiconductor News 13, p. 29 (2004)

10 R.L. Sellin, D. Bimberg, V. Ustinov, N.N. Ledentsov, I. Kaiander, M. Kuntz, M. Lämmlin, K.T. Tan, C. Marinelli, M.G. Thompson, A. Wonfor, R.V. Penty, I.H. White, D. O'Brien, S.P. Hegarty, G. Huyet, J.G. McInerney, J.K. White

High-power ultra-fast single- and multi-mode quantum-dot lasers with superior beam profile Proc. of SPIE’s Novel In-Plane Semiconductor Lasers III (Photonics West) 5365, p. 46 (2004)

11 M.G. Thompson, K.T. Tan, C. Marinelli, K.A. Williams, R.V. Penty, I.H. White,

M. Kuntz, D. Ouyang, D. Bimberg, V.M. Ustinov, A.E. Zhukov, A.R. Kovsh, N.N. Ledentsov, D.-J. Kang, M.G. Blamire

High-Q photonic-crystal nanocavity with self-assembled InGaAs quantum dots Technical Digest Intern. Symp. on Photonic and Electromagnetic Crystal Structures V PECS-V , p. 223 (2004)

12 M.G. Thompson, K.T. Tan, C. Marinelli, K.A. Williams, R.L. Sellin, R.V. Penty, I.H. White, M. Kuntz, M. Laemmlin, D. Ouyang, I.N. Kaiander, N.N. Ledentsov, D. Bimberg, V.M. Ustinov, A.E. Zhukov, A.R. Kovsh, F. Visinka, S. Jochum, S. Hansmann, D.-J. Kang,

Mode-locked quantum dot lasers for picosecond pulse generation Proc. of SPIE’s Novel In-Plane Semiconductor Lasers III (Photonics West) 5365, p. 107 (2004)

13 M.G. Thompson, K.T. Tan, C. Marinelli, K.A. Williams, R.L. Sellin, R.V.

Penty, I.H. White, M. Kuntz, D. Ouyang, I.N. Kaiander, N.N. Ledentsov, D. Bimberg, V.M. Ustinov, A.E. Zhukov, A.R. Kovsh, F. Visinka, S. Jochum, S. Hansmann, D.-J. Kang, M.G. Blamire

Mode-locking of InGaAs quantum dot lasers Proc. of SPIE’s Novel In-Plane Semiconductor Lasers III (Photonics West) 5452, p. 117 (2004)

14 M. Kuntz, G. Fiol, D. Bimberg Quantum dot lasers for high frequency systems

Technical Digest of OSA Topical Meetings: Optical Amplifiers and Their Applications Integrated Photonics Research, IPR , p. 3 pages (2004)

15 M.G. Thompson, K.T. Tan, C. Marinelli, K.A. Williams, R.V. Penty, I.H. White, M. Kuntz, D. Ouyang, D. Bimberg, V.M. Ustinov, A.E. Zhukov, A.R. Kovsh, N.N. Ledentsov, D.-J. Kang, M.G. Blamire

Transform-limited optical pulses from 18 GHz monolithic modelocked quantum dot lasers operating at ~ 1.3 µm Electr. Lett. 40, p. 346 (2004)

16 M. Kuntz, G. Fiol, M. Lämmlin, D. Bimberg, A.R. Kovsh, S.S. Mikhrin, A.V. Kozhukhov, N.N. Ledentsov, C. Schubert, V.M. Ustinov, A.E. Zhukov, Yu.M. Shernyakov, A. Jacob, and A. Umbach

10 Gb/s data modulation and 50 GHz mode locking using 1.3 µm InGaAs quantum dots lasers Proc. of 13th Int. Symp. Nanostructures: Physics and Technology, St Petersburg, Russia, 2005, Ioffe Physical Technical Institute , p. 79 (2005)

17 M. Kuntz, G. Fiol, M. Lämmlin, C. Schubert, A. Kovsh, A. Jacob, A. Umbach,

and D. Bimberg 10 Gb/s data modulation using 1.3 µm InGaAs quantum dots lasers

Electr. Lett. 41, No. 5, p. 48060 (2005)

18 M. Kuntz Nanophotonik – Nanostrukturen in der Kommunikationstechnologie

Jahrbuch der Berliner Wissenschaftlichen Gesellschaft , p. 273 (2005)

19 N.N. Ledentsov, A.R. Kovsh, V.A. Shchukin, S.S. Mikhrin, I.L. Krestnikov, A.V. Kozhukhov, L.Ya. Karachinsky, M.V. Maximov, I.I. Novikov, Yu.M. Shernyakov, I.P. Soshnikov, A.E. Zhukov, E.L. Portnoi, V.M. Ustinov, D.

Gerthsen, P. Battacharya, N.F. Zakharov, P. Werner, F. Hopfer, M. Kuntz, D. Bimberg

QP Lasers: Physics and Applications Semiconductor and Organic Optoelectronic Materials and Devices ed. By Chung-En Zah, Yi Luo, Shinji Tsuji, Proc. of SPIE, Vol. 5624, p. 335 (2005)

20 D. Bimberg, M. Kuntz, M. Lämmlin Quantum dot photonic devices for lightwave communication

Microelectronics J. , special issue: Low Dimensional Structures and Device Conference, (ed. M. Henini, I. Hernadez-Calderon) 36, p. 175 (2005)

21 D. Bimberg, M. Kuntz, M. Lämmlin Quantum dot photonic devices for lightwave communication

Applied Physics A 80, p. 1179 (2005)

9

Contents 0 Introduction ........................................................................................................11 1 QD laser design .................................................................................................16

1.1 Epitaxial structure of QD lasers, sample lists ..............................................16 1.2 Laser chip layout .........................................................................................20

1.2.1 Mesa definition and planarization.........................................................20 1.2.2 Contact definition .................................................................................22

1.3 High reflection coating.................................................................................23 1.4 Submount layout .........................................................................................23 1.5 Bonding.......................................................................................................25

2 Modeling of quantum dot edge emitters .............................................................27 2.1 Modeling of submount and laser chip..........................................................27

2.1.1 Submount ............................................................................................27 2.1.2 Laser chip ............................................................................................29

2.2 Modeling of intrinsic quantum dot lasers .....................................................36 2.2.1 Electronic band structure of modeled lasers ........................................38 2.2.2 Quasi-equilibrium model ......................................................................39 2.2.3 Relaxation time model (RT model).......................................................45 2.2.4 Simulation of QD laser cw operation....................................................50 2.2.5 Simulation of the large signal operation of QD lasers ..........................55 2.2.6 Simulation of the small signal operation of QD lasers..........................58 2.2.7 Limitation of the RT model, MEM model ..............................................67

3 Direct modulation of QD edge emitters ..............................................................73 3.1 Basic parameters of QD edge emitters .......................................................73

3.1.1 MOCVD grown 1.1 µm quantum dot lasers .........................................74 3.1.2 MBE grown 1.3 µm quantum dot lasers ...............................................75

3.2 Small signal operation.................................................................................83 3.2.1 S11 and S12 parameter measurements on 1.3 µm QD lasers ...............85 3.2.2 Limitations of modulation bandwidth - comparison to other groups .....92 3.2.3 Comparison to quantum well laser diodes ...........................................95

3.3 Large signal operation.................................................................................96 3.3.1 Relaxation oscillation measurements on 1.1 µm QD lasers.................97 3.3.2 Relaxation oscillation measurements on 1.3 µm QD lasers...............100 3.3.3 Digital modulation - eye diagrams of 1.3 µm QD lasers .....................102 3.3.4 Bit error rate measurements of 1.3 µm QD lasers .............................110

4 Direct modulation of 1.1 µm QD VCSELs ........................................................114 4.1 Structure, layout and static parameters.....................................................115 4.2 Small signal operation...............................................................................117

4.2.1 S11 parameter measurements............................................................117 4.2.2 S12 parameter measurements............................................................122

4.3 Large signal operation...............................................................................123 4.3.1 Streak camera measurements ...........................................................124

5 Short-pulse generation with QD lasers.............................................................129 5.1 Gain switching...........................................................................................129 5.2 Mode-locking.............................................................................................130

5.2.1 Passive mode-locking ........................................................................135 5.2.2 Hybrid mode-locking ..........................................................................140 5.2.3 Mode-locking limitations.....................................................................141 5.2.4 Ion-implanted section gap..................................................................144 5.2.5 Ion-implanted absorber section..........................................................145

10

6 Summary and outlook...................................................................................... 151 7 Nomenclature .................................................................................................. 153 8 Bibliography & Software .................................................................................. 155 9 Acknowledgement ........................................................................................... 165

11

0 Introduction Semiconductor laser diodes are the key component for a large number of technologies, among them fiber based communication, digital data storage, printing, material processing and display technology. Due to their high brightness, large efficiency, reliability, small foot print and low price they have superseded conventional light sources and light emitting diodes and enabled new applications. The victorious career of semiconductor laser diodes began with the invention of the double heterostructure (DHS) laser diode capable of room temperature operation in 1969 [1, 2]. One of the most important technological paradigm that led to the advent of the DHS laser diode is strain-free growth, i.e. only materials with almost identical lattice constant are grown on each other in order to have a defect free, coherent semiconductor structure. Suitable combinations of binary, ternary or even quaternary compounds based on InP, GaAs and GaSb can be found in diagrams like Fig. 1. GaxAl1-xAs has an almost x-independent lattice constant, as well as ternary compounds of GaInAs and AlInAs match perfectly with InP.

Fig. 1: Lattice parameter vs. energy gap (at room temperature) for various III–V compounds and their alloys [3] Whereas for the growth of optical confinement layers (waveguide) the paradigm still holds true, it changed for the carrier confinement and recombination zone (active

0 Introduction

12

zone). Quantum well (QW) lasers exploit lattice matched as well as strained quantum well layers. The introduction of strained layers allows the adjustment of the emission wavelength of the strained quantum well, depending on its thickness (a few nm) and composition. Still, the strained layer must not crack during growth, which puts a limit to the lattice mismatch allowed (typical a few %). Strained InGaAs QWs allow the emission wavelength of an AlGaAs-based laser to extend to longer wavelength, as well as strained InGaAs QWs on InP do. The latter combination, with an emission around 1.5 µm, is typically used for fiber transmission purposes, since the absorption minimum of standard quartz optical fibers lies in this range (Fig. 2).

Fig. 2: Fiber attenuation vs. wavelength for a standard single mode fiber [Corning® SMF-28™ CPC6, Corning Incorporated, 1998] Although InP based lasers up to now dominate the datacom laser market (1.3-1.6 µm), there is a twofold urge to extend the emission wavelength of GaAs based lasers into this region: First, GaAs is a factor 2 less expensive substrate for the fabrication of optoelectronic devices than InP. High-quality wafers up to 6” diameter are available. GaAs is already vastly employed for visible and near-IR emitters and thus provides a broader technological base. Second, nanostructuring (quantum dots and quantum wires) can be employed to extend the emission wavelength of GaAs based lasers further into the infrared region while at the same time the characteristics of the laser diode like threshold current density, temperature stability and modulation characteristics are drastically improved compared to QW lasers based on InP. Another challenge for future optoelectronic devices is their ability to be integrated with electronic circuits. Today, virtually all integrated electronic circuits are based on Si. Si, in contrast to GaAs and InP, is an indirect band gap material and therefore cannot be used for active devices like lasers in a straightforward way. Three different concepts for integration can be distinguished:

1) Purely Si based: A number of passive optoelectronic devices like waveguides, resonators and modulators have been fabricated on Si. Advantage of this technology is its compatibility with CMOS fabrication. Particularly successful is the Silicon-on-insulator (SOI) technology. Main drawback is the poor photoluminescence in Si, which might be overcome by quantum dots (e.g. Ge QD in Si, InGaAs QD on Si [4, 5])

0 Introduction

13

2) Hybrid devices with both Si and InP/GaAs based functional units: Optically active components are fabricated on an InP/GaAs material system and fused with the Si based components by wafer bonding etc. This gives maximum flexibility in design, but requires sophisticated processing and assembly.

3) Not Si-based: Devices, which are based on the InP or GaAs material system, comprising active and passive components which are monolithically integrated (e.g. transceiver module, i.e. laser + amplifier + optical modulator). This is the most mature technology, but also the most conventional one in the way that it does not address the problem of Si integration. In this context it is noteworthy that GaAs based electronic circuits (e.g. field effect transistors, FETs) are much faster than Si based ones. As soon as the main problem of an effective, easy-to-process insulation material on GaAs is solved, integration on GaAs might prove to be superior to Si.

Our work is focused on the third approach. Fig. 3 shows the compound roadmap of GaAs based lasers extending into the datacom wavelength range. Besides the growths of strained InGa(N)As QWs there is variety of InGaAs quantum dot structures (plain quantum dots, dots-in-a-well [DWELL] and dots grown on metamorphic buffers). For quantum dot structures, the paradigm of strain-free growth turns into its opposite: QDs only emerge from strongly strained semiconductor layers! In this work, devices based on growth schemes marked green in Fig. 3 were used, grown with either MOCVD or MBE.

InGaAs/InGaAs

QDs

InGaAs QDs InAs QDs InGaAs QWs

InGaNAsQWs

InGaNAsQDs

InGaNAsSbQWs

...

+ InGaAsQW + N

+ Sb

+ N

InAsSbQDs

+ Sb

+ Sb

In(Ga)As/GaAsN

QDs

1.3 µm

1.1 µm

1.5 µm

+ GaAsNQW

InGaAs/InGaAsmetamorphic QDs

+ InGaAsbuffer

InGaAs QDs /InGaP& InGaAs

templates

Fig. 3: Self-assembled InGaAs quantum dot laser roadmap, showing the extension of the QD laser emission to longer wavelength by various epitaxial methods, among them the dots-in-a-well structure and metamorphic buffer layers beneath the active region. The green boxes denote the technology used for the laser diodes presented in this work [courtesy R. Sellin]. Three-dimensional carrier confinement structures like quantum dots (or quantum boxes) promise a large material gain superior to all other semiconductor gain media architectures (quantum wells, quantum wires, bulk) due to their delta-function like density of states (DOS), assuming uniform quantum dots [6]. After a decade of research on pre-patterned three-dimensional carrier confinement structures yielding unsatisfyingly high threshold current densities the first Fabry-Perot injection laser based on self-assembled InGaAs/GaAs quantum dots was presented [7]. This laser had an emission wavelength of 940 nm and operated at 77 K. Since then, InGaAs/GaAs quantum dot lasers have considerably developed [8, 9] (for the latest review, see [10]):

0 Introduction

14

• Lasing wavelengths in the 1.3 µm spectral range, both for edge and surface

emitters using GaAs substrates [11, 12]. 1.5 µm emission wavelength of edge emitting lasers using metamorphic buffered substrates [13]

• Very low transparency current density (<6 A/cm2 per QD sheet) and internal losses (~1.5 cm-1), high internal quantum efficiency of 98% for a triple sheet QD-laser at 1.15 µm. 12 W output power, equivalent to a power density of 18.2 MW/cm2, for a 6-fold MOCVD grown stack. In lifetime tests at 1.0 W, 1.5 W and 50°C heat sink temperature no aging of these lasers within 3000 h could be observed [14, 15]

• Stability enhancement by 23 dB for external optical feedback at 1.3 µm [16, 17]

• Large tuning range of > 200 nm [18] • 12 GHz modulation bandwidth at room temperature [19] • 10 Gb/s error-free data modulation obtained at –2 dBm receiver power, 1.3 µm

emission wavelength [20, 21] • Passive mode-locking in the range of 5 to 50 GHz at wavelengths around

1.3 µm [22, 23] with pulse width down to 3 ps. • Pattern-free amplification at 40 Gb/s [24]

Several epitaxial improvements were proposed and partially realized to achieve the abovementioned results, i.e. growth of InGaAs/GaAs QDs on template layers [25], overgrowth of QDs with quantum well layers [26], stacking of QDs [27], close stacking of QDs leading to vertical coupling of the QD layers [28], defect reduction techniques [29], introduction of strain relaxation layers [30], p-doping of the GaAs barrier layers [31], and tunnel injection of carriers into the QDs through a thin barrier layer [32]. Besides that, the laser diode design has been optimized, including edge emitting lasers with symmetric far-fields [22] and single-mode emission [33] as well as intra-cavity contact single-mode VCSELs [34]. Some of these improvements were developed by my colleagues and collaborators from other work groups during the period of my thesis and are reflected by the continuous increase of the dynamic figure-of-merits like modulation bandwidth, repetition frequency (for mode-locking) and pulse width. To give a comprehensible overview of this development, my thesis is structured as follows: The first section gives an overview of the epitaxial structure, chip layout and high frequency mounting of the InGaAs quantum dot lasers we investigated during our work. The second section dives into the modeling of the laser chip vicinity and the quantum dot laser itself, discusses a few increasingly complex dynamic models of QD lasers and derives the most important static and dynamic parameters from these models. The main, third section deals with the dynamic properties of directly modulated QD edge emitters with 1.1 µm and 1.3 µm emission wavelength. Starting with an overview of the structural improvements of the lasers, we shortly discuss the static laser parameters before presenting the dynamic small and large signal measurements on various kinds of edge emitting QD lasers. From a comparison to dynamic modeling we try to explain the physical foundations of the dynamic limitations of QD lasers. The fourth section gives a short overview of the dynamic properties of InGaAs quantum dot VCSELs, along with a comparison to edge emitter performance.

0 Introduction

15

The last section of my thesis addresses hybrid and passive mode-locking of InGaAs quantum dot lasers, the required changes of device layout and experimental results. Frequently used symbols and quantities are listed in the nomenclature section.

1 QD laser design

16

1 QD laser design 1.1 Epitaxial structure of QD lasers, sample lists All quantum dot edge emitters investigated in this work contained a separate optical confinement (SC) double hetero structure (DHS). Fig. 4 shows the epitaxial structure of such a laser: On top of a n-doped GaAs substrate wafer, a GaAs buffer layer (ensuring surface smoothness), a AlGaAs lower cladding layer (typical thickness around 1 µm, Al content between 35 % and 80 %), a sequence of up to 15 layer bundles consisting of GaAs barrier layer, InAs wetting layer, QDs and (optionally) an InGaAs cap quantum well, an upper cladding layer and a highly p-doped contact layer were deposited.

Thinned Wafer150 µm

Quantum dot

Stacked quantumdot layers

Electricalcontact layer

Cladding layer

Cladding layer

GaAs wafer

Waveguide

Laser structure

GaAs wafersubstrate

Fig. 4: Schematic view of the epitaxial structure of a quantum dot edge emitting laser. The laser diodes investigated in this work were based on n-doped GaAs substrates. The cladding layers together with the GaAs waveguide provided the optical confinement, whereas the confinement of carriers was provided by the quantum dots and the adjacent wetting layers. QD laser typically contain more than one layer of QDs (between 2 and 15) in order to improve the gain of the device. This stacking requires a minimum spacer thickness between neighboring QD layers [35-37] to ensure a strain-free GaAs surface for the growth of each QD layer. Below this thickness correlation effects between the QD of adjacent layers appear (site correlation and anti-correlation, intermixing of electronic levels, change of photoluminescence efficiency etc.) [28, 37-47]. The intermixing of the electronic levels of vertically stacked QD leads to the formation of minibands and may be beneficial for carrier transport (this issue will be addressed later in context with dynamic limitations of QD lasers). All wafer structures investigated in this work contained non-coupled QDs with spacer thicknesses larger than 25 nm. In the past five years, the emission wavelength of QD lasers has been continuously shifted to longer wavelength. As shown on the QD laser roadmap (Fig. 3) we first investigated MOCVD grown InAs QDs in a GaAs matrix emitting at a wavelength of around 1.1 µm at room temperature. These samples were grown at the TU Berlin [14, 15, 48]. The concept of overgrowth with an InGaAs quantum well and subsequent decomposition of the QW lead to devices with emission wavelength between 1250 and 1300 nm [11, 26, 49-67].

1 QD laser design

17

Fig. 5: Self-organized grown InAs quantum dots (a) were overgrown with a 4 nm thick InGa(Al)As layer. The layer decomposed and caused In enrichment in the vicinity of the QDs (b), thus causing a red shift in the emission wavelength of the QDs. The structure was finally capped with GaAs barrier material, yielding a dot-in-a-well (DWELL) scheme [Courtesy M. Maximov] Fig. 5 shows the DWELL structure samples that were grown by MBE at the A.E.Ioffe Institute, St. Petersburg and recently by the company NL Semiconductors, Dortmund. Since these samples were suitable for standard measurement infrastructure (detectors, spectrometers, amplifiers etc.) at 1.3 µm, they can be considered as the “workhorse” of this thesis. Table 1 gives an overview of the diversity of samples that we investigated. The processing details will be explained in the next section. Origin Layers λ [nm] Mesa depth, width, contacts CharacterizationMOCVD TU 5382, QW 3 1080 Shallow, 3/5/10/30/50 µm Streak TU 5447 6 1120 Shallow, 3/5/10/30/50 µm Streak

MBE Ioffe 4-915 5 1300 Deep, 4/6/8/10 µm, MS SS, ML, EYE Shallow, 4/6/8/10 µm, MS SS Ioffe 4-920 5 1300 Shallow, 4/6/8/10 µm, MS LS, SS, ML Ioffe 4-924 10 1300 Shallow, 5/8/10/50 µm LS, SS, EYE Ioffe 5-600 5 1300 Deep, 1/1.5/2/4 µm, MS LS, SS, ML Deep, 4/6/8/10 µm, MS DO 57 10 1300 Deep, 1/1.5/2/4 µm, MS SS, EYE, BER DO 75 10 1300 Deep, 1/1.5/2/4 µm, MS SS, EYE, BER DO 224c 10 1300 Deep, 2/4 µm, GSG, MS SS, EYE, BER DO 453 15 1300 Deep, 2/4 µm, GSG, MS LS, SS

Table 1: Origin, sample number and main characteristics of the wafers and corresponding edge emitting devices that were investigated in the framework of dynamic measurements. The abbreviations for the device features are: MS - multi section, GSG – ground-signal-ground (top side) contacts, SS – small signal measurements, LS – large signal measurements, ML – mode locking, EYE – eye pattern measurements, BER – bit error rate measurements. Fig. 6 shows the typical structure of the MOCVD grown edge emitter wafers. To decrease interface roughness several transition layers have been introduced to the structure:

1 QD laser design

18

a) Below the lower cladding and on top of the upper cladding layer a graded AlGaAs layer was deposited.

b) Between cladding and waveguide 10fold AlGaAs/GaAs super-lattices were deposited to ensure good growth conditions for the QDs and to keep the surface roughness on top of the QDs at a minimum.

Typical quantum dot sheet densities lay around 10 25 10 cm−⋅ .

Fig. 6: Epitaxial structure for the wafer TU 5447. The quantum dots were grown in a Stransky-Krastanov self-assembled mode and subsequently covered by GaAs. All MBE samples were grown using similar roughness reduction techniques. In order to achieve 1.3 µm wavelength emission the aforementioned DWELL structure was implemented. QD laser samples with a number of 5, 10 and 15 quantum dot layers have been grown. Since the QD layers were separated by a GaAs spacer layer of more than 30 nm thickness, the waveguide thickness increased with the number of stacked QD layers. The cladding layer thickness was chosen to be large enough to avoid any leakage of the photonic mode into adjacent GaAs layers. Part of the samples were p-doped between the quantum dot layers to improve the laser properties [31]. Consequences of doping are discussed in the following section. For the DO samples, the Al content of the cladding layers was reduced from > 70 % to 35 % to achieve a broadening of the photonic mode and a better overlap with the outer quantum dot layers.

1 QD laser design

19

Fig. 7: Epitaxial structure for the wafer Ioffe 4-920 (left) and Ioffe 5-600 (right).

Fig. 8: Epitaxial structure for the wafer Ioffe DO 57/224c (left) and DO 453 (right). The latter structure contained 15 layers of QDs, causing a thickness of the waveguide > 500 nm.

1 QD laser design

20

Part of this work is also dedicated to dynamic measurements on QD vertical cavity surface emitting lasers (VCSELs). Table 2 lists the samples that were investigated. Origin Layers λ [nm] Processing CharacterizationMOCVD

TU NP 537 3 nom. 1100 ES 1000 (c) LS

TU NP 654 3x3 1100 (a) LS TU NP 800 3x3 1100 (a), (b) LS, SS

Table 2: Origin, sample number and main characteristics of the wafers and corresponding vertically emitting devices that were investigated in the framework of dynamic measurements. LS – large signal measurements, SS – small signal measurements. For the processing scheme, please refer to section 4. All theoretical and experimental considerations and results for VCSELs are found in section 4. 1.2 Laser chip layout

1.2.1 Mesa definition and planarization The main application of QD laser diodes at 1.3 µm, data transmission through optical fibers, requires a good coupling efficiency between laser and fiber, and at the same time only moderate output powers (a few mW, see Table 6). These demands were met by narrow stripe edge emitters with stripe width below 4 µm. Processing of such small structures is demanding and has considerable developed over the past years within our workgroup. For the first processing step, the definition of the mesa, two different types of processing schemes were employed for the samples in Table 1:

a) Wet etching: The MOCVD and early MBE samples were wet etched stopping within the upper cladding layer. The weak anisotropy of the wet etching process caused the sidewalls of the mesa to become uneven and tilted. Due to under-etching this process was unsuitable for stripe widths below 4 µm and etch depths beyond 2 µm.

b) Dry etching: The later MBE samples were dry etched with a Chemically Assisted Ion Beam Etching (CAIBE) facility. Due to the strong anisotropy of the ion beam etching process the side walls looked perfectly smooth and virtually no under-etching occurred (see Fig. 9).

1 QD laser design

21

Fig. 9: Cross section REM pictures of a wet etched (left) and a dry etched (right) laser mesa. The nominal width was 4 µm in both cases; the wet-etched ridge showed a pronounced under-etching due to isotropic nature of the wet etching process. Due to the limitations of the wet etching process the mesas of the corresponding samples were shallowly etched, meaning that the etching stops within the upper cladding layer (see Fig. 10, “shallow mesa”). This provided only weak lateral index guiding for the optical mode which was enhanced during laser operation by gain guiding. Since the optical confinement in vertical direction was much stronger, we observed a far-field asymmetry (ellipticity) of about 10, giving large losses when coupling to a (perfectly symmetric) fiber. An advantage of weak guiding was the suppression of higher lateral modes. These aspects of optical waveguides are discussed in detail in section 2.1.2. Dry etching enabled us to etch through the active layer to provide strong index guiding of the optical mode and suppression of current spreading (see Fig. 10, “deep mesa”). The strong index guiding combined with the small stripe width ensured a low asymmetry of the far-field (down to ellipticity 1.2) and a high coupling efficiency into optical fibers. Suppression of current spreading in QD layers lead to an improvement of the electrical high-frequency characteristics of laser diodes by reducing parasitic capacitances, as will be shown in section 3.2.1.

Electricalcontact layer

Cladding layer

Cladding layer

GaAs wafer

Vertical waveguide/Active zone

Lateral waveguide InsulatorInsulator Lateral waveguide InsulatorInsulator

“Shallow mesa” “Deep mesa” Fig. 10: Cross section scheme of narrow stripe laser structure with shallow mesa (left) and deep mesa (right). The difference between both types was the etch depth: For the deep mesa, the sides of the mesa were etched through the active layer, thus creating a stringent current path and a strong lateral optical confinement. After defining the mesa the sides of the ridge were covered with an insulating low refractive index material. For the shallow mesas, it was sufficient to cover the sides of

1 QD laser design

22

the mesa with a thin (400 nm) insulating silicon nitride layer. For deep mesas, the structure had to be planarized with a thick insulating layer (2-3 µm, depending on the etch depth) in order to be able to deposit proper contact layers. This was done with spin-on-glass (SOG) or, alternatively, with Benzo-Cyclo-Butene (BCB). The SOG planarization layer can be seen in Fig. 9 (right picture) as the dark layer left and right from the mesa. This picture also shows one of the technological difficulties that were to overcome: The SOG layer shrank during processing, leaving a gap between the SOG and the mesa. This problem was finally solved with BCB.

1.2.2 Contact definition The contact layer has to fulfill several tasks: It provides good ohmic contact to the semiconductor layer beneath, it should stick firmly to the underlying layer, and it should be stable enough to be bonded with an ultrasonic wire bonder. Besides that, it should impose no parasitic limitation on the device, i.e. the pad size should be as small as possible, and neighboring contact pads should be as far apart as possible. Starting from a simple full-coverage p-contact metallization, two designs for single and multi-contact metallization were developed.

Fig. 11: Top-side n-contacts (golden pads) arranged in a GSG scheme with pitch 250 µm (left) and multi-sectional metallization with 20 µm gap (right). The mesas run vertically, with twin mesas of 6/10 µm and 4/8 µm width (right) and 2/2 and 4/4 width (left), coded with A/b and C/d. Modeling of parasitic influences of the contact metallization (see section 2.1.2) showed that a bond pad size of 200x100 µm is both suitable for bonding and for high frequency modulation up to 10 GHz. Fig. 11 (left picture) shows a microscopic view of ground-signal-ground (GSG) contact structure with p-contact pads (reddish) and top-side n-contacts (golden pads). The pitch between the p- and n-contact pads was 250 µm. This device could be contacted via GSG probe head or bond wires. It had an additional backside n-contact. Fig. 11 (right picture) shows a microscopic view of a multi-sectional contact metallization. The bond pad size was 200x200 µm, the gap in the mesa metallization was 20 µm wide. The separate sections of length 1000 µm could be biased individually, as it was necessary for passive and hybrid mode-locking. The minimum possible length of the absorption and gain section was 100 and 500 µm, respectively. Insulation between the sections was enhanced by removal of the p-contact layer by dry etching.

1 QD laser design

23

1.3 High reflection coating In order to minimize output from the rear laser facet and to decrease mirror losses for short (< 800 µm) devices we applied high reflection coatings to selected samples. The HR coating consisted of pairs of SiO2 and SiNx layers with nominal thickness of 210 nm and 140 nm, respectively. Layer deposition was done with an Ar plasma sputtering facility comprising SiO2 and SiNx targets, a temperature stabilized sputtering plate and a thickness measurement sensor for in-situ monitoring and control of the deposited layer thickness. The sputtering rates were carefully calibrated by ex-situ sample control with ellipsometry. Fig. 12 shows the good agreement of simulated and measured back reflection spectra from laser facets with 4 and 2 pairs of dielectric layers. Simulation was done with a standard chain matrix model implemented with Mathematica [68].

800 1000 1200 1400 1600 18000.0

0.2

0.4

0.6

0.8

1.0

Ref

lect

ivity

Wavelength [nm]800 1000 1200 1400 1600 1800

0.0

0.2

0.4

0.6

0.8

1.0

Ref

lect

ivity

Wavelength [nm]

Fig. 12: Normal incidence back reflection spectra of HR coated laser facets for 4 pairs (left) and 2 pairs (right) of dielectric layers for six identical laser bars. The scatter points denote the simulated reflection spectrum. The peak reflectivity at 1.3 µm was 95 % and 80 %, respectively. 95 % reflectivity was employed for rear facets, while 80 % reflectivity was used for front facets of very short devices. 1.4 Submount layout For high frequency modulation and hybrid mode-locking measurements on QD laser diodes we had to make sure that the electrical connection between microwave cables and the mounted laser diode, i.e. the submount, did not limit the bandwidth of the mounted diode. As our goal for the direct modulation bandwidth is around 10 GHz, the submount should have a transmission bandwidth of at least 15 GHz. At the same time, the submount should fulfill other requirements:

• efficient heat sink • termination in a standard microwave adapter (SMA) port • short bond wiring • suitable for insertion into cryostat

Therefore we decided to use a copper block with a PTFE based micro strip line and an SMA port attached to it. The laser diode was glued to the front part of the copper block using a two component conductive epoxy. The assembly of the submount (see Fig. 13) is described in the technical appendix (not included with printed thesis). The dimensions of the copper block heat sink were chosen to fit into an Oxford contact gas cryostat CF 204 with 20 mm sample room diameter. The SMA connector

1 QD laser design

24

attached to the block had a nominal bandwidth of 16 GHz and was compatible with standard microwave cables. The strip line chip consisted of a two-sided gold-plated copper metallization on a PTFE carrier with 250 µm thickness. The back side of the chip was uniformly metallized, whereas the top side was structured into an S-shaped 50 Ohm strip line connecting the SMA connector and the sample. In order to be able to mount and contact two-sectional mode-locked laser diodes, a similar submount with two microwave connectors and a double 50 Ohm strip line was designed and fabricated. Fig. 14 shows the strip line layout as it was simulated with Sonnet [69], a 2D numerical microwave simulator.

Fig. 13: Single contact submount with RF connector, strip line and laser diode (front, left). The copper base provided mechanical stability and served as efficient heat sink. The RF characterization of the assembled submounts (without laser diode) was done with a fully calibrated network analyzer (NA) set-up. Both the transmission and the reflection of the submount were characterized. For the transmission measurement we butt-coupled two identical single submounts with a short bond ribbon and shortened the two strip lines of the double submount, respectively (see Fig. 14).

Fig. 14: Single (left) and double (right) section layout of the strip line chip. The laser diode position was in the left lower corner. The strip line width was 700 µm, the thickness was 40 µm. The gold plating of the lines was suitable for supersonic bonding and soldering. Two single submounts were butt-coupled for two-port S parameter measurements.

1 QD laser design

25

Fig. 15 shows both the S11 and S12 measurements and simulations for the butt-coupled single mounts and the double mount. The underlying model is explained in section 2.1.1. Unfortunately, the coupled single mounts exhibited strong box resonances due to standing waves between the SMA ports (left picture). Therefore it was not possible to judge the transmission properties of the strip line from this measurement. Instead, we relied on the measurements of the double mount that showed a linear increase / decrease of S11 / S12 due to the inductivity of the bond wire connecting both strip lines as well as small ripples due to a slight deviation of the strip line impedance from 50 Ohm. Since the bond wires for our samples were considerably shorter, they imposed no limit to the transmission bandwidth up to 15 GHz.

0 5 10 150.0

0.2

0.4

0.6

0.8

1.0

S P

aram

eter

Frequency [GHz]

S11 parameter Measured Model

S12 parameter Measured Model

0 5 10 150.0

0.2

0.4

0.6

0.8

1.0

S P

aram

eter

S11 parameter Measured Microwave model

S12 parameter Measured Microwave model

Frequency [GHz]

Fig. 15: Comparison of measured and simulated S parameters for two butt-coupled single mounts (left) and a short-ended double mount (right). The coupled single mounts show two strong resonance peaks, due to a standing wave resonance in the coupled device. The increase/decrease with frequency was due to the inductivity of the bond wires, the slight ripples showed a deviation of the strip line resistance from 50 Ohm. In conclusion, the submounts presented a trade-off between transmission optimization („as small as possible“) and handling consideration („as large as possible“) and were suitable for devices with a bandwidth up to 15 GHz. 1.5 Bonding The electrical connection between the strip line of the submount and the bond pad of the laser device was provided by one or more gold bond wires or ribbons. Typical dimensions were 20 to 25 µm diameter for the wires and 12x100 µm for the ribbon. The inductivity of the bond wire was about 1 nH/mm, whereas the bond ribbon had considerably lower inductivity in the range below 0.3 nH/mm. Bond wires were fabricated using a semi-automatic supersonic bonder; in lack of a ribbon bonding machine the ribbon bonds were attached manually using epoxy glue. Although it was advantageous to use low L bond ribbons, we machine-bonded most of the samples with wires since this ensure low contact resistance, reproducibility and high work speed. Fig. 16 (left) shows an almost finished wire bond between single submount stripe line and bond pad. The length of the bond wire was ~400 µm. The usual bond direction (sample submount) was swapped for most of the samples, because the final wedge bond induced less tensile stress to the bond pads. Otherwise it happened that the bond wire ripped off the bond pad.

1 QD laser design

26

0 500 1000 1500 2000 25000

1

2

3

4

5 Ribbon bond Wire bond

Ioffe 4-915, 800x4 µm, deeply etched

RC

freq

uenc

y [G

Hz]

Current density [A/cm2]

Fig. 16: Wire bonded laser diode (left) and comparison of wire and ribbon bond performance for identical laser device (right). Both ribbon and wire bond did not influence the RC bandwidth of the device. Fig. 16 (right) shows the comparison of the RF characteristics of wire bonded samples and ribbon bonded (ribbon width 100 µm, length 200 µm) samples. No influence of both bond types could be seen, as predicted by simulation. For the explanation of the measurement, please refer to section 3.2.1.

2 Modeling of quantum dot edge emitters

27

2 Modeling of quantum dot edge emitters To reduce the complexity of the modeling a QD laser device, we divide the laser in a Matrjoshka1-like way into three functional units:

1) Intrinsic QD laser: This part comprises the gain medium and the waveguide section (the active layer).

2) QD laser chip: This part comprises the semiconductor structure surrounding the active layer (the cladding and contact layers), the contact metallization and the bond wire(s).

3) Submount: The submount consists of the heat sink (optional heat spreader), electrical circuitry (strip lines, impedance matching networks) and terminates with one or more standardized microwave ports and bias connectors.

Chip design:• small series resistance• negligible parasitic capacitance• efficient fiber coupling

Submount:• effective heat sink• impedance matching• short bond wires• compact, reproducible

Active zone: • high quantum efficiency• high modulation

bandwidth

Fig. 17: Improvement chart for mounted QD laser diodes showing three functional units of the device: submount, laser chip and active zone (intrinsic QD laser). The improvements of these three units are associated with different technological challenges, which require different tools of modeling. The modeling of the three functional units is done with different tools. The following sections present details of the modeling, with an emphasis on understanding the properties of the intrinsic QD laser. 2.1 Modeling of submount and laser chip

2.1.1 Submount The frequency dependent electrical properties of the submount influence every measurement of the attached laser diode. Even a perfectly matched, high bandwidth submount still acts as a phase shifting transfer line. Since most of the high frequency measurements on lasers (e.g. S parameter measurements) are phase sensitive, it is necessary to de-embed the measurement of the mounted laser diode, i.e. exclude the characteristics of the submount. There are two ways to accomplish this task:

1 Russian hand-crafted doll made from wood that contains smaller copies of itself.


28

1) Network analyzers for frequency dependent measurements offer the possibility to calibrate the electrical transmission line (microwave cables, SMA ports) and set the measurement reference plane to a point near the device-under-test (DUT). For calibration, it is necessary to provide standardized calibration terminations (short, open, 50 Ohm load termination) to do a computational de-embedding on board the network analyzer. Calibration is routinely done for cables and connectors using a standard calibration kit. However, in order to de-embed the submount, the terminations have to be placed at the far end of the submount stripe line (where the laser diode is connected). This can only be done by the fabrication of identical submounts with suitable high bandwidth micro-terminations (short, …). This is not practicable for our purposes.

2) Given a complete description of the transmission and reflection characteristics of the submount, the de-embedding can be done by re-computation of the measured data with the help of microwave circuit simulation software.

ZS MA Zfeed thru Ls older

Lbond

SMA port

RcontactZstr ip line

εsubstrate, Zsubstrate

Fig. 18: Equivalent circuit of single submount comprising the SMA connector, solder inductance, stripe line, contact resistance and bond wire. The stripe line is based on a sandwich metal-dielectric-metal structure with appropriate PTFE dielectric characteristics. Hence we need a complete electrical model of the submounts described in section 1.4. Fig. 18 and Fig. 19 show the equivalent electric circuits for the single and double submount, respectively, implemented with Microwave Office [70]. The models include the properties of the stripe line chip material, the SMA ports, an inductive discontinuity at the port-stripe line interface and the bond wire. The dimensions of the model parameters correspond to the actual dimensions of the submounts.

SMA port 2

ZS MA Zfeed thru Ls older

Ls older

Lbond

ZS MA

SMA port 1

Zfeed thru

Zstr ip line Rcontact

RcontactZstr ip line

εsubstrate, Zsubstrate

Fig. 19: Equivalent circuit of two port submount comprising two SMA connectors, solder inductance, stripe lines, contact resistances and an additional bond wire for testing. The correctness of the model was checked by measurements of the bare submounts (without device). Fig. 15 shows the comparison of simulation and measurement of


29

the submounts. While the measurements of the single submount showed additional resonances that where not and could not be included in the model, the measurements of the double submount showed good agreement with the simulation, both for amplitude and phase (not shown) of the S11 and S12 scattering parameters. Both models were used to de-embed S11 parameter measurements of mounted single and two section laser devices in order to find the true S11 characteristics and thereby the RC parameters of the laser chip and intrinsic laser. For samples contacted with a calibrated GSG probe head the de-embedding was obsolete.

2.1.2 Laser chip Electric properties The electrical properties of the complex laser chip structure comprising the cladding layers, contact layer, substrate, ohmic contact layer, metallization and insulation can be described in terms of an amazingly simple electric equivalent circuit. Fig. 20 shows a RC circuit including the bond wire inductivity, where R is associated with the series resistance

serI

URI →∞

∂=

∂

and C is associated with the capacitance parallel to R, i.e. mainly the parasitic bond pad capacitance. The intrinsic laser diode comprises the active zone and is modeled separately in section 2.2.

Rser

Intrinsic LD

Lbond

Cmetal

Fig. 20: Simple equivalent circuit model for the laser chip, including the bond wire. The intrinsic laser diode represents the electric properties of the active layer. Rser denotes the series resistance of the laser diode, Cmetal denotes the capacitance parallel to Rser, mainly given by the capacitance of the p-contact bond pad. The circuit shown in Fig. 20 acts as a frequency low pass between input and intrinsic laser diode with a bandwidth (reduction of current modulation amplitude to one half) of

31

2dBfRCπ− = (2.1)


30

neglecting the influence of L. Taking L into account, no analytical expression for 3dBf− can be given. Therefore, Fig. 21 shows a numeric simulation of the influence of L on the transmission of the parasitic low-pass performed with Microwave Office [70].

0 5 10 15 200.0

0.2

0.4

0.6

0.8

1.0

1.2

L = 0 nH L = 0.5 nH

Para

sitic

tran

smis

sion

[a.u

.]

