Micromachined Transmission Lines for Microwave Applications

Micromachined Transmission Lines for Microwave Applications

Dissertation zur Erlangung des Doktorgrades

der Fakultät für Angewandte Wissenschaften

der Albert-Ludwigs Universität Freiburg im Breisgau

Ricardo Osorio

2003

Dekan: Prof. Dr. T. Ottmann

Referenten: Prof. Dr. J. G. Korvink, Prof. Dr. J. Wilde

Datum: 28. Oktober 2003

C

ONTENTS

Contents 3

Abstract 5

Zusammenfassung 7

1 Introduction 9

1.1 High frequency requirements of modern electronic systems 10

1.2 State-of-the-art MEMS micromachining 12

1.3 State-of-the-art transmission lines and waveguides 15

1.4 Organization of the thesis 21

1.5 Major Results 21

2 Simulation 23

2.1 Maxwell’ s Equations 23

2.2 Telegrapher equation in circuit theory 33

2.3 Quasi-static Simulation and Modeling 38

2.4 Full-Wave Simulation 46

3 Technology and Fabrication 59

3.1 SU-8 as dielectric and micromachined material 59

3.2 SU-8 process recipe 64

3.3 Technology considerations 65

3.4 Technology of metallization 69

3.5 Fabrication sequence of the strip line 74

3.6 Layout 77

3.7 Fabrication results 86

4 Characterization and modeling 91

4.1 On-wafer microwave measurements 91

4.2 Line parameters from S-parameters 93

4.3 Line parameters of strip lines 94

4.4 Equivalent circuit model for the strip line 100

4.5 Strip line filters 109

5 Final remarks 111

5.1 Summary 111

5.2 Conclusion 112

5.3 Outlook 113

Appendix 115

A.1 Scattering (S)-parameter 115

References 123

Acknowledgments 129

Curriculum Vitae 131

Abbreviations and Symbols 133

5

A

BSTRACT

This thesis reports on the design, fabrication, characterization, and modeling ofmicromachined strip lines. The challenge of structuring this three-dimensionaltransmission line is solved by using the photosensitive resin SU-8 as the microma-chinable material and as the dielectric in the strip line. Additionally, electrodepo-sition is applied to reinforce conductive structures to a thickness of and tofill out deep vias. The fabrication of the strip line, which is independent ofthe substrate, is described in detail. The characterization of the strip lines is per-formed directly on-wafer with microwave coplanar probes. The S-parameters ofthe strip lines are measured with frequencies of up to the millimeter-wave range( ). Based on these measurements the transmission line properties of thestrip line are analyzed and the corresponding equivalent circuit model is alsoextracted. To the author’s best knowledge, this is the first time that the dielectricconstant and the loss tangent of SU-8 are measured in the millimeter-wave fre-quency region.

Micromachining techniques applied to microwave transmission lines were limitedto planar ones, like microstrip or coplanar lines. In this work the property ofmicromachining techniques to fabricate three-dimensional lines, such as the stripline, is demonstrated. The value of the dielectric thickness in the strip line is

. The conductors in the strip line consist of a sputtered TiW-Ni seed layerfollowed by a electrodeposited thick Cu-layer. The structuring of SU-8 isperformed by using the simplest method of IC-technology: spin-on and photoli-thography. In particular, with SU-8 excellent structures with large aspect ratioscan be fabricated. Moreover, SU-8 itself is photosensitive making an additionalprocess step superfluous. The feasibility of SU-8 as the micromachinable materialand as dielectric in strip lines is investigated. In spite of the simple processing ofSU–8, there were some problems, which are reported: poor adhesion and crack-ing. These problems are systematically solved leading in the end to an improvedSU–8 process. In this process there is almost no cracking and adhesion of SU-8 to

3µm15µm

48GHz

30µm3µm

6

copper and nickel layers is improved. The total dielectric thickness was achievedby deposition and structuring of two thick SU-8 layers.

Strip lines with strip lengths ranging between and and with stripwidth values between and are designed in order to completely char-acterize the strip lines. The transition from the strip line to the contact pads, alsoplaced on the wafer, is discussed. These contact pads, which have coplanar con-figuration and characteristic impedance, are indispensable for on-wafercharacterization of the strip lines.

The Finite Element (FE) code was programmed in order to calculate the charac-teristic impedance of the strip line by solving the Laplace equation of the electricalpotential along the line’s cross section, which is a two-dimensional domain. Thisprogram can be applied to sensitivity calculations of the characteristic impedanceon deviations related to the process and the geometrical dimensions.