Frequency [GHz]

Fig. 21: Influence of bond wire inductivity on the transmission of the parasitic low-pass. The bandwidth is 9.5 GHz for 0 nH and 8.2 GHz for 0.5 nH, corresponding to a bond wire of 25 µm diameter and 600 µm length. To make sure that the bond wire is not limiting device performance we restrict the bond wires used in our submounts to lengths below 400 µm. The metallization capacitance of the laser chip can be estimated from a simple plate capacitor model:

0ACd

ε ε= (2.2)

where ε is the electrical susceptibility and d the thickness of the insulating layer (spin-on-glass or BCB, respectively) and A the area of the capacitor (the size of the bond pads). ε is 2.2 for SOG and 3 for BCB. For bond pads of size 200x200 µm and an average thickness d of > 1 µm this results in a capacitance per pad of less than 0.8 pF for SOG and 1.1 pF for BCB. Since a typical value for the series resistance of 1 mm long narrow stripe lasers (with two pads) lies between 5 and 10 Ω, this corresponds to bandwidth between 15 and 8 GHz. The bandwidth can be further enhanced by reducing the bond pad size and increasing the thickness of the insulating layer (for sample DO 453: d > 2 µm, pad size 200x100 µm). The estimation of the series resistance of the laser chip is far more demanding, since it depends on the particular epitaxial structure and doping of the device. A simulation including these features was done using the semiconductor simulation software DIOS [71] including the TESCA module for optoelectronic devices. A description of the corresponding model and subsequent fitting of parameters is beyond the scope of the theoretical part of this thesis. I-V curves including the series resistance and power characteristics could be successfully modeled with TESCA but need further adaptation of the model parameters. Generally, the etch depth of the mesa has a major influence on the series resistance. Deep etched mesas suppress current spreading and lead to an increase of the series resistance. Furthermore, we expect a linear dependence of the series resistance on the ridge width.


31

Thermal properties Fig. 4 shows the scaling of the different epitaxial layers with respect to the GaAs wafer thickness. It becomes clear that the heat generated by the laser structure is much more efficiently removed for devices mounted epi-side down on a copper or diamond heat sink, since these materials have a much larger thermal conductivity than the GaAs substrate (see Table 3). However, the actual thermal conductivity of a doped and electrically pumped GaAs substrate may differ from the given value.

Material Thermal conductivity at 300 K Wcm K

⎡ ⎤⎢ ⎥⋅⎣ ⎦

Reference

Copper 4 [72] Diamond 20 [72] SiO2 0.014 [72] GaAs (undoped) 0.46 [73]

Table 3: Thermal conductivity of common heat sink materials, glass and GaAs at room temperature. For broad area lasers with mesa widths above 10-20 µm epi-side down mounting is mandatory in case they are supposed to operate cw. For narrow stripe laser with widths below 4 µm epi-side down mounting is not necessary. Heating of the device can be monitored by comparison of pulsed (1-10 µs pulse length) and cw measurements. In the case of absence of a spectral shift of the emission or a change in the output-current curve we can assume to have no device heating. Besides, epi-side down mounting comprises several drawbacks for high-speed laser diodes:

a) In order to do a proper dye bonding of the epi-side with the heat sink (which means essentially soldering both surfaces with In), the epi-side is completely metallized. This gives us a considerable increase of the parasitic contact capacitance (factor 5-10).

b) It is not possible to choose a multi-contact layout for the laser (no GSG structure, no multi-sectional devices).

From this we concluded to mount all investigated samples epi-side up. For narrow mesas the thermal conductivity on the sides of the active zone plays an important role. Fig. 10 shows the two principal types of laser structures we investigated. For deep mesas, the insulating layer generally provides a bad thermal heat sink (see Table 3). Therefore, these structures are more likely to heat up during operation. Optical properties The optical properties of the waveguide are decisive for a number of important characteristics of a laser diode:

1) Number of guided lateral and vertical modes 2) Far-field shape and divergence 3) Optical losses inside the cavity (waveguide losses) 4) Modal gain as described by the G factor (i.e. the overlap of the active zone

with the optical mode)


32

We separate the mode distribution inside the waveguide structure of a laser diode into the one-dimensional longitudinal mode structure of a plane wave in z direction and the transversal mode structure of the waveguide cross section: ( ) ( ), , ( , ) ( ) ( , ) zi k zE x y z E x y E z E x y e−= ⋅ = ⋅ (2.3) The longitudinal mode structure can be described in terms of plane waves satisfying the cavity condition

,2effn L m mλ

= ∈ (2.4)

where L is the geometric length of the laser cavity, effn is the effective index of refraction given by the transversal mode order, and λ is the emission wavelength of the device. The longitudinal mode distance is then given by

2

2 effn LλλΔ = (2.5)

The transversal (lateral and vertical) modal structure described by ( , )E x y is simulated with the 2D numerical mode solver BPM-CAD [74]. The input of the mode solver consists of the geometry of the cross sectional waveguide structure and the corresponding dielectric constants (see Fig. 22). The solver computes the eigenvalues (the effective index of refraction) and the eigenfunctions (the optical modes) of the electromagnetic wave equations discretized on a finite spatial grid for a given wavelength (1.3 µm in our case).

SiO2

GaAs

SiO2Al0.80Ga As0.20

Al0.80Ga As0.20

Fig. 22: Deep mesa waveguide structure used for simulation of the transversal mode profile. The influence of electrical pumping, the QDs, the wetting layers and metallization is neglected. Fig. 23 shows typical results for the calculated optical modes. These are the 1st order modes of deep and shallow mesa structures with ridge width 4 µm, waveguide thickness 300 nm and an emission wavelength of 1.3 µm. The deep mesa mode is elliptic with a ratio x yω ω of 1.8 µm / 0.43 µm, corresponding to an ellipticity of 4, and an effective index of refraction of 3.26. The shallow mesa mode is elliptic with a ratio

x yω ω of 3.1 µm / 0.42 µm, corresponding to an ellipticity of 7, and a similar effective index of refraction of 3.26.


33

Fig. 23: Simulation of 1st order optical mode cross section for mesa width 4 µm for a deep etched mesa (left) and a shallow etched mesa with 150 nm of remaining p-cladding (right). The mode diameter is nearly a factor of 2 larger for the shallow mesa. Note that the graphs are tilted. For increasing mesa width the waveguide supports more and more lateral modes. Due to the strong vertical optical confinement, no higher vertical modes are found, so we restrict the indexing of transversal modes to lateral modes. Fig. 24 (right) shows the calculated number of lateral modes for deep and shallow mesas with widths between 1 and 8 µm. As expected, due to the weaker index guiding for structure etched back 150 nm above the active zone, only a few modes are supported. Single mode operation should be feasible for mesa widths at least up to 5 µm. For deep mesas, in contrast, it is necessary to fabricate ridge widths of 1 µm and below to ensure operation in single lateral mode.

1 2 3 4 5 6 7 8 90

2

4

6

8

10 deep mesa shallow mesa

Num

ber o

f mod

es

Waveguide width [µm]1 2 3 4 5 6 7

3.00

3.05

3.10

3.15

3.20

3.25

3.30

Effe

ctiv

e re

fract

ion

inde

x

Transversal mode order

Deep mesa, 4 µm ridge width

Fig. 24: Calculated number of guided modes in deep and shallow mesa structures for different mesa (waveguide) widths 1-8 µm (left). The assumed waveguide thickness is 300 nm; the sides of the mesa are planarized with SiO2. The right graph shows the decrease of the effective refractive index with higher lateral mode order. Due to the different spatial distribution of the light field intensity of lateral modes inside the laser cavity they couple to different spatial sub-ensembles of quantum dots. This may cause additional output noise associated with the competition of the QD sub-ensembles for carriers. For the same reason, the appearance of higher order transversal mode may have a disturbing influence on directly modulated lasers. As for mode-locked QD lasers, higher order transversal modes may show independent longitudinal mode-locking, causing the oscillation of additional optical pulses in the cavity. These issues will be further discussed in the corresponding chapters 3.3.3 and 5.2.


34

In total, for a deep mesa with ridge width of 4 µm seven transversal modes are found by the solver. Fig. 24 (right) shows the effective indices of refraction for all modes. They show up as additional longitudinal mode groups in the optical spectrum of the laser. The transversal modal distance is given by

transversaleff

nn

λ λ ΔΔ = (2.6)

where nΔ is the refractive index difference. Since the transverse mode distance

transversalλΔ is much larger (~ 10 nm) than the longitudinal mode distance (< nm), the neighboring peaks in the spectral overlap of several mode groups appear at quasi-random distances. The different mode groups can be clearly distinguished in a high resolution lasing spectrum (see Fig. 25).

1295 1296 1297 1298 1299 1300-80

-70

-60

-50

-40

-30Δλtransversal

Lase

r Out

put [

dB]

Wavelength [nm]

DO 224c, 500x4µm, HR coated facets

Δλlongitudinal

1295 1296 1297 1298 1299 1300-80

-70

-60

-50

-40

-30

La

ser O

utpu

t [dB

]

Wavelength [nm]

DO 224c, 500x2µm, HR coated facets

Fig. 25: Part of high resolution optical spectrum of a short (500 µm) cavity QD laser with 4 µm (left) and 2 µm (right) mesa width. The longitudinal mode distance is ~0.5 nm, corresponding to the distance between the adjacent peaks of similar height. For the 4 µm ridge, two lateral mode groups can be distinguished; the 2 µm ridge is in single transversal mode. The number of lasing transversal modes, their relative intensity and the shape of the transverse optical modes determine the shape of the laser far-field. For the following considerations we restrict us to the 1st order transversal mode and assume a two-dimensional Gaussian field and intensity distribution for this mode:

2 22 2

222 20 0( , ) , ( , ) ( , )y yx x

y yx x

E x y E e e I x y E x y E e eω ωω ω

⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞−⎜ ⎟ − ⎜ ⎟− −⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠= = = (2.7)

where xω and yω are the beam waist diameters of the transversal mode in lateral and vertical direction. The far-field divergence is characterized by a two dimensional Gaussian-shaped lobe with divergence angles xθ , yθ (in radians) given by the mode waist diameter:

,x yx y

λ λθ θπω πω

= = (2.8)

The calculated 1st order transversal mode of a deep mesa with 4 µm width has 13°/55° lateral and vertical far-field divergence, respectively.


35

The large far-field divergence in vertical direction causes coupling losses, since most fiber coupling optics have a numerical aperture below 0.5, corresponding to a full acceptance angle of 50°. Another limitation is given by the asymmetry of the far field. The maximum (ideal) coupling efficiency of an asymmetric far field with ellipticity

x yε ω ω= to a symmetrical optical fiber is

( )2

41

εηε

=+

(2.9)

For the calculated 1st order transversal mode of a deep mesa with 4 µm width this corresponds to a maximum coupling efficiency of 62 %. The shape of the transversal optical field not only influences purely optical properties of the laser diode, but also the coupling of the optical mode to the gain medium. The overlap of the optical mode with the gain medium (in our case the quantum dots) determines the modal gain and is described in terms of a lateral and vertical Γ factor:

( / 2, )

1 ( / 2, )

( , ) ( , )ilayer

i

w y hN

i w y

I x y dxdy I x y dxdy+ + ∞

= − −∞

Γ = ∑ ∫ ∫ (2.10)

where w is the width of the pumped active zone (corresponds to ridge width for deep mesas), iy is the vertical position of the ith QD layer and h its thickness, if treated as a homogeneous layer. For a two-dimensional Gaussian transversal mode the Γ factor can be separated into a lateral and a vertical Γ factor:

( )( / 2)

1( / 2) ( )

( ) ( ) , ( ) ( )ilayer

i

y hw N

x yiw y

I x dx I x dx I y dy I y dy++ ∞ ∞

=− −∞ −∞

Γ = Γ = ∑∫ ∫ ∫ ∫ (2.11)

The first equation is readily solved using a numerical approximation of the Gaussian integral. To solve the second equation, we assume a constant intensity over each quantum dot layer, giving:

1

( ) ( )layerN

y ii

h I y I y dy∞

= −∞

Γ = ⋅∑ ∫ (2.12)

Fig. 26 shows the calculated Γ factors depending on the waveguide dimension and the QD layer thickness and spacing. As expected, xΓ should be larger for strong optical confinement ( 2lateral wσ < ) than for weak confinement.


36

0.5 1.0 1.5 2.00.6

0.7

0.8

0.9

1.0

Late

ral Γ

x fac

tor

2σlateral / wpumped zone

102 103 10410-3

10-2

10-1 Spacer thickness 35∗h 25∗h 15∗h

Verti

cal Γ

y fac

tor

σvertical / h

Fig. 26: Dependence of lateral xΓ factor (left) and vertical yΓ factor (right) on the relative width

of the mode intensity distribution. yΓ is calculated for a structure with 15 QD layers and three

different spacer thicknesses (layer distances). For a narrow vertical mode (small verticalσ ) the outer QD layers do not overlap with the mode at all. For a large spacer thickness this effect sets in first. Associated with the optical confinement is the internal loss of the waveguide. It typically ranges between 2 and 10 cm-1 and has its origin in free-carrier absorption and defect center scattering. A quantitative analysis of internal loss in QD lasers is beyond the scope of this work. Nevertheless, we expect more free-carrier absorption for shallow mesas than for deep ones due to the leakage of the sides (lower xΓ ) of the lateral mode into low-pumped QD layers regions. On the other hand, the etched-through side-walls of the deep mesa may cause stronger scattering of the photons. 2.2 Modeling of intrinsic quantum dot lasers The intrinsic QD laser comprises the active zone of the laser, i.e. the GaAs waveguide (“barrier”, “matrix”), the InAs wetting layers including the InGaAs quantum well of a DWELL structure, and finally the InAs QDs. Modeling of the static and dynamic characteristics of the active zone of quantum dot lasers is a complex task. Several assumptions made in semi-classical semiconductor laser theory have to be revised:

1) The concept of band structures, electrons and holes with effective masses that can be treated as quasi-free particles, is based on the assumption of delocalized carriers. In any QD device, this is still true for the epitaxial layers above or below the QDs, but certainly not for the QDs themselves, as they cause a strong localization of carriers. Therefore, QDs are treated as artificial atoms, with discrete energy levels and electron wave functions [75].

2) Due to the strong localization, carriers trapped in different QDs are not necessarily in thermal equilibrium. Typically, below a certain temperature that ranges somewhere from 150 K to more than 300 K, a common Fermi level can no longer be assumed. Instead, the carrier distribution has to be described in terms of individual QD microstates [76].

3) In contrast to the screening of Coulomb interaction in high carrier density bulk semiconductors excitonic binding and the involved shift of energies play a major role for electrons and holes confined to the same QD [77].


37

Depending on the existence of partial thermal equilibriums, i.e. basically on the device temperature and the pumping current, we propose different models to describe QD lasers:

• Quasi-Fermi levels

Quasi-static model

differential gainreduction

• NO Quasi-Fermi levels

Reduced MEM modelNo carrier escapeLess computing

Full MEM modelIncluding carrier escapeExtensive computing!

• Quasi-Fermi levels ?

Rate equation modelStrong damping, ROs

Incorrect capture modeling!

MEM modelStrong damping, ROsExtensive computing!

• NO Quasi-Fermi levels

MEM modelOnly valid model

Extensive computing!

1 10 100 1000 100000

100

200

300

400

500

Tem

pera

ture

[K]


Fig. 27: Validity and key features of different dynamic QD laser models. Four different regions of device operation are distinguished, separated by a characteristic current and temperature given by the threshold current density (typical threshold values are in the range of 100 A/cm2) and the temperature (typically between 150 and 250 K) separating the region with temperature-independent threshold ( 0T → ∞ ) from the region of conventional threshold increase

( 0 100T K< ). i) Device below or slightly above threshold, at elevated temperatures The intra-band relaxation and escape is much faster than any e-h-recombination process (radiative and nonradiative decay). Carriers redistribute rapidly through thermal escape and relaxation. Thermal equilibriums (quasi-Fermi levels) for electrons and holes exist. The carrier distribution, gain etc. can be calculated in an analytical way [78]. ii) Device below or slightly above threshold, very low temperature A “trickle-down” model without any thermal escape mechanisms is assumed. Due to the non-existence of thermal equilibrium, a microstate model has to be used.

- If the intra-band relaxation is much faster than any e-h-recombination process, a simplified ground state MEM model with infinitely fast carrier relaxation can be assumed. This approach leads to a Poisson statistic and coupled differential equations, which can be readily solved [76, 79-81].

- If we assume finite intra-band relaxation times, the multi-level MEM model is only deployable in the framework of extensive Monte-Carlo simulations [81].

iii) Device above threshold, elevated temperatures We assume fast thermal escape, but no equilibrium due to the strong pump current and lasing. Since the e-h-recombination process is now much faster due to lasing, the carrier distribution in lasing QDs is essentially non-thermal.

- A rate equation (RE) model is an easy way to model most features of the static and dynamic laser operation, if the inter-dot carrier distribution tends towards equilibrium. Coupled differential equations can be readily solved and


38

approximated analytically [82-84]. An alternative approach uses a relaxation time model [85].

- Only a MEM model has full validity, but requires extensive, power and time consuming Monte-Carlo simulation. The accurateness of the model depends on the quantity of microstates involved.

iv) Device above threshold, low temperatures Only a MEM model has full validity (see above). In this framework we deal with three types of models, the quasi-static model, a combined relaxation time rate equation model and a Monte-Carlo MEM model.

2.2.1 Electronic band structure of modeled lasers The barrier is described in terms of unstrained bulk GaAs with a CB edge of 1.51 eV and VB edge set to 0 eV at 0 K. The wetting layer is modeled as a thin quantum well layer with thickness 0.5 nm. Only the ground sub band of the confined states is taken into account. In case of a DWELL structure, the WL is replaced by an InGaAs QW with 5 nm thickness. The quantum dots are modeled including 4 CB levels and 8 VB levels. Fig. 28 shows the CB and VB edges of the QD and the DWELL QW ground sub band with respect to the GaAs band edges at 300 K, as calculated by Stier et al. [86] for a 18 nm base length QD emitting around 1.3 µm. Unfortunately, not all VB QD levels have been computed. To account for additional VB levels, a DOS factor is included with the 8th VB level (index 8), increasing the maximum level occupation of 2 by a factor between 2 and 10.

0 1 2 3 4 5 6 7 8 9 100

200

400

600

800

1000

1200

1400

H31

0

H30

0

H21

0

H20

0

H11

0

H02

0

H01

0

H00

0

E011

E030

E001

E300

E110

E020

E200W

L

E010

E100

Ene

rgy

offs

et to

G

aAs-

VB e

dge

[meV

]

Level index

T=300K

E000

Fig. 28: Electronic levels of InGaAs QD (levels 1-10), surrounding quantum well (level 0) and barrier band edge (at room temperature) for an InAs QD with 18 nm base length. The table gives the energy levels at room temperature used for modeling. The size dispersion (inhomogeneous broadening) and thus the energy level dispersion of the QDs is included to the MEM model by a Gaussian distribution

( )20

222

( )2

E

inhomQD

inhom

Nn e

ε

σεπσ

−−⋅= (2.13)

Index CB level [meV] VB level [meV]WL 1279 134 1 1139 189 2 1190 187 3 1204 168 4 1242 164 5 158 6 151 7 145 8 137


39

where ( )n ε describes the DOS of an ensemble of QDN quantum dots with a center energy level of 0E and a broadening inhomσ . The intrinsic QD laser is essentially undoped apart from weak background p-doping due to residual carbon impurities during MBE growth. In case of explicit p-doping of the barrier the additional holes are taken into account by a band offset of the QDs with respect to WL (DWELL QW) and barrier.

2.2.2 Quasi-equilibrium model This model is meant to give an understanding of important features of the QD gain medium, namely the gain vs. carrier density curve and the mechanism of differential gain reduction. It describes the static quasi-equilibrium carrier distribution below and slightly above threshold (where the carrier distribution is clamped to the threshold values). It also allows us to calculate sub-threshold spectra. All QDs, wetting layer and barrier are in partial thermal equilibrium. Quasi-Fermi levels for electrons and holed ,F eE and ,F hE exist. The corresponding occupation probability is

,

1( )1

F ee E EkT

f Ee

−=+

(2.14)

Carrier densities for barrier, wetting layer, QD states will be calculated by use of the following DOS expressions: Barrier carrier density The expression for the carrier density in a continuous bulk layer is [73]:

, ,, , 1/ 2

2( , ) ( ) F e barrier ebarrier e F e e

E En E T N T F

kTπ−⎡ ⎤

= ⎢ ⎥⎣ ⎦

(2.15)

with the effective carrier density

3

2

2( ) 22

ee

mN T kTπ

⎛ ⎞= ⎜ ⎟⎝ ⎠

(2.16)

and the Fermi-Dirac integral defined as

1/ 20

( )1 FFF d

eη η

ηη η

∞

−=+∫ . (2.17)

The effective carrier density for GaAs and its ternary compounds can be found in various text books, e.g. [73]. Wetting layer carrier density The single level wetting layer is treated as a quantum well with thickness wld .The carrier volume density n [cm-3] in quantum wells is defined with respect to their area carrier density 2Dn [cm-2] and actual thickness QWd


40

2 /D QWn n d=

, , ,, , 2

1( , ) ln 1 expe WL F e WL eWL e F e

WL

m E En E T kT

d kTπ⎛ − ⎞⎡ ⎤

= ⋅ +⎜ ⎟⎢ ⎥⎣ ⎦⎝ ⎠

, (2.18)

where ,WL eE is the (ground state) energy level of the quantum well layer. QD carrier density The carrier volume density of a layer of quantum dots is defined with respect to their discrete number of states and their volume density. While their area density is a common figure, the thickness of a single dot layer and subsequently the QD volume density is somewhat difficult to define. In modern QD laser structures we always deal with stacked layers of QDs. Since the thickness of the spacers between the layers has a lower boundary due to growth mechanisms, thus limiting the maximum QD density in a given waveguide structure, we include this limitation to the volume density by defining: The volume density of QDs is the average QD volume density in a stack of QD layers. Then the carrier volume density is defined as: 2 /D Layern n d= where Layerd is the distance between two adjacent layers. Due to this definition, the differential gain values involved in simulation are considerably lower than those for calculations based on different quantities from other researchers. The corresponding carrier density for identical dots and for spin degeneracy 2 is

0 ,0, ,

1( , ) 21

QD F e

QDQD e F e E E

Layer kT

Nn E T

de

−= ⋅

+

(2.19)

with QDN being the area density and 0QDE the ground state electron level of the QDs. Similar equations for barrier, QW and QDs hold true for holes. Assuming four electronic CB levels and eight VB levels in the quantum dot (see Fig. 28) and increasing the 8th VB level DOS by a factor of 5, we can calculate the total carrier density of the quantum dot ensemble

, , ,

, ,8 , , , ,

4

, ,1

7

, ,1

1( , ) 21

1 1( , ) 2 51 1

QD e l F e

QD h F h QD h l F h

QDQD e F e E E

lLayer kT

QDQD h F h E E E E

lLayer kT kT

Nn E T

de

Nn E T

de e

−=

− −=

=

+⎛ ⎞⎜ ⎟= ⋅ +⎜ ⎟

+ +⎝ ⎠

∑

∑ (2.20)

in dependence on the Fermi levels and the temperature. The material parameters used for the calculations are as follows:


41

Symbol Quantity Value Reference

em GaAs bulk electron mass 00.0667 m⋅ [73]

hm GaAs bulk hole mass 00.377 m⋅ [73]

,e WLm In0.15Ga0.85As electron mass ( )2

In In 00.0667 - 0.0419 c - 0.00254 c m⋅ ⋅ ⋅ [3]

,h WLm In0.15Ga0.85As hole mass 00.377 m⋅ [3]

,barrier eE GaAs CB edge 1515 meV @ 0 K [3]

,barrier hE GaAs VB edge 0 meV Scale origin

,WL eE In0.15Ga0.85As CB edge 1370 meV @ 0 K [86] +

EL spectra

,WL hE In0.15Ga0.85As VB edge 144 meV @ 0 K [86] +

EL spectra QDN QD sheet density 14 21 10 10 m−− ⋅

Table 4: Material constants of the intrinsic QD laser structure used for modeling. Guffarth et al. [87, 88] have shown that the DWELL quantum well may undergo decomposition. However, with an Indium content of 15 %, this effect is found to be still small. We therefore neglect it. DWELL QW and wetting layer show an intermixing DOS and may be treated as a single quantum well with characteristics close to those of the DWELL quantum well. We set the ground state transition energy of the intermixed layers according to the photon energy found in our photo- and electroluminescence experiments. The band offset is set proportional to the band offset of the InAs wetting layer, as given in [86]. Later we will adjust the band offset for QD neutrality reasons. Since we want to model the carrier distribution at room temperature, a temperature shift of the energy levels with respect to the GaAs VB edge has to be included for the QD, WL and barrier. This shift is computed according to the Vashni shift parameters for InAs and GaAs [3].The shift for ternary compounds of IncGa1-cAs with an Indium content of Inc (like the DWELL quantum well) is included by a simple linear interpolation:

( )( )

( )

2 2

In In

InIn In

0.276 T 0.55 Tc 415 - + 1 - c 1515 - T + 83 T + 225

c ,c 415+ 1 - c 1515shiftL T

⎛ ⎞ ⎛ ⎞⋅ ⋅⋅⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠=

⋅ (2.21)

In the following we present the calculated data for the QD laser structure DO 453, incorporating 15 layers of QDs in an In0.15Ga0.85As quantum well. Assuming total neutrality for the device: , ,e hn nα α

α α

=∑ ∑ ,


42

the quasi-Fermi levels are linked to each other, and we obtain a single parameter , ,F e F heU E E= − , where U is the voltage applied to the p-n-junction. In this case, the

QD ensemble itself is not necessarily neutral, i.e. in general , ,

1..4 1..8QD e QD hn nα α

α α= =

≠∑ ∑ .

For our structure, the QDs are charged with a considerable electron surplus of a factor of 3. Most theoretical models of QD gain media, however, assume QD neutrality. For purely excitonic models this is even an implicit condition. The demand of neutrality of the QDs can be met by a relative shift of the QD CB and VB levels with respect to the wetting layer states. This shift will be denoted as a band offset of the QDs. For our structure, the necessary offset to ensure QD neutrality is -40 meV. In the following, we discuss both the charged (no band offset) and the neutral case (-40 meV band offset). Fig. 29 shows the shift of the quasi-Fermi levels with increasing junction voltage

, ,F e F heU E E= − . We note that the CB Fermi level shifts faster than the VB Fermi level due to the lower DOS of the CB levels in QDs, DWELL QW and barrier.

0.9 1.0 1.1 1.2 1.3 1.4 1.50.0

0.1

0.2

0.3

1.1

1.2

1.3

1.4

1.5

EF,e (conduction band) EF,h (valence band)

NQD = 1.5∗1014 m-2

DO 453, charged QD

Ferm

i ene

rgy

[meV

]

Junction voltage [V]0.9 1.0 1.1 1.2 1.3 1.4 1.5

0.0

0.1

0.2

0.3

1.1

1.2

1.3

1.4

1.5

EF,e (conduction band) EF,h (valence band)

NQD = 1.5∗1014 m-2

DO 453, neutral QD

Ferm

i ene

rgy

[meV

]

Junction voltage [V]

Fig. 29: Dependence of quasi-Fermi levels on the junction voltage for negatively charged QDs (left) and for neutral QDs (right). In both cases, the CB Fermi level shifts faster than the VB Fermi level due to the lower DOS of the CB levels. Along with the junction voltage the carrier density in the structure increases. Fig. 30 shows the dependency of the QD ground state occupation probability for electrons and holes on the total carrier density in the active zone (i.e. the electron-hole number of barrier, DWELL layers and QDs with respect to the active zone volume). It reveals an important feature of the quantum dot gain medium: The occupation probability for electrons is always considerably larger than for holes, due to lower density of QD CB states. At the time the hole occupation probability reaches 0.5, the electron state is almost saturated. The effect is obviously more pronounced for negatively charged than for neutral dots. For large quantum dot sheet densities the curves are simply shifted to higher carrier density, since more carriers are needed to fill the QDs. The imbalance of ground state occupation has a serious impact on gain and differential gain. Fig. 31 shows the calculated gain curve for a maximum modal gain of 45 cm-1. This maximum is approached only for large carrier densities 18 3> 10 cm− , whereas inversion (Gain = 0) is reached for very low carrier densities, 18 3~0.05 10 cm−⋅ .


43

The gain for charged QDs follows a logarithmic curve (linear slope in Fig. 31, left graph). For neutral quantum dots, the slope of the linear part in Fig. 31, right graph, is steeper, thus providing more gain for a given carrier density than charged QDs, but levels off to a sub-logarithmic growth for 18 3> 0.2 10 cm−⋅ .

0.01 0.1 10.0

0.2

0.4

0.6

0.8

1.0

CB VB

DO 453, charged QD

1∗1014 m-2

1.5∗1014 m-2

2.5∗1014 m-2

5∗1014 m-2

10∗1014 m-2

Carrier density [1018 cm-3]

QD

GS

Occ

upat

ion

prob

abilit

y

0.01 0.1 10.0

0.2

0.4

0.6

0.8

1.0 CB VB

DO 453, neutral QD

1∗1014 m-2

1.5∗1014 m-2

2.5∗1014 m-2

5∗1014 m-2

10∗1014 m-2


QD

GS

Occ

upat

ion

prob

abilit

y

Fig. 30: QD ground state occupation probability for electrons (CB) and holes (VB) vs. the total carrier density in the active zone. Due to the lower CB quantum dot DOS the electron ground state is much stronger populated than the hole state. For negatively charged dots, this effect is even more pronounced. The larger dot density at fixed gain merely increases the necessary carrier density.

0.01 0.1 1

-40

-20

0

20

40

Mod

al g

ain

[cm

-1]

DO 453, charged QD

1∗1014 m-2

1.5∗1014 m-2

2.5∗1014 m-2

5∗1014 m-2

10∗1014 m-2


0.01 0.1 1

-40

-20

0

20

40

DO 453, neutral QD

Mod

al g

ain

[cm

-1]

1∗1014 m-2

1.5∗1014 m-2

2.5∗1014 m-2

5∗1014 m-2

10∗1014 m-2


Fig. 31: Modal gain of QD ground state transition vs. total carrier density for different dot sheet densities. The maximum gain (loss) is 45 cm-1. The inversion carrier density (Gain=0) is about the same for charged dots (left) and neutral dots (right), but gain increases faster for neutral dots. A crucial parameter for the dynamic behavior of QD lasers is the differential gain, since it is the most important link between electrical modulation of the laser (i.e. of the carrier density) and the optical modulation (i.e. the photon density), as denoted in the basic equation for the resonance frequency of a semiconductor laser:

0

'12

gres

phot

v Gf P

π τ= (2.22)


44

where G’ is the differential modal gain. The differentiation of the curves from Fig. 31 yields the differential gain shown in Fig. 32 in dependence on the modal gain. We see a strong decrease of the differential gain with increasing modal gain. Whereas at inversion threshold the differential gain starts with values around 15 20.5 10 cm−⋅ , it decreases by a factor of 2 at a typical threshold gain value of 15 cm-1. This differential gain reduction is even more pronounced for the negatively charged quantum dots. It represents a severe limitation for the modulation bandwidth of QD laser devices.

0 10 20 30 400.0

0.2

0.4

0.6

0.8

1.0

Diff

eren

tial g

ain

[10-1

5 cm

2 ]

DO 453, charged QD

1∗1014 m-2

1.5∗1014 m-2

2.5∗1014 m-2

5∗1014 m-2

10∗1014 m-2

Modal gain [cm-1]

0 10 20 30 400.0

0.2

0.4

0.6

0.8

1.0DO 453, neutral QD

1∗1014 m-2

1.5∗1014 m-2

2.5∗1014 m-2

5∗1014 m-2

10∗1014 m-2

Modal gain [cm-1]

Diff

eren

tial g

ain

[10-1

5 cm

2 ]

Fig. 32: Differential modal gain, assuming a maximum modal gain of 45 cm-1, vs. modal gain. Charged QDs (left) show a strong decrease in differential gain due to the QD electron ground state saturation. The effect is also present for neutral QDs. The equation above can be transformed into

( )2

01 '

21 '

2

res g m i

g m iout

p m

f v G P

vG P

hv V

α απ

α απ α

= +

+=

⋅

(2.23)

using the fact that above threshold the modal gain equals the losses that are associated with the photon lifetime. outP denotes the total output power of the device.

For devices of reasonable length < 2000 µm the term m i

m

α αα+ is close to unity.

Therefore, the resonance frequency for a given output power is mainly determined by the differential gain G’. For high resonance frequencies, laser working at a low modal gain value (long devices) should be preferred. However, longer devices consume more electrical power and are subjected to cavity resonance effects at modulation frequencies coinciding with the cavity round trip frequency (e.g. 10 GHz for a 4 mm long device). Issues like power consumption and detailed modulation characteristics can only be addressed within the framework of a dynamic model, as presented in the next section.


45

2.2.3 Relaxation time model (RT model) Any real semiconductor laser operation, especially the switching behavior in the range below 1 ns, is governed by non-equilibrium carrier distributions varying in time and position inside the active zone. There is a hierarchy of relaxation and recombination processes involved [85]: 1) Fast carrier-carrier scattering in the barrier with a time constant (1) 1Barrier psτ < drives the carrier distribution towards a separate Fermi distribution of electrons and holes with distinct temperature 2T (not necessarily lattice temperature) and Fermi energy

(1), ,F barrier eE , (1)

, ,F barrier hE . 2) Carrier-phonon scattering in the barrier with a time constant (2) 1Barrier psτ < drives the Fermi distribution of carriers towards the lattice temperature (the lattice is assumed to be an efficient reservoir at constant temperature T ). Along with this we introduce two new Fermi levels (2)

, ,F barrier eE , (2), ,F barrier hE .

3) Similar processes (carrier-carrier, carrier-phonon scattering) drive the carrier distribution in the wetting layer (or DWELL QW) towards Fermi distributions (2)

, ,F WL eE , (2), ,F WL hE at lattice temperature T.

4) The interaction of carriers in the barrier and the wetting layers leads to the formation of joint Fermi levels (2)

, ,F B WL eE + , (2), ,F B WL hE + . Since there are between 5 and

15 stacked layers of QDs embedded in the barrier, this interaction also causes thermal equilibration of the WL and QDs of these different layers. The time constant of this process is assumed to be fast ( (2) 1Barrier WL psτ ↔ < ). There might be a dependence on the number of stacked QD layers. 5) Carrier-carrier scattering between carriers in the QDs and the wetting layer / barrier are finally driving the QD distribution and thus the total carrier distribution in the VC and the VB towards Fermi distributions ,F eE , ,F hE of temperature T due the fast WL/barrier temperature relaxation. The time constant for this process is mainly given by the carrier capture time of the QDs and lies around ~ 5WL QD psτ ↔ . 6) At all levels, carriers can recombine, thus decreasing the number of carriers and (in case of radiative recombination) increase the number of photons. We include a non-radiative recombination constant for the barrier, wetting layer and all QD levels and radiative recombination for all QD levels according to the possible optical transitions (transition arrows in Fig. 28). All recombination times lie in the range of a nanosecond. We enable stimulated emission for the ground state and the next-to-ground-state transition (thick lines in Fig. 28) with a rate given by the modal gain of both transitions. The dynamic behavior of the model arises from the tendency of the real carrier densities to approach the partial equilibriums within the corresponding relaxation time and, of course, from the lasing process.


46

To reduce the computational complexity of the model we make the following assumptions: a) The scattering time constants are actually different for electrons and holes due to

their different effective mass and energy level spacing; we assume identical values.

b) According to microscopic scattering parameter calculations [85] the values for the scattering time constants involving the barrier and the wetting layer levels are in the range between 0.1 and 1 ps. We therefore neglect the dynamics of processes (1), (2) and (3) since they are much faster than any other relaxation or recombination process like WL and QD carrier capture, non-radiative and radiative recombination. Hence the carrier distribution in the barrier and the wetting layers can be described in terms of integrated carrier densities:

, , , ,( ), ( ), ( ), ( )Barrier e Barrier h WL e WL hn t n t n t n t c) We assume an ideal ensemble of QDs without inhomogeneous broadening. Thus,

we neglect wavelength shifts and the effect of spectral broadening due to spectral hole burning.

d) The various scattering processes influence the phase decay (homogeneous line width) of the QD radiative recombination. Since we do not take inhomogeneous broadening into account, we also neglect homogenous broadening and include both entities in the (modal) gain, which is easily derived from experimental results.

e) Within the framework of the approximations c) and d), the carrier distribution in the QD ensemble is described by ensemble average populations for the different CB and VB levels of the QDs, i.e. for the above model we have a set of 12 variables:

1, 2, 3, 4,

1, 2, 8,

( ), ( ), ( ), ( )

( ), ( ),..., ( )QD e QD e QD e QD e

QD h QD h QD h

n t n t n t n t

n t n t n t

The ensemble average model holds true as long as we assume the scattering of carriers between different QDs with the time constant ~ 5WL QD psτ ↔ to be fast compared to non-radiative and radiative recombination in the QDs (~ns).

f) We include two photon modes, one each for the ground state and the next-to-ground-state transition.

Finally, the relaxation time model that we use for dynamic simulation consists of 24 coupled rate equations: 4 QD lasing level occupation equations:

( )( )

( )( )

1,1, , , 1,

1, , , 1,

1, 1,max,1 1

1, 1, 1,,

1..8

( ) 1 2 , ( ), ( )

1 2 , ( ), ( )

( ) ( )1 ( )

2( ) ( ) ( )

( )

QD eQD e F QD e QD e

QD

QD e F total e QD etotal

QD e QD hg

QD e QD h QD eQD h

rad nonrad

dn tf E E t T n t

dt

f E E t T n t

n t n tv G P t

n t n t n tn tα

α

τ

τ

τ τ =

= −

+ −

+⎛ ⎞− −⎜ ⎟

⎝ ⎠⋅

− − ∑

(2.24)


47

and similarly for 1, 2, 4,( ), ( ), ( )QD h QD e QD hdn t dn t dn t , the two latter radiating into mode 2 ( )P t , 8 QD non-lasing level occupation equations:

( )( )

( )( )

3,3, , , 3,

3, , , 3,

3, 2, 3,,

1..8

( ) 1 2 , ( ), ( )

1 2 , ( ), ( )

( ) ( ) ( )( )

QD eQD e F QD e QD e

QD

QD e F total e QD etotal

QD e QD h QD eQD h

rad nonrad

dn tf E E t T n t

dt

f E E t T n t

n t n t n tn tα

α

τ

τ

τ τ =

= −

+ −

⋅− − ∑

(2.25)

and similarly for 4, 3, 5, 6, 7, 8,( ), ( ), ( ), ( ), ( ), ( )QD e QD h QD h QD h QD h QD hdn t dn t dn t dn t dn t dn t , including the factor δ DOS enhancement of VB level 8:

( )( )8,8, , , 8,

( ) 1 2 , ( ), ( ) ...QD hQD h F QD h QD h

QD

dn tf E E t T n t

dtδ

τ= ⋅ − + , (2.26)

2 wetting layer (or DWELL QW) carrier density equations:

( )( )

( )( )

,, , , ,

, , , ,

, ,

, , ,

( ) 1 , ( ), ( )

1 , ( ), ( )

( ) ( )1( ) ( )

WL eWL e F Barrier WL e WL e

Barrier WL

WL e F total e WL etotal

WL e WL h

nonrad WL WL e WL h

dn tn E E t T n t

dt

n E E t T n t

n t n tn t n t

τ

τ

τ

↔↔

= −

+ −

⋅−

+

(2.27)

similarly for , ( )WL hn t ,

2 barrier carrier density equations including the pump term:

( )( )

( )( )

,, , , ,

, , , ,

, ,

, , ,

( ) 1 , ( ), ( )

1 , ( ), ( )

( ) ( )1 (( ) ( )

Barrier eBarrier e F Barrier WL e Barrier e

Barrier WL

Barrier e F total e Barrier etotal

Barrier e Barrier h

nonrad Barrier Barrier e Barrier h

dn tn E E t T n t

dt

n E E t T n t

n t n t Jn t n t

τ

τ

ητ

↔↔

= −

+ −

⋅− + ⋅

+)t

e

(2.28)

similarly for , ( )Barrier hn t ,

6 equations which account for electron and hole number conservation in all relaxation processes:


48

( ) ( ) ( ), , , , , , , , ,

1..4

, , ,1..4

, ( ), , ( ), 2 , ( ),

( ) ( ) ( )

Barrier e F total e layer WL e F total e QD QD e F total e

Barrier e layer WL e QD QD e

n E E t T N n E E t T N f E E t T

n t N n t N n t

αα

αα

=

=

⎛ ⎞+ +⎜ ⎟⎝ ⎠

⎛ ⎞= + +⎜ ⎟

⎝ ⎠

∑

∑(2.29)

( ) ( ), , , , , ,

, ,

, ( ), , ( ),

( ) ( )Barrier e F Barrier WL e layer WL e F Barrier WL e

Barrier e layer WL e

n E E t T N n E E t T

n t N n t↔ ↔+

= + (2.30)

( ), , , ,1..4 1..4

2 , ( ), ( )QD e F QD e QD ef E E t T n tα αα α= =

=∑ ∑ , (2.31)

and three similar equations holding for the VB states, as well as two equations for the photon modes:

1, 1,1 1max,1 1

1, 1,

( ) ( )( ) ( )1 ( )2

( ) ( )

QD e QD hlayers g

phot

QD e QD hlayers

rad

n t n tdP t P tN v G P tdt

n t n tN

τ

βτ

+⎛ ⎞= − −⎜ ⎟

⎝ ⎠⋅

+ ⋅

(2.32)

similarly for 2 ( )P t .

QDN denotes the single sheet QD density, layersN gives the number of stacked QD layers. maxG denotes the maximum modal gain of the first and second photon mode. The barrier and the wetting layer carrier densities are given as area densities. The photon number is converted into output power by ,1 1( ) ( )out g m QDP t h v N L W P tν α= ⋅ ⋅ ⋅ ⋅ ⋅ , (2.33) with L and W being the laser length and width, respectively. The initial conditions for the Fermi levels are

, , , , , ,

, , , , , ,

(0) (0) (0) 1000

(0) (0) (0) 340F total e F Barrier WL e F QD e

F total h F Barrier WL h F QD h

E E E meV

E E E meV↔

↔

= = =

= = =

for a numerical reason: Starting with equal quasi-Fermi levels for electrons and holes, similar to the situation in an un-pumped semiconductor, causes convergence problems of the numerical solver due to the exponential increase / decrease of the Fermi levels with the pump current. The initial carrier densities and carrier numbers for all levels are set to the values corresponding to the initial Fermi levels. The initial photon densities are set to zero. Numerical solutions of this differential equations system depending on the input current function ( )J t yield the temporal behavior of carrier densities and photon density. The calculation itself is implemented with Mathematica 5.1 [68] and uses the NDSolve[ ] command with a maximum step number of 109.


49

Relaxation and recombination time parameters For quantum dots, a wide range of values for capture, relaxation and recombination times exist, ranging from sub-ps to a several tens of ps [89-92]. In our model, all time constants are actually fit parameters determined by the comparison of the simulation and measurements of the dynamic behavior of QD lasers, i.e. small signal and large signal modulation. Typical ranges for time constants used for the simulation of our QD lasers are:

Symbol Quantity Range for calculation

QDτ Intra-dot relaxation time 1-4 ps

Barrier WLτ ↔ Barrier to wetting layer relaxation time 0.1-1 ps

totalτ 1-10 ps

Wetting layer to QD relaxation time, total, therefore slowest relaxation time

radτ QD radiative recombination time ~ 1 ns

nonradτ QD non-radiative recombination time ~ 1 ns

,nonrad WLτ WL radiative recombination time ~ 2 ns

,nonrad barrierτ Barrier radiative recombination time ~ 1 ns η Pump efficiency 0.5-1.0

max,1 max,2,G G Maximum modal gain per QD layer 1-10 cm-1 Table 5: Range of relaxation and recombination time constants used for modeling. Simulation of gain-current curve The gain-current curve of the intrinsic QD laser is calculated assuming a step-function like current pulse and a non-lasing device (infinite mirror loss, like an anti-reflection coated semiconductor amplifier). The RTM equations are solved for successive current densities and evaluated for the steady state modal gain and differential modal gain at steady state time (typically ~10 ns) after the pulse leading edge. Fig. 33 shows the corresponding curves for charged and neutral dots. For neutral dots a gain up to 30 cm-1 can be realized with threshold current densities below 1 kA/cm-2. The differential gain lies between 0.4 and 15 21 10 cm−⋅ for reasonable laser length.


50

0 500 1000 1500 2000 2500

-40

-30

-20

-10

0

10

20

30

40

DO 453

Neutral QDs (-) charged QDs


Mod

al g

ain

[cm

-1]

0 500 1000 1500 2000 25000.01

0.1

1

Neutral QDs (-) charged QDs

Diff

. mod

al g

ain

[10-1

5 cm2 ]

DO 453


Fig. 33: Calculated modal gain and differential modal gain in DO 453 for neutral and charged QDs for a dot density of 10 21.5 10 cm−⋅ . The threshold current density for common QD laser devices lies in the range between 200 and 1000 A/cm2. The gain-current curves shown in Fig. 33 can be roughly approximated by the two-parameter function

( ) lninv

jG j Aj

⎛ ⎞= ⋅ ⎜ ⎟

⎝ ⎠, (2.34)

where A and invj denote the gain slope and the inversion current density. This interpolation function is useful for the analytical description of the laser properties. We compared the calculated gain-current curve for the DO 453 structure with the experimental results of gain measurements on a SOA structure (investigated by my colleague M. Lämmlin). After the correction for the fiber coupling losses of the device, we observed a good correspondence between the measured and the simulated data, including a gain saturation effect at an optical input power of 0.3 mW.

0 20 40 60 80 100 120 140-70-60-50-40-30-20-10

010203040

Experiment Fiber-to-fiber gain 20 dB coupling loss

Simulation Chip gain @ 0.01 mW input Chip gain @ 0.1 mW input Chip gain @ 0.3 mW input Chip gain @ 0.5 mW input

Chi

p ga

in [d

B]

Current [mA]

DO 453, 4000x4µm

Fig. 34: Comparison of chip gain measurement and simulation of a DO 453 SOA structure with length 4 mm, ridge width 4 µm. The best fit is achieved for 20 dB coupling loss (a plausible value) and 0.3 mW optical input power.

2.2.4 Simulation of QD laser cw operation Assuming a step-function like current pulse and laser structures of different length (1, 2, 3, 4 mm, as-cleaved facets, internal losses 2 cm-1), the RTM equations are solved for successive current densities and evaluated for the steady state photon density


51

1( )P t at time ~10 ns after the pulse leading edge. The criterion for the steady state time is the stability of the optical output (relaxation oscillations fully damped out). Fig. 35 shows the measured and averaged PI curves for a number of devices (see section 3.1) and the corresponding simulation results. Since the simulation parameters were chosen to fit the PI data (besides the dynamic measurements), the agreement is quite good. All thresholds are correctly modeled, as well as the slopes for the longer devices. The deviation of the slope for short devices maybe due to spectrally dependent gain compression effects which are not included in the model.

0 500 1000 1500 2000 25000

20

40

60

80

100 1 mm 2 mm 3 mm 4 mm Simulation

To

tal o

utpu

t pow

er [m

W]


DO 453, 4 µm, as cleaved

Fig. 35: Measured PI curves for DO 453 QD lasers with length 1-4 mm, ridge width 4 µm. The scatter points show the simulated results. From the set of experimental PI curves for different device length we can derive the internal quantum efficiency int,maxη , the internal optical losses iα and the transparency current density ( )thrj L → ∞ according to the linear laser model:

( )int,max( ) mout thr

m i

hP J J Je

αν ηα α

= ⋅ ⋅ −+

(2.35)

with 1 2

1 1ln2m L R R

α⎛ ⎞

= ⎜ ⎟⎝ ⎠

The transparency current density is usually found by extrapolation of the threshold current density dependence on the device length for infinitely long cavities. Our model and the experimental results show that a linear extrapolation is not suitable in most cases due to the strong nonlinearity of the gain-current curve. Including this nonlinearity to the extrapolation function in the shape of the 2 parametric gain approximation (2.34) yields the following exponential dependence:

( )

1( )1 1

( ) ln

1( ) 1 ( )i m i

thr thr inv i m

LA A

thr inv inv m

G j A j j

j L j e j e LA

α α α

α α

α−+

− −

= ⋅ = +

⎛ ⎞= ⋅ ≈ ⋅ +⎜ ⎟⎝ ⎠

(2.36)

The linear approximation is only valid for 1( )mA Lα − , i.e. for long devices.


52

The term i

Ainvj e

α

⋅ denotes the transparency current density transpj of the waveguide structure. Fig. 36 (right) shows the corresponding curve (similar to the curve derived from the RT model) and experimental data for four different device lengths. The threshold current dependence predicts an nonlinear increase of the threshold currents for short (~500 µm) devices.

0.0 0.5 1.0 1.5 2.00

200

400

600

800

1000

DO453, 4µm, as cleaved

jtransp=170 A/cm2

Measurement Linear fit

Thre

sh. c

urre

nt d

ensi

ty [A

/cm

-2]

Reciprocal length [mm-1]

0.0 0.5 1.0 1.5 2.0 2.50

500

1000

1500

2000

2500

Measurement Nonlinear fit

DO 75, 4 µm

jtransp= 570 A/cm2

Thre

shol

d cu

rrent

den

s. [A

/cm

2 ]

Reciprocal length [mm-1]

Fig. 36: Linear (left) and exponential (right) extrapolation of the dependence of threshold current density on the inverse cavity length. The linear extrapolation is valid for large modal gain, long devices as found for the 15fold QD stack sample Do 453 (left). From the slope of the P-I curve at threshold the external quantum efficiency is derived. The linear dependence of the external quantum efficiency on the laser length

( )1 2

1int,max int,max

21 1 1( ) 1 1ln

i i

diff m R R

L Lα αη α η η

⎛ ⎞⎛ ⎞ ⎜ ⎟= + = +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ (2.37)

gives us an estimate of the maximum internal quantum efficiency and the waveguide losses. This model holds for constant maximum internal quantum efficiency and internal losses, independent of the cavity length. In the case of lasing close in the gain saturation region, i.e. for short cavities, the differential quantum efficiency is found to decrease in quantum dot lasers (see Fig. 37). This effect might be caused by three mechanisms: 1) The larger photon density in short cavities leads to a more pronounced gain

compression effect and to a decrease of the internal quantum efficiency. This effect will be included by a gain compression factor.

2) Due to the large current density higher states are more populated. If these states have a larger non-radiative recombination rate, the overall recombination rate increases. The differential quantum efficiency then decreases with length due to the decrease of the internal quantum efficiency. This effect is, to a much smaller extent than in experiment, also present in the RT model.

3) The larger carrier density in short devices leads to an increase of free carrier absorption and subsequently to an increase of the internal optical losses. The difficulty of quantitative estimation of internal losses was already discussed in section 2.1.2. Carrier density dependent optical losses are therefore not included into our models.

The effect of nonlinear dependence was found for all quantum dot lasers we investigated.


53

0 1 2 3 40.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5 Measurement Theory with gain compression

ηint, 0 ~ 100 %αint = 2.4 cm-1

ε ~ 10-19 m3

DO453, 4µm, as cleaved

1/η ex

t

Device length [mm]

Fig. 37: Differential quantum efficiency vs. device length for 4 different device lengths. The values for short devices deviate from the a linear dependence, the quantum efficiency even decreases for 1 mm long devices. The nonlinear model is explained below. The model of a linearly increasing PI curve is of course limited for any real laser by following (reversible) effects: 1) Gain compression: Due to the large photon density inside the cavity the

stimulated recombination time of the QD ground state electrons and holes becomes so short, that it eventually lies in the range of the QD carrier capture and relaxation time. The QD states are tend to be depleted (spectral hole burning). Since the gain of the QD medium still needs to compensate the losses, the carrier density and therefore the current density increase.

2) Thermal effects: Since 50 % of the power consumed by the laser diode is converted to thermal energy, the device heats up for large current densities. The increasing lattice temperature leads to a redistribution of carriers in favor of higher energy states. Therefore, the carrier density and current density (for constant gain) increase.

Thermal effects can be avoided to a certain extent by efficient heat removal and pulsed operation. The gain compression mechanism is inherent and cannot be circumvented. The gain compression effect is present in our model; thermal effects can be partially included by changing the lattice temperature manually. In our model, gain compression starts to set in only for very large (>10 kA/cm2) current densities, seemingly in agreement with experimental results. Since gain compression is held responsible as the limiting factor for modulation dynamics [32, 93, 94], we derive an estimation of the gain compression from the PI curve. The phenomenological model of gain compression expresses the gain compressed modal gain dependent on the photon density P :

1 ,1

out

g m p

PG G PP h v Vε ν α

→ =+ ⋅ ⋅ ⋅

. (2.38)

The influence of gain compression on the PI curve is written in the form of a power dependent threshold current density. Therefore we rewrite the threshold current density as a Taylor sum with the help of the logarithmic gain approximation ( )thrG j :


54

( )( ) ( ) ( ) 21

,0

11

1( ) 1 ...2

i m

i m

Pi m i mA

thr inv thr

GP

j P j e j P PA A

α α ε

α αε

α α α αε ε

+ +

= ++

⎡ ⎤+ +⎛ ⎞⎢ ⎥= = ⋅ + + +⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

(2.39)

The output power is then given implicitly by

2

00 1 2

( ) ( )( ) ( ) ...out outout

g m p g m p

P P j P jP j P j C Cj h v V h v V

ε εν α ν α

⎡ ⎤⎛ ⎞∂ ⎢ ⎥= − ⋅ + ⋅ +⎜ ⎟⎜ ⎟∂ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅⎢ ⎥⎝ ⎠⎣ ⎦ (2.40)

where 0 ( )P j is the PI curve, ,0thrj the threshold current density in the absence of gain compression. The 1st order effect of gain compression is a decrease of the external quantum efficiency:

( )0 11 ,0

(1) (0)

1 1( ) 1 , i mthr

ext ext g m p

P CL C jj h v V A

α αε

η η ν α⎛ ⎞ +∂

= ⋅ + =⎜ ⎟⎜ ⎟∂ ⋅ ⋅ ⋅⎝ ⎠ (2.41)

The 2nd order effect is a curvature of the PI curve. The 1st and 2nd order effect have been included to a simulation of the LI curve for different gain compression factors.

0 500 1000 1500 2000 25000

10

20

30

40

50 Measurement ε = 10-21 m3

ε = 10-20 m3

ε = 5 x 10-20 m3

ε = 10-19 m3

Out

put p

ower

[mW

]


Do 453, 1000x4 µm

Fig. 38: Simulation of the influence of gain compression on PI curve for different gain compression factors. The dotted curve is a measured cw PI curve. A bend in both simulated curves can be seen, that is not present in the experimental results. Fig. 38 shows the simulated influence of gain compression for a DO 453, 1000x4 µm sample. Several effects may cause a linear decrease of the slope besides gain compression, for example an increase of the internal losses. The criterion for the influence of gain compression is therefore the 2nd order curvature, i.e. the deviation from a linear slope. For the simulated PI curves in Fig. 38, this deviation is clearly visible for gain compression factor 20 310 mε −> . However, the measured LI curve shows no curvature. From comparison we might conclude that the gain compression factor for this sample is smaller than 20 310 m− . However, a more detailed analysis of the spectrally resolved output power in section 2.2.7 reveals that the spectral gain


55

compression is much larger in QD lasers. The curvature of the spectrally resolved output power is larger and would agree well with notion of a large gain compression

19 310 mε −> and a strong nonlinear behavior of the external quantum efficiency. The following expression derived from equation (2.41) gives a quantitative understanding of the nonlinear dependence of the inverse differential efficiency on the device length (see Fig. 37):

( ) ( ) ( )( )

,0

(1) (0)

1 1 1thr i

ext ext g m

j LL L

e A v H Lαε

η η α⎛ ⎞

= + +⎜ ⎟⎜ ⎟⋅ ⋅ ⎝ ⎠ (2.42)

Combined with the measured threshold current dependence ( ),0thrj L the fit yields an estimate of the internal losses and the gain compression factor (for known A ).

2.2.5 Simulation of the large signal operation of QD lasers Numerical solutions of the differential equations system of the RT model yield the temporal behavior of all time-dependent variables, among them carrier densities, the Fermi levels and the photon density. Fig. 39 shows a typical result for the simulation of the pulsed operation of a quantum dot laser diode. The electrical pulse width is 5 ns, the pulse amplitude lies well above the threshold. For numerical reasons, the leading edge of the current pulse has a smooth slope with a rising time of 100 ps (typical rise time for pulse generators).

0 1 2 3 4 5 60

10

20

30

40

50

60

70

0

20

40

60

80

100

Cur

rent

[mA]

Time [ns]

Out

put p

ower

[mW

]

0 1 2 3 4 5 60.0

0.2

0.4

0.6

0.8

1.0

electrons holes

Occ

upat

ion

prob

abilit

y

Time [ns]

Fig. 39: Simulated pulsed laser operation current and output power transient (left) and corresponding quantum dot ground state occupation probability for electrons and holes (right) for DO 453 sample parameters. The power transient shows a turn-on delay and strongly damped relaxation oscillations. The occupation probabilities show the imbalance between electron and hole occupation due to the different DOS. A typical feature of the turn-on process is relaxation oscillations of carrier and photon density. They occur during the first nanoseconds of laser operation. Their origin is the imbalance of carrier density and photon density during turn-on: The inflow of carriers due to pumping increases the carrier density of the QD lasing levels. As long as the occupation probability is well below the inversion condition, carriers recombine slowly by spontaneous emission. Since the filling speed is larger than the recombination speed, the occupation builds up till it reaches and exceeds inversion. Now stimulated emission sets in, and the photon density rises


56

exponentially. Eventually the carrier recombination speed due to stimulated emission becomes larger than the filling speed, leading to a decrease of the carrier density. The subsequent reduction of the photon density closes the relaxation cycle. The oscillations typically damp out after a few cycles and lead to steady-state lasing. After the current is turned off, the photon density decreases exponential due to stimulated emission within a few 10th of picoseconds. The carrier densities decrease only slowly after lasing turns off. The relaxation oscillation process can be roughly described by a relaxation frequency and a damping constant. Here is a connection to the small signal analysis described in the next section: The relaxation frequency is approximately given by the resonance frequency resf and the damping behavior by the damping coefficient γ (see Fig. 40, left). The dependence of resf and γ on laser parameters like differential gain and photon lifetime is discussed in the next section. A simple analytical expression for the turn-on delay (time interval between onset of current and lasing) can be derived from a simple rate equation model [95]:

0ln 1 lnturn on spon sponspon thr

e d jnj j j

τ τ ττ−

⎛ ⎞ ⎛ ⎞⋅= − − ≈⎜ ⎟ ⎜ ⎟⎜ ⎟⋅ −⎝ ⎠⎝ ⎠

(2.43)

where sponτ is the time constant of spontaneous emission, thrj the threshold current density. Fig. 40 (right) shows the good agreement of the logarithmic dependence with experimental data. Measurement of the turn-on delay is a simple way to determine

sponτ .

0.0 0.5 1.0 1.5 2.00

20

40

60

80

1001/fres

Measurement Simulation

Out

put p

ower

[mW

]

Time [ns]

τturn-on

~ γ

0.0 0.5 1.0 1.5 2.0 2.5 3.00

1

2

3

4

5

τspon = 1.04 ns

Turn

-on

dela

y [n

s]

Ln(I/(I-Ithr))

Fig. 40: Measured and simulated turn-on transient of a DO453, 1000x4 µm laser diode for a particular pulse current (left) and the corresponding turn-on delay in units of spontaneous emission time τ for different pulse currents (right). Another important large signal mechanism is the turn-off of the laser. In contrast to the slow turn-on due to sponτ being typically in the ns range, the turn-off is governed by the fast carrier relaxation times and the photon lifetime photτ , all in the range of tens of ps. The slowest of these processes dominates the exponential decrease of the photon density. Therefore, no simple analytical expression for the turn-off behavior can be given.


57

The large signal behavior of a laser diode determines its capability for digital data modulation. For optical data modulation, the laser diode is biased above threshold and switched between two output power levels, defining the low and the high digital optical signal level (see Fig. 41). Operating the laser diode above threshold avoids the disturbing influence of a long turn-on delay, but decreases the contrast between Hi and Lo optical level. 000110100111010110 000110100111010110

Fig. 41: Digital optical data modulation scheme: A digital stream of electrical signals enters the laser diode and is converted to a stream of optical signals. Both the Lo and Hi electric levels lie above threshold. The modulation scheme shown is a Non-Return-to-Zero (NRZ) amplitude modulation scheme. There is a close relation between large signal and small signal modulation: The small signal relaxation frequency and damping of the laser diode increase with output power (see next section). Since for large signal modulation, the output of the laser is switched between two states, Hi and Lo, both states correspond to different relaxation frequencies. Clearly, the slow resonance frequency and slower damping at the Lo signal level has a larger influence on the large signal quality than the fast relaxation at the Hi signal. Generally, the maximum large signal modulation frequency lies in the range of the maximum modulation bandwidth of the laser diode derived from small signal measurements.

In order to evaluate the large signal behavior of a laser diode with respect to digital data modulation, so-called eye pattern diagrams of a laser diode are measured. Eye pattern measurements show the capability of a laser to send data at a certain transmission rate (e.g. 1.25 / 2.5 / 5 / 10 Gb/s) and a certain output power. Fig. 42 illustrates the composition of an eye pattern diagram. The electrical signal stream employed for modulation is a Pseudo-Random Bit Sequence (PRBS, index N) containing all possible permutations of N bits in a fixed, most condensed bit frame. Fig. 42: An eye pattern diagram consists of the successive bitwise superposition of an optical signal stream. The signal stream itself has a fixed pattern (Pseudo-Random Bit Sequence) for maximum variation of bit patterns in a given time frame. A measured eye pattern consists of single data points rather than of transients due to the sampling measurement scheme of the set-up.


58

An eye pattern diagram consists of the successive bitwise superposition of an optical signal stream with a fixed PRBS pattern. It shows the four possible transitions between two successive bits (0 0, 0 1, 1 0, 1 1) and their dependence on N-1 preceding bits. Eye diagrams are simulated in the framework of the RT model using appropriate PRBS signal streams as current input. Since the length of a PRB sequence (the word frame length) depends exponentially on the number of bits involved ( 2N ), the computational time for an eye pattern increases accordingly, demanding ~1 h computational time on a 1 GHz Pentium III for a PRBS 7. Fig. 43 shows the simulated eye patterns for a DO 453, 1000x4 µm QD laser diode.

0 100 200 300 400 50040

60

80

100

120PRBS4, 2.5 Gb/s

Lase

r Out

put [

mW

]

Time [ps]0 100 200

20

40

60

80

100

120

140

Lase

r Out

put [

mW

]

Time [ps]

PRBS4, 10 Gb/s

Fig. 43: RTM simulated eye patterns for a DO 453, 1000x4 µm QD laser diode at 2.5 Gb/s (left) and 10 Gb/s (right) data rate. A PRBS 4 is applied as simulation input, switching between 2.5 kA/cm2 and 5 kA/cm2 input current density. Due to strong damping of relaxation oscillations, both diagrams show almost symmetric eye patterns. The 10 Gb/s pattern shows bandwidth limitation effects; there is no straight upper or lower level. One important parameter for optimum performance of the laser is the “openness” of the eye pattern, i.e. the signal-to-noise ratio of the Hi and Lo level. A characteristic feature of QD laser eye patterns is the low distortion of the Hi and Lo level due to strong damping of laser oscillations. Therefore, as shown in Fig. 43, the eye patterns appear symmetric. The maximum data rate is limited by the modulation bandwidth of the laser diode. As the data rate approaches the maximum bandwidth, the eye starts to close. Separation between upper and lower signal level is no longer possible. This effect can already be seen in the right graph of Fig. 43. Detailed analysis of eye pattern diagrams and subsequent bit error rate measurements is done in section 3.3.3.

2.2.6 Simulation of the small signal operation of QD lasers In order to be able to compare measured small signal parameters of the QD laser diodes (S parameter) with the time-resolved RTM simulation, we employ a time-to-frequency conversion algorithm: A current modulation with frequencies between 0.5 and 20 GHz is superimposed with the step-like current pulse. The modulation amplitude is a small fraction of the pulse current (typical modulation power -10 dBm, corresponding to a few A/cm2), since we aim at small signal modulation (see Fig. 44). After solving the RTM we evaluate the amplitude and phase of persistent modulation (turn-on fluctuations must be damped

out at this point) of the junction voltage , ,( ) ( )( ) F e F hE t E t

U te−

= and the photon density


59

1( )P t by Fourier analysis. From the complex amplitudes ( , )U f JΔ and 1( , )P f JΔ the S parameters are calculated according to the following equations:

11

112

( , )( , )

( , )( , )( , )

( , )1( , )

serU f JR f J RJ L B

R f J ZS f JR f J Z

P f JS f Jh e J L Bν

Δ= +

Δ ⋅ ⋅−

=+

Δ=

⋅ Δ ⋅ ⋅

(2.44)

serR is an additional resistance constant accounting for the series resistance of a real

device. Note that the definition for 12 ( , )S f J implicitly includes the assumption of 100 % conversion efficiency of the optical output into current by an ideal detector. In the experiment, 12 ( , )S f J is considerably lowered by a constant factor due to coupling and conversion losses. This simulation is done for successive current densities and frequencies ( , )f J , thus constructing modulation response curves for different current densities (i.e. output powers).

0 2 4 6 80

1000

2000

3000

4000

5000

Cur

rent

den

sity

[A/c

m2 ]

Time [ns]

Pump pulse

0 2 4 6 80.6

0.7

0.8

0.9

1.0

1.1Voltage drop over junction

Volta

ge d

rop

[V]

Time [ns]

0 2 4 6 80

50

100

150Optical pulse

Out

put p

ower

[mW

]

Time [ns]

Fig. 44: Step-like current density function with superimposed current modulation at 3 GHz (left), simulated drop voltage (middle) and simulated optical pulse with turn-on delay, relaxation oscillation peak and persistent modulation (right). The simulated and measured modulation response curves are compared to improve the RTM. The main parameters to achieve good agreement are the modal gain and the relaxation time constants. The latter determine the degree of suppression of the resonance frequency peak in the modulation response curve. Both the S11 and the S12 parameter curve contain information about the high-speed modulation characteristics of the laser diode. S11 parameter (input impedance) simulation The S11 parameter characteristics are phenomenologically interpreted in terms of an equivalent electrical circuit similar to the one used for description of the laser chip. Fig. 45 shows the equivalent circuit for the whole laser diode with the intrinsic LD model marked grey. The intrinsic QD laser can be described in terms of a low pass RC circuit, where the diode sign denotes the voltage drop of ~1 V across the pn junction.


60

Rdiff

Rser

eφ

Cdiff

Cmeta

Lbond

Intrinsic LD

Fig. 45: Equivalent circuit for QD laser chip comprising bond inductivity, series resistance, parasitic metallization capacitance, junction resistance and junction capacitance. The grey box denotes the equivalent model for the intrinsic laser diode. The corresponding current density dependent resistance diffR is identified with the differential pn-junction resistance. For an ideal laser diode, diffR should drop to zero above threshold, since the junction voltage and gain are clamped and do not change with current (see Fig. 44, middle graph). However, for a real laser there are several mechanisms that cause a finite, current dependent diffR :

• As the output power (photon density) increases, the carrier recombination times become shorter. Due to finite capture and relaxation times, the lasing levels (QD) are emptied faster than refilled. In order to keep the carrier density in the lasing state constant, the total carrier density rises, along with the voltage drop over the junction. This is the gain compression mechanism that eventually leads to gain saturation and is included in the RT model.

• The carrier transport within the barrier causes a shift of the quasi-Fermi levels, leading to a larger effective voltage drop over the active zone. The difference to the single layer voltage drop decreases with current (see Fig. 46). This effect should be prominent for QD VCSELs, since they have a very wide barrier region (> 1 µm), for QD edge emitters with a large number of stacked QD layers (> 0.5 µm), and for a non-p-doped barrier region.

Our RT model does not take the voltage drop over the intrinsic region into account, since it only calculates the quasi-Fermi level differences of a single QD layer and omits a possible tilting of the Fermi levels across the stack of QD layers, i.e. diffR is underestimated. The actual occurrence of a discrepancy between simulated and experimental data (see section 3.2.1) is also a hint that the pumping of stacked QD layers may be not uniform, with negative effect for the modal gain of the QD laser structure. The current density dependent capacitance from the RC circuit model in Fig. 45 is simply there to describe the high-frequency roll-off of the electrical bandwidth. diffC is determined by the speed, with which the population of barrier, wetting layers and QDs can be changed (by carrier transport, capture / reemission and, indirectly, by


61

carrier recombination / absorption). The larger diffC with respect to diffR , the slower the laser diode reacts to changes of the current density under modulation.

AlGaAs

EFermi,e

EFermi,h

GaAs + QDAlGaAs

1

2 eφintrinsic

eφQD layer

Fig. 46: Sketch of QD laser band structure and the position of the quasi-Fermi levels under lasing operation. The effective voltage drop over all QD layers is larger than the voltage drop over a single layer due to carrier transport limitation. Fig. 47 shows the simulated S11 parameter curves and typical experimental data for different current densities. The simulated S11 data show a typical RC low pass behavior and give the correct low pass cut-off frequency. However, for most of the QD laser diodes we investigated the variation of the simulated data (i.e. the value of

diffR ) is too small to fit the experimental data, due to the aforementioned limitation of the RT model.

0 5 10 150.795

0.800

0.805

0.810

0.815

0.820

S11

para

met

er

Frequency [GHz]

500 - 2500 A/m-1

0 5 10 150.0

0.2

0.4

0.6

0.8

1.0

Ref

lect

ion

(S11

)

Frequency [GHz]

Fig. 47: Simulated S11 parameters (left) and the comparison with the typical experimental data (right). The variation of the simulated S11 is too small to fit the experimental data. The discrepancy is due to the limitations of the RT model. The frequency dependent S11 parameter characteristics of the equivalent circuit are simulated and fitted to the experimental data with Microwave Office. Additional modeling of the submount and chip characteristics allows fitting of de-embedded data (see section 2.1.1). From the fitted circuit we derive the frequency dependent values for the equivalent circuit elements, i.e. series resistance, differential resistance and differential capacitance (the bond inductivity and parasitic metallization capacitance


62

can be neglected due to proper chip design and mounting, see sections 1.2.2 and 1.5). Fig. 48 shows the experimental data and a typical fit curve (left) and the dependence of the derived differential resistance and differential capacitance on frequency (right). Both the RT model (Fig. 47) and the experimental results (Fig. 48) yield a decreasing differential resistance and a slightly increasing differential capacitance. The intrinsic RC bandwidth of the laser is derived from both entities:

3 ,1

2dB intrinsicdiff diff

fR Cπ− = (2.45)

Whereas the RT model gives the correct RC bandwidth, i.e. the correct product

diff diffR C , the differential resistance is underestimated (and the capacitance value is too large) by a factor of ~10 for this particular QD laser diode.

0.1 1 100.0

0.2

0.4

0.6

0.8

1.0

DO224, 500x2µm, HR-HR

0 kA/cm2

1 kA/cm2

2 kA/cm2

5 kA/cm2

10 kA/cm2

Fit

|S11

|

Frequency [GHz]

0 2000 4000 6000 8000 100000

5

10

15

20

0

2

4

6

8

10DO224c, 500x2µm, HR-HR

Junc

tion

resi

stan

ce R

diff [

Ω]


Cap

acita

nce

Cdi

ff [pF]

Fig. 48: S11 parameter measurements and typical equivalent circuit fit for a DO224c, 500x2 µm sample (left). The agreement between measurement and simulation is very good. The right graph shows the current density dependence of differential resistance and capacitance derived from the fit curves in the left graph. As we expect, the differential resistance decreases with current due to the decreasing carrier lifetime in the active region. The capacitance is more or less stable, meaning that the response of the active region becomes faster with increasing current. A detailed, spatially resolved simulation of the carrier density inside the active layer is necessary to include the effect of carrier transport into modeling (see considerations in section 2.1.2) and to achieve correct values for diffR and diffC . This was too time consuming to be accomplished for this work. However, such modeling has been done for quantum well lasers in the past, e.g. in [96, 97], highlighting the effects we also expected to find in QD lasers incorporating stacked DWELL structures: The carrier transport time across the stacked QW layers depends on the width of the optical confinement region, the carrier mobilities in the barrier and the capture / reemission time constants of the QW. Wide confinement regions (> 100 nm) with a large number (> 3) of QW lead to an inhomogeneous distribution of carriers. Hole and electron density show a slope like depicted in Fig. 46. The effect is much stronger for holes, since they have a smaller barrier mobility and a larger probability of being trapped in a QW. The subsequent accumulation of holes on the p-side of


63

the active zone attracts electrons via Coulomb interaction, leading to a larger total carrier density on the p-side of the active layer. Due to different carrier densities in adjacent quantum wells and band-gap renormalization, different QW show different emission wavelengths, leading to gain broadening of the active zone. During turn-on of the MQW laser, QWs close to the p-side of the active zone reach inversion first and cause the onset of lasing. The stimulated emission of photons and their absorption in the non-inverted QWs on the n-side lead to a faster distribution of carriers (photon-assisted transport). Relaxation oscillations are strongly damped due to slow carrier transport, the corresponding carrier density oscillations in the different QWs are partly out of phase. A large carrier transport time causes a capacitive-like roll-off of the input impedance, represented in the equivalent circuit by a low RC bandwidth. S12 parameter (transmission function) simulation The transmission function of a laser diode describes the ability of the diode to convert a modulation of the pump current into an output power modulation. Of course S12 is intimately linked to S11. The bandwidth of the transmission function is almost similar to the electrical RC bandwidth except for resonance enhancement due to the resonant interplay of photon density and electronic lasing levels. This becomes immediately clear if we recapitulate the influence of carrier capture/reemission and recombination on the modulation speed: An oscillating pump current in phase with a depletion of the lasing levels by an oscillating photon density enhances the modulation response of the laser at this particular frequency. Prerequisite for a resonance enhancement is a fast relaxation of carriers from the barrier down to the QD lasing levels. As presented in the experimental small signal analysis section of this work (section 3.2), QD lasers show no or just a small resonance enhancement. In our RT model, this behavior is implemented by the relaxation time parameters (see Table 5). Fig. 49 shows simulated and measured S12 parameter curves for different current densities. The good agreement between the RT model simulation and the measured data is achieved by a careful choice of relaxation time constants.

0 2 4 6 8 10-30

-25

-20

-15

-10

-5

Mod

ulat

ion

resp

onse

[a.u

.]

Frequency [GHz]

500 - 2500 A/m-1

0 2 4 6 8 10-30

-25

-20

-15

-10

-5

Experiment Simulation

Mod

ulat

ion

resp

onse

[a.u

.]

Frequency [GHz]

500 - 2500 A/cm-2

Fig. 49: Simulated S12 parameters (left) and the comparison with the typical experimental data (right). The agreement that can be achieved by proper selection of the model parameters is very good. The QD capture time is 4 ps, the barrier and well relaxation time 0.1 ps. The shape of the transmission function in its simplest, normalized form is described analytically by a two parameter curve:


64

( ) ( )

22 2

2 2 2

44 2

res

res

fP fI f f i f

ππ πγ

∂=

∂ − + (2.46)

where resf is the current density dependent resonance frequency and γ is the current density dependent damping factor. The equation is derived from a simple single excitonic level rate equation model [95]. Three typical curves for different relations of resf and γ are shown in the left graph of Fig. 50. For small damping we observe a strong resonance peak, in this case the -3 dB bandwidth is approximately given by 3 01.55dBf f− ≈ . For large damping, the -3 dB bandwidth is given by 3 0dBf f− ≈ .

0 2 4 60.1

1

10

-3 dB

+3 dB

fres = 2.2 GHz

Res

pons

e [a

.u.]

Frequency [GHz]

γ = ω γ = 4 ω γ = 10 ω

0 2 4 6 8 100.1

1

10

500 A/cm2

... 5000 A/cm2

Tran

smis

sion

func

tion

[nor

m.]

Frequency [GHz]

-3dB

Fig. 50: Transmission function curves for different damping constants γ (left). The resonance frequency is set to 2.2 GHz. Small damping causes a strong resonance peak, strong damping makes the resonance disappear and decreases the -3 dB bandwidth. For data transmission purposes we define a 3 dB corridor that encloses the transmission function curve within the -3 dB frequency range. The right graph shows the increase and saturation of the bandwidth with drive current density. The 3 dB corridor shown in Fig. 50 (left) is important for the evaluation of the data transmission properties of the laser diode and is discussed in section 3.3.3. Corresponding curves for increasing current density are shown in the right graph of Fig. 50. Both the resf and γ increase with the output power of the laser diode:

0 0

20 0 0

1( ) '2

( ) ( )

gres

phot

res

vf P G P

P K f P

π τ

γ γ

=

= ⋅ +

(2.47)

Both equations are derived from the rate equation model, e.g. [95]. The corresponding -3 dB frequency can be derived as a function of the resonance frequency and the damping constant:

( )

( ) ( )3

*3 0

12

, , ,

dB

dB res res

P fI

f F f F f Kγ γ

−

−

∂=

∂= =

(2.48)


65

Since the damping constant increases linearly with output power, while the resonance frequency increases as a square root function, the -3 dB bandwidth levels off for high output powers and tends do decrease for even higher powers. Fig. 51 shows the experimental data and corresponding fit curve for a laser diode with a maximum bandwidth of 6 GHz.

0 1000 2000 3000 4000 50000

10

20

30

40

(f -3dB

)2 [GH

z2 ]

(j-jthr) [A/cm2]

K=1.4 ns

0 10 20 30 400

10

20

30

40

50

60

70

γ0=17 GHzK=1.2 ns

fres2 [GHz2]

Dam

ping

γ [G

Hz]

Fig. 51: Typical square -3dB modulation bandwidth dependence on the net drive current density (left). The bandwidth values are derived from the S12 parameter measurements. Alternatively, the parameters resf and γ can be found by fitting the successive S12 parameter

measurements and plotted (right graph) to find the values for K , 0γ and the maximum bandwidth. The maximum bandwidth is approximately given by the K factor according to:

3 ,22dB maxfKπ

− = (2.49)

The K factor itself depends on basic laser diode properties like the photon lifetime inside the cavity, the differential gain and the gain compression factor [8]:

24'phot

g

Kv G

επ τ⎛ ⎞

= +⎜ ⎟⎜ ⎟⋅⎝ ⎠ (2.50)

The maximum bandwidth solely due to the photon lifetime is quite large, even for 2 mm long devices with photon lifetimes of ~10 ps the bandwidth limit is still as large as 22 GHz. Fig. 52 (left) shows the dependence of the maximum bandwidth limited by the photon lifetime on the cavity length and for different internal losses and facet reflectivity. In fact the maximum modulation bandwidth of the QD lasers we investigated is limited by the differential gain and gain compression factor. The gain compression factor is mainly dependent on the QD carrier relaxation / capture time. Even a small gain compression factor for our QD lasers of 22 31 10 mε − −< ⋅ yields a severe bandwidth limitation if combined with the small differential gain of QD lasers 19 2' 1 10G m−< ⋅ . Fig. 52 (right) shows the dependence of the modulation bandwidth maximum according to equation (2.50) for the modeled differential gain from Fig. 33 and three different gain compression factors. The curves exhibit maximums between 0.5 and 1.5 mm device length due to the trade-off between increasing differential gain and increasing photon


66

lifetime. The gain compression is assumed to be constant. The optimization of basic device parameters like length, facet coating and bias current density with the help of these theoretical considerations is important for maximum data transmission performance of our QD devices.

0.1 1 10

10

100

as-cleaved facets, αi=2cm-1

HR coated rear facet, αi=2cm-1

as-cleaved facets, αi=5cm-1

Max

imum

f -3dB

[GH

z]

Device length [mm]1 10

1

10

100

ε = 10-22 m3

ε = 5∗10-23 m3

ε = 10-23 m3

τphoton limit

Max

imum

f -3dB

[GH

z]Device length [mm]

Fig. 52: Maximum -3 dB bandwidth of a laser diode vs. device length due to the limitation by photon lifetime (left). HR coatings reduce the bandwidth; internal losses determine the theoretical limit for very long (~10 mm) devices. The right graph shows the photon limit curve for as-cleaved facets, 12i cmα −= and the corresponding curves for additional limitation by gain compression for different ε and differential gain according to Fig. 33. Due to the strong differential gain reduction for short devices (high threshold gain) even a small ε imposes a severe limit on the maximum modulation bandwidth. However, there is a discrepancy between the large compression 20 31 10 mε − −> ⋅ found in the previous section 2.2.4 and the actual bandwidth of the devices. Modeling according to analytical equations like (2.51) may be too simple. We therefore rely on the dynamic relaxation time model. Measured S12 parameter curves and those simulated with the RT model (see Fig. 49, right) show a slight roll-off for frequencies below 1 GHz. This feature cannot be described analytically by a two parameter curve, so a third parameter 21/ e

τ has to be included:

( ) ( )2

22 2

2 2 21/

411 2 4 2

res

rese

fP fI f f f i f

ππ τ π πγ

∂= ⋅

∂ + ⋅ − + (2.52)

21/ e

τ is defined as being the inverse frequency where the roll-off reaches 2e− of the initial value. It is interpreted as a time constant describing an additional low pass behavior (capacitive-like roll-off) of the intrinsic QD laser due to a slow carrier transport process. Fig. 53 depicts the influence of an additional transport time of 50 ps.


67

0 2 4 6 8 100.1

1

10

500 A/cm2

... 5000 A/cm2

Tran

smis

sion

func

tion

[nor

m.]

Frequency [GHz]

-3dB

Fig. 53: Influence of slow carrier transport process in intrinsic QD laser on shape of transmission function and modulation bandwidth. The parameters resf and γ are similar to

those in Fig. 50 (right graph) except an additional transport time term 21/50

epsτ = . A strong

decrease of the modulation bandwidth follows. The influence of an additional slow transport time found in experimental data might be due to slow transport of carriers across the barrier to the DWELL layers or from the wetting layer to the quantum dots. There is a direct connection to gain compression, since a slow carrier transport might also cause gain compression. However, the amount of gain compression depends on the proximity of the slow transport, capture or relaxation process to the lasing levels. A slow capture into the QDs causes stronger gain compression than a slow capture from the barrier to the DWELL layer, since the latter is buffered by the DWELL QW carrier reservoir. A slow transport of carriers across the barrier is expected to yield no gain compression at all. We believe that there is experimental evidence (as will be shown in the next chapters) that the main contribution to bandwidth limitation of current QD lasers is due to three different effects:

• Low differential gain 'G due to the asymmetric DOS of holes and electrons in quantum dots, as explained with the quasi-equilibrium model

• Large gain compression factor ε due to slow capture of the carriers into the quantum dots

• Capacitive-like roll-off of transmission function due to wide active zone (up to 500 nm) and, as a consequence, long carrier transport times across the active zone

However, the actual bandwidth of a laser device will also be influenced by the dimensions of the device, facet reflectivities, losses, current confinement etc.

2.2.7 Limitation of the RT model, MEM model Whereas the relaxation time model is very useful for the simulation of transient behavior, it does not include the spectral dimension. Only a single photon mode for ground state emission is considered. The effects of non-equilibrium population of spectrally different QDs, especially spectral broadening, are not included.


68

1270 1280 1290 1300 1310 13200.0

0.1

0.2

0.3

0.4

0.5

0.6

1 kA/cm2

3 kA/cm2

10 kA/cm2

La

ser O

utpu

t [lin

ear]

Wavelength [nm]

DO 224c, 500x2µm, HR-HR

0 2000 4000 6000 8000 100000.00

0.02

0.04

0.06

0.08

0

5

10

15

Peak

/ to

tal p

ower

[a.u

.]


Spec

tral w

idth

[nm

]

Fig. 54: Spectral broadening of QD laser emission with increasing current (left) and corresponding width and peak power vs. current density (right). The spectral peak power decreases with respect to the total output power, at the same time the spectrum broadens considerably. The integrated PI curve shows a perfect linear slope. The broadening of the laser emission spectrum with increasing output power is a very common feature of quantum dot lasers. A 30 nm wide spectrum for low temperature (< 200 K) is not unusual (see experimental section). Even at room temperature spectral broadening takes place. Fig. 54 shows the dependence of spectral broadening and peak power on the bias current for a QD laser diode at room temperature. Although there are no signs of gain compression (no PI curve curvature) for the integrated PI curve, there is a saturation of spectral power, i.e. the maximum output power within a given wavelength range (say 1 nm). The reason for this “spectral gain compression” effect is most probably a relatively slow (~10 ps) capture of carriers into QDs and/or relaxation within the QDs. With increasing output power the lasing quantum dots are depleted faster than refilled. Whereas in conventional (QW) lasers this would cause a readjustment of the quasi-Fermi levels in order to keep up the gain condition, this does not happen for QD lasers, since there are no common Fermi levels for the holes and electrons in the QDs. Instead, the quasi-Fermi levels of the WL increases, causing an increased capture for all QDs, but with a stronger impact on QDs below and close to threshold. As soon as these QDs start lasing, they provide additional current sinks. The spectral gain compression mechanism should be clearly visible for devices that are forced to operate in a spectrally narrow range, e.g.