The S-parameters of the fabricated strip lines are measured on-wafer with fre-quencies of up to . From the S-parameters the characteristic impedancesand the propagation constants for the strip lines are calculated and the elementsper unit length of the corresponding equivalent circuit model are extracted. For thefirst time the relative dielectric constant and loss tangent of SU-8 are measuredwith millimeter-wave frequencies. At , the relative dielectric constant ofSU-8 is and the loss tangent is . The strip line with characteristicimpedance shows an attenuation constant of at . From full-wave simulations, an amount of is assigned to the skin-effect in thecopper conductive layers, whereas corresponds to the loss tangentof the SU-8 dielectric.

15µm

0.5mm 3mm4µm 30µm

50Ω

48GHz

48GHz3.2 0.043 48.2Ω

0.58dB mm⁄ 48GHz0.2dB mm⁄

0.38dB mm⁄

7

Z

USAMMENFASSUNG

Diese Dissertation befaßt sich mit dem Entwurf, der Herstellung, der Charakteri-sierung und der Modellierung von Strip-Leitungen. Dabei werden Techniken ausder Mikrosystemtechnik eingesetzt, um der Herausforderung der dreidimensiona-len Strukturierung der Strip-Leitungen besser zu begegnen. Einerseits wurde Gal-vanik zur Verstärkung von metallischen Strukturen auf und zum Auffüllenvon vias eingesetzt, und andererseits wurde der photoempfindliche SU-8Lack, gleichzeitig, als das mikrostrukturierbares Material und als Dielektrikumder Strip-Leitung verwendet. Auf die vollständige Herstellung der Strip-Leitun-gen, welche substratunabhängig ist, wird detailliert eingegangen. Die Charakteri-sierung der Strip-Leitungen erfolgt direkt auf dem Substrat (on-wafer) mit kopla-naren, mikrowellentauglichen Testspitzen, mit denen die S-Parametern der Strip-Leitung bei Frequenzen bis zum millimeterwellen Bereich ( ) gemessenwerden. Anhand der Messungen werden die Leitungseigenschaften analysiert undschließlich ein Ersatzschaltbildmodell für die Strip-Leitung extrahiert. Laut derbisherigen Recherche des Autors, werden, zum ersten Mal, die relative Dielektri-zitätszahl und der Verlustwinkel von SU-8 im millimeterwellen Bereich gemes-sen.

Der Einsatz der Mikrosystemtechnik im Bereich der Mikrowellenleitungen hatsich bisher auf planare Leitungen, wie Microstrip- und Koplanarleitungen,beschränkt. Diese Arbeit setzt Techniken der Mikrostrukturierung bei der Herstel-lung von dreidimensionalen Mikrowellenleitungen ein, wie dies die Strip-Leitungdarstellt. Das Dielektrikum der Strip-Leitung erreicht eine nominelle Höhe von

. Die leitenden Strukturen der Strip-Leitung bestehen aus einer gesputtertenTiW-Ni Startschicht und einer auf galvanisch verstärkten Kupferschicht.Der SU-8 Lack läßt sich mit den einfachsten Mitteln der IC-Technologie struktu-rieren: Aufschleudern und Photolithographie. Das besondere dabei ist allerdings,daß damit Strukturen mit großen Aspektverhältnissen erreicht werden können.Dazu kommt, daß SU-8 selbst photoempfindlich ist und dadurch ein zusätzlicherProzeßschritt gespart wird. Der Einsatz von SU-8 als mikrostrukturierbares Mate-

3µm15µm

48GHz

30µm3µm

8

rial und als Dielektrikum bei der Herstellung von Strip-Leitungen wird untersucht.Trotz des einfachen technologischen Prozesses von SU-8, stößt man auf Schwie-rigkeiten, wie Haftungsprobleme und Risse im Lack. Diese Schwierigkeitenwerden systematisch aufgehoben, mit dem Ergebnis, daß ein ausgereifter SU-8Prozeß entsteht. Bei diesem Prozeß sind dann die Risse der SU-8 Strukturennahezu verschwunden und die Haftungseigenschaften zu galvanischer Nickel-und Kupferschichten deutlich verbessert. Die Gesamthöhe des Dielektrikumswurde durch zwei SU-8 Schichten von jeweils Dicke erreicht.