• small aperture single mode QD VCSELs • DBR or DFB QD edge emitting lasers • QD semiconductor optical amplifiers pumped with a single wavelength

Significant gain compression has been found in DFB devices with quantum dots, limiting the output power and dynamic properties [93, 98]. Small aperture QD VCSELs (as presented in section 4.1) show a strong thermal roll-over of the output power in cw operation that masks the gain compression. Even for pulsed measurements it is difficult to distinguish between thermal and gain compression effects. The most reliable way to find out the saturation characteristics of QDs is by SOA measurements since they offer the possibility to access electrical bias current and optical power separately.


69

Preliminary measurements on QD SOAs (see Fig. 34) show that for moderate current densities (< 1000 A/cm2) the optical amplification starts showing saturation effects for output powers (amplified power) below 1 mW. Further investigations have to be made to clarify this effect. Gain compression has a major influence on the modulation characteristics of laser diodes since it reduces the coupling between the carrier reservoir and the photons. We include gain compression into the RT model by choice of the relaxation time constants. However, we cannot reproduce the spectral properties and temperature dependence of the threshold (T0). The broadening of the spectrum is more pronounced for low temperatures, due to the decreasing thermal coupling between the QDs. In this case, the assumption of thermal equilibrium among the CB and VB carriers and the existence of Fermi levels is no longer valid. It has been shown that in this case the modeling of carrier dynamics in quantum dot ensembles gives qualitatively erroneous results [81]. The limitations of the RT model are overcome by the microscopic modeling of the QD states inside the lasers. In this case, quantum dots are no longer described by an ensemble average occupation of a certain electronic level, but by a particular carrier configuration, the so-called microstate [76, 79-81]. For the QDs described in the previous section the definition of a microstate is simple: Each electronic level (see Fig. 28) can be occupied by two electrons (holes) with spin up/down. A single QD with N levels can therefore be notated as a binary number of length 2N:

1, 1, 2, 2, , ,, , , ,..., ,

{0,1}N Ns s s s s s

s↑ ↓ ↑ ↓ ↑ ↓Δ =

∈ (2.53)

For N levels, there are 22 N different microstates. The interaction between the QDs, the wetting layer and the photon mode(s) can now be implemented in several ways:

1) MEM differential equation system: The QD ensemble state is given as the ensemble average of microstate occupation, i.e. 22 N variables giving the number of all QDs in a particular microstate. These variables are linked with each other, to the WL occupation and the photon densities via differential equations. For 12 electronic levels, this corresponds to more than 16 million coupled differential equations. Therefore most models are restricted to a few electronic levels, excitonic capture and relaxation or even to a ground state condition [76, 79-81]. We must be aware that the reduction of levels distorts the true carrier storage capability of the QDs, which has a major influence on modulation dynamics. A ground state condition is definitely not valid for highly pumped QDs at room temperature.

2) Monte-Carlo-Simulation: This is a kind of brute force attack of the modeling issue. The QD ensemble is described by a large number of single QD microstates. For 1.000.000 QDs and 12 levels, this corresponds to a moderate memory demand of 3 MB. The interaction of the QDs and relaxations are described in terms of a random elementary processes scheme. Elementary processes are spin flip, relaxation from one level to an adjacent level, capture into a level (from the WL), non-radiative recombination and radiative recombination/ generation. The latter is associated with the generation/ absorption of a photon with suitable wavelength. The elementary processes


70

take place with adjustable rates corresponding to the relaxation / recombination times, but at a random time.

The Monte-Carlo simulation has the advantage of great simplicity. However, in order to reduce statistical noise, a large number of QDs (> 10000) and a short time step (~10 fs, depending on the number of QDs) have to be implemented. Computational limits are approached fast. The model has nevertheless been implemented with Microsoft Visual C++, comprising four independent electronic QD levels (2 CB + 2 VB, no excitonic binding), spin degree of freedom, and a single photon mode. The microstates of individual quantum dots are then described by binary numbers of 8 bit. The elementary processes mentioned above are all implemented in a way similar to the example of spin-flip below: /*Spin flip Up*/ if (Random(TimeSpinRelax) < 1) { IndexDot = (int)Random(NumberDots); if (CBStates[IndexDot][2*IndexState] == 0 && CBStates[IndexDot][2*IndexState+1] == 1) { CBStates[IndexDot][2*IndexState] = 1; CBStates[IndexDot][2*IndexState+1] = 0; } }

The Random function ensures the occurrence of a spin-flip event with a certain rate, given by the time constant TimeSpinRelax (e.g. 500, so it happens to be “true” every 500th time), but at a random time. The program then picks a random dot (numbered by the variable IndexDot) and checks, whether a spin-flip is possible, that means the spin-down state is occupied and the spin-up state is empty, or not. If possible, it performs the flip operation by setting the microstate variable CBStates[IndexDot][Level][Spin] to their complementary values. Elementary processes involving carrier-photon interaction (like stimulated emission) are implemented in a similar way: /*GS [1] recombination for e - Spin Up, h - Spin Down, stimulated emission */ IndexDot = (int)Random(NumberDots); if (Random(TimeRadReco) < Photons) { if (CBStates[IndexDot][0] == 1 && VBStates[IndexDot][1] == 1) { CBStates[IndexDot][0] = 0; VBStates[IndexDot][1] = 0; Photons = Photons + 1; } }

Please note the increase of the stimulated emission probability with increasing photon number. Similar random processes are implemented for the photon number to account for optical loss due to waveguide absorption and mirrors, summarized in a photon lifetime. Electrical drive current is provided by a constant flow of carriers into the wetting layers: /* Drive current density [A/cm^2] */ CBWLStates = CBWLStates + (int) CurrentIncrement; VBWLStates = VBWLStates + (int) CurrentIncrement;


71

Of course the current may also be temporarily varied, for example in a short pulse. Most computational time is spent on the evaluation of IF statements, of which the program is essentially made of. An improvement of the implementation in terms of reduction of IF statements would have the largest impact. By proper choice of the relaxation and recombination rates, turn-on characteristics similar to the ones calculated with the RT model are found (see Fig. 55).

0 200 400 600 800 10000.0

0.2

0.4

0.6

0.8

e GS e ES

Popu

latio

n pr

obab

ility

Time [ps]0 200 400 600 800 1000

0.0

0.5

1.0

1.5

2.0

Lase

r Out

put [

a.u.

]Time [ps]

Fig. 55: Monte-Carlo modeling of turn-on process of a QD laser diode, averaging over 10.000 QDs. The left figure shows the CB ground and excited state occupation transient, whereas the right graph shows the photon number inside the cavity (i.e. the output power). Strong damping of the relaxation oscillation is easily modeled by large relaxation time constants. In order to extend the model to a spectral dimension, we included inhomogeneous (equation (2.13)) and homogeneous broadening according to the Lorentzian model

( )

2

2 20

( ) p

p

Lγ

ωω ω γ

=− +

(2.54)

where pγ is the decay rate of the excitonic polarization, and a number of photon modes, corresponding to the longitudinal modes of a laser diode (~100-500 modes). The inhomogeneous broadening of the quantum dots is implemented by assigning a random shift to the electronic levels of individual dots before starting the computation, arriving at a Gaussian distribution of dot number vs. energy shift centered at zero shift. The homogeneous broadening is implemented by a random energy offset between recombination energy of CB VB ground state and the photon energy during recombination and absorption with a Lorentzian distribution centered at zero offset. The photons generated by recombination can now distribute over all modes, causing a large increase of statistical noise for a single mode due to its low occupation. In order to lower this noise, the number of QDs in the simulation has to be increased to more than a million, causing a computational time of several days / weeks for a single 2 ns transient (1 GHz Pentium III). Further optimization of the program code and an implementation on a 16 node computational cluster, as it is available in our group, was not accomplished yet.


72

For modeling of our experimental data we therefore rely on the quasi-equilibrium and the RT model and restrict our modeling to room temperature (see Fig. 27). Besides the computational issue, the main problem of QD laser diode modeling is the estimation of carrier relaxation and recombination rates. No reliable data have so far been derived from ab initio calculations. As already mentioned, the rates serve as fitting parameters for all our models, opening the modeling to a considerable degree of arbitrariness.

3 Direct modulation of QD edge emitters

73

3 Direct modulation of QD edge emitters Dynamic measurements on quantum dot edge emitters serve two purposes: Firstly, by comparison of the experimental results with corresponding models we try to understand the fundamental mechanisms and limitations of fast (< 1 ns) current-to-light conversion in quantum dot lasers. Secondly, by testing the QD lasers with standardized datacom schemes, we evaluate their applicability for optical data transmission with data rates up to 10 Gb/s. Besides the speed of the QD lasers a bundle of parameters has to be optimized in order to meet the specification of laser diodes suitable for data transmission. Table 6 lists the most important parameters and compares the specs with the currently available devices based on InGaAs quantum dot laser technology.

Parameter Requirement QD laser module Fiber coupled power (dBm) -3 0 Wavelength (nm) 1270-1355 1285-1290 SMSR (dB) multimode multimode Extinction ratio (dB) > 5 5 RIN (dBc/Hz) -130 N/A Temperature range (°C) 0-85 0-30 Modulation bandwidth (GHz) 10.6 7 Error-free data rate (Gb/s, BER < 10-12) 10 10 Rise / fall time (20%-80%) (ps) < 30 70 Eye signal-to-noise ratio (dB) > 10 7 Modulation voltage (V) 1.2 2.5 Threshold current (mA) 30 5 Operation c.w. c.w.

Table 6: Requirements for data transmission laser diodes and comparison to state-of-the-art quantum dot laser characteristics. The corresponding QD device is the QD laser module described in the following sections. Parameters that do not meet the specifications or were not measured are marked [Courtesy J. Marsh]. Over the past five years, QD edge emitters have made substantial progress regarding their wavelength and their modulation speed. However, not all of the specifications are fulfilled. The next sections will give an overview of the measurement techniques, experimental results, improvements and persistent problems of QD lasers regarding the aforementioned parameters. 3.1 Basic parameters of QD edge emitters Prior to dynamic measurements, basic parameters of quantum dot lasers like wavelength, internal losses, quantum efficiencies, temperature behavior and fiber coupling properties had to be characterized. The necessary measurements were accomplished with standard techniques, which will not be discussed in detail.


74

Evaluation of the experimental data was done according to the models that were presented in section 2.

3.1.1 MOCVD grown 1.1 µm quantum dot lasers TU 5447 and TU 5382 samples – quantum dot versus quantum well The TU 5447 quantum dot laser with 6-fold stacked QD layers was grown as briefly described in section 1.1. A similar laser structure incorporating three quantum wells instead of the QDs was fabricated for comparison of QD and QW laser performance. Ridge waveguide laser diodes with mesa widths of 3, 5, and 10 µm were fabricated using wet etching techniques (see section 1.2.1) and provided with large (covering almost the complete top side) bond pads. The comparison of QW and QD devices revealed typical features of self-organized quantum dots. Fig. 56 shows the optical spectrum of both laser types for large range of temperature. The spectra were measured in pulsed mode to avoid device heating.

1000 1020 1040 1060 1080 1100 1120 11400

5

10

15

20

25

10K 20K 50K 100K 200K 300K

Spec

tral i

nten

sity

[a.u

.]

Wavelength [nm]1000 1020 1040 1060 1080 1100

0.0

0.2

0.4

0.6

0.8

1.0 20K 50K 100K 150K 200K 250K

Spec

tral i

nten

sity

[a.u

.]

Wavelength [nm]

Fig. 56: Optical spectra for a QD laser diode TU 5447, 1000x10 µm (left) and a QW laser TU 5382, 1000x3 µm (right) depending on the device temperature. Both lasers exhibited a spectral shift due to the band gap change. The spectra of the QD laser broadened significantly for low temperatures, whereas the QW laser showed narrow emission. At room temperature both QW and QD laser had a narrow emission spectrum with a FWHM between 3 and 8 nm. For cryogenic temperatures, however the QD laser spectrum broadened significantly due to the onset of lasing of additional quantum dot sub-ensembles within the range of inhomogeneous broadening (QD size distribution), as discussed in section 2.2.7. The FWHM of the spectrum at 10 K of more than 40 nm agreed with an inhomogeneous broadening of 30-40 meV. However, the integrated output power of the QD laser was about the same for all temperatures. The spectral width of the quantum well laser, in contrast, even narrowed for low temperatures. The broadening mechanism of QD lasers had another important consequence, i.e. the temperature independence of the threshold current density. Fig. 57 (right graph) shows the temperature dependence of threshold for the QW and QD laser. Whereas the QW device showed an increase of threshold with temperature, that was typically modeled as exponential increase

00( )

TTj T j e= ⋅ , (2.55)

with 0T being the characteristic temperature, the QD laser exhibited a constant threshold with a small decrease below room temperature, followed by an increase.


75

This effect was seen for all QD samples that we investigated and was also found by various other groups [99-110].

0.0 0.5 1.0 1.50

200

400

600

800

1000TU 5447, 5 µm, jtransp< 200 A/cm2

Th

resh

old

curre

nt d

ens.

[A/c

m2 ]

Reciprocal length [mm-1]0 50 100 150 200 250 300

0

100

200

300

400

500

Thre

shol

d cu

rrent

den

s. [A

/cm

2 ]

Temperature [K]

QD TU 5447, T0 -> infinite QW TU 5382, T0 = 190 K

Fig. 57: Threshold current dependence of sample TU 5447 with 5 µm ridge width on length (left). A minimum threshold current density of 200 A/cm2 was measured. The right graph shows a comparison of the temperature dependence of threshold for similarly processed QW and QD lasers. The QD laser showed an almost ideal T0. After these preliminary characterizations, the samples were tested under large signal modulation, as discussed in section 3.3.1.

3.1.2 MBE grown 1.3 µm quantum dot lasers The most important specification for datacom laser diodes is certainly the emission wavelength. The corresponding fiber dispersion minimum wavelength range around 1.3 µm was first scratched by MBE grown QD laser diodes emitting at wavelength between 1260 and 1320 nm. QD growth at this wavelength requires a trade-off between gain and extension of the wavelength [36], therefore all devices we present in this section lay at the short wavelength limit of the datacom range. Several epitaxial and diode design changes have since then been implemented. In this section we will briefly go through all stages of QD laser improvement:

a) Deep etching of mesa for higher speed, better coupling efficiency b) Decrease of ridge width down to 1 µm for better coupling efficiency c) Lowering of series resistance, p-modulation doping for higher speed and

higher characteristic temperature d) Top-side probe head contact scheme for fast and reliable testing e) Extensive stacking of QD layers up to 15 for more modal gain

Ioffe 4-915 samples – deep vs. shallow mesa Mesas etched through the waveguide provide a strong index guiding and increase the lateral far-field divergence. Since the optical confinement in vertical direction is stronger than in lateral direction, this leads to a more symmetric far-field and an improved coupling into (symmetric) optical fibers. At the same time strong lateral index guiding improves the lateral overlap of the optical mode and the pumped waveguide and should reduce the waveguide losses due to free-carrier absorption at the sides of the optical mode. The most important question to answer is whether etching through the active layer causes more non-radiative recombination of carriers and/or increases the internal losses due to scattering at the side walls of the ridge.


76

Fivefold stacked Ioffe 4-915 quantum dot lasers where processed into shallow and deeply etched ridge waveguide lasers of 4/6/8/10 µm width for direct comparison. The contact layout was multi-sectional for maximum versatility (cf. Fig. 11, right).

0.0 0.5 1.0 1.50

200

400

600

800

1000 Deeply etched Shallowly etched

jtransp~ 100 A/cm2

Thre

shol

d cu

rrent

den

s. [A

/cm

2 ]

Reciprocal length [mm-1]0 1000 2000 3000 4000

0

1

2

3

4

Shallow: ηint = 76 %

αint = 7 cm-1

Deep: ηint = 66 %

αint = 5 cm-1

1/η ex

t

Device length [µm]

Fig. 58: Threshold current density (left) and differential quantum efficiency (right) of Ioffe 4-915 samples, ridge width 4 µm, for shallow and deep etched mesas. The transparency current density and internal losses are comparable. From a series of devices with different length we determined internal losses of 5 cm-1 / 7 cm-1, an internal quantum efficiency of 76 % / 66 % and a transparency current density of 100 A/cm2 for deep / shallow mesas, respectively (see Fig. 58). Taken into account the experimental uncertainty due to processing variations across the wafers, this indicated that the deep-mesa etching had not created a significant amount of defects within the active layer. Deep etching, on the other hand, decreased the far field asymmetry (ellipticity) of 1:10 to 1:6 for 4 µm stripe width, as shown in Fig. 59. The left graph shows the corresponding spectrum of the deep etched sample.

1240 1260 1280 1300-70

-60

-50

-40

-30

-20

-10

01130x4 µm @ 500 A/cm2

Spec

tral p

ower

[dBm

]

Wavelength [nm]-20 0 20

-80

-60

-40

-20

0

20

40

60

80

lateral scan (°)

verti

cal s

can

(°)

-20 0 20

-80

-60

-40

-20

0

20

40

60

80

lateral scan (°)

Fig. 59: Ioffe 4-915 spectrum (left) and far-field scans of two Ioffe 4-915 samples with shallow mesa (middle) and deep etched mesa (right), respectively. An improvement of the symmetry from 1:10 to 1:6 was achieved [Courtesy M. Lämmlin]. Ioffe 5-600 samples – improvement of far-field symmetry 5-fold stacked Ioffe 5-600 samples similar to the previous sample, but with a narrow ridge layout with widths between 1 and 4 µm (additionally 4 to10 µm for larger output powers) were processed. The basic parameters like internal losses, threshold current


77

and differential quantum efficiency were comparable to those of the previous sample. No systematic investigation of the dependence of these parameters on stripe widths was performed due to the poor reproducibility of the results for nominally identical devices. The reason for that were processing variations across the wafer. By reducing the ridge width to 1 µm, we even achieved a symmetric far-field with a 1/e² divergence of 60°. Fig. 60 shows the improvement of the far-field symmetry for deep mesa lasers as a function of ridge width.

-60 -40 -20 0 20 40 60-60

-40

-20

0

20

40

60

verti

cal a

xis

(°)

horizontal axis (°)

-60 -40 -20 0 20 40 60-60

-40

-20

0

20

40

60

verti

cal a

xis

(°)


-60 -40 -20 0 20 40 60-60

-40

-20

0

20

40

60

verti

cal a

xis

(°)


Fig. 60: Far-field improvement of Ioffe 5-600 samples with deep etched mesas for decreasing ridge width: 4 µm, 2 µm and 1 µm (from left to right) [Courtesy M. Lämmlin]. Still, we have to be aware of the large far-field divergence associated with the symmetric far-field. Carefully adjusted coupling optics with a large numerical aperture of 0.6 would be necessary to collect the light from the narrow stripe QD lasers. A decrease of the divergence could be achieved by a widening of the vertical waveguide (so-called large optical cavity – LOC) and a step-back to 2-4 µm ridge width. LOC structures work with higher order vertical modes (unlike the presented QD lasers, see section 2.1.2 for waveguide properties) and require a complete redesign of the epitaxial structure. For cavities with large waveguide thickness, electrical properties similar to those of VCSELs may occur (see section 4). For moderate current densities, no higher order transversal modes were detected in high-resolution optical spectra (see Fig. 61) for 4 µm ridge width. Instead, a strong mode grouping can be seen: One longitudinal mode sticks out from a group of 4-5 modes. The origin of this mode grouping was discussed in [111].

1250 1260 1270 1280 1290 1300 1310-70

-60

-50

-40

-30

-20

-10

01000x4 µm @ 2.5 kA/cm2

Spec

tral p

ower

[dBm

]

Wavelength [nm]1276 1277 1278 1279 1280

-70

-60

-50

-40

-30

-20

-10

01000x4 µm @ 2.5 kA/cm2

Spec

tral p

ower

[dBm

]

Wavelength [nm]

Fig. 61: Spectrum of Ioffe 5-600 sample: The high resolution detail (right) showed no transverse modes, but mode grouping of 3-4 adjacent longitudinal modes.


78

A possible impact of the deep etching layout on the temperature dependence of the threshold current was checked. Fig. 62 shows the experimental results for two different temperature ranges.

50 100 150 200 250 3000

100

200

300

400

Thre

shol

d cu

rrent

den

s. [A

/cm

2 ]

T0 = 61 K

Temperature [K]

Ioffe 5-600, 1000x4 µm

10 20 30 40 50 60 70 80

100

200

300

400500

Ioffe 4-915, 2000x4 µm, deep mesa

T0=53 K

Thre

shol

d cu

rrent

den

s. [A

/cm

2 ]

Temperature [°C]

Fig. 62: Temperature dependence of the threshold for Ioffe 5-600, 1000x4 µm (left) and Ioffe 4-915, 2000x4 µm (right). The broad range measurement showed a minimum of threshold current for 225 K and an exponential increase beyond this temperature. The room temperature T0 was comparable to those of quantum well lasers. In contrast to the 1.1 µm MOCVD quantum dot lasers presented in the previous section, the temperature independent threshold currents of the 1.3 µm samples doubled for room temperature. This increase was attributed to the enhanced thermal re-emission of carriers into the wetting layer state(s) of the DWELL layer due to the larger proximity of QD levels and DWELL levels (~140 meV for electrons, 55 meV for holes, cf. Fig. 28) compared to a wetting layer structure (250 meV for electrons, 80 meV for holes, cf. [86]). No impact of the deep etching on the T0 was found. In order to benefit from the temperature stability of QD lasers, the stable region has to be extended to larger temperature, preferably up to 80 °C. P-modulation doping [31] and tunnel injection of carriers into the quantum dots [108] have been proposed to reach this aim. The decisive influence of deep etching on the modulation properties of the QD laser is discussed in section 3.2.1. DO 57/ Do 75 samples – improvement of IV characteristics and p-doping P-doping of the waveguide between the QD layers will affect both the electrical and the optical properties of the QD lasers. For comparison, two batches of QD lasers were grown incorporating 10 stacks of quantum dots, being undoped (DO 57) and p-doped (DO 75, 17 35 10 cm−⋅ ) in the active region (for sample structure, see section 1.1). The wafers were processed into deep etched ridge waveguide structures with the contact layout depicted in the right graph of Fig. 11. First, we checked the electrical properties of the layout. Both samples showed no significant difference in their IV characteristic. However, as shown in Fig. 63, they demonstrated a decrease of the differential resistance by a factor of 3-5 compared to the previous samples Ioffe 4-915 and Ioffe 5-600. The reason for that was a change of the MBE facility along with a substantial improvement of the doping level reliability. The DO QD lasers consumed less power (better wall plug efficiency) and showed less heating.


79

0 500 1000 1500 2000 25000

1

2

3 Ioffe 4-915 Ioffe 5-600 DO 57 DO 75 DO 224 DO 453

Volta

ge [V

]


Fig. 63: Improvement of series resistance due to better doping level control for the DO samples. P-doped and undoped samples showed no significant differences. The experimental results on the threshold current density and differential quantum efficiency revealed a negative impact of p-modulation doping: The doped sample, DO 75, showed a much higher transparency current density (700 A/cm2) than the undoped sample (275 A/cm2). The data for the differential quantum efficiency showed a large variation due to processing inhomogeneities across the wafer, but still the differential efficiency for the undoped sample was larger than for the doped one.

0.0 0.5 1.0 1.5 2.0 2.50

500

1000

1500

2000

2500 DO 57, 4 µm, jtransp=245 A/cm2

DO 75, 4 µm, jtransp=570 A/cm2

Thre

shol

d cu

rrent

den

s. [A

/cm

2 ]

Reciprocal length [mm-1]0.0 0.5 1.0 1.5 2.0 2.5

0

1

2

3

4

5

DO 57, 4 µm DO 75, 4 µm

1/η di

ff

Device length [mm]

Fig. 64: Threshold current density (left) and differential quantum efficiency (right) of DO 57 and 75 samples with ridge width 4 µm. The transparency current density and internal losses were lower for the undoped samples. The differential quantum efficiency varied due to processing discontinuities; no internal losses were evaluated. The p-modulation doping also affected the temperature dependence of the threshold current, as shown in Fig. 65. A high T0 region of the DO 75 sample could be seen below 40°C, but at higher temperature the threshold started to increase. Above 70°C the DO 75 sample turned off due to insufficient modal gain (gain saturation). The reasons for the large threshold current and the peculiar T0 characteristics were most probably processing imperfections, since all later p-doped sample (DO 224, DO 453) achieved lower threshold current density values and showed a hyper-exponential increase of threshold with temperature, marking the transition region between high and low T0 regions.


80

0 10 20 30 40 50 60100

1000

DO 57, 1000x4 µm DO 75, 1000x4 µm

T0 = 50 K

T0 = Inf

T0 = 40 K

Th

resh

old

curre

nt d

ens.

[A/c

m2 ]

Temperature [°C]10 20 30 40 50 60 70

100

1000 4 µm ridge 2 µm ridge

T0=50-60 K

DO224, 500 µm, HR/HR

Thr.

curre

nt d

ens.

[A/c

m2 ]

Temperature [°C]

Fig. 65: Temperature dependence of threshold current density for p-modulation doped (DO 75) and undoped (DO 57) QD laser samples (left) and another p-doped QD laser sample (DO 224, right). The DO 75 sample showed a room temperature region of ideal T0, but in total had a larger threshold current density compared to the undoped sample. The DO 224 showed a hyper-exponential increase of threshold without a plateau. The impact of p-doping on the modulation characteristics is discussed in section 3.2. Fig. 66 shows the corresponding room temperature spectra for undoped and doped samples. The center emission wavelength of both samples was 1275 nm, no grouping effects were present. No influence of p-doping on the spectral properties of the QD laser diodes was detectable.

1220 1240 1260 1280 1300 1320-100

0

100

200

100 mA

40 mA

20 mA

DO-57, 1000x4µm (1)

Lase

r Out

put [

dB]

Wavelength [nm]1220 1240 1260 1280 1300 1320

-100

0

100

200

100 mA

60 mA

40 mA

DO-75, 1000x4µm (1)

Lase

r Out

put [

dB]

Wavelength [nm]

Fig. 66: Spectra for undoped DO 57 (left) and p-doped DO 75 (right) samples with dimensions 1000x4 µm. No influence of p-doping on the spectra was detected. DO 224 samples – improvement of contact scheme In order to increase the speed and reliability of our experimental work, in particular the contacting of the samples, we redesigned the contact layout of the laser diodes to be suitable for top-side ground-signal-ground probe head testing. The layout (see Fig. 11, left graph) was also compatible with mounting and wire bonding. The DO 224 wafer was subsequently processed into ridge waveguide lasers with deep etched mesas of width of 2 and 4 µm. However, the new contact design required the back-structuring of the planarization layer for the deposition of the top-side n-contacts. Whereas the contact scheme showed perfectly ohmic characteristics for both the n- and p-contacts, the back-structuring caused cracks in the SOG planarization layer, leading to a low device yield of the DO 224 wafer. Planarization with SOG was finally given up in favor of BCB.


81

DO 453 samples – improvement of gain The 15-fold stacked p-modulation doped DO 453 samples were processed into deeply etched ridge waveguide laser with 2 and 4 µm ridge widths, comprising all aforementioned improvements. Processing was done with large accuracy and skill, yielding virtually 100 % device functionality. Due to the large number of QD layers, the laser diodes showed an extraordinary large modal gain, which allowed operating as-cleaved samples with length below 500 µm. Fig. 67 shows the basic characteristics of the DO 453 samples. The transparency current density of 140 A/cm2 was by a factor of 5 lower than for the DO 75 p-doped sample. The transparency current density per QD layer was only 9 A/cm2, which was an excellent value, comparable to the lowest values ever measured for quantum dot lasers. Due to the large modal gain, the dependence of threshold current density on the device length was linear. 2 µm ridges showed a considerably larger threshold current, due to larger internal losses. The emission wavelength lay at 1290 nm, being absolutely suitable for datacom purposes.

0.0 0.2 0.4 0.6 0.8 1.00

100

200

300

400

500

600

4 µm ridge, jtransp=137 A/cm2

2 µm ridge, jtransp=240 A/cm2

Thre

shol

d cu

rrent

den

s. [A

/cm

2 ]

Reciprocal length [mm-1]0 1 2 3 4

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4 µm ridge, ηint = 70 %, αint = 2 cm-1

2 µm ridge, ηint = 72 %, αint = 4 cm-1

1/η di

ff

Device length [mm]

Fig. 67: Threshold current density (left) and differential quantum efficiency (right) of DO 453 samples with ridge width 2 and 4 µm. The transparency current density and internal losses were lower for the 4 µm ridge. DO 57 QD laser module A DO 57 QD laser diode with dimension 1000x1 µm, HR coated rear facet, was packaged into a commercial fiber optic module, comprising a fiber pigtail, temperature control and a impedance matching network for optimized electrical modulation. Packaging was done by the company u2t photonics.

TEC

HF-Platine

Submount

Fig. 68: Schematic view of the QD laser module, the microwave connector for the electrical signal line was situated to the left, the fiber pigtail to the right hand side [Courtesy G. Jacumeit, u2t photonics].


82

The elements of the impedance matching network (see Fig. 69) were carefully dimensioned to achieve a low signal reflectance at the module and maximum coupling of the RF signal to the laser diode. To minimize the signal reflection, the matching resistor of the network was chosen to add up to 50 Ohm (the standard microwave cable impedance) with the diode resistance: 50match diodeR R+ = Ω Frequency independent matching can only be achieved, if the matching resistor and the diode are placed very close to each other (with a distance much smaller than a quarter wavelength of the maximum modulation frequency). For 10 GHz this corresponds to a distance of < 5 mm, which is a challenging task. Frequency dependent matching, in contrast, helps to increase the module bandwidth. The reflection of the signal oscillates with frequency between the values

( )( )

min

2

max 2

0

/

/match diode

match diode

r

R Z R Zr

R Z R Z

=

+ −=

+ +

(2.56)

with a period of / 2f c LεΔ = and ε being the dielectric constant of the transmission line. The power coupled into the laser diode oscillates accordingly between the two values ( 0P denotes the input power):

min 0

22

max 0 2

( )

2 /( )/

diode

diode diode

diode match

RP r PZ

R Z RP r PZ Z R R Z

=

⎛ ⎞⋅= ⎜ ⎟+ +⎝ ⎠

(2.57)

This corresponds to a current enhancement of

2

max2

min

2 //

diode

diode match

I Z RI Z R R Z

⋅=

+ +, (2.58)

which for the first time occurs at the frequency / 4c Lε . The transmission line length between the matching resistor and the laser diode was chosen to yield a current enhancement at a frequency of 7 GHz, thereby lifting the modulation bandwidth of the device. The bias network in Fig. 69 was completed by a capacitor serving as the RF link and an inductor for the low pass bias current supply of the laser diode.


83

rf

dc

gnd

transmission line

transmission line

inductor

laser diode

resistor

capacitor

rf

dc

gnd

transmission line

transmission line

inductor

laser diode

resistor

capacitor

Fig. 69: Impedance matching and bias network connecting the microwave port (rf), the bias current port (dc) and the QD laser diode (denoted by the diode sign) [Courtesy G. Jacumeit]. All QD laser module measurements were performed with the temperature control set to 23°C. Fig. 70 shows a photograph of the QD laser module mounted on a connection board and the corresponding PI curve. The threshold current of the module was 8 mA (corresponding to a threshold current density of 800 A/cm2). The fiber coupling efficiency inside the module was 10 %, due to the large far-field divergence of the laser diode.

0 10 20 30 40 50 600.0

0.2

0.4

0.6

0.8

1.0

Out

put i

n fib

er [m

W]

Current [mA]

Fig. 70: Photograph of the QD laser module (left) and its output power in fiber (right). The module was transported several times, including large temperature variation, and has up to now shown no degradation of performance. 3.2 Small signal operation Characterization of QD laser diodes for optical data transmission applications requires the measurement of their transmission function, i.e. the ratio of output power modulation to electrical input modulation for a frequency range from DC to 10-20 GHz. The transmission function (see section 2.2.3 for modeling) depends on static laser diode parameters, e.g. cavity length, width, facet reflectivity, and bias current (output power). If the transmission function is independent of the current modulation amplitude, we speak of small signal operation. In contrast, large signal operation


84

characteristics depend on the modulation amplitude (turn-on of a laser is a large signal operation). Related to the small signal transmission function (S12) is the frequency dependent impedance of the laser diode (S11), i.e. the frequency dependent reflection of an electrical modulation signal at the laser diode.

50 Ghz detectorLaser diode

Optical fiberwith isolator

Bias current

Network analyzer

Cryostat withLaser diode

Optics

Bias current

Detector Amplifier

Network analyzer

Fig. 71: Set-up for small signal measurements at room temperature (left) and at cryogenic temperatures (right). Room temperature samples were mounted on a temperature controlled heat sink. S11 and S12 parameters were measured with a HP 8722C 40 GHz network analyzer. Both parameters were measured with a network analyzer (NA). A network analyzer is a frequency generator and electrical spectrum analyzer in one. Sending an electrical sine wave signal with a certain frequency to the laser diode, it determines amplitude and phase of the reflected sine wave signal (S11) as well as the amplitude and phase of the transmitted sine wave signal (S12). Since a laser diode has an optical output, the optical signal is converted to an electrical signal by a fast detector to be analyzed by the NA. Fig. 71 shows the small signal measurement set-up for laser diode characterization at room and cryogenic temperatures. A HP 8722C 40 GHz network analyzer was connected to the laser diode under test with a broadband 26 GHz microwave line (the cryostat sample holder provided a rigid broadband microwave cable both as sample fastening and signal transmission line). The bias current was fed to the sample by an internal bias-T of the NA. The optical signal from the diode was converted with a broadband 50 GHz detector (XPDV2020R, u2t photonics) and fed into the second port of the NA. An additional broadband amplifier was inserted between detector and NA for cryostat measurements to compensate the small (1 %) coupling efficiency of light to the detector. All electrical transmission lines were carefully calibrated prior to measurements with a suitable calibration kit comprising broadband short, load and open terminations. Computer-controlled measurements were performed for a frequency range between 0.05 – 20 GHz, a modulation amplitude of -10 dBm (corresponding to 2 mA current amplitude at 50 Ohm), and for various bias currents. Typical results for impedance and transmission curves are shown in Fig. 48 and Fig. 49. From the S11 and S12 curve we directly derived the -3 dB bandwidth and, by a fit with a suitable model, additional parameters like equivalent circuit resistance and capacitances (see section 2.2.3).


85

3.2.1 S11 and S12 parameter measurements on 1.3 µm QD lasers The relation of the small signal modulation S parameters to the dynamic properties of the intrinsic QD laser has already been discussed in section 2.2.6. The experimental results for devices with different design (shallow, deep mesa, top contacts), epitaxial structure (varying number of QD stacks, p-doping), and dimensions were compared to identify the limiting factors for the dynamic performance of QD laser diodes emitting at 1.3 µm. The implications of the results for future device improvement are discussed in the following section 3.2.2. Ioffe 4-915 - improvement due to deep etching Etching through the active layer of QD laser diodes had proved to be beneficial for the far-field properties of the devices (see section 3.1.2). By small signal analysis we investigated the influence of deep etching on the dynamic properties of the corresponding QD laser diodes. Both the S11 parameter (reflection) and the S12 parameter (transmission) were measured for several samples of the 5-fold stacked Ioffe 4-915 sample, with varying lengths and a ridge width of 4 µm. All QD laser diodes were mounted on our standard single submounts and characterized at room temperature with the set-up shown in Fig. 71 (left).

0.1 1 100.0

0.2

0.4

0.6

0.8

1.0

0 mA 20 mA 40 mA 60 mA 80 mA 100 mA

|S11

|

Frequency [GHz]0.1 1 10

0.01

0.1

1

20 mA 40 mA 100 mA

-3 dB: 4.2 GHz

Mod

ulat

ion

resp

onse

[a.u

.]

Frequency [GHz]

Fig. 72: S11 (left) and normalized S12 (right) measurement of a Ioffe 4-915, 1130x4 µm, deep etched sample at various bias currents. The maximum bandwidth was 4-5 GHz. Fig. 72 shows the typical results for a deep etched sample with dimensions 1130x4 µm. The S11 parameter for zero bias was close to one (full reflection of the input signal with positive sign due to large resistance of laser diode) and changed to values between -1 and 0 for non-zero bias current (reflection of input signal with negative sign due to small resistance of laser diode below 50 Ohm). The left graph of Fig. 72 only shows the absolute value of S11, which increased for increasing bias current due to the decreasing resistance of the laser diode. The right graph of Fig. 72 shows the transmission measurement results. The modulation bandwidth increased with bias current and saturated between 4 and 5 GHz. The transmission curve had no resonance peak, corresponding to a strong damping of relaxation oscillations (compare to Fig. 50). The transmission curves were normalized for comparison. The RC bandwidth derived from the reflection measurements were fitted to the intrinsic part of the electric equivalent circuit shown in Fig. 45 in order to derive the


86

RC bandwidth of the device at different currents. Due to strong damping, the simple low pass model was suitable for QD laser diodes. Simulation of the equivalent circuit and fitting was done with Microwave Office [70]. Fig. 73 (left) shows the results for the RC bandwidth derived for deep etched and shallow etched samples. A significant increase of the RC bandwidth to 4 GHz for deep etched samples was found.

0 500 1000 1500 2000 25000

1

2

3

4

5Ioffe 4-915, ridge width 4µm

2000 µm d.e. 1130 µm d.e. 2000 µm sh.e. 1340 µm sh.e.

RC

ban

dwid

th [G

Hz]


0 500 1000 1500 2000 25000

5

10

15

20

25 2000x4 µm d.e. 1130 µm d.e. 2000 µm sh.e. 1340 µm sh.e.

(f -3dB

)2 [GH

z2 ](j-jthr) [A/cm2]

Fig. 73: RC bandwidth (left) and modulation bandwidth (right) dependence on bias current density for Ioffe 4-915 samples with shallow (sh.e.) and deep (d.e.) etched ridges. A significant increase of the RC bandwidth for the deep mesa devices was found. The modulation bandwidth increased accordingly. The improvement was due to the elimination of the parasitic capacitance associated with the lateral diffusion of barrier and DWELL level carriers into the sides of the active layer by etching through the active layer. At the same time, the resistance of the deep etched samples was larger for a given current bias density due to the narrowing of the current path. The transmission response curves (S12) for different net bias current densities ( thrj j− ) were evaluated for their modulation bandwidth and plotted versus the net bias current density. Fig. 73 (right graph) shows the results for deep and shallow etched samples. Related to the improvement of the RC bandwidth was the increase of the maximum modulation bandwidth for deep etched samples from 3 GHz to 4.7 GHz. All curves show the expected saturation of modulation bandwidth for high current densities. The devices were clearly capable of 5 Gb/s digital modulation, as shown in section 3.3.3. From a fit of these data with the function 3 ( )dB thrf j j− − derived from equations (2.47) and (2.48) we calculated the K factor and the amount of initial damping 0γ . The K factors agreed with the maximum modulation bandwidth according to equation (2.49). Modeling of the S11 and S12 characteristics of the Ioffe 4-915 samples was not completed since the S11 parameter showed a strong deviation from the simulated results: The differential resistance predicted by the model was by factor of 10-50 smaller than the experimentally derived value. The reason for this were low doping levels in the p- and n-doped region of the laser structures that caused a substantial Fermi level bending across the active region and the adjacent layers. The effect of low doping (below the nominal value) was also present in the I-V curve shown in Fig. 63.


87

Ioffe 5-600 – comparison of modulation dynamics for narrow ridges Next we investigated the influence of narrow (< 2 µm) stripe width on the modulation characteristics. The 5-fold stacked Ioffe 5-600 sample, similar to the Ioffe 4-915 structure, was processed into deep etched devices with stripe widths 1/1.5/2/4 µm. Due to the very delicate processing of these high-aspect ratio mesas (the mesa height was about 2 µm) only a few of the 1 and 1.5 µm devices showed proper lasing. Fig. 74 shows the comparison for a 4 µm and a 1.5 µm device: Both devices reached the same maximum RC and modulation bandwidth, although the necessary current density was larger for the narrow stripe laser, probably due to lower internal quantum efficiency. Since we could not complete a comparison of the internal parameters of devices with different stripe widths, the modulation characteristics of the Ioffe 5-600 devices present merely a best-performance survey.

0 1000 2000 3000 4000 50000

1

2

3

4

5

5-600, 1000x4 µm 5-600, 1500x1.5 µm

RC

ban

dwid

th [G

Hz]


0 1000 2000 3000 40000

5

10

15

20

(j-jthr) [A/cm2]

5-600, 1000x4 µm, K=2.2 ns 5-600, 1500x1.5 µm, K=2.6 ns

(f -3dB

)2 [GH

z2 ]

Fig. 74: RC bandwidth (left) and modulation bandwidth (right) for DO 5-600 with two different stripe width (and length). The 1.5 µm ridge device required higher bias current densities, probably due to lower internal quantum efficiency. DO 57 and 75 – impact of p-doping on modulation bandwidth P-doping of QD laser structures was intended to increase both modal gain of the QD lasers and their modulation bandwidth [31]. No significant improvement of the modal gain (for example ground state lasing for very short devices) had been found for the DO 75 samples. We investigated a number of devices with both doped and undoped active zone. Fig. 75 shows the transmission function measurement for the sample DO 57, 1000x4 µm and DO 75, 1000x4 µm. They show similar modulation characteristics with almost identical maximum modulation bandwidth. Both samples showed transmission functions without resonance peak – a feature that is responsible for low patterning eye diagrams!


88

1 100.01

0.1

1

DO-57, 1000x4µm

-3 dB:5 GHz

20 mA 40 mA 100 mA

Mod

ulat

ion

resp

onse

[a.u

.]

Frequency [GHz]1 10

0.01

0.1

1 -3 dB: 5.2 GHz

DO-75, 1000x4µm 40 mA 60 mA 100 mA

Mod

ulat

ion

resp

onse

[a.u

.]

Frequency [GHz]

Fig. 75: S12 transmission function measurements for undoped DO 57 (left) and p-doped DO 75 (right) 1000x4 µm samples at different bias currents. The transmission function showed no resonance peak. No difference between both samples was detected; the maximum bandwidth in both cases was 5-6 GHz. Fig. 76 shows the modulation bandwidth for both samples. All p-doped samples that we investigated showed no significantly larger bandwidth than their undoped twins. The lower bandwidth saturation at high power for the DO 75 sample, as depicted in Fig. 76, was attributed to device variations.

0 500 1000 1500 2000 25000

10

20

30

DO-57, 1000x4µm, K=1.7 ns DO-75, 1000x4µm, K=1.6 ns

(j-jthr) [A/cm2]

(f -3dB

)2 [GH

z2 ]

Fig. 76: Modulation bandwidth dependence on net bias current density for p-doped (DO 75) and undoped (DO 57) samples. The p-doped sample showed a slight increase of the maximum modulation bandwidth. From the previous section on static properties we know that for the p-doped DO 75 samples threshold currents were factors of 3 larger than for the DO 57 samples. The reason could be an enhanced non-radiative recombination rate of carriers inside the DWELL quantum well layer and the QDs due to a larger number of holes. A larger number of holes inside the QDs should give a higher differential gain. The absence of the latter might indicate that the additional holes reside mainly in the excited states or QW states. If we assume neutral dots, additional holes may only reside in the QW layers. Since there was no convincing theoretical clue for this effect, p-doping was nevertheless continued for the next samples.


89

QD laser module – bandwidth improvement due to impedance matching The QD laser module comprising optical coupling and an impedance matching bias network was tested prior to eye pattern measurements. Fig. 77 (left) shows the reflection measurement, revealing the beneficial influence of proper impedance matching: Back reflection was reduced (S11 = 0) for low frequencies and multiples of 13 GHz. In between the reflection reaches a maximum value of 0.7, in good agreement with the theoretical value of 0.8 calculated from equation (2.56) for

6diodeR = Ω . This corresponds to a current enhancement at 10 GHz of approximately 1.6. Since the maximum modulation bandwidth of the QD laser diode shown in the right graph of Fig. 77 was 6 GHz, the current enhancement had only a small influence on the module bandwidth. More important was the suppression of noise due to reflection of the electrical signal by the impedance matching network. Due to the power limitations of the bias network, the module was driven with moderate current densities below 6000 A/cm2.

0 5 10 15 200.0

0.2

0.4

0.6

0.8

1.0 60 mAQD-Laser-Modul

DO 57, 1000x1 µm

|S11

|

Frequency [GHz]

0 2000 4000 60000

10

20

30

40

50QD laser moduleDO-57, 1000x1µm, K=1.4 ns

(j-jthr) [A/cm2]

(f -3dB

)2 [GH

z2 ]

Fig. 77: Typical S11 (left) and modulation bandwidth (right) results for the QD laser module, containing a DO 57, 1000x1 µm sample with HR coated rear facet. The S11 curve showed oscillations with matching points at 0 and 13 GHz due to the impedance matching network. According to the small signal analysis, the QD laser module should be capable of 10 Gb/s digital modulation. DO 224 – GSG scheme improvement The 10-fold stacked, p-doped DO 224 sample was processed into top contact laser diodes suitable for testing with a GSG probe head. Ridge widths of 2 and 4 µm were realized in our tried and tested deep etching scheme. HR coating of 0.5 mm bars with 95 % backside, 80 % front facet reflectivity should ensure ground state lasing and maximum photon density for fast dynamics. Thanks to the new contact scheme, complete laser bars were mounted on a copper heat sink on a temperature controlled stage for small signal analysis. Fig. 78 (left) shows the perfectly smooth S11 curves for a 500x4 µm sample. Distortion of the signal by submount and bonding were completely removed. However, both the S11 and the S12 measurement in Fig. 78 exhibited the well-known characteristics: strong damping, saturation of the modulation bandwidth at 7 GHz. The dependence of the S11 curve on current was still deviating from the model predictions; the increase of the low frequency reflection was a factor of 2-3 stronger for the experimental results.


90

0.1 1 100.0

0.2

0.4

0.6

0.8

1.0

0 A/cm2

1 kA/cm2

2 kA/cm2

5 kA/cm2

9 kA/cm2DO224, 500x4µm, HR-HR

|S11

|


0.1

1

10

1 kA/cm2

2 kA/cm2

5 kA/cm2

9 kA/cm2


Mod

ulat

ion

resp

onse

[a.u

.]

Frequency [GHz]

7 GHz

Fig. 78: S11 (left) and S12 (right) measurement of a DO 224, 500x4 µm, HR coated sample at various bias currents. The maximum bandwidth was 7 GHz. Fig. 79 (right) shows the modulation bandwidths for DO 224 samples with different ridge width. The 4 µm device showed a significantly larger maximum modulation bandwidth. At the same time, the 4 µm device needed twice the current and generated approximately twice the output power (10 mW at 2500 A/cm2). Depending on the need for maximum bandwidth or low power consumption, both devices have their applications.

0 2000 4000 6000 8000 100000

2

4

6

8

( )( )

( )


RC

ban

dwid

th [G

Hz]

(j-jthr) [A/cm2]

( )

0 2000 4000 6000 8000 100000

10

20

30

40

50

500x2µm, HR-HR, K=1.5 ns 500x4µm, HR-HR, K=1.2 ns

(f -3dB

)2 [GH

z2 ]

(j-jthr) [A/cm2]

Fig. 79: Reflection for DO 224, 500x2 µm (left) and modulation bandwidth (right) for DO 224, 500x2 µm and 500x4 µm, both with HR coated facets. The maximum bandwidth for the 4 µm device was larger. The data points in brackets denote the RC circuit fitting accuracy limit due to the small differential resistance at large currents. The maximum bandwidth of the DO 224, 500x4 µm sample at 70°C was still 6 GHz. The RC bandwidth in Fig. 79 showed a smooth increase with current. For large current densities, the differential resistance became too small in relation to the 50 Ohm network impedance to be accurately fitted with the RC equivalent circuit model. For broader or longer devices this limitation was even more severe. Therefore we only evaluated the RC bandwidth for the smallest device. DO 453 samples – impact of large modal gain The DO 453 sample incorporated 15 QD layers for maximum modal gain. If the modulation bandwidth of InGaAs QD laser diodes was limited by the low differential gain, this sample should have shown a significant improvement compared to the


91

previous, 5-fold and 10-fold stacked ones. Devices with lengths between 0.5 and 4 mm, 2 and 4 µm ridge widths were processed and bar-tested with the GSG probe head set-up. Fig. 80 shows the S11 and the S12 measurements for a 1000x4 µm sample, results for 500x(2/4) µm with HR coated facets are similar. The transmission function exhibited the usual strong damping and bandwidth saturation at 6 GHz, whereas the S11 curve showed an odd behavior for large frequency: The reflection decreased. Due to this effect and the aforementioned vanishingly small differential resistance at large bias current densities, no RC bandwidth of the samples could be retrieved.

0.1 1 100.5

0.6

0.7

0.8

0.9

1.0

|S11

|

Frequency [GHz]

0 A/cm2

500 A/cm2

1000 A/cm2

2000 A/cm2

4000 A/cm2

DO453, 1000x4µm

0.1 1 100.01

0.1

1

500 A/cm2

1000 A/cm2

2000 A/cm2

4000 A/cm2

DO453, 1000x4µm

Mod

ulat

ion

resp

onse

[a.u

.]

Frequency [GHz]

6 GHz

Fig. 80: S11 (left) and S12 (right) measurement of a DO 453, 1000x4 µm sample at various bias currents. The maximum modulation bandwidth was 6 GHz. Fig. 81 shows the modulation bandwidth of a 2 and 4 µm device, with a maximum modulation bandwidth of 4.7 and 6 GHz, respectively. Due to the reliable processing of the DO 453 samples the modulation characteristics were reproduced for several samples, giving the same result: No improvement of the maximum modulation bandwidth compared to 5-fold and 10-fold stacked samples was found.

0 1000 2000 3000 4000 50000

10

20

30

40

(f -3dB

)2 [GH

z2 ]

(j-jthr) [A/cm2]

DO 453, 1000x4 µm, K=1.4 ns DO 453, 1000x2 µm, K=1.8 ns

Fig. 81: Modulation bandwidth for DO 453, 1000x4 µm and 1000x2 µm samples. The 4 µm ridge device showed a larger maximum bandwidth. This result was consistent with the bandwidth limitation found in other dynamic measurements (relaxation oscillation measurements, digital modulation) on the same samples. In the following section we discuss the origin of the bandwidth limitation and possible means of improvement.


92

3.2.2 Limitations of modulation bandwidth - comparison to other groups In order to understand the influence of the intrinsic parameters of QD lasers (relaxation time, DOS, recombination times etc.) we compared simulations with different sets of parameters. As a starting-point of the simulation we fitted the model to the cw, small and large signal characteristics of a DO 453, 1000x4 µm sample. Fig. 35, Fig. 83 and Fig. 92 show the corresponding measurements and simulated data.

1 10-30

-25

-20

-15

-10

-5DO 453, 1000x4 µm

500 A/cm2

1000 A/cm2

1500 A/cm2

2000 A/cm2

2500 A/cm2

M

odul

atio

n re

spon

se [a

.u.]

Frequency [GHz]

Fig. 82: Measured transmission functions of the sample DO 453, 1000x4 µm and the corresponding simulated transmission function (data points) fitted by careful choice of the simulation parameters. The simulation showed a light discrepancy for low current densities, the resonance peak was overestimated by the model. Additional fits to the characteristics of devices with different lengths (1,2,3,4 µm) and different number of QD layers (5, 10, 15) obtained by simply changing length or layer number while keeping all other parameters fixed ensured the reliability of the model parameter set. We simulated the influence of certain parameters on the modulation characteristics by varying them while keeping all other parameters fixed. Fig. 83 shows the comparison of the transmission function for the actual device and the simulated one for halved capture and relaxation times.

0 2 4 6 8 100.01

0.1

1

Tran

smis

sion

func

tion

[a.u

.]

0.5 kA/cm2

1 kA/cm2

1.5 kA/cm2

2 kA/cm2

3.5 kA/cm2

5 kA/cm2

Frequency [GHz]0 2 4 6 8 10

0.01

0.1

1

0.5 kA/cm2

1 kA/cm2

2.5 kA/cm2

5 kA/cm2

7.5 kA/cm2

10 kA/cm2

Tran

smis

sion

func

tion

[a.u

.]

Frequency [GHz]

Fig. 83: Modeled transmission function for the Do 453, 1000x4 µm laser diode (left) and corresponding transmission function for the same sample with halved QD capture and relaxation time (right). The transmission function now showed a resonance peak at low current densities, along with an increased modulation bandwidth for large current densities.


93

Fig. 84 shows the corresponding modulation bandwidth versus current density. As expected, the simulated modulation bandwidth of the device increased for smaller relaxation times by a factor of 1.5.

0 2000 4000 6000 8000 100000

20

40

60

80

τcap=4 ps, τrelax=2 ps, K=1.6 τcap=2 ps, τrelax=1 ps, K=0.98

(f -3dB

)2 [GH

z2 ]


Fig. 84: Modeling results for modulation bandwidth of a DO 453, 1000x4 µm QD laser with two different sets of parameters: experimental data and fit (capture time 4 ps, relaxation time 2 ps) and simulation for improved bandwidth (capture time 2 ps, relaxation time 1 ps). The maximum bandwidth increased from ~6 to ~9 GHz. The differential gain in a laser diode can be maximized for a given epitaxial structure by fabrication of low mirror loss devices, i.e. by long and/or HR coated laser diodes. As long as the modulation bandwidth was not limited by the photon lifetime (see Fig. 52), even a 5-fold stacked laser achieved a similar maximum bandwidth as a 15-fold stacked QD laser. The reason for that is the independence of the dynamic properties of a single QD layer from adjacent layers. Fig. 85 shows the curves for maximum modulation bandwidth for a different number of QD layers (with optimized mirror losses) and for different modal gain per layer.

0 2 4 6 8 100.01

0.1

1

Tran

smis

sion

func

tion

[a.u

.]

Gain/layer = 3 cm-1

15 layers 10 layers, 95% 5 layers, 80%/95%

Frequency [GHz]0 2 4 6 8 10

0.01

0.1

1

Tran

smis

sion

func

tion

[a.u

.]

15 QD layers Gain/layer = 2 cm-1

Gain/layer = 3 cm-1

Gain/layer = 4 cm-1

Frequency [GHz]

Fig. 85: Dependence of maximum modulation bandwidth transmission function on QD layer number (left) and modal gain per layer (right). While the layer number only influences the output power of the device (offset in left figure), an increasing modal gain per layer drastically improves the maximum possible bandwidth. Let’s recapitulate the three main contributions to bandwidth limitation of current QD lasers:

- Low differential gain 'G due to the asymmetric DOS of holes and electrons in quantum dots, as explained with the quasi-equilibrium model

- Large gain compression factor ε due to slow capture of the carriers into the quantum dots


94

- Capacitive-like roll-off of transmission function due to wide active zone (up to 500 nm) and, as a consequence, long carrier transport times across the active zone

The first two effects are confirmed by our modeling. The third effect is not included in our model, but there are a few measurements (Fig. 86) were the capacitive-like roll-off is clearly visible.

0 5 10 15 200.0

0.5

1.0

τ1/e2=0 ps

τ1/e2=100 ps

fres = 7.5 GHzγ = 48 GHz

Mod

ulat

ion

resp

onse

[a.u

.]

Frequency [GHz]

Fig. 86: Measured transmission functions of the sample DO 224, 500x4 µm, HR-HR coating, and the corresponding three-parameter transmission function according to the equation in section 2.2.6. The capacitive-like roll-off of the transmission function is described by a time constant of 100 ps. The red curve shows the hypothetical curve for 0 ps. The comparison of the three-parameter fit and the hypothetical curve with the same resonance frequency and damping, but for vanishing roll-off shows the strong influence of the transport time on the modulation bandwidth of the laser: The bandwidth without transport limitation is almost twice as large. Our simulations and theoretical estimations agree well with the results of our measurements. An improvement of the intrinsic modulation bandwidth of QD laser diodes can therefore only be accomplished by:

- Enlargement of the modal gain per layer (by increasing the QD density, the oscillator strength, by decreasing the inhomogeneous broadening)

- Improvement of the transport, relaxation and capture time (by coupling of QD layers, tunnel injection of carriers, by DWELL QW tailoring, narrowing of active section)

All of these tasks are very challenging, if at the same time all other parameters of the laser diodes are to be kept constant (wavelength, losses, threshold current etc.). Comparison to other groups Tunnel injection (TI) of carriers into quantum dots was proposed and realized by the group of P. Bhattacharya [32, 91, 94, 112, 113]. A maximum modulation bandwidth of 24 GHz at an emission wavelength of 1.1 µm and 8 GHz at 1.24 µm wavelength was achieved. It has to be added that all small signal measurements have been performed under pulsed operation, with a rather poor S/N ratio. There is a considerable concern that the performance of the devices will be worse under cw operation. The TI scheme has up to now not been reproduced by any other workgroup. It comprises not only an injection barrier layer, but also closely stacked (and therefore coupled) QD layers. The difference in performance to our lasers might be due to either the injection scheme or the strong vertical QD coupling.


95

1.3 µm InGaAs QD lasers with InGaP cladding and buffer layers incorporating vertically coupled QD stacks with 18 nm spacer thickness were grown and investigated by the group of J. Harris [19]. A maximum modulation bandwidth of 12 GHz is achieved, limited by gain saturation and switching to excited state lasing. 7 GHz modulation bandwidth, 10 Gb/s eye pattern measurements were presented by a Fujitsu consortium, employing a p-doped InGaAs QD laser structure similar to our 1.3 µm MBE grown samples [114]. More than 6 dB extinction ratio was achieved between 20°C and 70°C without current adjustment. These results are comparable to ours, except for the improved temperature stability. InGaAs QD laser devices with single mode emission yielded 5 GHz modulation bandwidth [115] and a 2.5 Gb/s open eye pattern [98], respectively. Single mode devices seem to be strongly subjected to gain compression limitations.

3.2.3 Comparison to quantum well laser diodes Quantum well laser devices incorporating a single or multiple QW (MQW) as gain medium are the well-established semiconductor lasers suitable for high-speed applications. Directly modulated QW lasers have reached modulation bandwidths beyond 20 GHz [116-119] more than ten years ago, and have since then been optimized regarding their wavelength, power consumption and temperature dependence. Commercial QW laser diodes with a modulation bandwidth > 10 GHz are available. With the help of tunnel injection, a bandwidth as large as 48 GHz could be achieved [120], although this particular device was not relevant for data transmission due to its strong resonance enhancement (>10 dB). Single mode emission at 1310 nm with a data rate of 10 Gb/s for uncooled operation up to 100°C and low current drive of 14 mAp-p has been recently demonstrated [121]. The main features that distinguish QW from QD devices are:

- Gain per layer: Due to the larger DOS of QW (> 1012 cm2) compared to the area density of QDs (1010-1011 cm2) QW layers have an up to ten times larger modal gain. MQW lasers usually contain 3-5 layers of QWs.

- QW lasers show a larger threshold current dependence on temperature (T0 ~ 50-70 K).

- Due to the smaller number of relaxation and capture processes involved in QW devices, the total relaxation time is smaller (~1 ps range [96], compared to several ps in QD devices) and causes less gain compression.

- QD devices with a large number of stacks (for maximum gain) and large spacer thickness (for optimum growth of successive QD layers) have wide active areas (> 500 nm), imposing a modulation bandwidth limitation by slow carrier transport. Since QW devices work with a smaller number of layers, the transport problem is not as dominant.

So far, the aforementioned limitations of QD devices have prevented them from surpassing the conventional QW devices in the field of direct modulation. Due to the more complex design of QD lasers, we expect them to gradually improve along with a better theoretical understanding of the interplay of carrier dynamics and epitaxial structure.


96

3.3 Large signal operation Laser diode operation is considered as large signal modulation, if the small signal analysis is no longer valid, i.e. the nonlinearity of changes in gain and carrier density is essential. As a rule of thumb we keep in mind that large signal modulation always provokes relaxation oscillations. Investigation of the large signal modulation behavior of quantum dot lasers is of considerable interest both for understanding the complex physics of QD gain media and for evaluating their benefit for application in optical datacom. In comparison to conventional quantum well lasers, QD lasers exhibit a number of novel properties, e.g. strongly damped relaxation oscillations, a broad emission spectrum, especially at low temperatures, low chirp, and a large characteristic temperature. Part of these characteristics can only be accessed by large signal measurements. On the other hand, applications like digital data transmission are large signal operation schemes This chapter is therefore essentially twofold: First, time resolved turn-on measurements will be presented for 1.1 and 1.3 µm QD lasers. The second part of the chapter deals with digital modulation and data transmission with 1.3 µm QD lasers.

5 6 7 8 9 100

2

4

6

RC bandwidth 10 GHz 1 GHz 500 MHz 200 MHz

Inte

nsity

[a.u

.]

Time [ns]

Fig. 87: Simulated turn-on behavior of a laser diode with a built-in parasitic RC bandwidth between 0.2 and 10 GHz. The calculation was done with a simple rate equation model numerically solved for a rectangular current pulse input. The relaxation peak positions are only slightly delayed when the RC bandwidth decreases. As already stated in section 2.2.3, there is a close relationship between relaxation oscillations and small signal transmission function, where resonance frequency resf and damping γ can be associated with the transmission curve parameters. This implies an interesting feature of large signal RO measurements: Laser diodes with a poor electrical signal injection (low bandwidth submounts, even needle-contacted samples) or with strong parasitic contact capacitances are not suitable for small signal transmission measurements due to the strong perturbation of the signal on its way to the active region, but might still be accessible for large signal modulation pulses. It is true that the large signal pulse is also perturbed by a low bandwidth signal line; however due to the long turn-on delay of semiconductor lasers in the range of 1 ns the distorted pulse entering the active region is still capable of provoking relaxation oscillations. Fig. 87 shows simulated turn-on relaxation oscillations with a resonance frequency of 2 GHz for different submount bandwidths,


97

ranging from an undistorted pulse (10 GHz) down to a flattened pulse with a rise time well above 1 ns (200 MHz). The submount bandwidth influences mainly the damping of the relaxation oscillations; generally, low bandwidth submounts tend to smooth out the relaxation oscillation peaks. The resonance frequency, however, stays almost the same. Thus, even for a non-optimized laser diode the intrinsic speed of the relaxation oscillation can be retrieved. We employed this method when studying the modulation characteristics of the first QD edge emitting laser samples and for QD VCSELs. It is clear that this experimental trick does not release us from the task of elimination of parasitic elements, since in any data transmission scheme, a slow relaxation into steady state like in Fig. 87 would obscure the digital signal levels.

3.3.1 Relaxation oscillation measurements on 1.1 µm QD lasers Theoretical considerations [122] imply that the turn-on dynamics of quantum dot lasers might be too complex to be completely revealed in a spectrally integrated transient. This is, for example, the case when the laser diode shows independently emitting ensembles of quantum dots. It is expected that spectrally different sub-ensembles of QDs start lasing with different turn-on delays, relaxation frequencies and damping. We used both temporally and spectrally resolved measurements to investigate the turn-on behavior of 1.1 µm and 1.3 µm quantum dot lasers. Since the coupling between the QDs depends on temperature, we included the sample temperature as third parameter to our investigations.

cryostat withlaserdiode double spectrometer

streak camera+ reticon

pulse generator to computer

bias tee

bias

Fig. 88: Experimental set-up for relaxation oscillation measurements with temporal, spectral and temperature resolution. The laser diode placed in a He flow cryostat was fed with a pulsed current through a microwave cable reaching into the cryostat chamber. The optical output from the laser diode through the cryostat window was focused into a subtractively butt-coupled double spectrometer. The selected wavelength was then focused on the S1 cathode of an Imacon 500 synchroscan streak camera. The camera screen was read out with a cooled CCD line (Reticon) and fed to the computer. The complete set-up was computer controlled. The set-up for both temporally and spectrally turn-on measurements at cryogenic temperatures is shown in Fig. 88. It comprised an Oxford CF 204 helium flow cryostat for temperatures between 5 and 300 K, two butt-coupled Spectra Physics 300 mm imaging grating spectrometers providing a maximum spectral resolution of 100 pm in the range between 800 and 1600 nm (single spectrometer) and a Imacon 500


98

synchroscan streak camera with long wavelength S1 photo cathode. The streak camera worked at a fixed repetition rate of 38 MHz and integrated (~10 ms) incoming pulses in order to enhance sensitivity. The wavelength range lay between 1 and 1.3 µm. The temporal resolution of the set-up lay in the range of 5 ps, transients as long as 10 ns could be measured by combination of successive streak measurements. To ensure a ps time resolution, light path differences in the mm range had to be considered. That was why we used a second spectrometer for the compensation of path differences of the interfering beams from the spectrometer grating. As an electrical pulse source we employed a HP 8131A pulse generator with a typical rise time of 100 ps and a maximum voltage of 5 V, corresponding to 200 mA maximum current into 50 Ohm.

Fig. 89: Spectro-temporal turn-on intensity profile of a TU 5447, 1000x10 µm QD laser diode at temperatures 20, 100, 200, and 300 K (from top left to bottom right). The laser diode was driven with 60 mA amplitude, 5 ns duration electrical pulses. All graphs span the same wavelength range, although with different offset due to the spectral shift of emission. TU 5447 and TU 5382 samples – quantum dots vs. quantum well Several TU 5447 QD laser diodes with dimensions 1000x10 µm were investigated to find out whether QD laser modes turn on synchronously or not. At the same time


99

spectral broadening, wavelength shift, mode grouping and relaxation characteristics were measured. For comparison, a TU 5382 quantum well sample processed similar to the QD sample, with dimensions 800x3 µm was also tested. Fig. 89 shows the spectro-temporal measurements with dependence on the laser diode temperature. As expected, the QD laser spectrum broadened significantly for lower temperatures. Whereas for room temperature, the spectral FWHM was 6 nm, it was 30 nm for 200 K and 40 nm for 20 K. The reason for spectral broadening has already been discussed in section 2.2.7. For room temperature, a narrowing of the spectrum of about 50 % set in after the relaxation oscillation peak. For all temperatures, the relaxation oscillation was strongly damped, so that only the first peak appeared. Furthermore, this first peak had the same position for all longitudinal modes! There was no sign for an independent or even temporally shifted relaxation oscillation for different wavelengths. The low temperature measurements had been repeated with a number of QD laser diodes, all with similar results. The synchronous turn-on of all longitudinal modes at low temperatures is based on one of the following mechanisms:

1) The homogeneous broadening of the QD emission is in the range of or larger than the inhomogeneous broadening ( 30inhom meVσ ≈ ) of the QD ensemble due to size distribution. In this case, all quantum dots overlap spectrally, contributing to a synchronous bunch of longitudinal modes. At the same time we would expect a narrowing of the optical spectrum [122], which is not observed within the measured time range of 1 ns. However, narrowing is counteracted by spectral gain compression of the central modes.

2) The homogeneous broadening is small compared to inhomσ , but the modes are synchronized by carrier dynamics. This is a doubtful explanation, since the carrier relaxation between different dots is definitely slow (hence the broadening) and cannot account for the synchronization.

Fig. 90: Spectro-temporal turn-on intensity profile of a TU 5382, 800x3 µm quantum well laser diode at temperatures 20 (left) and 300 K (right). The laser diode was driven with 1.5 V amplitude, 5 ns duration electrical pulses. The QW laser emission spectrum was considerably smaller than the QD laser emission at low temperatures. The comparison of the quantum dot laser turn-on measurements with quantum well laser turn-on revealed the unique properties of QD lasers. Fig. 90 shows the


100

corresponding measurements for q TU 5382 QW sample. At room temperature we observed a narrow emission (~ 1 nm) with clearly resolved relaxation oscillation peaks. Damping of the RO was considerably lower for this QW sample (which is typical for QW lasers) than for the QD sample. At low temperature, the emission of the QW laser became even narrower (< 1 nm) due to Fermi distribution narrowing. The experimental results show that for low temperatures, carrier in QD lasers are essentially non-thermally distributed, as pointed out in section 2.2.7.

3.3.2 Relaxation oscillation measurements on 1.3 µm QD lasers Ioffe 4-920 sample Similar RO measurements were performed for QD laser diodes emitting at 1.3 µm. We investigated a Ioffe 4-920 sample incorporating a 5-fold stack of InGaAs quantum dots (similar to Ioffe 4-915) with a stripe width of 30 µm, a length of 1900 µm and a shallow mesa. The laser was mounted p-side up on our standard single submount. The measurements were carried out at room temperature and 200 K. The threshold current density of this device was 290 A/cm2 (170 A/cm2) resulting in a threshold current of 165 mA (95 mA) at 300 K (200 K). Spectrally resolved transients were measured by means of the Synchroscan streak camera set-up described in the previous section (see Fig. 88). The laser diodes were driven with electrical pulses of 5 ns length and the obligatory 38 MHz repetition rate. Due to the pulse generators maximum output current of 200 mA and the rather high threshold current of the sample all measurements were carried out with a sub-threshold bias of 150 mA (40 mA) at 300 K (200 K).

0 1 2 3 4 5

1200

1210

1220

1230

Time [ns]

Wav

elen

gth

[nm

]

0 1 2 3 4 5

1250

1260

1270

1280In

tens

ity [a

.u.]

Time [ns]

Wav

elen

gth

[nm

]

0

1

2

3

4

5

Fig. 91: Spectro-temporal turn-on intensity profile of a Ioffe 4-920, 1900x30 µm QD laser diode at 200 (left) and 300 K (right). Both graphs span the same wavelength range, but with different offset due to the spectral shift of emission. Time-resolved spectra of the QD laser at maximum excitation level (bias plus 190 mA pulse) are shown in Fig. 91. The central emission wavelength of the laser at room temperature was 1263 nm, which corresponded to the ground state transition for these DWELL quantum dots. The full width at half maximum (FWHM) of the emission was 7 nm. As the mode spacing of 120 pm was in the range of the spectral resolution of the set-up, single modes were not resolved. A mode grouping structure with a spacing of 1.5 nm could be seen. The origin of this mode grouping was already discussed in


101

section 3.1. The mode grouping became more pronounced with increasing duration of the laser pulse. The side mode suppression ratio (SMSR) within the mode grouping comb increased from about 1.3 dB at the beginning of the pulse to more than 10 dB near the end of the pulse. The central emission wavelength of the laser at 200 K was 1212 nm corresponding to the thermal shift of the ground state transition. The FWHM of emission was about 20 nm as compared to 7 nm at 300 K due to the weaker thermal coupling between dots, similar to the results for 1.1 µm quantum dot lasers. The spectral spacing of 1 nm between the mode groups was 1/3 smaller than in the room temperature case. Also the temporal development of the mode grouping had changed with temperature: The SMSR within the mode grouping comb was larger than 10 dB even at the beginning of the pulse. At both temperatures the oscillations of the different mode groups were synchronous, similar to the results for 1.1 µm quantum dot lasers. Due to the strong damping of the relaxation oscillations no second peak of the oscillation was detectable. It was therefore not possible to obtain an estimation of modulation speed of the laser diode. Further information about the modulation characteristics are derived from small signal measurements (section 3.2.1). DO 453 samples – comparison of small and large signal characterization Most of the quantum dot lasers we investigated (Ioffe 4-915, Ioffe 5-600, DO 57) showed turn-on characteristics similar to the previous sample. For the DO 453 samples, however, it was possible to evaluate first and second RO peak. Spectrally integrated turn-on transients were measured with a 50 GHz detector and a 40 GHz oscilloscope for different pulse amplitudes. Fig. 92 (left) shows a selection of results for a DO 453, 1000x4 µm sample. Both the current dependent turn-on delay and the RO frequency were derived from the transients. Fig. 92 (right) shows the dependence of the turn-on delay time on the current, plotted according to the linearity predicted by equation (2.43). The linear fit of the data yielded a reasonable carrier lifetime of 1.2 ns. The RT model simulation of the turn-on behavior gave similar results and is shown in Fig. 92 for comparison.

0 1 2 3 4 50.00

0.02

0.04

0.06

0.08Measurement

500 A/cm2

750 A/cm2

... 1500 A/cm2

Simulation

Lase

r Out

put [

a.u.

]

Time [ns]

0.0 0.5 1.0 1.5 2.00

500

1000

1500

2000

2500 Experiment Simulation + linear fit

τ = 1.2 ns

Turn

-on

dela

y [p

s]

Ln(I/(I-Ithr)

Fig. 92: Turn-on transients of a DO 453, 1000x4 µm sample at different currents (left) and corresponding turn-on delay vs. current (right) with the derived carrier lifetime. The electrical pulse in the left graph started at 0 ns and has a total length of 5 ns. Fig. 93 shows the square RO frequencies plotted versus the net current density according to equation (2.47). We found a fairly linear dependence, in agreement with


102

theory. Fig. 93 also gives the modulation bandwidth derived from small signal measurements. Both frequencies are experimentally related by 3 1.2dB ROf f− = ⋅ , as expected from equation (2.46) for strong damping.

0 500 1000 15000

10

20

30

-3 dB bandwidth RO frequency

Freq

uenc

y2 [GH

z2 ]

(j-jthr) [A/cm2]

Fig. 93: Relaxation oscillation frequency and modulation bandwidth of a DO 453, 1000x4 µm sample at different currents. The modulation bandwidth was derived from S12 measurements; the RO frequency was derived from the turn-on measurements (Fig. 92). The comparison illustrates the ambiguity of modulation bandwidth estimation from RO frequencies: The low damping relation 3 1.55dB ROf f− = ⋅ is not valid for QD lasers, which means that besides the RO frequency the exact amount of damping has to be derived from the RO measurements in order to give the correct relation. Extraction of the damping constant γ from measurements like those presented in Fig. 92 is only possible with a large error due to the small amplitude of the second RO peak. For modulation bandwidth characterization we therefore generally rely on small signal measurements.

3.3.3 Digital modulation - eye diagrams of 1.3 µm QD lasers Digital modulation of 1.3 µm quantum dot lasers is the most important milestone on the road to application of QD lasers in datacom. Digital modulation eye patterns and bit error rates (BER) have been measured for a number of samples (see Table 1, marked EYE) at the Heinrich-Hertz-Institute with the help of the group of Dr. Weber, namely Colja Schubert and Vincent Marembert.


103

DC current

10 Ghz Detector

Bias-T

Amplifier

Bit Pattern Generator

Laser diodeOptical fiber

Oscilloscope Fig. 94: Schematic set-up for eye pattern measurements. A master oscillator (not shown) feeds the transmission base frequency (e.g. 10 GHz) to the bit pattern generator (SHF BPG 4x10). The PRBS signal from the BPG is amplified with a suitable broad band low noise amplifier (SHF 80) for higher input power at the laser diode. PRBS signal and bias current are fed to the laser through a Bias-T. The output from the laser is coupled into a SMF with optical isolator and converted in a broad band detector. Both the bandwidth of the detector and connected sampling oscilloscope are matched with the signal bandwidth (max. 10 GHz) to avoid additional high frequency noise. The eye pattern measurement set-up is a genuine optical data transmission system, albeit a very short optical fiber length of a few meters. Fig. 94 shows the schematic set-up that was employed for all eye pattern measurements presented in this work. The electrical input is a pseudo-random bit sequence (PRBS) no-return-to-zero (NRZ) pulse train, i.e. bit pattern of length 1215 − bit containing all possible sequences of 15 bits from (000000000000000) to (111111111111111). Part of the PRBS signal is shown in the left graph of Fig. 95. This is the most demanding sequence, since it represents the highest and lowest frequency components of the PRBS signal. The left part of Fig. 95 shows the eye pattern of the electrical output of the BPG, as measured for calibration purposes.

0 1 2 3 4 5

-2

-1

0

1

2

Sign

al le

vel [

a.u.

]

Time [ns]

0 100 200

-2

0

2

4

Sign

al le

vel [

a.u.

]

Time [ps]

Fig. 95: Direct measurement of the BPG electrical output signal: Part of the BPG PRBS 15 signal stream (left) and the corresponding eye pattern. The PRBS sequence shown contains a sequence of alternating “0” and “1”, 15 successive “0” and 15 successive “1”. The eye pattern is of course in perfect shape, since has not yet undergone any electro-optic conversion. In order to check the system test bed for our lasers we performed 10 Gb/s test eye pattern measurements on a commercial quantum well laser diode (Optospeed


104

Germany), specified for 10 Gb/s and mounted on a submount similar to the QD lasers. Fig. 96 proves the functionality both of our set-up and submount.

0 1 2 3 4 50

5

10

15

20

Sign

al le

vel [

a.u.

]

Time [ns]

0 100 200-4

-2

0

2

4

Sign

al le

vel [

a.u.

]

Time [ps]

Fig. 96: Part of the 10 Gb/s bit pattern (left) and eye diagram (right) of a commercial quantum well laser diode specified for 10 Gb/s. A clearly open eye was observed. The bit pattern corresponds to the electrical pattern shown in Fig. 95 except that Hi and Lo are swapped because the QW diode was driven with negative bias current (p-doped substrate). There were a large number of parameters derived from eye pattern measurements. We selected four crucial parameters for eye pattern evaluation:

1) average power of signal 2) extinction ratio 3) signal-to-noise ratio 4) timing jitter (peak-to-peak)

The quantities are depicted and explained in Fig. 97 and Fig. 98. The parameters were automatically evaluated by the oscilloscope during measurement. In order to achieve an eye pattern trace with low statistic sampling noise, we integrated at least 600 PRBS word frames; for a sampling rate of 1 M sample/s this took about 20 seconds. Long measurements (> 10 min) exhibited drift effects due to temperature changes or changes in the laser-to-fiber coupling efficiency. Therefore we limited the measurements time to below 10 min.

0 100 2000

2

4

6

8

10

Pow

er [m

W]

Time [ps]

Average power

0 100 2000

2

4

6

8

10

Pow

er [m

W]

Time [ps]

Extinction ratio

Fig. 97: The average power (left graph) in fiber determines the maximum range of the optical signal until it has to be amplified (and regenerated). Since the PRBS contains an equal number of Lo’s and Hi’s, the average power lies more or less in the middle between both levels. The extinction ratio (right graph) gives the ratio of Lo power level to Hi power level (the level contrast). A large extinction ratio (low Lo level) saves laser power and increases the decision accuracy of the detector.


105

0 100 200-4

-2

0

2

4

Sign

al le

vel [

a.u.

]

Time [ps]

Signal-to-noise ratio

0 100 200-4

-2

0

2

4

Sign

al le

vel [

a.u.

]

Time [ps]

Timing jitter (p-p)

Fig. 98: The signal-to-noise (S/N) ratio (left) is defined as the average S/N ratio of both Hi level and Lo level noise with respect to the eye opening. The noise itself is the standard deviation width of the corresponding eye pattern trace (width of the color coded profile). The timing jitter is given as the temporal distance between the hit-free eye areas at the crossing point (peak-to-peak timing jitter). The p-p jitter is larger than the rms jitter, which is defined as FWHM of the trace at the crossing point. Both quantities characterize the quality of the eye opening. All eye pattern parameters depend on the following quantities:

- laser drive current (typically 10-100mA), current density 1-10 kA/cm2 - bit pattern generator amplitude (typically 1-2.5 V) - additional amplification of the BPG signal - electrical impedance of laser diode (typically 1 to 20 Ω) - maximum modulation bandwidth of QD laser diode (up to 7 GHz)

Ioffe 4-924 samples Preliminary eye pattern measurements were done with a shallow etched 10-fold stacked QD sample Ioffe 4-924, 730x10 µm with HR-coated rear facet. The corresponding eye diagram in Fig. 99 showed the capability of this laser for 2.5 Gb/s optical data modulation. This agreed well with modulation bandwidth measured for this device showing a bandwidth of 3 GHz.

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

Sign

al le

vel [

a.u.

]

Time [ns]

0 500 1000

-2

0

2

4

Sign

al le

vel [

a.u.

]

Time [ps]

Fig. 99: Part of a 2.5 Gb/s bit pattern (left) and eye diagram (right) of the sample Ioffe 4-924, 730x10 µm, HR-coated rear facet. A low S/N ratio and a slow trailing edge were observed. The bit pattern corresponds to the electrical pattern shown in Fig. 95. It shows the increase of the Lo level during the alternating sequence,


106

From these very first measurements we concluded that major improvements had to be made in the design and processing of QD lasers in order to be able to achieve a proper eye pattern at 2.5 Gb/s and beyond. The corresponding improvements are discussed in detail in the sections 1.2 and 3.1. Ioffe 4-915 samples The most important improvement was certainly the deep etching of QD laser mesas. A Ioffe 4-915 5-fold stacked 1130x4µm laser diode, deep etched, with as-cleaved facets, was eye pattern tested with bit rates of 2.5 and 5 Gb/s. The diode was biased at 7 thrI⋅ (60 mA) by a low noise DC source. The average output power of the laser diode was 24 mW (both facets).

0 100 200 300 400 500-4

-2

0

2

4

Sign

al le

vel [

a.u.

]

Time [ps]0 100 200 300 400 500

-4

-2

0

2

4

Sign

al le

vel [

a.u.

]

Time [ps]

Fig. 100: Eye pattern measurements on the sample Ioffe 4-915, 1130x4 µm, deep etched, at 2.5 Gb/s (left) and 5 Gb/s (right). Fig. 100 shows the measured 2.5 and 5 Gb/s pattern generated with a 15 bit PRBS and 1 V amplitude. A clear open eye with a signal-to-noise ratio of approx. 10 was observed. In agreement with the flat S12 parameter (transmission) measurement presented in section 3.2.1 the eye pattern was quite symmetric with a small HI level overshoot of about 10 %. The timing jitter was 16 ps. The laser emitted at a wavelength of 1275 nm. An open eye pattern at 10 Gb/s was not found, in agreement with the maximum small signal modulation bandwidth of this sample of 5 GHz. Fig. 101 shows simulated eye patterns derived from the RT model (see modeling section 2.2.3). The simulation reproduces important characteristics like low overshoot, symmetric shape of the eye pattern and the Lo and Hi level distortion. Statistical effects are not present in the simulation, but could in principle be added to the model. However, this extension of the model leads to unacceptable computational demands.


107

0 100 200 300 400 50040

60

80

100

120

Lase

r Out

put [

mW

]

Time [ps]0 100 200 300 400 500

40

60

80

100

120

Lase

r Out

put [

mW

]

Time [ps]

Fig. 101: Simulated eye patterns of a 2.5 Gb/s (left) and a 5 Gb/s (right) eye pattern employing the RT model based on a PRBS 7 signal stream. There was no visible difference for longer bit frames (e.g. PRBS 15, the measurement standard). The broadening of the traces due to amplitude and timing jitter was not reproduced by the model, since it did not feature statistic elements. DO 75 and 57 samples In order to improve the modulation speed of QD lasers, p-doping of the active layer was proposed (see section 3.1.2). We investigated the 10-fold stacked samples DO 57 and 75 similar in growth and processing except for p-doping of 5x1017cm-3 between the QD layers for DO 75. Both undoped and p-doped devices had a maximum small signal modulation bandwidth of 5-6 GHz (see section 3.2.1).

0 100 200 300 400 500

-2

0

2

4

Sign

al le

vel [

a.u.

]

Time [ps]0 100 200

-2

0

2

4

Sign

al le

vel [

a.u.

]

Time [ps]

Fig. 102: Eye pattern measurements on the sample DO 75, 1000x4 µm, deep etched, HR coated rear facet, at 5 Gb/s (left) and 10 Gb/s (right). The 10 Gb/s eye is almost closed and not suitable for data transmission. The measurements presented in Fig. 102 show no major differences compared to the previous eye patterns of a 5-fold stacked QD laser (Fig. 100), in agreement with the small signal analysis. An increase of differential gain due to the larger number of QD layers was not detected. To give an impression of the impact of bandwidth limitation on the eye patterns, Fig. 102 shows an almost closed 10 Gb/s eye pattern. Besides the design and processing of the QD laser diodes the mounting of the devices played an important role for the eye pattern improvement. Along with the devices mounted on our standard single submount a couple of devices were


108

integrated into a fiber coupled module with impedance matching network (see section 3.1) in co-operation with the company u2t photonics, Berlin. Although the small signal transmission characteristics for the module were similar to those of standard submount devices, the suppressed reflection of the input signal due to the impedance matching network yielded a dramatic improvement of the timing jitter and S/N ratio parameters of the QD laser module.

0 100 200

-2

0

2

4

Sign

al le

vel [

a.u.

]

Time [ps]0 100 200

-2

0

2

4

Sign

al le

vel [

a.u.

]Time [ps]

Fig. 103: Eye pattern measurements on the QD laser module containing the sample DO 75, 1000x1 µm, deep etched, HR coated rear facet, at 10 Gb/s (left) and 12 Gb/s (right). The corresponding parameters were 60 mA bias current, 2.5 V signal amplitude for both the 10 Gb/s eye and the 12 Gb/s eye. Eye pattern measurements were carried out back-to-back with the module biased at 3 6 thrI− ⋅ and a NRZ PRBS 15 with up to 2.5 Vp-p amplitude (12 dBm). The average output power into fiber was 1 mW. Fig. 103 shows the measured 10 Gb/s and 12 Gb/s patterns for the QD laser module. Both eyes were open, with a signal-to-noise (S/N) ratio of 6.8 / 6.0, an extinction ratio of 4.9 dB / 3.8 dB and a peak-to-peak timing jitter of 30 ps / 42 ps for the 10 Gb/s and 12 Gb/s pattern, respectively. Both patterns exhibited a double trace at the trailing edge of the bits, which we assigned to the influence of the impedance matching network. Due to the strong damping of relaxation oscillations in QD lasers, both eye patterns showed very little overshoot.

Ext. Ratio [5 dB]

[1/25 ps] Recipr. jitter

Power [1 mW]

S/N ratio [10]

30 mA, 1V40 mA, 1V50 mA, 1V60 mA, 1V30 mA, 1.25V40 mA, 1.25V50 mA, 1.25V60 mA, 1.25V

Fig. 104: Optimization chart for the four main eye pattern parameters, measured for different bias currents and signal amplitudes on the QD laser module. The larger the enclosed area, the better the eye pattern diagram. Extinction ratio and output power showed a typical trade-off behavior. Optimum performance was achieved for 60 mA, 1.25 V.


109

In order to find the best working parameters for the QD laser module, a series of eye patterns was measured and evaluated for the four basic eye pattern parameters already mentioned. Optimum performance was reached at 60 mA, 1.25 V with a signal-to-noise (S/N) ratio of 8.9, an extinction ratio of 2.1 dB and a peak-to-peak timing jitter of 28 ps. We achieved a lower timing jitter, lower S/N ratio as for standard submount devices due to the impedance matching network! After thorough bias point optimization, we expected the laser module to be capable of error-free 10 Gb/s data modulation (see section 3.3.4). DO 224c samples Besides wire-bonded QD laser diodes with and without impedance matching network we also checked on probe head contacted samples. Two DO224c (10-fold stacked) laser diodes with 500 µm length, HR coated rear and front facet (95 and 60 %, respectively) and 2 and 4 µm ridge width designed in a top-contact GSG structure were investigated. The GSG probe head contact provided lossless transmission of the electrical signal, but was not impedance matched. Due to the shorter cavities of the laser compared to the DO 57/75 samples and different epitaxial structure, the series resistance of the samples lay closer to 50 Ohm, causing less reflection at the sample. Eye pattern measurements were carried out back-to-back with diodes biased at 5 10 thrI− ⋅ under the same conditions as the aforementioned DO 57/75 series. The average output power into fiber was 1-3 mW. Eye pattern performance was optimized, as shown in the charts in Fig. 105.

Ext. Ratio [5 dB]

[1/25 ps] Recipr. Jitter

Power [2.5 mW]

S/N ratio [10]

60 mA, 1V70 mA, 1.25V80 mA, 1.7V100 mA, 2.5V

Ext. Ratio [5 dB]

[1/25 ps] Recipr. Jitter

Power [2 mW]

S/N ratio [10]

50 mA, 1V60 mA, 1.25V80 mA, 1.7V100 mA, 2.5V

Fig. 105: Eye pattern optimization charts for the samples DO 224c, 500x4 µm (left) and 500x2 µm (right). For both lasers, optimum performance was found for 100 mA, 2.5 V amplitude. This means double current density for the 2 µm laser compared to the 4µm laser, with a lower output power. Fig. 106 shows the optimized 10 Gb/s patterns for both lasers. The eyes were symmetric, with a signal-to-noise (S/N) ratio of 6.1/ 5.6, an extinction ratio of 3.3 dB/ 3.1 dB and a peak-to-peak timing jitter of 29 ps/ 41 ps for the 4 µm / 2 µm sample, respectively. Since the 4 µm sample had a larger output power, it was preferable for subsequent bit error rate measurements.


110

0 100 200

-4

-2

0

2

Sign

al le

vel [

a.u.

]

Time [ps]0 100 200

-4

-2

0

2

Sign

al le

vel [

a.u.

]

Time [ps]

Fig. 106: Eye pattern measurements on the samples DO 224c, 500x4 µm (left) and 500x2 µm (right), both deep etched, HR coated rear facet, at 10 Gb/s. The corresponding parameters were 100 mA bias current, 2.5 V signal amplitude for both. Fig. 107 (left) shows a simulated 10 Gb/s eye pattern, calculated for the DO 224c, 500x4 µm sample. The simulation showed a remarkable agreement with the measurement (Fig. 106) including the slight asymmetry of leading and trailing edges. Although the model did not include statistical broadening, it reproduced level broadening due to the splitting of traces (double traces). Besides the laser parameters we also varied the temperature of the set-up. When increasing the temperature from room temperature to 80°C, the 10 Gb/s eye pattern started to deteriorate due to increasing amplitude noise. Fig. 107 (right) shows the corresponding measurement. Since QD lasers had shown temperature independent cw operation up to 60-80°C, we hoped to prove this for modulation properties, too.

0 100 20020

40

60

80

100

120

Lase

r Out

put [

mW

]

Time [ps]0 100 200

-2

0

2

4

Sign

al le

vel [

a.u.

]

Time [ps]

Fig. 107: Simulated eye patterns of a 10 Gb/s eye pattern (left). The agreement with the actual measurement (Fig. 106) was quite good. The right graph shows a 10 Gb/s eye pattern measurement at 80°C for the 4 µm sample. The increasing temperature led to a deterioration of the eye pattern.

3.3.4 Bit error rate measurements of 1.3 µm QD lasers Bit error rate (BER) measurements are the closest-to-application test measurements for digitally modulated laser diodes. Even though an eye pattern diagram may have parameters seemingly suitable for data transmission, it might turn out to have a BER


111

floor at 10-6, rendering the device useless for transmission. The BER measurement set-up is shown and explained in Fig. 108.

DC current

10 Ghz Detector

Bias-T Amplifier

Bit Pattern Generator

Laser diode Optical fiber

Bit Error Rate Tester

SOA

Variableopticalattenuator

Fig. 108: The bit error rate measurements set-up is in parts similar to the eye pattern set-up, except for an additional optical amplifier in the optical fiber, a variable optical attenuator, an electrical amplifier behind the detector and a bite error rate tester (BERT) instead of a scope. The BERT was not triggered by the BPG, but derived the clock from the optical input. It locked on the PRBS word frame and counted the number of errors for Lo and Hi bits. The BER was measured for different values of optical attenuation and plotted versus the optical power at the detector. For statistical certainty, at least 10 erroneous bits had to accumulate. For a data rate of 10 Gb/s and a BER of 10-12 this meant a measurement time of 20 min. Alternatively, BER measurements can be simulated by mask testing of the eye pattern diagram, i.e. defining a certain area (the mask) of the eye opening as ambiguous for signal detection and counting the hits inside this mask as erroneous bits. The main difference between both measurement schemes is that the mask testing sampling oscilloscope is triggered by the BPG, whereas the BERT does its own clock recovery. Insofar the BERT measurement is one step closer to application. DO 57 QD Laser Module BER measurements were carried out at data rates of 8, 10, 11 and 12 Gb/s, keeping the optimized eye pattern measurement settings. We inserted a semiconductor optical amplifier between laser and BER tester to compensate for optical losses due to a low laser-to-fiber coupling efficiency of 10 %. Fig. 109 shows the BER measurements for the QD laser module. Both for 8 and 10 Gb/s, we achieved error free operation (BER = 10-12) at -4.5 dBm and -2 dBm receiver power, respectively. No error floor could be detected. Although best eye pattern performance was found for 60 mA, 1.25 V, the best BER performance at 10 Gb/s was found for 60 mA, 2.5 V amplitude. The BER curves for both lasers at 8 Gb/s followed more or less straight lines whereas the data for 10 Gb/s showed a curvature that was unexpected. A possible reason for this effect might be a saturation of the RF-amplifier used to amplify the electrical signal at the BER tester.


112

-8 -6 -4 -2 0 2 410-12

10-10

10-8

10-6

10-4

10-2

8 Gb/s 10 Gb/s

Bit e

rror r

ate

Receiver power [dBm]

60 mAAmpl=2.5VT=20°C

Fig. 109: BER measurements for QD laser module containing a DO57, 1000x1 µm sample. No error floor down to 10-12 could be detected. The power penalty for the increase of the data rate is 2.5 dBm. When we increased the data rate to 12 Gb/s, the lowest BER was approximately 10-3. This underlines the notion of failing BER measurements despite open eye pattern diagrams. DO 224c sample Fig. 110 shows the BER measurements for the GSG QD laser diode. Both for 8 and 10 Gb/s, we achieved error free operation (BER <10-11) at –5 dBm and +4 dBm receiver power, respectively. No error floor could be detected. Still, there was a considerable power penalty of 9 dB when moving from 8 to 10 Gb/s data rate. At 11 Gb/s (not shown), we observed an error floor of 10-4, and at 12 Gb/s BER measurements were no more possible (BER = 0.1). This was in agreement with the maximum modulation bandwidth limitation of 7 GHz.

-8 -6 -4 -2 0 2 410-12

10-10

10-8

10-6

10-4

10-2

8 Gb/s 10 Gb/s

Bit e

rror r

ate

Receiver power [dBm]

I=80 mAAmpl=2.5VT=20°C

Fig. 110: BER measurements for the DO224c, 500x4 µm sample. No error floor down to 10-11 was detected. The power penalty for the increase of the data rate was 9 dBm. The error floor for a data rate of 11 Gb/s was approximately 10-4; the error floor for 12 Gb/s was ~10-1. No measurement of the BER dependence on receiver power was possible beyond 10 Gb/s, although the eye pattern diagrams were still open at


113

11/12 GHz. The error floor for 10 Gb/s data rate at the elevated temperature of 80°C was ~10-5; no BER measurements were possible at this temperature. Compared to the QD laser module, the penalty when moving from 8 to 10 Gb/s bit rate was much larger. The difference was probably due to the impedance matching, which reduces reflections and thus noise at the electrical input of the diode inside the QD module. Careful design of the QD laser diodes, improvement of the epitaxial structure of the QD gain medium and proper packaging of the QD device have lead to a successful test of error free data modulation with 1.3 µm QD laser diodes at a data rate of 10 Gb/s.

4 Direct modulation of 1.1 µm QD VCSELs

114

4 Direct modulation of 1.1 µm QD VCSELs Vertical cavity surface emitting lasers (VCSELs) represent the main alternative design for semiconductor laser diodes. The advantages of their design (see Fig. 111) compared to edge emitters are:

- VCSELs are fabricated without wafer cleaving, allowing fast parallel processing and testing of the devices

- VCSELs can be easily grouped in arrays and have a small footprint (~100x100 µm)

- VCSELs have a low beam divergence due to their large aperture and a symmetric far-field, which makes them ideal for fiber coupling

- VCSELs are longitudinally single-mode, transversally single mode for small apertures

- VCSELs have very small threshold current densities due to the anisotropy of spontaneous emission in micro-cavities [123].

With all these advantages, its clear that they also posses some drawbacks, mainly the sophisticated processing and the limited output power.

Bond wire

+ Contact

- Contact

Waveguide

Gain medium

Substrate

Edge emitter (“conventional design”)

- Contact

+ Contact

Botttom mirror

Top mirror

Gain medium

Substrate

Surface emitting laser

Fig. 111: Schematic design of edge emitting laser diode (left) and VCSEL (right). The shown VCSEL has intra-cavity ring contacts. Alternative layouts work with conductive mirrors, providing a p-contact on top of the top mirror and a plain backside n-contact. [Courtesy V. Türck] Similar to edge emitting laser diodes, a number of material systems and gain media exist for VCSELs. Among them are GaAs-based QW VCSELs for wavelength below 1 µm, InP-based QW VCSELs, GaInNAs-based QW VCSELs and GaAs-based InGaAs quantum dot VCSELs for datacom wavelength range [11, 12, 124-129] (compare to section 0). GaAs-based devices offer specific advantages for VCSELs because of the large index of refraction difference and good thermal conductivity of GaAs/AlGaAs layers. The positive aspects of nano-structuring the active zone (quantum dots, quantum wires) are the same as for edge emitters: extension of wavelength into the infrared region for GaAs, low threshold current densities, high temperature stability, low chirp, and low modulation patterning. In this work we present dynamic measurements on MOCVD grown InGaAs quantum dot VCSELs emitting near 1.1 µm. The samples were grown with alternative precursors, the wavelength was chosen to yield optimum QD growth. The results were obtained in close cooperation with F. Hopfer and represent a small contribution to his extensive work on QD VCSELs [34]. A detailed description of growth, processing and static properties of QD VCSELs can be found there. Section 4.1


115

merely summarizes the most important facts, before we present the results of dynamic measurements in section 4.2 ff. 4.1 Structure, layout and static parameters MOCVD grown quantum dot VCSELs with a single 3-fold stack of quantum dot layers (NP 537) and with tripled 3-fold stacks (NP654, NP800) were realized. Each three-fold stack was placed at a maximum of the longitudinal optical mode distribution. Table 2 lists the VCSEL samples that were investigated in the framework of dynamic measurements. The structures were structured using dry and selective wet etching techniques. Intra-cavity contacts were formed by metal deposition. The oxide aperture and the mirrors were oxidized by wet thermal oxidation. The structure was planarized with BCB and contact pads were deposited on top of the planarization layer. Fig. 112 shows the schematic structure of a GaAs-based QD VCSEL (without planarization layers).

GaAs Substrate

Quantum Dot µ-Cavity

1.75 λ (n)GaAs

Metal contacts

Laser light

DBR

1.75 λ (p)GaAs

GaAsAlGaAs

AlO

InGaAs Quantum Dots

Fig. 112: Schematic cross-section of a GaAs-based quantum dot VCSEL with intra-cavity contacts and oxide aperture. The REM inset shows three stacked layers of quantum dots. In order to minimize parasitic contact metallization capacitances, several contact pad layouts were tested. Fig. 113 shows the three different layouts. The reduction of the semiconductor-metal contact area, as it was realized with the asymmetric contact design, caused an increase of the contact resistance at the same time, thus making a trade-off between both quantities necessary.

Fig. 113: Photographs of three evolutionary stages of contact metallization layouts for intra-cavity QD VCSELs: The left layout had two ring contacts with a p-n-contact overlap. The middle layout had a ring p-contact and an asymmetric n-contact; the right design featured fully asymmetric contacts for minimum contact capacitance. The latter two layouts had GSG-compatible contact pad structure (not shown) and no contact overlap.


116

QD excited state (ES) lasing was achieved for the TU NP 537 sample at low temperatures (230 K and below). Room temperature ground state (GS) lasing was not possible do to insufficient gain. Different from edge emitters, for lasing in VCSELs care has to be taken that one of the widely spaced longitudinal modes (~100 nm modal distance) overlaps with the spectral gain maximum. Since both the gain maximum and the longitudinal modes shift with temperature differently, excited state lasing can only be realized within a certain temperature range. QD ground state single mode lasing at room temperature was achieved for the samples TU NP 654 and NP 800, with very small threshold currents down to 103 µA. A maximum output power of 0.7 mW and a differential quantum efficiency of 43 % were measured for a 3.5 µm aperture diameter. Corresponding PIV curves are depicted in Fig. 114.

0.0 0.5 1.0 1.50

1

2

3

0

1

2

3

4

Ithr=700µA

Rser=470 Ω @ 1.2 mAType16/10, 230 K

Volta

ge [V

]

Current [mA]

Out

put p

ower

[µW

]

0 1 2 3 4 50

1

2

3

4

0.00

0.05

0.10

0.15

0.20

Volta

ge [V

]

Current [mA]

11.5 µm 9.5 µm 7.5 µm 5.5 µm 3.5 µm 1.5 µm

Pow

er in

MM

fibe

r [m

W]

Fig. 114: PIV curves for a NP 537 sample at 230 K with 10 µm aperture diameter (left) and for NP 654 samples with aperture diameters between 1.5 and 11.5 µm (right). The single IV curve in the right graph belongs to an 11.5 µm aperture laser. Please note that the output is given as power coupled into a multi-mode fiber. The actual output power was larger. For cw operation it was limited by thermal effects.

986 988 990 992 994

200 K, 2 mA,6 µm aperture

log.

Inte

nsity

(a.

u.)

wavelength (nm)1080 1085 1090 1095 1100 1105 1110

-50

-40

-30

-20

-10

0

10 654-2: 3_7Aperture 3.5 µm, 3.5 V, 0.97 mA, 140 µW in MM fiber

SSR = 35 dB

Inte

nsity

(dB)

Wavelenght (nm)

Fig. 115: Spectra of a NP 537 sample at 200 K with 6 µm aperture diameter (left) and for a NP 654 sample with aperture diameter 3.5 µm (right) at RT. Both QD VCSELs were single mode, with side mode suppression ratios of 25 dB and 35 dB, respectively. VCSELs with apertures larger than ~5 µm showed multimode lasing.


117

4.2 Small signal operation

4.2.1 S11 parameter measurements Modeling of QD VCSEL impedance The gain medium is the same as for the QD edge emitters, which means that the intrinsic QD laser model from section 2.2 is in principle also valid for QD VCSELs. Of course, values for losses, cavity dimension and gain have to be fitted to the VCSEL parameters. Extensive modeling of the optical, thermal and electrical properties are discussed in [34]. Modeling of the dynamic properties of a VCSEL diode is done based on an equivalent electrical circuit model similar to the one used for edge emitters. The simple picture of the intrinsic laser as an RC circuit is included to this model. In contrast to edge emitters, VCSELs have a much larger total resistance (above 100 Ohm) due to their small diameter and thick active region; parasitic capacitance may play a larger role due to the proximity of the intra-cavity contacts and the oxide aperture. Fig. 116 shows the corresponding model.

Rser

Rap

Cpar

Cap

Rdiff Cdiff

Fig. 116: Equivalent circuit model of a VCSEL, comprising the metallization capacitance, series resistance, differential resistance and capacitance of the pn junction, and resistance and capacitance of the aperture. The input impedance of the QD VCSEL samples is measured with a network analyzer set-up similar to the one discussed in section 3.2.1. All devices were contacted with probe heads, no mounted VCSELs were investigated for small signal analysis. This allows us to obtain low noise S11 parameter data. S11 parameters were measured in dependence on the bias current in the frequency range between 0.05 and 20 GHz. The data were then fitted with the aforementioned equivalent circuit model using Microwave Office [70]. Fig. 117 shows the measured


118

and fitted data for a NP 537 sample with 10 µm aperture diameter. For the fit we omitted the metallization capacitance and the aperture RC circuit. The series resistance serR was set constant for all bias conditions. diffR and diffC were varied for every bias current, i.e. we obtained a set of N differential resistances and capacitances for N measurements. The differential resistance for zero bias was of course large (>100 kOhm) and set constant.

0 1.0

1.0

-1.0

10.0

10.0

-10.0

5.0

5.0

-5.0

2.0

2.0

-2.0

3.0

3.0

-3.0

4.0

4.0

-4.0

0.2

0.2

-0.2

0.4

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

S11 at 0 mASwp Max

20GHz

Swp Min0.05GHz

S11VCSEL

S11Modell

0 1.0

1.0

-1.0

10.0

10.0

-10.0

5.0

5.0

-5.0

2.0

2.0

-2.0

3.0

3.0

-3.0

4.0

4.0

-4.0

0.2

0.2

-0.2

0.4

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

S11 at 0.1 mASwp Max

20GHz

Swp Min0.05GHz

S11VCSEL

S11Modell

0 1.0

1.0

-1.0

10.0

10.0

-10.0

5.0

5.0

-5.0

2.0

2.0

-2.0

3.0

3.0

-3.0

4.0

4.0

-4.0

0.2

0.2

-0.2

0.4

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

VCSEL at 3.5 mASwp Max

20GHz

Swp Min0.05GHz

S11VCSEL

S11VCSEL

Fig. 117: Smith charts showing the frequency dependence of the complex S11 parameter of a QD VCSEL for three different bias conditions. For zero bias, we observed full reflection of the input signal (S11 close to unity) for low frequencies, for increasing bias the reflection decreased due to the decreasing series resistance. All charts show the typical high frequency capacitance roll-off (half circle to the left). Both the measured and fitted curves are shown. Single 3-fold stack VCSELs Similar measurements and fits were made for a series of NP 537 QD VCSELs with different aperture and top mirror diameter. We should keep in mind that these samples did not show lasing at room temperature, even though they consume milliamps of current. Fig. 118 shows the dependence of two of the derived parameters, i.e. the inverse differential resistance and the capacitance, on the VCSEL dimensions. The corresponding series resistance was 10-20 Ohm and almost constant for all devices, the metallization capacitance and the bond inductivity were omitted.

1 10 100

1

10

~ aperture1.5

Aperture diameter [µm]

Con

duct

ivity

[1/k

Ω] at 2500 A/cm2

1 10 1000.1

1

10

at 2500 A/cm2


Cap

acita

nce

[pF]

~ aperture0.5

Fig. 118: Dependence of the device conductivity (left) and capacitance (right) of NP 537 QD VCSELs on the aperture diameter. A non-quadratic slope was observed. The top mirror diameter has no influence.


119

For a homogeneous current distribution we expected a quadratic increase both of conductivity and capacitance with aperture diameter for a given current density. Instead, we observed a slower decrease in both cases, with an exponent of 1.5 and 0.5 for conductivity and capacitance, respectively. Since the conductivity increased faster with aperture diameter, the RC bandwidth increased approximately linear for large apertures (see Fig. 120). There are at least two possible reasons for this deviation from a quadratic dependence:

- The effectively pumped zone for small aperture diameters is larger than the nominal aperture (current spreading), leading to a larger capacitance and lower conductivity. This effect was also found in 2-dimensional modeling.

- An influence of the metallization capacitance, which is essentially increasing step-wise with aperture diameter, causes the most of the increase in capacitance. In this case, part of the parallel resistance is due to the contact resistance of the device.

Another surprising result was that the differential resistance was much larger (by a factor of 10 to 100) than the series resistance. This means that the main voltage drop in the device is associated with a low pass behavior, i.e. with a parallel capacitance. The metallization capacitance cannot be responsible, because it would simply short-circuit for high frequencies. Two possibilities (or a mix of both) are left:

- The voltage drops mainly over the intrinsic GaAs zone, i.e. diffR is large. This seems plausible for VCSELs, since the active region is quite thick (> 1 µm) and undoped. The mechanism of a Fermi level shift was already discussed in section 2.2.3.

- The voltage drops in the aperture region, due to the current path narrowing. The weak dependence of the resistance and capacitance on the aperture diameter favors the first mechanism. Subsequent modeling of these effects is beyond the scope of this work. Triple 3-fold stack VCSELs In order to quantify the influence of QD layers on the electrical properties of the device, corresponding measurements for VCSELs with 3x3-fold stacked quantum dots were performed (see Fig. 119). The data were evaluated for a current density of 7500 A/cm2 to ensure the same current density per QD layer as for the NP 537 sample. However, we must keep in mind that the NP 537 devices were not lasing during the measurement.


120

1 10 100

1

10

~ aperture1.2


Con

duct

ivity

[1/k

Ω] at 7500 A/cm2

1 10 1000.1

1

10

Cap

acita

nce

[pF]

Top mirror diameter 12 µm 16 µm

~ aperture0.4


at 7500 A/cm2

Fig. 119: Dependence of the conductivity (left) and the capacitance (right) of NP 654 QD VCSELs on the aperture diameter. Again, we observed a non-quadratic slope of both quantities. The results were similar to the previous measurement. A slight influence of the top mirror diameter was found for the capacitance. Both the conductivity and capacitance values from the fits were similar to the results for the single 3-fold stacked sample NP 537. This is a surprising result, regarding the larger cavity and the larger number of QD layers. The drawbacks of a larger cavity were balanced by the improvement of gain and by laser operation. Fig. 120 shows a comparison of the RC bandwidths for both samples, with the triple 3-fold stacked samples ahead. The maximum bandwidth lay between 1.6 and 1.8 GHz. Large aperture VCSELs showed the largest RC bandwidth due to the reduction of current spreading.

0 10 20 30 40 500.0

0.5

1.0

1.5

2.0

NP 537 @ 2500 A/cm2 NP 654 @ 7500 A/cm2


RC

ban

dwid

th [G

Hz]

Fig. 120: Increase of the RC bandwidth of the NP 537 and NP 654 QD VCSELs for increasing aperture at a fixed current density. The maximum RC bandwidth for the devices was slightly larger (~10 %). The NP 654 samples had a larger RC bandwidth. This small RC bandwidth imposed a severe limit to the application of QD VCSELs as data transmitters. As it was not yet clear which mechanism is responsible for the limitation, the design of the QD VCSEL contact metallization was optimized in order to exclude the parasitic influence of the metallization capacitance.


121

Triple 3-fold stack VCSELs – contact layout evaluation QD VCSELs with triple 3-fold stacked QD layers were fabricated using two different contact layouts (a) and (b) (see Fig. 113). S11 parameter measurements were performed for a series of VCSEL with aperture between 2 and 15 µm. The data were evaluated with a three parameter fit yielding differential resistance, differential capacitance and series resistance. The series resistance for the symmetric layout lay between 30 and 40 Ohm, for the asymmetric layout it lay between 70 and 80 Ohms.

1 10 1000.1

1

10

NP 800, symmetric NP 800, asymmetric

3-30 kA/cm2

~ aperture0.7


Con

duct

ivity

[1/k

Ω]

1 10 1000.1

1

10


3-30 kA/cm2

Cap

acita

nce

[pF]

~ aperture0.3


Fig. 121: Inverse differential resistance (left) and differential capacitance (right) in dependence on aperture size and contact layout for NP 800 VCSELs. Both conductivity and capacitance increased sub-linear with increasing aperture. The asymmetric layout showed slightly smaller capacitances. The increase was caused by larger contact resistance due to smaller contact pads. Fig. 121 shows the corresponding values for the fitted parameters. Only for the capacitance we found a small improvement due to the asymmetric layout, leading to a minor enhancement of the RC bandwidth (see Fig. 122).

0 2 4 6 8 10 12 14 160.0

0.2

0.4

0.6

0.8

1.0

1.2

3-30 kA/cm2



RC

ban

dwid

th [G

Hz]

Fig. 122: RC bandwidth in dependence on aperture and contact size at different bias currents for NP 800 VCSELs with symmetric contacts (left) and asymmetric contacts (right). The bandwidth increased with increasing aperture size and was only weakly dependent on the contact size and layout. The differences of both QD VCSEL layouts may be attributed not to a decrease of metallization capacitance, but to a change of the current path inside the cavity. The


122

main limitation for the RC bandwidth of the QD VCSELs lay within the cavity. Improvement of the VCSEL performance is associated with a redesign of the epitaxial structure and doping levels. Coupling of QD layers and p-doping of the barrier region, along with a decrease of the inhomogeneous broadening of the quantum dots, will increase the RC bandwidth.

4.2.2 S12 parameter measurements Although the S11 parameter measurements showing a RC bandwidth limitation of 1-2 GHz lead to the assumption of a low modulation bandwidth in the same region, only a transmission measurement yields the true modulation characteristics. Transmission measurements for QD VCSELs are quite challenging due to the small output powers of the lasers. The network analyzer based S12 parameter measurement set-up (see section 3.2.1) was completed with a 20 GHz multi-mode fiber (MMF) detector (APhS Allegra 20MM) instead of the 50 GHz single mode fiber detector and a broadband amplifier. Light from the VCSELs was coupled into a MMF with a micro-lensed fiber end and fed to the MMF optimized detector. Fig. 123 shows a detail from the measurement set-up. Single 3-fold stack VCSELs The output power of these devices was too small to be measured with this set-up. Large signal measurements were instead performed for these samples (see next section).

Fig. 123: Photograph of a VCSEL wafer piece on a chuck, contacted with a GSG probe head and coupled to a lensed vertical fiber (left). The right graph shows the microscopic view of the VCSEL, the probe head is situated at the right, and the fiber can be made out as a grey spot covering the VCSEL beneath. Triple 3-fold stack VCSELs S12 parameters were measured in dependence on the bias current in the frequency range between 0.05 and 20 GHz for the NP 800 samples with symmetric and asymmetric layout. For larger output power devices with mirrors of 5 DBR pairs were investigated. Fig. 124 shows the transmission measurements for VCSELs with an aperture size of 8 µm and both layouts.


123

0.1 1 100

2

4

6

8

10 2 mA 3 mA 4 mA 5 mA

Mod

ulat

ion

resp

onse

[a.u

.]


0

1

2

3

4

5

2 mA 3 mA 4 mA 5 mA

Mod

ulat

ion

resp

onse

[a.u

.]

Frequency [GHz]

Fig. 124: Room temperature modulation response measurements for NP 800 VCSELs with 8 µm aperture, 5 DBR pairs top mirrors, with symmetric (left) and asymmetric (right) layout. In both cases the modulation bandwidth saturates at 1.5 GHz for an output power of 1 mW. Both devices were limited to bandwidths below 1.5 GHz. The modulation bandwidth saturated with 1 mW output powers, larger currents lead to a decrease of both power and bandwidth. As expected for QD devices, the transmission curve showed a strong influence of damping, with a slightly larger damping for the asymmetric sample. The impact of mirror losses was determined by comparison to a QD VCSEL with a 6 DBR pairs top mirror instead of 5. The lower mirror losses lead to a decrease of the threshold of the device, the modulation bandwidth saturated at 2 GHz due to larger differential gain and photon density. On the other hand the output power was considerably smaller (~0.2 mW). Fig. 125 shows the corresponding measurement.

0.1 1 100

1

2

3 1 mA 2 mA 3 mA 4 mA 5 mA

Lase

r Out

put [

a.u.

]

Frequency [GHz]

Fig. 125: Room temperature modulation response measurements for NP 800 VCSELs with 8 µm aperture, 6 DBR pairs top mirrors and symmetric layout. Due to the larger reflectivity of the top mirror, the threshold current is smaller (lasing at 1 mA), and the modulation bandwidth saturates at 2 GHz for an output power of only 0.2 mW. QD VCSELs with apertures larger than 6 µm showed similar results. Small aperture VCSELs show smaller bandwidths due to the unfavorable carrier distribution inside the cavity. 4.3 Large signal operation Large signal modulation of QD edge emitters has already taught us a lot about QD specific characteristics, e.g. a strongly damped relaxation oscillation and suppressed


124

chirp. We expect similar behavior of quantum dot VCSELs concerning the damping, since it is caused by the QD gain medium. Large signal measurements help us to determine the intrinsic modulation properties of QD VCSELs. Due to the pulsed operation thermal effects limiting the VCSEL performance is suppressed. The large sensitivity of the streak camera set-up permits dynamic measurements even for very small output powers or in a cryostat. The chirp characteristics of QD VCSELs may be different to those of QD edge emitters, because the mode structure of a VCSEL corresponds to different spatial transversal modes. Non-equilibrium carrier distribution within the active zone of the VCSEL during turn-on may cause a complex spectral behavior.

4.3.1 Streak camera measurements Spectrally, time and temperature resolved measurements with the set-up described in section 3.3.1. were performed with a couple of devices from each of the samples listed in Table 2. Single 3-fold stack VCSELs Preliminary large signal measurements were performed with the NP 537 single 3-fold stack VCSEL structure. Since this sample did not show ground state lasing at room temperature, the devices had to be mounted and inserted to a cryostat. Mounting and bonding the devices were quite challenging tasks, as can be seen in Fig. 126. Bonding was done in two stages: First, the VCSEL bond pads were connected to nearby large bond pads with 20 µm Au wires. In the second step, the strip line of the submount was connected to the large pads. Spectro-temporally resolved scans were recorded at a temperature of 230 K. Fig. 127 shows the corresponding graphs. The emission for small currents was single-mode, despite the large aperture. For currents larger than 3 mA, additional transversal modes appeared on the short wavelength side (the high energy side) of the first mode (not shown), with a modal distance of 1 nm. A first RO peak can be seen in Fig. 127, but due to strong damping no second peak could be detected. Unfortunately, this made it impossible for us to determine a RO frequency. None of the large signal measurements of 1.1 µm VCSELs was suitable for RO frequency estimation.

Fig. 126: Photograph of a wire bonded VCSEL for low temperature experiments; the wire thickness is 20 µm (left). The VCSEL array was mounted on a standard submount and


125

connected to the strip line via additional bond pads made from edge emitters (right). The pictures give an impression of the small size of VCSELs, compared to conventional lasers. Multimode operation of this device could only be found in pulsed mode; for cw operation the VCSEL turned of due to thermal limitations.

0.0 0.5 1.0 1.5994

996

998

1000

Time [ns]

Wav

elen

gth

[nm

]

0.0 0.5 1.0 1.50

2

4

6

8

10

Lase

r Out

put [

a.u.

]Time [ns]

Fig. 127: Spectro-temporally resolved scan of a laser pulse from a NP 537 VCSEL with 10 µm aperture at 230 K (left). The electrical pulse had a length of 2.5 ns and amplitude of 2.7 mA. The optical pulse started left. The right graph shows the spectrally integrated transient. An initial relaxation peak can be seen, but no further oscillations. As we know from modeling of QD gain media, the strong damping of relaxation oscillations is mainly caused by gain saturation and differential gain reduction. For a device with insufficient ground state gain, this effect appears to be very clear. Similar to edge emitters, VCSELs can be gain switched in order to achieve short optical pulses (see section 5.1). By driving the device with a 900 ps short electrical pulse the VCSEL was gain switched. Fig. 128 shows the corresponding graphs. We achieve a short optical pulse with a FWHM of 200 ps.

0.0 0.2 0.4 0.6 0.8 1.0994

996

998

1000

Time [ns]

Wav

elen

gth

[nm

]

0 200 400 600 800 10000

5

10

15

20

FWHM 200 ps

Lase

r Out

put [

a.u.

]

Time [ns]

Fig. 128: Spectro-temporally resolved scan of a gain switched NP 537 VCSEL with 10 µm aperture at 230 K (left). The pulse width was 0.9 ns. The right graph shows the spectrally integrated pulse with a FWHM of 200 ps. Short pulses of gain switched VCSELs with small apertures are spectrally narrow due to the single-mode operation of the device. The spectral width of the pulse shown in Fig. 128 is limited by the resolution of the spectrometer to < 100 pm.


126

Triple 3-fold stack VCSELs Due to their larger gain, the NP 800 samples showed ground state lasing at room temperature. Optical output of the devices was coupled into a 50 m multi-mode fiber (MMF) using the on-wafer test set-up described in section 4.2.2, the fiber was then linked to the streak camera set-up. The dispersion of 50 m of MMF lay in the range of 60 ps nm km⋅ and caused a temporal offset of 30 ps every 10 nm. However, this offset was too small to disturb the spectrally resolved measurement. Fig. 129 shows the turn-on behavior of a NP 800 VCSEL with a nominal aperture (according to processing) of 5 µm. The device showed single mode operation. No relaxation oscillation peak was detected. A determination of the RO frequency was therefore not possible.

0.0 0.5 1.0 1.51100

1105

1110

1115

1120

Time [ns]

Wav

elen

gth

[nm

]

0.0 0.5 1.0 1.50.0

0.5

1.0

1.5

2.0

La

ser O

utpu

t [a.

u.]

Time [ns]

Fig. 129: Spectro-temporally resolved scan of a laser pulse from a NP 800 VCSEL with a nominal aperture of 5 µm and asymmetric layout at room temperature (left). The electrical pulse had a length of 5 ns and amplitude of 2 V. The right graph shows the spectrally integrated transient. No relaxation peak can be seen. The spectral position of the emission was very stable, no transversal mode hopping occurred. No chirp of the mode could be detected (< 200 pm, being the resolution of the spectrometer for this measurement). This makes single mode VCSELs ideal for applications with densely spaced optical channels. VCSELs with apertures larger than 4 µm show multimode operation. Fig. 130 shows the turn-on spectrum of a NP 800 VCSEL with a nominal aperture of 9 µm. Six modes started lasing; the first RO peak was synchronous for all modes. The spectral width of the emission was 7 nm. No chirp could be detected. The spectrally integrated emission allowed us to estimate a relaxation frequency of 1.7 GHz. This is in good agreement with the results from small signal analysis.


127

0.0 0.5 1.0 1.51100

1105

1110

1115

1120

Time [ns]

Wav

elen

gth

[nm

]

0.0 0.5 1.0 1.50.0

0.2

0.4

0.6

0.8

1.0

Inte

grat

ed O

utpu

t [a.

u.]

Time [ns]

Fig. 130: Spectro-temporally resolved scan of a laser pulse from a NP 800 VCSEL with a nominal aperture of 9 µm and symmetric layout (left). The electrical pulse had a length of 5 ns and amplitude of 2 V. Several transversal modes started lasing. The right graph shows the spectrally integrated transient. The intention of dynamic measurements on QD VCSELs was to find out whether the devices are limited in their performance by parasitic elements or by intrinsic parameters. We investigated both the symmetric and asymmetric contact layout. Fig. 131 shows the results for a similar device like in Fig. 130, except for an asymmetric layout. The spectral behavior was similar. The RO peak appeared to be slightly more damped (no second RO) in agreement with the result found for the small signal analysis. However, the differences might be due to device variations.

0.0 0.5 1.0 1.51100

1105

1110

1115

1120

Time [ns]

Wav

elen

gth

[nm

]

0.0 0.5 1.0 1.5

0.0

0.2

0.4

0.6

0.8

1.0

Inte

grat

ed O

utpu

t [a.

u.]

Time [ns]

Fig. 131: Spectro-temporally resolved scan of a laser pulse from a NP 800 VCSEL with a nominal aperture of 9 µm and asymmetric layout (left). The electrical pulse had a length of 5 ns and amplitude of 2 V. The right graph shows the spectrally integrated transient. An interesting feature of strongly pumped QD VCSELs is their ability to start lasing synchronously for ground and excited QD states. Fig. 132 shows a wide wavelength scan of the turn-on behavior of a NP 800 VCSEL with an aperture of 7 µm. The emission showed several transversal modes, as expected, and an additional longitudinal mode, corresponding to excited state emission. The large initial carrier density inside the cavity provided enough gain for the excited mode to briefly turn-on. Since the excited mode exhibited a strong, gain switching like RO peak, we assumed a strong non-equilibrium occupation of the QDs prior to lasing.


128

0.0 0.5 1.0 1.51000

1020

1040

1060

1080

1100

1120

Dispersive shift in 50 m multimode fiber

Time [ns]

Wav

elen

gth

[nm

]

0.5 1.0 1.5 2.0

0.0

0.5

1.0

1.5

2.0 Excited state (1000 nm) Ground state (1110 nm)

Lase

r Out

put [

a.u.

]

Time [ns]

Fig. 132: Spectro-temporally resolved scan of a laser pulse from a NP 800 VCSEL with a nominal aperture of 7 µm (left). The electrical pulse had a length of 5 ns and amplitude of 3 V. Initial lasing on both ground and excited state was detected. The right graph shows the spectrally integrated transient for GS and ES emission, corrected for fiber dispersion. Although such large spectral variation of emission offers interesting insights of QD lasing mechanisms, it is unwelcome for any application. The effect can be suppressed by use of narrow mirror stop bands. From small and large signal measurements we determined the modulation bandwidth of 1.1 µm QD VCSELs to be in the range of 1-2 GHz. The main limitations for the bandwidth are:

- relatively small gain and differential gain of the QD gain medium, - large capacitance of the QD region, - thermal limitation of the devices, leading to power and bandwidth roll-off.

So besides the limitations known for edge emitting devices, VCSELs are subjected to additional restrictions. Eye pattern measurements at 2.5 Gb/s seem feasible, given 2 Gb/s bandwidth of the NP 800 QD VCSELs. VCSELs with small apertures are suitable for data transmission due to their single mode emission. However, small aperture QD VCSELs have shown to have a smaller RC bandwidth and modulation bandwidth due to current spreading effects inside the cavity. Besides, they have a small (< 1 mW) output power. Optimum performance will be achieved with a trade-off between these parameters.

5 Short-pulse generation with QD lasers

129

5 Short-pulse generation with QD lasers Short optical pulses are involved in virtually all applications of semiconductor lasers: Pump-and-probe analysis, medical applications and, most important, fiber data communication, to name just a few. There are a number of methods to generate short (~ps duration) optical pulses with semiconductor lasers, as shown in Fig. 133. The principle of gain switching becomes immediately clear when we call to mind the turn-on behavior of a semiconductor laser: A gain switched pulse is generated simply by switching the laser off after the first relaxation oscillation peak. Gain switching can be implemented with any simple laser diode. Q-switching involves a means of changing the cavity losses (the “Q”) of the laser diode after the electrical pump process. This can be accomplished by a passive saturable absorber section or by an externally controlled loss section (e.g. an electrically driven absorber section) within the cavity. In any case, the laser diode has to be specially designed for Q-switching. A sudden decrease of the cavity losses (Q-switch) causes the laser diode to cross the lasing threshold and start lasing until the stored carriers are used up. Mode-locking (ML) essentially means to phase lock the longitudinal modes of a laser diode in order to compose a modal interference beat, the ML pulse stream. Active ML is achieved by external electrical modulation of the laser diode and can be implemented with plain laser diodes. Passive and hybrid ML involves an absorber section similar to Q-switching.

Passive ML Active ML

Mode-Locking

„Synchronize longitudinallaser modes“

Gain Switching

„Using the first relaxation oscillation“

Hybrid ML

Passive QS Active QS

Q-Switching

„ Lower thresholdafter pump pulse“

Fig. 133: Semiconductor laser operating modes for short pulse generation. Whereas gain switching and Q switching can produce single pulses, mode-locking generates a regular pulse comb with a repetition rate given by the cavity round trip frequency. In this work, passive and hybrid mode-locking of QD lasers was extensively investigated. This chapter takes a quick look at gain switching of QD lasers before passive and hybrid mode-locking of QD lasers are presented in detail. 5.1 Gain switching


130

The basic idea of gain switching is to generate a single short (10th of ps) optical pulse with a long (~ns) electrical pump pulse [130, 131]. Since both the optical and the electrical pulse terminate after the first relaxation oscillation peak, the length of the electrical pulse is given by the turn-on delay and the duration of the first relaxation oscillation. In section 3.3.2 we learned that the turn-on delay of QD laser diodes lies in the range between 0.5 and 2 ns, depending on the pump current intensity, and is much longer than the duration of the first RO (~100 ps). Therefore, the length of the electrical pulse for gain switching ranges in the ns region. All practical and theoretical considerations concerning gain switching are included in the turn-on process of QD lasers (see section 3.3.2). Hence Fig. 134 gives just an example for a gain switched QD laser diode. The measurement was done with the streak camera set-up presented in the aforementioned section. The sample (10-fold stacked Ioffe 4-924, 700x10 µm, HR coated rear facet) was driven with maximum power (5 V output); the pulse length was adjusted to achieve minimum optical pulse width at maximum pulse power.

400 500 600 700 800 9001245

1250

1255

1260

1265

1270

Time [ps]

Wav

elen

gth

[nm

]

0 200 400 600 800 1000 1200 14000

50

100

150

200

FWHM 140 ps

Lase

r Out

put [

a.u.

]

Time [ns]

Fig. 134: Spectro-temporal intensity profile (left) and integrated intensity (right) of the gain switched QD laser diode Ioffe 4-924, 700x10 µm, HR coated rear facet. The laser diode was driven with a 5 V, 1.2 ns electrical pulse. The FWHM of the pulse was 140 ps; the spectral width was about 6 nm. The optical pulse showed a slight asymmetry, a trailing edge occurred due to the finite fall time (~100 ps) of the electrical pulse and the lifetime of the carriers stored in the laser diode. The minimum width of the optical pulse was in this case limited by the available pulse power. 5.2 Mode-locking Mode-locked QD lasers [22, 23, 132-135], like directly modulated QD lasers, are useful for data communication. Since mode-locked lasers provide a regular optical pulse train, an optical modulator has to be added to provide the encoding of digital optical data (see Fig. 135). The maximum data rate is then given by the round trip frequency of the mode-locked laser diode and thus by its cavity length. Besides high data rates it is also advantageous to generate the shortest possible pulses, because they can then be added with other pulses in a time division multiplexing scheme. The third figure-of-merit of mode-locking is the spectral width of the pulses. Spectrally narrow pulses are suitable for closely spaced optical communication channels running through the same optical fiber (wavelength division multiplexing). A


131

fundamental limit, the Fourier limit, stating that for Gaussian shaped pulses with spectral FWHM νΔ and temporal FWHM τΔ 0.44ν τΔ ⋅ Δ ≥ , (2.59) forces us to bring mode-locked QD lasers as close as possible to the Fourier limit and search a trade-off between spectral and temporal width. Mode-locked QD lasers should yield pulse width below 1 ps due to their broad emission spectrum.

000110100111010110

000110100111010110

Fig. 135: Data transmission scheme using a mode-locked laser (left). The actual digital signal (black curve) is encoded by an optical modulator (middle) by in- and out-fading of the optical pulses from the laser according to the signal stream. The resulting optical signal (right) has a return-to-zero (RZ) scheme. In the following section we present results on passive and hybrid mode-locking of monolithic QD laser samples with lengths between 800 and 8000 µm, corresponding to round trip frequencies between 5 and 50 GHz. The limitations of data rates and pulse width are discussed and possible device improvements are suggested. In the following we give a short phenomenological description of the mode locking mechanism. Fig. 136 shows a schematic view of a monolithic two-sectional laser cavity and a sketch of the photon density distribution along the longitudinal axis during build-up of the oscillating optical pulse. For passive mode-locking, the absorber is biased with a reverse voltage, and the gain section is biased with a forward current sufficiently high to sustain lasing of the device. Initially, the photon density is supposed to be static inside the cavity, and the absorber section acts

merely as a leaky facet, i.e. creates loss. Now, in contrast to a leaky facet, the absorber section shows saturation characteristics, i.e. the absorption loss decreases with the intensity of the incident light. As the photon density fluctuates ( 1T ), bunches of increased photon density pass the absorption section with less attenuation than those with decreased density, leading to a pile-up of photons in one or more oscillating pulses ( 2T ). After a few round trips, the pulses reach a final shape, given by the absorption and gain characteristics of both sections ( 3T ) and lead to a pulsed output at both facets of the cavity. Fig. 136: Longitudinal photon density distribution during build-up of passive (hybrid) mode-locking in monolithic two-sectional laser cavity and schematic view of two-sectional cavity. The arrows denote the direction of the moving pulse.

Reverse bias Bias

I

I

I

GainAbs.

Time T1

Time T2

Time T3


132

The two main pulse shaping mechanisms are absorber bleaching (saturation) and gain bleaching (saturation). Fig. 137 illustrates their impact on an incoming pulse.

-15 -10 -5 0 5 10 150.0

0.5

1.0

1.5 Incoming pulse Attenuated pulse Attenuated pulse, normalized

Puls

e am

plitu

de [a

.u.]

Time [ps]-20 -15 -10 -5 0 5 10

0.0

0.5

1.0

1.5 Incoming pulse Amplified pulse Amplified pulse,

normalized

Puls

e am

plitu

de [a

.u.]

Time [ps]

Fig. 137: Schematic view of the pulse shaping characteristics of the absorber section (left) and the gain section (right). Both section saturate around 0t = and do not recover within the pulse width (slow absorber, slow gain recovery). Accordingly, the absorber shapes mainly the leading edge of the pulse, whereas the gain section shapes the trailing edge. Both mechanisms together cause pulse shortening. The arrows denote the moving direction of the pulses. Depending on the recovery speed of the absorber, it shapes only the leading edge of the pulse (slow absorber, recovery > 10 ps), or the entire pulse (fast absorber, recovery time < 1 ps). Gain recovery is assumed to be slow (> 10 ps). The impact of the absorber section also depends on the reflectivity of the adjacent facet: For a high reflection absorber facet, the optical pulse is fully reflected and overlaps with itself, creating a stronger saturation in the absorber. This effect should lead to shorter pulses. A subsequent modeling of QD mode locking operation based on microscopic model of the quantum dot gain medium is still under development and is not included with this work.

Fig. 138: Schematic view of a mounted two-sectional laser diode with absorber section (left section) and gain section (right section). Both sections are biased and can additionally be modulated with a RF signal. As already mentioned, passive and hybrid mode-locked laser require a saturable absorber section within the laser cavity. For monolithic devices this can be accomplished by a two-sectional design of the laser diode contacts and metallization


133

(see section 1.2.2). The two-section QD laser devices for mode-locking consisted of a long gain section operated at positive bias and a short absorber (typically 10-20 % of the total length) section operated at reverse bias levels between 0 and –6 V. Fig. 138 gives a schematic view of the device and the bias conditions. For hybrid mode-locking both the absorber and/or the gain section can be additionally modulated with an RF signal coupled to the device via a high-frequency suitable two-port submount (see section 1.4). The mounted two-section devices are fixed on a temperature-controlled heat sink, connected to the bias current and voltage sources via microwave cables and coupled into a SMF by taper. The SMF incorporates an optical isolator to avoid back reflection into the laser diode. Fig. 139 shows the two main set-ups for time resolved measurements on mode-locked QD lasers: For hybrid mode-locked devices with repetition rates below 10 GHz and long pulses (> 20 ps) a 40 GHz sampling oscilloscope (Hewlett Packard 54120A) combined with a 50 GHz detector (XPDV2020R, u2t photonics) and an 40 GHz RF signal generator (Agilent 8247C) and 20 GHz amplifier is used. This set-up also allows measuring the timing and amplitude jitter of the optical pulses and the true pulse shape.

Reverse bias

DC current

50 Ghz Detector

Bias-T

Frequency generator

Two-sectionallaser diode

Optical fiber

40 GHz Oscilloscope

Trigger line

Reverse bias

DC current Bias-T

Frequency generator

Two-sectionallaser diode

Optical fiber

Autocorrelator

Computer

Fig. 139: Set-up for measurement of mode-locked laser diodes based on a fast detector and sampling oscilloscope (left) and on an autocorrelator (right). The oscilloscope set-up is restricted to hybrid ML since a trigger signal is required. For all other samples, an autocorrelation set-up is used to determine the convoluted pulse shape. The self-assembled autocorrelator works with a second harmonic generating (SHG) nonlinear Lithium niobate crystal, a cooled phototube for maximum sensitivity and is adjusted for background-free measurement. The linear mechanical stage for variable delay allows fs resolution with a maximum time window of 600 ps! The main drawback of autocorrelation traces is their ambiguity with respect to the true pulse shape and width. The deconvolution of the SHG signal can only be made assuming a certain (e.g. Gaussian) pulse shape. Asymmetric pulses always appear symmetric. Deconvolution is accomplished with a small computer program implemented with LabVIEW [136]. It fits the convolution of any pulse shape function described by a finite set of parameters (not necessarily symmetric) to the measured curve and derives the most suitable parameters. Unambiguousness of the deconvoluted function is not checked. The main result of this calculation is the FWHM of the optical pulse. From the measurement of auto- and first order cross-correlation we can derive the timing jitter between two adjacent pulses (uncorrelated jitter). The cross-correlation


134

( )C t corresponds to the convolution of the autocorrelations of the pulse ( )A t and the jitter distribution ( )( )j j t∗ . Deconvolution of the cross-correlation with the auto-correlation yields the autocorrelation of the jitter distribution, from which (after deconvolution) the uncorrelated jitter distribution ( )j t can be derived. The deconvolution of cross- with auto-correlation is done with the Fourier transforms of the correlation functions using the well-known convolution theorem:

1

( ) ( )( ) ( ) ( )

( ( )) 2 ( ( )) ( )

( ( ))( )2 ( ( ))

A t f fC t A t j j

F C t F A t F j j

F C tj j FF A t

π

π−

= ∗= ∗ ∗

= ⋅ ⋅ ∗

⎛ ⎞∗ = ⎜ ⎟

⋅⎝ ⎠

(2.60)

The full timing jitter can be substantially larger than the uncorrelated jitter. The radio frequency (RF) spectrum of the mode-locked pulses is measured with a 50 GHz detector (XPDV2020R, u2t photonics) and a 22 GHz electrical spectrum analyzer (HP 8562A). It allows us to determine the exact repetition rate of the mode-locked pulse, the stability of the frequency, and the locking range (for hybrid mode-locking). RF spectra can also be used to derive an estimate for the full timing jitter of mode-locked lasers (including correlated jitter between non-adjacent pulses). The sideband noise of the repetition frequency is measured and integrated (typically from 100 Hz to 10 MHz offset) to give the noise power and, subsequently, the jitter. For this measurement, the spectrum analyzer has to be calibrated, which was not possible for our equipment. We therefore omit sideband noise measurements. Prior to mode locking measurements we investigated the characteristics of the saturable absorber section. P-I curves of two-sectional devices were measured for conventionally pumped gain section and varying absorber bias voltages. Fig. 140 (left) shows the results for a Ioffe 5-600, (700+100)x4 µm, HR coated rear facet sample showing a clear hysteresis for currents just above threshold.

0 20 40 60 80 1000

5

10

15

20Reverse bias

voltage -1 V -2 V -3 V

cw L

aser

Out

put [

mW

]

Current [mA]0 20 40 60 80 100

0

1

2

3

4

5

0

2

4

6

8

10

12Reverse bias

voltage -1 V -2 V -3 V -4 V

Phot

ocur

rent

[mA]

Gain current [mA]

Pow

er A

bsor

ptio

n [m

W]

Fig. 140: PI curve hysteresis of the two-sectional sample Ioffe 5-600, (700+100)x4 µm, HR coated rear facet, for different absorber bias voltages (left) and the corresponding photocurrent measurement at the absorber section (right). At low voltages, the absorber is easily saturated, yields only a small hysteresis and a moderate saturation photocurrent. The efficiency of the absorber and the photocurrent increase with bias voltage.


135

As expected, the hysteresis becomes larger for higher reverse bias due to stronger absorption and higher saturation intensity. The fact that the laser starts lasing at higher currents shows that the gain section can compensate for the absorber losses – the mode locking section is not too long. The saturation of the absorber is proved by the right graph of Fig. 140. The measured photocurrent across the absorber section shows a voltage dependent behavior: For small reverse voltages it saturates faster, because the carrier sweep-out time in the waveguide region of the absorber section is long. An absorber section length of 100 µm is saturated at low absorption powers of a few mW; therefore we regard this length as the shortest suitable one. The layout of the two-sectional contacts takes this into consideration.

5.2.1 Passive mode-locking Passive mode locking at 5 GHz Passive mode-locking was first investigated by us using long devices, since there is a considerable interest in low frequency optical clocks for computer applications [137]. Quantum dot lasers, with their low threshold current densities and small internal losses are ideal for long devices. Several 5-fold stacked Ioffe 4-915 samples with dimensions 8100x4 µm and shallow etched mesas, were cleaved and mounted on two-port submounts. The absorber section was 600 µm long, the gain section 7500 µm. Due to the multi-sectional design of the contacts the gain sections consisted of 9 successive sections, which were short-ended with 7500 µm long bond ribbons in order to work as one section. The devices operated at ~150 mA forward current (gain section) and -4 V reverse bias voltage. All measurements were carried out at room temperature without temperature stabilization. Fig. 141 shows the autocorrelation measurement of the mode-locked laser. The deconvolution of the autocorrelation pulse assuming a Gaussian pulse shape yielded a FWHM of 9 ps. This value was limited basically by the maximum reverse bias voltage we apply to the absorber section; in order not to destroy the laser we worked only at moderate voltages down to -4 V.

-40 -20 0 20 400.0

0.5

1.0

1.5 Autocorrelation Deconvoluted pulse

FWHM (deconv.) 9 ps

Inte

nsity

[a.u

.]

Time [ps]

-50 0 50 100 150 200 2500.0

0.5

1.0

1.5

1280 1290 1300

-60

-40

-20

0

Cross correlation

Autocorrelation

SHG

sig

nal [

a.u.

]

Time [ps]

Pow

er [d

Bm]

λ [nm]

Fig. 141: The left diagram shows the autocorrelation measurement for the sample Ioffe 4-915, (7500+600)x4 µm, from which a Gaussian shaped pulse with FWHM of 9 ps was deconvoluted. The right diagram additionally shows the adjacent cross correlation peak, which allowed us to estimate the uncorrelated jitter to be < 2 ps. The inset shows the corresponding spectrum of the laser.


136

The right graph additionally shows the first adjacent cross correlation peak, i.e. the convolution of two successive optical pulses. According to the repetition frequency of 5 GHz, both peaks had a distance of 200 ps. The decrease in amplitude was due to a slight misalignment of the mechanical delay stage, which became prominent for a long delay (~3 cm). The cross correlation peak bears information about the variation of the relative position of successive pulses, the uncorrelated jitter: A large jitter broadens and flattens the cross correlation peak. Based on an estimation of the measurement accuracy of our system we derived an upper limit for the uncorrelated jitter of 2 ps. The peak power of the mode-locked pulses was calculated from the average output power (32 mW from laser, 4 mW in fiber):

2peak averageFWHM

TP Pτ

≈ ⋅ (2.61)

where T was the pulse period (200 ps) and FWHMτ was the pulse width, assuming a triangular pulse shape. The pulse energy was 20 fJ in fiber (160 fJ ex laser). Passive mode-locking at 20 and 35 GHz For datacom applications, typical base frequencies for mode-locked devices range from 10 to 40 GHz, corresponding to device lengths between 4 and 1 mm. The Ioffe 4-915 two-section devices for mode-locking at 20 and 35 GHz consisted of a long gain and a short absorber section with length 1500/500 µm for the 2000 µm and 980/150 µm for the 1130 µm long device, respectively. Time-domain measurements were carried out with the autocorrelator set-up.

30 40 50 60

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

FWH

M P

ulse

Wid

th [p

s]

Nolasing

incomplete ML+ cw lasing

Gain Current [mA]

Rev

erse

Bia

s Vo

ltage

[V]

7

11

16

20

-60 -40 -20 0 20 40 600.0

0.5

1.0

1.5

2.0

1280 1285 1290

-60

-40

-20

0

Pow

er [d

Bm]

λ [nm]

Autocorrelation Deconvoluted

Gaussian

SHG

sig

nal [

a.u.

]

Time [ps]

Fig. 142: Passive mode-locking parameter scan (left) and typical autocorrelation trace and deconvoluted pulse shape (right) for the sample Ioffe 4-915, (1500+500)x4 µm. The inset shows the corresponding spectrum. The pulse repetition frequency was 20.2 GHz.

Fig. 142 (right) shows a typical autocorrelation measurement from the 2000 µm device. It shows both the autocorrelation (middle peak) and the cross correlation (side peaks) of the pulses. The autocorrelation trace was deconvoluted assuming a Gaussian pulse shape. The dashed curve shows the calculated pulse shape with a FWHM of 12 ps. This value is in good agreement with the Fourier limit ( 0.44ν τΔ ⋅ Δ = ) of 13 ps estimated from the spectral FWHM of 180 pm. The inset of


137

Fig. 142 (right) shows the spectrum of the mode-locked laser centered at a wavelength of 1286 nm. In order to characterize the dependence of the pulses on parameters like reverse bias and gain current, we did arrays of autocorrelation scans with a fully automated set-up. The 2000 µm laser was passively mode-locked at currents between 30 mA and 70 mA and reverse bias voltages between -2.5 and 0 V. The results of the scan are depicted in Fig. 142 (left): The diagram shows the different regimes of device operation versus reverse bias and gain current. The center region, which corresponds to mode-locking operation, shows the grey scale coded deconvoluted FWHM pulse width of the autocorrelation traces. With increasing reverse bias, the onset of lasing shifted to larger currents, due to the increasing absorption within the waveguide. The onset of lasing occurred abruptly as mode-locking; we observed no transition region (e.g. Q-switching). With increasing current, the pulses became broader, until we observed a cw offset, i.e. incomplete mode-locking. At even higher currents, we observed a transition region with all kinds of pulse patterns (e.g. self pulsation) until all intensity fluctuations flattened out to cw lasing. The pulse width ranged from 8 to 18 ps. As expected, the shortest pulses occurred at large reverse bias voltages, were it was possible to go to larger gain currents with the laser still capable of mode-locking. The minimum pulse width was once again limited by the maximum reverse bias voltage we estimated here to be not harmful for the device. Comparison of autocorrelation and cross correlation allowed us to estimate the uncorrelated jitter to be less than 1 ps. However, we expect the main jitter contribution to be correlated jitter. The 1130 µm long laser was passively mode-locked at currents between 40 and 70 mA and reverse bias voltages between –3 and 0 V. The mode-locking frequency was 35 GHz.

40 50 60 70

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

FWH

M P

ulse

Wid

th [p

s]

Nolasing

Incompletemode locking

Gain Current [mA]

Rev

erse

Bia

s Vo

ltage

[V]

5

7

8

9

11

-20 -10 0 10 200.0

0.5

1.0

1.5

2.0 Autocorrelation Deconvoluted

Gaussian

1275 1280 1285 1290

-60

-40

-20

0

Pow

er [d

Bm]

λ [nm]

SHG

sig

nal [

a.u.

]

Time [ps]

Fig. 143: Passive mode-locking parameter scan (right) and typical autocorrelation trace and deconvoluted pulse shape (left) for the sample Ioffe 4-915, (980+150)x4 µm. The inset shows the corresponding spectrum. Fig. 143 (right) shows the autocorrelation measurement of the laser pulses. The minimum pulse width we achieved with this device was 7 ps, which is again in agreement with the Fourier transform limit. The uncorrelated jitter estimated from the cross correlation was less than 2 ps. The peak power from one facet of the mode-locked laser was 6 mW.


138

Fig. 143 (left) shows the reverse bias vs. current scan of the autocorrelation traces and the corresponding FWHM pulse widths. In comparison to the results on the longer device shown in Fig. 142 we observed a much smaller region of mode-locking. This is due to the shorter absorber section of 180 µm which saturates already at low gain currents. We estimate the saturation absorption to be comparable to the saturation gain, i.e. 15 cm-1. The trade-off between absorber, gain and total length establishes the current pulse width limitation of 7 ps. Mode locking of Ioffe 5-600 samples Passive mode-locking results at 20 GHz were achieved with Ioffe 5-600 samples with dimension similar to the Ioffe 4-915, (1500+500)x4 µm device. Both samples contained the same number of QD stacks and were deep etched. Fig. 144 shows a typical autocorrelation and the parameter scan. From the scan we see that the mode-locking range of the sample was considerably larger than those of the corresponding Ioffe 4-915 sample. Variations in the processing and the improvement of the electrical properties (lower differential resistance) account for these differences.

50 100 150 200

-3

-2

-1

0

FWH

M P

ulse

Wid

th [p

s]

NL


Gain Current [mA]

Rev

erse

Bia

s Vo

ltage

[V]

5

10

15

20

-60 -40 -20 0 20 40 600.0

0.5

1.0

1.5

2.0

1295 1300 1305

-60

-40

-20

0

SHG

sig

nal [

a.u.

]

Time [ps]

Pow

er [d

Bm]

λ [nm]

Fig. 144: Passive mode-locking parameter scan (left) and typical autocorrelation trace (right) for the sample Ioffe 5-600, (1500+500)x6 µm. The inset shows the corresponding spectrum. Passive mode-locking at 40 and 50 GHz For devices with as-cleaved facets and 5 QD stacks, a cavity length of 1.1 mm, including a 100 µm absorber, is the almost shortest possible length still lasing due to gain saturation. In order to achieve mode-locking with even shorter, faster devices, an HR coating is applied to the rear facet of the two-sectional laser bars.


139

30 40 50 60 70

-6

-5

-4

-3

-2incompletemode-locking

FWH

M P

ulse

Wid

th [p

s]

Nolasing

Gain Current [mA]

Rev

erse

Bia

s Vo

ltage

[V]

3

4

6

7

-40 -20 0 20 400.0

0.5

1.0

1.5

2.0

1260 1265 1270 1275 1280

-60

-40

-20

0

SHG

sig

nal [

a.u.

]

Time [ps]

Pow

er [d

Bm]

λ [nm]

Fig. 145: Passive mode-locking parameter scan (left) and typical autocorrelation trace (right) for the sample Ioffe 5-600, (900+100)x4 µm, HR coated rear facet. The inset shows the corresponding spectrum. Ioffe 5-600 samples with dimension (900+100)x4 µm and (700+100)x4 µm with HR coated rear facet were investigated. Fig. 145 shows results for the 1000 µm device. The right graph shows both the autocorrelation (middle peak) and the cross correlation (side peaks) of the pulses. The FWHM pulse width at –6 V absorber bias was 3.2 ps. This value, regarding the spectral FWHM, corresponds to a Fourier limited pulse. The inset of the right graph shows the spectrum of the mode-locked laser centered at a wavelength of 1273 nm. The parameter scan results for passive mode-locking of the 1000 µm device (40 GHz) are depicted in Fig. 145 (left): The pulse widths ranged from 3 to 7 ps. As for all devices we investigated (working at frequencies 5, 10, 20, and 50 GHz), the shortest pulses occurred at large reverse bias voltages. The highest mode-locking frequency we achieved was 50 GHz. Fig. 146 (right) shows both the autocorrelation and the cross correlation measurement of the laser pulses. The Fourier transform limited minimum pulse width we achieved with this device was 3 ps. The peak power from one facet of the mode-locked laser was 6 mW. Besides pulse shape and width we also determined the timing and amplitude jitter of the pulses. Comparison of autocorrelation and cross correlation [19] allowed us to estimate the uncorrelated jitter to be less than 1 ps.

40 60 80 100

-6

-5

-4

-3

-2

FWH

M P

ulse

Wid

th [p

s]

Nolasing

incompletemode-locking

Gain Current [mA]

Rev

erse

Bia

s Vo

ltage

[V]

2

4

5

7

-30 -20 -10 0 10 20 300.0

0.5

1.0

1.5

2.0

1270 1280 1290

-60

-40

-20

0

SHG

sig

nal [

a.u.

]

Time [ps]

Pow

er [d

Bm]

λ [nm]

Fig. 146: Passive mode-locking parameter scan (left) and typical autocorrelation trace (right) for the sample Ioffe 5-600, (700+100)x4 µm, HR coated rear facet. The inset shows the corresponding spectrum.


140

Fig. 146 (left) shows parameter scan of the autocorrelation traces and the corresponding FWHM pulse widths. In comparison to the results on the longer device shown in Fig. 145 the region of mode-locking has shrunken considerably. Below -4.5 V the laser does not turn on at all. This is due to the short gain section which saturates already at moderate absorber gain currents. This situation is somewhat different to the results observed for the uncoated 35 GHz device that showed lasing, but no ML below a certain voltage. The reason for this discrepancy is unclear. However, we made sure that it is not a simple turn-on hysteresis effect.

5.2.2 Hybrid mode-locking For hybrid mode-locking up to frequencies of 20 GHz we applied a RF power of up to 25 dBm to the absorber section (see Fig. 139). The large RF power was necessary in order to compensate the strong damping of the electrical signal on its way to the active region of the laser diode. From S11 parameter measurements in section 3.2.1 we know that the RC bandwidth of the investigated samples for zero bias lies in the range of < 1 GHz due to the junction capacitance, and the voltage coupled to the active layer decreases 20 dB/decade. The additional modulation of the absorber voltage with a frequency close to the repetition rate of the cavity yields an amplification of the pulse shaping process in the absorber section due to the sinusoidal change of absorber loss. Therefore we expect a decrease of pulse width and an enhancement of the mode-locking region. For hybrid mode-locking, both the repetition rate and the phase of the pulse stream are locked to the external RF signal.

30 40 50 60

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

FWH

M P

ulse

Wid

th [p

s]

Nolasing


Gain Current [mA]

Rev

erse

Bia

s Vo

ltage

[V]

7

11

16

20

30 40 50 60 70

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

FWH

M P

ulse

Wid

th [p

s]

Nolasing

Mode locking


Gain Current [mA]

Rev

erse

Bia

s Vo

ltage

[V]

8

11

13

16

18

Fig. 147: Comparison of passive (left) and hybrid (right) mode locking of the sample Ioffe 4-915, (1500+500)x4 µm. 20 dBm RF power were applied for hybrid mode-locking. For hybrid mode-locking of the sample Ioffe 4-915, (1500+500)x4 µm, however, we observed quite similar results as for passive mode-locking except for a slight increase of the mode-locking regime towards larger currents (+5 mA) (see Fig. 147). The pulse widths did not change significantly, which indicated that, as expected from the S11 measurements, most of the 20 dBm RF power did not enter the device and thus did not contribute to absorption modulation. We characterized the influence of the RF power on the mode-locking frequency tuning range, i.e. the range of RF frequencies for which the mode-locking frequency is pinned to the RF frequency.


141

20.24 20.26 20.28 20.30-70

-60

-50

-40

-30

Spec

tral p

ower

[dBm

]

Frequency [GHz]0 5 10 15 20 25 30

0

20

40

60

80

100

Lock

ing

rang

e [M

Hz]

RF Power [dBm]

Fig. 148: Radio frequency spectrum (left) of the sample Ioffe 4-915, (1500+500)x4 µm under hybrid mode-locking with successive external locking frequencies ( 5f MHzΔ = ). The distance between the framing peaks denotes the locking range of ~45 MHz for this sample at 22.5 dBm RF power. The right graph shows the increase of locking range with applied RF power. A maximum locking range of 90 MHz is achieved for 25 dBm RF power. Fig. 148 (left) shows the RF spectrum of the mode-locked pulses for different external locking frequencies with a spacing of 5 MHz within the locking range of the device. As soon as the locking frequency is detuned too much, two lines appear in the RF spectrum, the locking frequency and the native cavity round trip frequency. Fig. 148 (right) shows the tuning range versus the applied RF power. The maximum tuning range was 90 MHz (0.5 % of the locking frequency). As expected, the locking range increases with increasing RF power. The RF power is limited by the maximum output power of the RF source and amplifier. The locking range can be further increased by an improvement of the RC bandwidth of the laser (see section 3.2.1). A more efficient coupling of RF power to the absorber section should also help to improve pulse shape and jitter characteristics.

5.2.3 Mode-locking limitations Table 7 gives a summary of measured passively mode-locking devices with corresponding (minimum) pulse width and pulse-to-period ratio. Frequency = Length Hybrid ML Passive ML 5 GHz 8.2 mm Pulse width Pulse / Period 9 ps 5 % 12 GHz 3.3 mm 21 ps 25 % 22 ps 25 % 20 GHz 2 mm 11 ps 25 % 11 ps 25 % 35 GHz 1.1 mm - 7 ps 25 % 40 GHz 1 mm 3 ps 12 % 50 GHz 0.8 mm 3 ps 15 %

In the following we discuss the limitations of these mode-locking parameters and means to overcome these limitations.

Table 7: Measured mode-locking frequencies, corresponding device lengths, minimum pulse widths and pulse-to-period ratios. The best ratio was achieved for the 5 GHz devices.


142

Repetition frequency limit The maximum frequency of passive mode-locking is limited by the shortest possible cavity length still capable of lasing. Lets assume that the maximum possible gain in the gain section has the same absolute value as the maximum possible loss (from section 2.2.2 we know that the maximum possible gain of a quantum dot active layer is only achieved for very large carrier densities, so this is just the upper limit for the gain). The absorption section always gives maximum loss because it is not pumped at all (saturation effects shall be omitted). It then takes a strongly pumped gain section of about the same length as the absorber section to compensate for the losses. The remaining part of the gain section has to compensate the mirror and waveguide losses. This gives us an estimate of the minimum gain section length still capable of lasing for a given maximum modal gain, absorber section length, facet reflectivity and internal losses.

0.1 1 1040

60

80

100100 10

Modal gain limit(Theory)

10 cm-1

15 cm-1

20 cm-1

25 cm-1

Measured devices [Rep. rate]

Gai

n se

ctio

n le

ngth

[% d

evic

e le

ngth

]

Device length [mm]

510

1220

35

ML Frequency [GHz]

0.1 1 1040

60

80

100100 10

Modal gain(Theory)

10 cm-1

15 cm-1

20 cm-1

25 cm-1

Measured devices [rep. rate]

G

ain

sect

ion

leng

th[%

dev

ice

leng

th]

Device length [mm]

40

50

ML Frequency [GHz]

Fig. 149: Limitation for mode-locking repetition rate for QD lasers with as-cleaved facets (left) and HR coated rear facet (right). Different values for the maximum modal gain of the QD gain medium are given; the data points mark the dimensions of the actual devices presented in the previous sections. HR coating helps to increase the maximum repetition frequency to approximately 60 GHz. Fig. 149 shows the corresponding calculations for uncoated (left) and HR coated (right) single facet, along with data points marking the actual devices that were presented in the previous section. The lines denote the limit for a certain modal gain value; the area below the curves is the non-lasing parameter zone. For a reasonable maximum modal gain of 20 cm-1 for the 5-fold stacked samples all data points lie within the lasing zone. It also becomes clear that for repetition rates higher than 60 GHz, additional improvements have to be made to ensure lasing. Higher repetition frequencies can be achieved by

- Stacking of more QD layers (increase of modal gain) - HR coating of front facet (trade-off: output power decreases) - Colliding pulse mode-locking scheme with middle absorber section (doubles

the repetition rate) Output power limit The current range where mode-locking appears typically lies between thrI and 2 thrI⋅ , where thrI denotes the threshold current with applied reverse bias. It is limited by the


143

occurrence of a cw background added to the mode-locking pulse, i.e. incomplete mode-locking. Since the most powerful pulses are emitted close to the high current limit, striving for larger output powers requires mode-locking at even higher currents. Due to the different carrier densities in the absorber and the gain section, there might be some principle limit for the maximum mode-locking current. We investigated the optical spectra of a two-sectional device with the absorber switched on and off. Fig. 150 shows the results for the sample Ioffe 5-600, (900+100)x4 µm, HR coated rear facet presented in the previous section.

1220 1240 1260 1280 1300 1320-60

-40

-20

0 Bias 0V, 40 mA Bias -4V, 45 mA

Pow

er [d

Bm]

Wavelength [nm]1220 1240 1260 1280 1300 1320

-60

-40

-20

0 Bias 0V, 140 mA Bias -4V, 130 mA

Pow

er [d

Bm]

Wavelength [nm]

Fig. 150: Comparison of spectra for the sample Ioffe 5-600, (900+100)x4 µm, HR coated rear facet, at different bias current and voltages. The curve for -4 V bias in the left graph corresponds to mode-locking operation. The spectra in the right graph both correspond to cw lasing. The emission in the left graph of Fig. 150 is centered at 1270 nm. For switched-on absorber the spectrum narrows symmetrically. Mode-locking is observed. In the right graph we see that for switched on absorber, the spectrum only shrinks at the short wavelength edge, corresponding to the still unaltered center wavelength of the absorber section of 1270 nm. Most probably the wavelength of maximum absorption remains unchanged, while the gain maximum broadens and shifts to larger wavelength. Due to the decreasing spectral overlap mode-locking is no longer possible. At least two mechanisms cause such a red shift:

- Band gap renormalization - Gain section heating (thermal shift)

In the case of gain section heating it should be possible to reduce the warmth to some extent by use of narrow ridges (2 µm). Pulse width limit The ultimate limitation for the minimum pulse width of mode-locked lasers is the width of the gain spectrum. As we are yet deploying only 2 % of the intrinsic spectral width of the quantum dot gain medium, there is still plenty of room for reducing the pulse width to levels in the range or below 1 ps. Fig. 151 illustrates this assumption by showing the optical spectrum of a free-running QD laser and a mode-locked one. Shorter pulses should become possible with stronger absorbers. There are basically three ideas to enhance absorption:

- Stacking of more QD layers - Ion-implantation of the absorber section to create more absorption centers - Higher absorber voltages


144

The application of higher voltages is limited by the break-through voltage limit of the pn-junction and by the leakage current between gain and absorber section. The latter can be reduced by ion-implantation of the gap. Insulation resistances as large as 10 MOhm have been reached this way. Our work on ion-implanted absorbers and gaps are presented in the next sections.

1271 1272 1273 12740

2

4

6

Spec

tral p

ower

[lin

ear]

Wavelength [nm]

Mode-locked operation @ 40 GHz

1240 1260 1280 1300

-50

0

50

100

Free running laser

Mode-locked operation@ 40 GHz

Spec

tral p

ower

[dB]

Wavelength [nm]

Fig. 151: High resolution optical spectrum (left) of a mode-locked QD laser Ioffe 5-600, (900+100)x4 µm. The longitudinal mode distance corresponds to a repetition rate of 40 GHz, between 5 and 7 modes are locked. The right graph shows the same mode-locking spectrum (with logarithmic scale) in comparison to a non-mode-locked QD laser. The spectrum of free-running QD lasers at large output powers is about a factor 10-20 larger than typical mode-locking spectra.

5.2.4 Ion-implanted section gap In order to achieve better insulation between the absorber section and gain section and to minimize leakage currents Portnoi et al. (private communication) proposed to make the gap semi-insulating by ion-implantation. For ion-implantation of the section gaps we prepared a wafer piece that would later be separated into single devices. The gain and absorber sections which are not intended to be implanted must be shielded from the ion beam, e.g. by a thick (~10 µm) layer of lithographic resist or by gold layer. We deposited a 15 µm thick Au layer on top of the mesas by Au plating the contact metallization. The gaps were left blank by a plating mask.

0 200 400 600 800 1000

0

10

20

Thic

knes

s [µ

m]

Horizontal position [µm]

Fig. 152: Galvanized multi-sectional sample prepared for ion implantation (left) and corresponding profile of Au thickness showing 15 µm Au on top of the mesas (right). The to-be-implanted gap sections are the three dark horizontal ribbons crossing the Au-plated mesas.


145

Fig. 152 shows a photograph of the plated sample and the corresponding Au thickness measurement. The implantation was done at the ion beam facilities of the Hahn-Meitner-Institut, Berlin. The samples were exposed to a beam of Ar4+ ions with energy of 5 MeV. Starting with gap insulation resistances between 4 and 7 kOhm depending on the ridge width, after the first implantation with a dose of 10 26 10 /ions cm⋅ the resistance had only increased by 20 % (the resistance was measured with an accuracy of 1 %). After the second run with an increased dose of 11 28 10 /ions cm⋅ the resistance rocketed to 5-7 MOhm (see Fig. 153). The increase of resistance was hyper-exponential.

0 2 4 6 8 10

10-3

10-2

10-1

100

10000

1000

100

10

1

pre-implant Dose 6x1010

Dose 8x1011

Con

duct

ivity

[mS]

Ridge width [µm]

Res

ista

nce

[kΩ

]

0.0 2.0x1011 4.0x1011 6.0x1011 8.0x10111

10

100

1000

10000Ridge width

4 µm 6 µm 8 µm 10 µm

Hyper-exponentialslope!

Gap

resi

stan

ce [k

Ω]

Dose [ions/cm2]

Fig. 153: Increase of the gap resistance after implantation, for different ridge width. The right graph shows the extrapolation of an exponential increase of the resistance and the measured value, which exceeded the extrapolation by two magnitudes. The final resistance lay between 5 and 7.3 MOhm. The large gap resistance was nevertheless suitable for mode-locked devices. Unfortunately, the thick Au plating made proper cleaving of the facets impossible. Although the electrical properties of the two-sectional samples were excellent, no lasing could be achieved due to facet damage during cleaving. Use of a removable resist mask should solve this problem.

5.2.5 Ion-implanted absorber section The ion-implantation of saturable absorbers is a well-established technique for the fabrication of monolithic mode-locking device, e.g. [138-140]. In most applications, the ions are implanted through the facet of the laser diode. Depending on the ion energy and mass, typical penetration depth and according absorber length of 10 µm are realized. This method is relatively simple and requires no additional preparation of the sample. In principle it is also possible to implant the ions through the top side of the laser diode. This method has two advantages: The ion beam does not interfere with the delicate laser facet, and the length of the absorber can be adjusted by masking. A drawback is the masking preparation. Both techniques were used by us for the ion-implantation of absorber sections in quantum dot lasers. Top-side implantation, 1. Session


146

Prior to implantation, the suitable energy, mass and dose of ions had to be determined. Energy and mass define the penetration depth and the defect generation rate of the ions. Fig. 154 shows the simulated vertical distribution of defects in a GaAs/AlGaAs structure. The right graph shows an ideal defect distribution, with its maximum inside the active layer.

Fig. 154: Simulation of vertical vacancies distribution profile for Ar1+ ions with 2.4 MeV (left) and 4.4 MeV energy (right) in a GaAs/GaAlAs structure simulating the vertical waveguide. The target depth, the active zone, lies in the middle of the diagram. The penetration depth for the lower energy (1.5 µm) is too small; the higher energy (depth 2.1 µm) is suitable [Courtesy O.Schulz]. After the choice of the ion energy a suitable mask for the non-implanted section had to be found. The easiest way to protect the laser mesas from ion bombardment is the reinforcement of the ridge metallization by Au plating. Only the gain section was gold-plated, the absorber section (which is to be implanted) remains uncoated. Fig. 155 shows the corresponding height profile of the gold-plated laser ridges. The gold with thickness > 2 µm provided sufficient screening of the ion beam without obstruction of the facet cleaving. Six samples Ioffe 4-915, (1500+500)x4 µm and (1500+500)x6 µm were prepared and characterized prior to implantation with respect to their PIV curve characteristics.

0 100 200 300 4000

2

4

6

~ 2 µm

Hei

ght [

µm]

Position [µm]

Fig. 155: Height profile of gold plated contact metallization. The gold layer is quite rough, but has a sufficient average thickness of 2 µm.


147

The optimum energy of the Ar1+ ions was not available at the time of our implantation session, so implantation was done with 2.4 MeV. The lower energy caused a less efficient generation of defects in the active zone (see Fig. 154), therefore implantation was done in two steps with an rather large accumulated dose of

12 21 10 /ions cm⋅ . Fig. 156 shows the results before and after implantation. The sample shows an increase of the threshold and decrease of the differential quantum efficiency.

0 50 100 150 2000.0

0.5

1.0

1.5

2.0

2.5

0

2

4

6

8

10

12

14

Before After implantation After 10 min lasing

Volta

ge [V

]

Current [mA]

Out

put p

ower

[mW

]

Fig. 156: PIV characteristics of the sample Ioffe 4-915, 2000x4 µm, implanted with a dose of

12 21 10 /ions cm⋅ . The implantation caused an increase in threshold, above 150 mA the laser switched to excited state lasing. The differential quantum efficiency was also substantially decreased, but both effects were partly removed by annealing. Like for the facet implantation session, the implanted laser diodes showed partial annealing, that was forced by lasing operation (due to the devices heating). This effect can be attributed to the annealing of lattice defects created by the ions. The original PI curve was not recovered, due to the remaining defects and ions inside the cavity. However, no passive mode locking could be observed with these samples, despite the fact that the implanted section can be additionally pumped / depleted via the electrical contact of the absorption section. A possible explanation is that the ion implanted absorber offers very efficient recombination centers. Therefore, saturation of the absorber is no longer possible. Top-side implantation, 2. Session For the second session four samples Ioffe 5-600, (1500+500) µm with deep etched mesa widths 4 and 6 µm were prepared for top-side implantation (masking, electro-plating, mounting, characterization) similar to the previous session. All samples showed mode locking prior to implantation. This time, an ideal Ar1+ ion energy of 4.4 MeV was provided. Implantation was done in a single run with a low dose of

10 24.2 10 /ions cm⋅ . Fig. 157 shows the impact of the implantation on the IV characteristics of both the absorber and gain section. While the gain section resistance is not altered, the absorber section became semi-insulating due to strong implantation. No lasing of the devices could be achieved after implantation, no annealing effect could be observed. A possible explanation besides excessive losses due to defect absorption could be GaAs/AlGaAs intermixing, resulting in the destruction of the waveguide.


148

Due to limitations in switching time of the ion beam shutter (minimum beam shutter open-close time was in the range of sec, corresponding to ~ 1010 ions/cm2) the application of a smaller dose is not feasible. Possible solutions to achieve lasing and mode-locking by top-side implantation are

- Alter ion mass, reduction of ion defect creation rate, - Reduction of the length of the implanted section to ~100 µm to overcome

excessive losses, - Facet implantation.

Further investigations will have to clear this question.

0 1000 2000 30000

1

2

3

preimp, long section postimp, long section postimp, short section

U [V

]

Current density [A/cm²]0 1000 2000 3000

0

1

2

3

preimp, long section postimp, long section postimp, short section

U [V

]

Current density [A/cm²]

Fig. 157: IV characteristics of the samples Ioffe 5-600, 2000x4 µm (left) and 2000x6 µm (right), both implanted with a dose of 10 24.2 10 /ions cm⋅ . The implantation caused a semi-insulating characteristic of the implanted section, lasing was impossible due to large optical losses. No annealing effect was observed. The graphs show the IV curve of the un-implanted gain section for comparison. Ion implantation through facet Determining the ion energy and mass for facet implantation was not as crucial as for top-side implantation, since we preferred maximum absorber length, i.e. maximum penetration depth. Therefore, the samples were exposed to a beam of N4+ ions with the large energy of 17 MeV. Fig. 158 shows the simulated lateral vacancies distribution profile for the nitrogen ions. The distribution was rather inhomogeneous due to the larger collision cross-section of slow ions, with a maximum density at a depth of 9 µm. Four samples Ioffe 4-915, shallow etched mesa, with dimensions 1000x4 µm and 2000x4 µm were prepared for implantation, as shown in Fig. 158. Prior to implantation, the devices were characterized concerning threshold and output power. The implantation was done in two steps: In the first run, doses of 12 21 10 /ions cm⋅ and

12 22 10 /ions cm⋅ were each applied to a pair of 1000/2000 µm devices. The PIV curve showed no significant change after the first run, so a second run with doses of

13 21 10 /ions cm⋅ and 13 22 10 /ions cm⋅ was done, giving an accumulated dose of 13 21.1 10 /ions cm⋅ and 13 22.2 10 /ions cm⋅ , respectively.


149

Fig. 158: Simulation of lateral vacancies distribution profile for N4+ ions with 17 MeV in GaAs (left), the penetration depth is about 10 µm, with a maximum defect density around 9 µm. The photograph shows the sample holder for facet ion implantation with four mounted laser samples attached. Fig. 159 shows the impact of the implantation on the PIV curves of the two devices with the large dose: Due to an increase of the internal optical losses the threshold current increased and the differential quantum efficiency decreased. The effect was much stronger for the short cavity, since it was closer to gain saturation than the long one.

0 20 40 60 80 1000.0

0.5

1.0

1.5

2.0

0

5

10

15

20 Before 1 day after 2 days after

Volta

ge [V

]

Current [mA]

Out

put P

ower

SF

[mW

]

0 20 40 60 800.0

0.5

1.0

1.5

2.0

0

5

10

15 Before 1 day after 2 days after

Volta

ge [V

]

Current [mA]

Out

put P

ower

SF

[mW

]

Fig. 159: PIV characteristics of the samples Ioffe 4-915, 1000x4 µm (left) and 2000x4 µm (right), both implanted with a dose of 13 22.2 10 /ions cm⋅ . The implantation caused an increase in threshold and a decrease of the differential quantum efficiency, but the effect was partly removed by annealing. All implanted laser diodes show annealing, i.e. part of the implantation effect is removed. This happens most probably due to annealing of the ion induced lattice defects. A residual effect of the implantation remains, which is due to implanted ions. Despite the absorber effect of the implanted section it was not possible to obtain passive mode locking with these samples. Reasons for this might be the insufficient length and absorption loss of the implanted section. If the implanted defects (ions, lattice defects) do not absorb light, but merely trap carriers, their impact is probably only a decrease of the internal quantum efficiency of the QD laser. Since QDs suppress lateral carrier diffusion, effective absorption-recombination interplay by carrier diffusion between QDs and defects may not take place (radiation hardness of QD lasers [141-143]). In this case, the concept of an ion-


150

implanted absorber for QD lasers is a disadvantage compared to reverse bias section absorbers, which have proved to work.

6 Summary

151

6 Summary and outlook In this work, we investigated the dynamic properties of InGaAs quantum dot lasers in three different configurations: edge emitting laser diodes, vertical surface emitting diodes and two-sectional mode-locked edge emitting diodes. Edge emitting laser diodes emitting at wavelengths between 1.1 µm and 1.3 µm were improved regarding their epitaxial structure and processing. Optimized laser diodes comprise 15-fold stacked QD layers, an etched-through ridge waveguide and top-side contacts suitable for fast probing and bonding. Subsequent modeling of the edge emitting lasers was done including equivalent circuit modeling of the laser chip and submount, quasi-static modeling of the active zone and a dynamic modeling of the active zone under operation. A rate equation based relaxation time model as well as a microstates model were implemented and used for the simulation of dynamic behavior of QD lasers. Simulation with a full microstates Monte-Carlo model was limited by the available computational resources. Small signal measurements, spectro-temporally resolved measurements and digital modulation measurements were performed to clarify the physical origin of dynamic properties like modulation bandwidth, damping, turn-on delay and spectral shaping. Emphasis was put on a distinction between intrinsic, quantum dot inherent effects and effects due to the device structure. The main goal of my work was the identification of these intrinsic limitations of the QD gain medium. Comparison of experimental results and modeling shows that the main limiting mechanisms are differential gain reduction due to state filling and moderate relaxation and capture time constants leading to spectral gain compression. Modulation bandwidths up to 7 GHz were achieved, with only weak dependence on the number of stacked QD layers. Eye pattern measurements with data rates between 2.5 and 12 Gb/s were performed showing symmetric, open eye traces. Bit error rate measurements were performed at 8 and 10 Gb/s data rate yielding error-free (error rate below 10-12) data modulation at a receiver power of -2 dBm at 1.3 µm emission wavelength. In order to increase the error-free transmission region (lower receiver power, lower input power etc.) of digitally modulated QD lasers at 10 Gb/s their modulation bandwidth has to be significantly increased to 12-15 GHz. No evidence for the benefits of p-doping and tunnel injection for the dynamic properties was found during our investigations. Improvement could probably be accomplished by vertical coupling of the QD stacks, the decrease of the inhomogeneous broadening of the QD ensemble, the increase of the QD density and the tailoring of the quantum well layer surrounding the quantum dots. QD VCSELs emitting at 1.1 µm wavelength were characterized regarding their modulation bandwidth in dependence on the contact layout and aperture size. From small and large signal measurements we determined the modulation bandwidth to be in the range of 1-2 GHz. The main limitations for the bandwidth are relatively small gain and differential gain of the QD gain medium, large capacitance of the QD region and the thermal limitation of the devices, leading to power and bandwidth roll-off. QD VCSELs are subjected to gain compression effects to a greater extent than multimodal edge emitting QD lasers.

6 Summary

152

QD VCSELs with small apertures are suitable for data transmission due to their single mode emission. However, small aperture QD VCSELs have shown to have a smaller RC bandwidth and modulation bandwidth due to current spreading effects inside the cavity. QD laser diodes for passive and hybrid mode-locking were processed based on edge emitting multi-stacked QD laser. A reverse bias absorber section was defined by a two-sectional contact layout. The electrical insulation between the absorber and gain section was optimized by etching and ion implantation. Definition of an absorber section by ion implantation through the facet or from the top side was not successful due to insufficient ion dose control. Devices with length between 800 µm and 8000 µm corresponding to repetition frequencies between 5 and 50 GHz were characterized comprising different absorber-gain section ratios. Stable passive mode-locking with Fourier-limited pulse widths with a typical width-to-period ratio of 10-20 % was found for reverse bias voltages in the range of -2 to -6 V. Hybrid mode-locking was achieved for 20 GHz repetition frequency, with a locking range of 100 MHz at 25 dBm input power. The pulse width was limited by the maximum reverse bias voltage, gain and absorption saturation. Shorter pulses can be achieved by stacking of more QD layers, application of larger bias voltages and adjustment of the absorber length. Future development of modulated InGaAs quantum dot devices will strongly depend on the substantial improvement of the intrinsic QD modulation properties. Guidance for epitaxial growth of faster quantum dot structures can only arise from a thorough understanding and modeling of the complete quantum dot structure. Whereas the requirements for modeling of quantum dot lasers have been clarified in the past years, no computationally feasible and complete dynamic model including crucial spectral and electronic features has been presented so far. Therefore, modeling and simulation of QD lasers are important milestones for the next years. At the same time, well-known issues like the excessive inhomogeneous broadening of self-assembled quantum dots have to be addressed to tap the full potential of zero-dimensional confinement.

7 Nomenclature

153

7 Nomenclature The table gives the most common quantities used in semiconductor laser physics, their symbol used in the text of the thesis and, if possible, their typical value for InGaAs quantum dot lasers. Symbol Quantity (typ.) Value ⋅ unit c Light speed in vacuum 82.9979 10 /m s⋅ ,e q Electronic charge -191.6022 10 C⋅

0ε Permittivity in vacuum -128.8542 10 A sV m

⋅⋅

⋅

0m Electron rest mass -319.1096 10 kg⋅ h Planck’s constant -346.6262 10 J s⋅ ⋅

, Bk k Boltzmann constant -231.3806 10 /J K⋅ k T⋅ Thermal energy at 300 K 0.0259 eV

Ba Bohr radius -115.2918 10 m⋅ a Lattice constant 0.6nm

iα Laser waveguide (internal) losses 12 5 cm−−

mα Laser cavity mirror loss 11 20 cm−− β Fraction of spontaneous emission into laser mode 510− C Capacitance 1 pF

, ,F gapE E E Energy, Fermi energy level, Energy band gap 191.6 10 1J eV−⋅ =

, ,,F e F hE E Quasi-Fermi levels for electrons, holes ,J eV , resf f Frequency, Laser resonance frequency 1 5GHz− ( , )F E T Fermi distribution

g , 'g Material gain, differential material gain 1cm− , 2cm G Modal gain 115 50cm−−

'G Differential modal gain 15 13 210 10 cm− −− Γ Optical confinement factor 4 210 10− −− γ RO damping coefficient 1-10GHz

pγ Polarization decay rate (homogeneous broad.) 31 10 GHz−

intη Internal quantum efficiency 0.6 0.8−

extη External (or total) quantum efficiency 0.4 0.6−

diffη Differential quantum (or slope) efficiency 0.5 W A⋅ , thrJ J Current, threshold current 35 50 10 A−− ⋅ , thrj j Current density, threshold current density 2100 1000 A cm− ⋅ , photκ κ Inverse photon lifetime, photon loss rate 11 11 2 10 s−− ⋅

L Laser cavity length 0.5 8mm− λ Photon wavelength 1100 1300nm−

7 Nomenclature

154

,e hm m Effective electron mass, effective hole mass 00.065 m⋅ , 00.377 m⋅

rm Reduced effective exciton mass , ,e hN N N Carrier number

, ,e hn n n Carrier density 24 3 18 310 10m cm− −=

transpn , 0n Transparency carrier density 17 310 cm−

thrn Threshold carrier density 17 310 cm− ,D AN N Donor, acceptor density 17 19 310 10 cm−−

ν Photon frequency 142.3 10 230Hz THz⋅ =

P Photon number inside laser cavity 610 p Photon density inside laser cavity 20 3 14 310 10m cm− −=

0P Equilibrium photon number inside laser cavity 0p Equilibrium photon density inside laser cavity

R Resistance 1 20− Ω

1 2,R R Laser facet reflectivity (vertical incidence) 0.3 0.95−

inhomσ Inhomogeneous broadening of QD ensemble 30meV t Time s T Absolute temperature 0 273.5K C= − °

photτ Photon lifetime 5 10 ps−

sponτ , radτ Excitonic radiative lifetime 1ns

nonradτ Excitonic non-radiative lifetime (all other recombination channels) 1ns

V Voltage 1V

pV Volume of photonic mode 15 31 10 m−⋅ gv Group velocity of light in cavity 80.9 10 m s⋅

ω Angular frequency, 2 fπ ⋅ Hz

8 Bibliography & Software

155

8 Bibliography & Software 1. Kroemer, H., A Proposed Class of Heterojunction Injection Lasers.

Proceedings of the IEEE, 1963. 51(12): p. 1782ff.

2. Alferov, Z.I., et al., Injection Properties of N-AlxGa1-XAs-P-GaAs Heterojunctions. Soviet Physics Semiconductors-USSR, 1969. 2(7): p. 843ff.

3. S. Adachi, R.B., R.P. Devaty, F. Fuchs, A. Hangleiter, W. Kulisch, Y. Kumashiro, B.K. Meyer, R. Sauer, Landolt-Börnstein - III Condensed Matter. Landolt-Börnstein. Vol. Semiconductors - Group IV Elements, IV-IV and III-V Compound. 2002: Springer.

4. Linder, K.K., et al., In(Ga)As/GaAs self-organized quantum dot light emitters grown on silicon substrates. Journal of Crystal Growth, 1999. 202: p. 1186-1189.

5. Linder, K.K., et al., Self-organized In0.4Ga0.6As quantum-dot lasers grown on Si substrates. Applied Physics Letters, 1999. 74(10): p. 1355-1357.

6. Asada, M., Gain and the threshold of three-dimensional quantum-box lasers. IEEE Journal of Quantum Electronics, 1986. QE-22: p. 1915-1921.

7. Kirstaedter, N., et al., Low-Threshold, Large T-O Injection-Laser Emission from (InGa)As Quantum Dots. Electronics Letters, 1994. 30(17): p. 1416-1417.

8. Bimberg, D., M. Grundmann, and N.N. Ledentsov, Quantum dot heterostructures. 1999, Chichester, [Eng.]; New York: John Wiley. 328 p.

9. Grundmann, M., Nano-optoelectronics : concepts, physics, and devices. Nanoscience and technology. 2002, Berlin ; New York: Springer. xvi, 442 p.

10. Bimberg, D., M. Kuntz, and M. Laemmlin, Quantum dot photonic devices for lightwave communication. Microelectronics Journal, 2005. 36(3-6): p. 175-179.

11. Ustinov, V.M., et al., 1.3 µm InAs/GaAs quantum dot lasers and VCSELs grown by molecular beam epitaxy. Journal of Crystal Growth, 2001. 227: p. 1155-1161.

12. Lott, J.A., et al., InAs-InGaAs quantum dot VCSELs on GaAs substrates emitting at 1.3 µm. Electronics Letters, 2000. 36(16): p. 1384-1385.

13. Novikov, I.I., et al., Ultrahigh gain and non-radiative recombination channels in 1.5 µm range metamorphic InAs-InGaAs quantum dot lasers on GaAs substrates. Semiconductor Science and Technology, 2005. 20(1): p. 33-37.

14. Sellin, R.L., et al., High-reliability MOCVD-grown quantum dot laser. Electronics Letters, 2002. 38(16): p. 883-884.

15. Sellin, R.L., et al., Close-to-ideal device characteristics of high-power InGaAs/GaAs quantum dot lasers. Applied Physics Letters, 2001. 78(9): p. 1207-1209.


156

16. O'Brien, D., et al., Feedback sensitivity of 1.3 µm InAs/GaAs quantum dot lasers. Electronics Letters, 2003. 39(25): p. 1819-1820.

17. Huyet, G., et al., Quantum dot semiconductor lasers with optical feedback. Physica Status Solidi a-Applied Research, 2004. 201(2): p. 345-352.

18. Varangis, P.M., et al., Low-threshold quantum dot lasers with 201 nm tuning range. Electronics Letters, 2000. 36(18): p. 1544-1545.

19. Kim, S.M., et al., High-frequency modulation characteristics of 1.3 µm InGaAs quantum dot lasers. Ieee Photonics Technology Letters, 2004. 16(2): p. 377-379.

20. Kuntz, M., et al., 10 Gbit/s data modulation using 1.3 µm InGaAs quantum dot lasers. Electronics Letters, 2005. 41(5): p. 244-245.

21. Tan, K.T., et al., High bit rate and elevated temperature data transmission using InGaAs quantum-dot lasers. IEEE Photonics Technology Letters, 2004. 16(5): p. 1415-1417.

22. Kuntz, M., et al., Direct modulation and mode locking of 1.3 µm quantum dot lasers. New Journal of Physics, 2004. 6: p. -.

23. Thompson, M.G., et al., Transform-limited optical pulses from 18 GHz monolithic modelocked quantum dot lasers operating at similar to 1.3 µm. Electronics Letters, 2004. 40(5): p. 346-347.

24. Akiyama, T., et al., Pattern-effect-free amplification and cross-gain modulation achieved by using ultrafast gain nonlinearity in quantum-dot semiconductor optical amplifiers. Physica Status Solidi B-Basic Research, 2003. 238(2): p. 301-304.

25. Mano, T., et al., Formation of InAs quantum dot arrays on GaAs (100) by self-organized anisotropic strain engineering of a (In,Ga)As superlattice template. Applied Physics Letters, 2002. 81(9): p. 1705-1707.

26. Kovsh, A.R., et al., Lasing at a wavelength close to 1.3 µm in InAs quantum-dot structures. Semiconductors, 1999. 33(8): p. 929-932.

27. Schmidt, O.G., et al., Prevention of gain saturation by multi-layer quantum dot lasers. Electronics Letters, 1996. 32(14): p. 1302-1304.

28. Alferov, Z.I., et al., An injection heterojunction laser based on arrays of vertically coupled InAs quantum dots in a GaAs matrix. Semiconductors, 1996. 30(2): p. 194-196.

29. Ledentsov, N.N. and D. Bimberg, Growth of self-organized quantum dots for optoelectronics applications: nanostructures, nanoepitaxy, defect engineering. Journal of Crystal Growth, 2003. 255(1-2): p. 68-80.

30. Nuntawong, N., et al., Effect of strain-compensation in stacked 1.3 µm InAs/GaAs quantum dot active regions grown by metalorganic chemical vapor deposition. Applied Physics Letters, 2004. 85(15): p. 3050-3052.


157

31. Deppe, D.G., H. Huang, and O.B. Shchekin, Modulation characteristics of quantum-dot lasers: The influence of p-type doping and the electronic density of states on obtaining high speed. IEEE Journal of Quantum Electronics, 2002. 38(12): p. 1587-1593.

32. Bhattacharya, P. and S. Ghosh, Tunnel injection In0.4Ga0.6As/GaAs quantum dot lasers with 15 GHz modulation bandwidth at room temperature. Applied Physics Letters, 2002. 80(19): p. 3482-3484.

33. Klopf, F., et al., InAs/GaInAs quantum dot DFB lasers emitting at 1.3 µm. Electronics Letters, 2001. 37(10): p. 634-636.

34. Hopfer, F., Oberflächenemittierende Quantenpunktlaser: Design, Technologie und Charakterisierung, in Institute of Solid State Physics. 2004, Technical University Berlin: Berlin.

35. Tsatsulnikov, A.F., et al., Photoluminescence of arrays of vertically coupled, stressed InAs quantum dots in a GaAs(100) matrix. Semiconductors, 1996. 30(10): p. 953-958.

36. Maximov, M.V., et al., Tuning quantum dot properties by activated phase separation of an InGa(Al)As alloy grown on InAs stressors. Physical Review B, 2000. 62(24): p. 16671-16680.

37. Heitz, R., et al., Excitation transfer in self-organized asymmetric quantum dot pairs. Physical Review B, 1998. 58(16): p. R10151-R10154.

38. Solomon, G.S., et al., Increased size uniformity through vertical quantum dot columns. Journal of Crystal Growth, 1997. 175: p. 707-712.

39. Shernyakov, Y.M., et al., Quantum-dot cw heterojunction injection laser operating at room temperature with an output power of 1 W. Technical Physics Letters, 1997. 23(2): p. 149-150.

40. Ustinov, V.M., et al., Low-threshold injection lasers based on vertically coupled quantum dots. Journal of Crystal Growth, 1997. 175: p. 689-695.

41. Zaitsev, S.V., et al., Radiation characteristics of injection lasers based on vertically coupled quantum dots. Superlattices and Microstructures, 1997. 21(4): p. 559-564.

42. Zaitsev, S.V., et al., Quantum-dot lasers: Principal components of the threshold current density. Semiconductors, 1997. 31(9): p. 947-949.

43. Zhukov, A.E., et al., Thermal stability of vertically coupled InAs-GaAs quantum dot arrays. Semiconductors, 1997. 31(1): p. 84-87.

44. Shernyakov, Y.M., et al., Operating characteristics and their anisotropy in a high-power laser (1.5 W, 300 K) with a quantum-dot active region. Technical Physics Letters, 1998. 24(5): p. 351-353.

45. Zhukov, A.E., et al., Injection lasers based on InGaAs quantum dots in an AlGaAs matrix. Journal of Electronic Materials, 1998. 27(3): p. 106-109.


158

46. Kovsh, A.R., et al., Quantum-dot injection heterolaser with 3.3 W output power. Technical Physics Letters, 1999. 25(6): p. 438-439.

47. Kovsh, A.R., et al., Molecular beam epitaxy (MBE) growth of composite (In,Al)As/(In,Ga)As vertically coupled quantum dots and their application in injection lasers. Journal of Crystal Growth, 1999. 202: p. 1117-1120.

48. Sellin, R.L., et al., Alternative-precursor metalorganic chemical vapor deposition of self-organized InGaAs/GaAs quantum dots and quantum-dot lasers. Applied Physics Letters, 2003. 82(6): p. 841-843.

49. Maximov, M.V., et al., Single transverse mode operation of long wavelength (similar to 1.3 µm) InAsGaAs quantum dot laser. Electronics Letters, 1999. 35(23): p. 2038-2039.

50. Park, G., et al., Room-temperature continuous-wave operation of a single-layered 1.3 µm quantum dot laser. Applied Physics Letters, 1999. 75(21): p. 3267-3269.

51. Zhukov, A.E., et al., Continuous-wave operation of long-wavelength quantum-dot diode laser on a GaAs substrate. IEEE Photonics Technology Letters, 1999. 11(11): p. 1345-1347.

52. Mikhrin, S.S., et al., A spatially single-mode laser for a range of 1.25-1.28 µm on the basis of InAs quantum dots on a GaAs substrate. Semiconductors, 2000. 34(1): p. 119-121.

53. Tsatsul'nikov, A.F., et al., 1.3 µm emission from quantum dots formed by 2 ML InAs deposition in a wide band gap (1.5-1.7 eV) InGaAlAs matrix. Compound Semiconductors 1999, 2000(166): p. 261-264.

54. Tsatsul'nikov, A.F., et al., Volmer-Weber and Stranski-Krastanov InAs-(Al,Ga)As quantum dots emitting at 1.3 µm. Journal of Applied Physics, 2000. 88(11): p. 6272-6275.

55. Ustinov, V.M., et al., Long-wavelength quantum dot lasers on GaAs substrates. Nanotechnology, 2000. 11(4): p. 397-400.

56. Ustinov, V.M., et al., High output power CW operation of a quantum dot laser. Compound Semiconductors 1999, 2000(166): p. 277-280.

57. Eliseev, P.G., et al., Ground-state emission and gain in ultralow-threshold InAs-InGaAs quantum-dot lasers. IEEE Journal of Selected Topics in Quantum Electronics, 2001. 7(2): p. 135-142.

58. Kovsh, A.R., et al., InAs/InGaAs/GaAs quantum dot lasers of 1.3 µm range with high (88%) differential efficiency. Electronics Letters, 2002. 38(19): p. 1104-1106.

59. Mikhrin, S.S., et al., High efficiency (ηD > 80%) long wavelength (λ > 1.25 µm) quantum dot diode lasers on GaAs substrates. Semiconductors, 2002. 36(11): p. 1315-1321.


159

60. Kovsh, A.R., et al., InAs/InGaAs/GaAs quantum dot lasers of 1.3 µm range with enhanced optical gain. Journal of Crystal Growth, 2003. 251(1-4): p. 729-736.

61. Kovsh, A.R., et al., High power lasers based on submonolayer InAs-GaAs quantum dots and InGaAs quantum wells. Microelectronics Journal, 2003. 34(5-8): p. 491-493.

62. Zhukov, A.E., et al., High external differential efficiency and high optical gain of long-wavelength quantum dot diode laser. Physica E-Low-Dimensional Systems & Nanostructures, 2003. 17(1-4): p. 589-592.

63. Sellers, I.R., et al., Lasing and spontaneous emission characteristics of 1.3 µm In(Ga)As quantum-dot lasers. Physica E-Low-Dimensional Systems & Nanostructures, 2005. 26(1-4): p. 382-385.

64. Ray, S.K., et al., Growth, fabrication, and operating characteristics of ultra-low threshold current density 1.3 µm quantum dot lasers. Japanese Journal of Applied Physics Part 1-Regular Papers Short Notes & Review Papers, 2005. 44(4B): p. 2520-2522.

65. Shernyakov, Y.M., et al., 1.3 µm GaAs-based laser using quantum dots obtained by activated spinodal decomposition. Electronics Letters, 1999. 35(11): p. 898-900.

66. Ustinov, V.M., et al., InAs/InGaAs quantum dot structures on GaAs substrates emitting at 1.3 µm. Applied Physics Letters, 1999. 74(19): p. 2815-2817.

67. Maximov, M.V., et al., Gain and threshold characteristics of long wavelength lasers based on InAs/GaAs quantum dots formed by activated alloy phase separation. IEEE Journal of Quantum Electronics, 2001. 37(5): p. 676-683.

68. Mathematica 5.1. 2004, Wolfram Research.

69. Sonnet. 2001, Sonnet Software Inc.

70. Microwave Office 2001. 2001, Applied Wave Research.

71. DIOS 2D Process Simulator. 1995, ISE Integrated Systems Engineering AG: Zurich.

72. Bergmann, L., Lehrbuch der Experimentalphysik - Bergmann/Schäfer. Vol. 1. 1990, Berlin, New York: De Gruyter.

73. Sze, S.M., Physics of semiconductor devices. 1981, New York: John Wiley & Sons.

74. BPM CAD. 1997, Optiwave Corp.

75. Stier, O., M. Grundmann, and D. Bimberg, Electronic and optical properties of strained quantum dots modeled by 8-band k center dot p theory. Physical Review B, 1999. 59(8): p. 5688-5701.


160

76. Grundmann, M., R. Heitz, and D. Bimberg, New approach to modeling carrier distribution in quantum dot ensembles: Gain and threshold of QD lasers and impact of phonon bottleneck. Physica E, 1998. 2(1-4): p. 725-728.

77. Grundmann, M., et al., Nature of optical transitions in self-organized InAs/GaAs quantum dots. Physical Review B, 1996. 53(16): p. 10509-10511.

78. Dery, H. and G. Eisenstein, The impact of energy band diagram and inhomogeneous broadening on the optical differential gain in nanostructure lasers. IEEE Journal of Quantum Electronics, 2005. 41(1): p. 26-35.

79. Grundmann, M., et al., Carrier dynamics in quantum dots: Modeling with master equations for the transitions between micro-states. Physica Status Solidi B-Basic Research, 1997. 203(1): p. 121-132.

80. Grundmann, M., R. Heitz, and D. Bimberg, Carrier statistics in quantum-dot lasers. Physics of the Solid State, 1998. 40(5): p. 772-774.

81. Grundmann, M. and D. Bimberg, Theory of random population for quantum dots. Physical Review B, 1997. 55(15): p. 9740-9745.

82. Sugawara, M., et al., Effect of homogeneous broadening of optical gain on lasing spectra in self-assembled InxGa1-xAs/GaAs quantum dot lasers. Physical Review B, 2000. 61(11): p. 7595-7603.

83. Deppe, D.G. and D.L. Huffaker, Quantum dimensionality, entropy, and the modulation response of quantum dot lasers. Applied Physics Letters, 2000. 77(21): p. 3325-3327.

84. Ishida, M., et al., Photon lifetime dependence of modulation efficiency and K factor in 1.3 µm self-assembled InAs/GaAs quantum-dot lasers: Impact of capture time and maximum modal gain on modulation bandwidth. Applied Physics Letters, 2004. 85(18): p. 4145-4147.

85. Chow, W.W. and S.W. Koch, Theory of semiconductor quantum-dot laser dynamics. IEEE Journal of Quantum Electronics, 2005. 41(4): p. 495-505.

86. Stier, O., Electronic and Optical Properties of Quantum Dots and Wires, in Institut für Festkörperphysik. 2001, Technische Universität Berlin: Berlin.

87. Guffarth, F., et al., Strain engineering of self-organized InAs quantum dots. Physical Review B, 2001. 6408(8): p. -.

88. Guffarth, F., et al., Electronic properties of InAs/GaAs quantum dots covered by an InxGa1-xAs quantum well. Physica Status Solidi B-Basic Research, 2001. 224(1): p. 61-65.

89. Borri, P., et al., Ultrafast carrier dynamics and dephasing in InAs quantum-dot amplifiers emitting near 1.3 µm-wavelength at room temperature. Applied Physics Letters, 2001. 79(16): p. 2633-2635.


161

90. Nielsen, T.R., P. Gartner, and F. Jahnke, Many-body theory of carrier capture and relaxation in semiconductor quantum-dot lasers. Physical Review B, 2004. 69(23): p. -.

91. Bhattacharya, P., et al., Carrier dynamics and high-speed modulation properties of tunnel injection InGaAs-GaAs quantum-dot lasers. IEEE Journal of Quantum Electronics, 2003. 39(8): p. 952-962.

92. Heitz, R., et al., Carrier capture and relaxation processes in InAs/GaAs quantum dots. Physics of Low-Dimensional Structures, 1997. 12: p. 163-171.

93. Su, H., et al., Linewidth study of InAs-InGaAs quantum dot distributed feedback lasers. IEEE Photonics Technology Letters, 2004. 16(10): p. 2206-2208.

94. Ghosh, S., S. Pradhan, and P. Bhattacharya, Dynamic characteristics of high-speed In0.4Ga0.6As/GaAs self-organized quantum dot lasers at room temperature. Applied Physics Letters, 2002. 81(16): p. 3055-3057.

95. Olshansky, R., Frequency response of 1.3 µm InGaAsP high speed semiconductor lasers. IEEE Journal of Quantum Electronics, 1987. QE-23(9): p. 1410-1418.

96. Tessler, N., R. Nagar, and G. Eisenstein, Structure Dependent Modulation Responses in Quantum-Well Lasers. IEEE Journal of Quantum Electronics, 1992. 28(10): p. 2242-2250.

97. Tessler, N. and G. Eisenstein, On Carrier Injection and Gain Dynamics in Quantum-Well Lasers. IEEE Journal of Quantum Electronics, 1993. 29(6): p. 1586-1595.

98. Su, H., et al., High external feedback resistance of laterally loss-coupled distributed feedback quantum dot semiconductor lasers. IEEE Photonics Technology Letters, 2003. 15(11): p. 1504-1506.

99. Maksimov, M.V., et al., Quantum dot injection heterolaser with ultrahigh thermal stability of the threshold current up to 50°C. Semiconductors, 1997. 31(2): p. 124-126.

100. Maximov, M.V., et al., InGaAs/GaAs quantum dot lasers with ultrahigh characteristic temperature (T0=385K) grown by metal organic chemical vapour deposition. Japanese Journal of Applied Physics Part 1-Regular Papers Short Notes & Review Papers, 1997. 36(6B): p. 4221-4223.

101. Maximov, M.V., et al., InGaAs/GaAs quantum dot lasers with ultrahigh characteristic temperature (T0=385k) grown by metal organic chemical vapor deposition. Compound Semiconductors 1996, 1997(155): p. 809-812.

102. Zhukov, A.E., et al., Injection heterolaser based on an array of vertically aligned InGaAs quantum dots in a AlGaAs matrix. Semiconductors, 1997. 31(4): p. 411-414.


162

103. Zou, Z., et al., Threshold temperature dependence of lateral-cavity quantum-dot lasers. IEEE Photonics Technology Letters, 1998. 10(12): p. 1673-1675.

104. Park, G., et al., Temperature dependence of lasing characteristics for long-wavelength (1.3 µm) GaAs-based quantum-dot lasers. IEEE Photonics Technology Letters, 1999. 11(3): p. 301-303.

105. Mukai, K., et al., High characteristic temperature of near-1.3 µm InGaAs/GaAs quantum-dot lasers at room temperature. Applied Physics Letters, 2000. 76(23): p. 3349-3351.

106. Shchekin, O.B., et al., Low-threshold, continous-wave two-stack quantum-dot laser with reduced temperature sensitivity. IEEE Photonics Technology Letters, 2000. 12(9): p. 1120-1122.

107. Shchekin, O.B., et al., Discrete energy level separation and the threshold temperature dependence of quantum dot lasers. Applied Physics Letters, 2000. 77(4): p. 466-468.

108. Pradhan, S., S. Ghosh, and P. Bhattacharya, Temperature dependent steady-state characteristics of high-performance tunnel injection quantum dot lasers. Electronics Letters, 2002. 38(23): p. 1449-1450.

109. Novikov, I.I., et al., Temperature characteristics of low-threshold high-efficiency quantum-dot lasers with the emission wavelength from 1.25 to 1.29 µm. Semiconductors, 2003. 37(10): p. 1239-1242.

110. Fathpour, S., et al., The role of Auger recombination in the temperature-dependent output characteristics (T0 = infinity) of p-doped 1.3 µm quantum dot lasers. Applied Physics Letters, 2004. 85(22): p. 5164-5166.

111. Ouyang, D., Characterization of lasers based on self-organized In(Ga)As quantum dots. 2003, Technical University Berlin: Berlin.

112. Bhattacharya, P. and S. Ghosh, Response to "Comment on 'Tunnel injection In0.4Ga0.6As/GaAs quantum dot lasers with 15 GHz modulation bandwidth at room temperature' " [Appl. Phys. Lett. 81, 2659 (2002)]. Applied Physics Letters, 2002. 81(14): p. 2661-2662.

113. Mi, Z., P. Bhattacharya, and S. Fathpour, High-speed 1.3 µm tunnel injection quantum-dot lasers. Applied Physics Letters, 2005. 86(15): p. -.

114. Otsubo, K., et al., Temperature-insensitive eye-opening under 10-Gb/s modulation of 1.3 µm p-doped quantum-dot lasers without current adjustments. Japanese Journal of Applied Physics Part 2-Letters & Express Letters, 2004. 43(8B): p. L1124-L1126.

115. Krebs, R., et al., High frequency characteristics of InAs/GaInAs quantum dot distributed feedback lasers emitting at 1.3 µm. Electronics Letters, 2001. 37(20): p. 1223-1225.


163

116. Kjebon, O., et al., 30GHz direct modulation bandwidth in detuned loaded InGaAsP DBR lasers at 1.55 mu m wavelength. Electronics Letters, 1997. 33(6): p. 488-489.

117. Lindgren, S., et al., 24-GHz modulation bandwidth and passive alignment of flip-chip mounted DFB laser diodes. Ieee Photonics Technology Letters, 1997. 9(3): p. 306-308.

118. Bach, L., et al., 22-GHz modulation bandwidth of long cavity DBR laser by using a weakly laterally coupled grating fabricated by focused ion beam lithography. Ieee Photonics Technology Letters, 2004. 16(1): p. 18-20.

119. Morton, P.A., et al., Packaged 1.55-Mu-M Dfb Laser with 25 Ghz Modulation Bandwidth. Electronics Letters, 1994. 30(24): p. 2044-2046.

120. Zhang, X., et al., 0.98-mu m multiple-quantum-well tunneling injection laser with 98-GHz intrinsic modulation bandwidth. Ieee Journal of Selected Topics in Quantum Electronics, 1997. 3(2): p. 309-314.

121. Aoki, M., et al., A 1310 nm InGaAlAs short-cavity DBR laser for 100°C, 10 Gbit/s operations with a 14 mAp-p current drive. ECOC 2005 Proceedings, 2005. 2: p. 293-294.

122. Grundmann, M., How a quantum-dot laser turns on. Applied Physics Letters, 2000. 77(10): p. 1428-1430.

123. Deppe, D.G., L.A. Graham, and D.L. Huffaker, Enhanced spontaneous emission using quantum dots and an apertured microcavity. IEEE Journal of Quantum Electronics, 1999. 35(10): p. 1502-1508.

124. Lott, J.A., et al., Vertical cavity lasers based on vertically coupled quantum dots. Electronics Letters, 1997. 33(13): p. 1150-1151.

125. Ledentsov, N.N., et al., Interconnection between gain spectrum and cavity mode in a quantum-dot vertical-cavity laser. Semiconductor Science and Technology, 1999. 14(1): p. 99-102.

126. Maleev, N.A., et al., InGaAs GaAs structures with quantum dots in vertical optical cavities for wavelengths near 1.3 µm. Semiconductors, 1999. 33(5): p. 586-589.

127. Zou, Z., et al., Ground state lasing from a quantum-dot oxide-confined vertical-cavity surface-emitting laser. Applied Physics Letters, 1999. 75(1): p. 22-24.

128. Sakharov, A.V., et al., 1.3 µm vertical microcavities with InAs/InGaAs quantum dots and devices based on them. Semiconductors, 2001. 35(7): p. 854-859.

129. Ledentsov, N., et al., Quantum dots for VCSEL applications at λ =1.3 µm. Physica E-Low-Dimensional Systems & Nanostructures, 2002. 13(2-4): p. 871-875.


164

130. Schell, M., et al., Low Jitter Single-Mode Pulse Generation by a Self-Seeded, Gain-Switched Fabry-Perot Semiconductor-Laser. Applied Physics Letters, 1994. 65(24): p. 3045-3047.

131. Schell, M., D. Huhse, and D. Bimberg, Generation of 2.5 ps Light-Pulses with 15 nm Wavelength Tunability at 1.3 µm by a Self-Seeded Gain-Switched Semiconductor-Laser. IEEE Photonics Technology Letters, 1993. 5(11): p. 1267-1269.

132. Huang, X.D., et al., Passive mode-locking in 1.3 µm two-section InAs quantum dot lasers. Applied Physics Letters, 2001. 78(19): p. 2825-2827.

133. Thompson, M.G., et al., Colliding-pulse modelocked quantum dot lasers. Electronics Letters, 2005. 41(5): p. 248-250.

134. Thompson, M.G., et al., 10GHz hybrid modelocking of monolithic InGaAs quantum dot lasers. Electronics Letters, 2003. 39(15): p. 1121-1122.

135. Kuntz, M., et al., 35 GHz mode-locking of 1.3 µm quantum dot lasers. Applied Physics Letters, 2004. 85(5): p. 843-845.

136. LabVIEW 6.1. 2001, National Instruments.

137. Kobrinsky, M., On-Chip Optical Interconnects. Intel Technology Journal, 2004. 8(2): p. 129-141.

138. Weber, A.G., et al., Generation of Single Femtosecond Pulses by Hybrid Mode-Locking of a Semiconductor-Laser. IEEE Journal of Quantum Electronics, 1992. 28(10): p. 2220-2229.

139. Yu, J., et al., Generation of 290 fs Pulses at 1.3 µm by Hybrid Mode-Locking of a Semiconductor-Laser and Optimization of the Time-Bandwidth Product. Applied Physics Letters, 1994. 65(19): p. 2395-2397.

140. Yu, J. and D. Bimberg, Suppression of Self-Pulsation for Tens of Gigahertz Optical Pulses from Passively Mode-Locked Semiconductor-Lasers. Applied Physics Letters, 1995. 67(22): p. 3245-3247.

141. Guffarth, F., et al., Radiation hardness of InGaAs/GaAs quantum dots. Applied Physics Letters, 2003. 82(12): p. 1941-1943.

142. Ribbat, C., et al., Enhanced radiation hardness of quantum dot lasers to high energy proton irradiation. Electronics Letters, 2001. 37(3): p. 174-175.

143. Sobolev, N.A., et al., Enhanced radiation hardness of InAs/GaAs quantum dot structures. Physica Status Solidi B-Basic Research, 2001. 224(1): p. 93-96.

9 Acknowledgement

165

9 Acknowledgement I am very grateful to Prof. Dieter Bimberg for giving me the opportunity to work on a fascinating topic of modern semiconductor physics, for providing excellent scientific, technical and financial resources and having a stimulating and never-tiring interest in the progress of my work. My sincerest thanks go to Prof. Nikolai N. Ledentsov for refereeing my thesis and for passionate and fruitful discussions on the dynamics of QD laser diodes. During the last years of my work I had the pleasure to collaborate with Gerrit Fiol, contributing to most of the results of this thesis by accurate, skillful and creative work, partly in the framework of his diploma thesis on the dynamic properties of QD lasers. If I ever felt privileged to be dependent on the work of so many co-workers involved in growth, processing and pre-characterization of the QD laser devices, it is due to my colleagues Matthias Lämmlin, Friedhelm Hopfer and the head of the epitaxy group of NL Nanosemiconductors, Alexey Kovsh. Virtually non of the progress reported in my thesis would have taken place without their willingness to sacrifice sweat and time2 for the growth and processing of state-of-the-art narrow ridge quantum dot lasers. In this context I express my thanks and appreciation for the invaluable labor of Oliver Schulz and Anatol Lochmann of setting up a completely new clean room facility (Center for NanoPhotonics) at the physics department of the TU Berlin. I am indebted to Sebastian “LabVIEW” Bognár for valuable help in all kinds of lab hardware control and budget issues. My gratitude is due to Sven Rodt and Konstantin Pötschke for maintenance of a fast and reliable computer network infrastructure and help in all software related tasks. I wish to thank all of my colleagues for contributing to the pleasant atmosphere of research, discussion and after-work relaxation. A large number of co-workers from other institutes and companies have contributed to my work, of which I at least want to name a few: My sincerest thanks to Dr. Niggebrügge (HHI) for facilitating crucial processing tasks using the outstanding HHI clean room infrastructure and to Dr. Colja Schubert and Vincent Marembert (HHI) for their major contribution to the measurement of eye patterns and bit error rates. I would like to thank Dr. Ronald Kaiser (HHI) and his co-workers for fruitful discussions on the mode-locking of semiconductor lasers. I am indebted to Dr. Andreas Umbach and Alexander Jacob for the efficient collaboration on the first 10 Gb/s QD laser module. The burden of my administrative duties was significantly lightened by Jinan Tso, Susanne Badawi and Ulrike Grupe, secretaries of the NanOp competence center and of the institute, respectively. 2 and a tiny bit of blood, too, due to the incompatibility of 1.95 m body length with certain clean room facilities.

9 Acknowledgement

166

My parents Ulla and Peter Kuntz have always taken great interest in my work and since ever given me the secure feeling of love and unhesitating support. And the sun will always shine on me being with Sandra (a.k.a. Dr. Brünken).

Documents

Modulated InGaAs/GaAs Quantum Dot Lasers · Modulated InGaAs/GaAs Quantum Dot Lasers vorgelegt von Diplom-Physiker Matthias Kuntz aus Berlin von der Fakultät II – Mathematik und