Strip-Leitungen mit Leitungslängen zwischen und , und Leitungs-breiten zwischen und werden entworfen, um die Strip-Leitung voll-ständig zu charakterisieren. Außerdem wird über den Übergang der Strip-Leitungzu den Kontaktflächen auf dem Substrat diskutiert. Diese Kontaktflächen, die einkoplanares Leitungsstück darstellt und Leitungsimpedanz aufweisen sollen,werden bei der on-wafer Messung der Strip-Leitungen benötigt. Das numerischeVerfahren der Finite Elemente (FE) wird einprogrammiert, um die Laplace-Glei-chung des elektrischen Potentials im Leitungsquerschnitt zu lösen um daraus dieLeitungsimpedanz der Strip-Leitung zu extrahieren. Das Programm kann auch beider Empfindlichkeitsanalyse der Leitungsimpedanz auf geometrischen Abwei-chungen, die mit Technologietoleranzen verbunden sind, eingesetzt werden.

Die S-parametern der hergestellten Strip-Leitungen werden direkt auf dem Sub-strat mit Frequenzen bis gemessen. Aus den S-parametern werden dieLeitunsgsimpedanzen und Ausbreitungskonstanten der Leitungen berechnet unddaraus die Elemente des Ersatzschaltbildmodells extrahiert. Ebenfalls aus diesenMikrowellenmessungen werden die elektrischen Eigenschaften von SU-8 zumersten Mal bei Frequenzen im millimeterwellen Bereich extrahiert. Eine relativeDielektrizitätszahl von 3.2 und einen Verlustwinkel von bei werden gemessen. Die Dämpfungskonstante für die Strip-Leitung mit Lei-tungsimpedanz beträgt bei . Aus full-wave Simulationenwerden dem Skin-Effekt der Kupferleitung und etwa dem Verlustwinkel des SU-8 Dielektrikums zugeordnet.

15µm

0.5mm 3mm4µm 30µm

50Ω

48GHz

0.043 48GHz50Ω

0.58dB mm⁄ 48GHz0.2dB mm⁄ 0.38dB mm⁄

9

1 I

NTRODUCTION

This work focuses on the relatively new area of microelectromechanical systems(MEMS) for radio-frequency applications, commonly known as RF-MEMS.MEMS technology can be conceived nowadays as the new revolution in micro-electronics. Similarly to monolithic integrated circuits, it enables the execution ofcomplex functions on several orders of magnitude lower than discrete devices.New with MEMS are fabrication techniques for 3D-structuring, including bulkmicromachining, surface micromachining, LIGA and wafer bonding. NowadaysMEMS technology is on the verge of revolutionizing the development of RF andwireless communication systems. In this sense RF-MEMS utilizes MEMS capa-bilities to realize new kinds of devices like micro-switches, micromachined capac-itors, micromachined inductors, micromachined antennas, micromachined trans-mission lines and micromachined resonators, which can work at high frequenciesup to the millimeter-wave region.

Considering market development, the acceleration sensor can be identified as thefirst breakthrough to come out of MEMS, and it now represents the largest singleMEMS application through its incorporation in airbag systems. Moreover it isassumed that RF-MEMS components will become the next major breakthrough toresult from MEMS. The market for RF-MEMS is constantly growing and a recentstudy [1] forecast more than US$ 1.0 billion for the total market of RF-MEMS by2007 (Figure 1.1). It represents a huge increase as an amount of less than US$ 50million was projected by the same study for 2002. Applications of RF-MEMS areexpected in the areas of mobile telephony of the third generation, collision-avoid-ance automotive radar, GPS and wireless LAN.

In order to satisfy this great demand, RF-MEMS devices must reach maturity forindustrial production. While much effort has been invested in micromachined fil-ters, switches, capacitors and inductors, investigations in transmission lines andwaveguides have until recently proceeded at a more modest pace. Coplanarwaveguides and microstrip transmission lines have been improved in terms ofattenuation by using micromachining techniques. Nevertheless the strip line,

1 Introduction

10

which is a typically three-dimensional transmission line, has not yet been investi-gated from the point of view of available microsystem technologies. This workintends to bridge this technological gap.

In the next sections, a brief review of topics related to micromachined transmis-sion lines up to the millimeter-wave region is presented. The first section dealswith the need of modern electronics for higher frequencies, the focus of researchin this area, and of the role RF-MEMS can play. The last section gives an over-view of micromachining techniques and transmission lines.

1.1 High frequency requirements of modern electronic systems

Looking back over the last decades, one can see that the 1990’s have brought adramatic change in radio frequency (RF) technology. The emerging informationage has created an increased interest and worldwide market for communicationsystems and networking of voice and data alike. This transition of RF technologyto a new era has been very exciting, resulting in a movement from large central-ized systems to smaller distributed mobile and, in many cases, hand-held systems.The digital cellular and personal communications bands around 0.9 and 1.9 GHzcomprise much of the frequency spectrum being used for cellular purposes. Future

Figure 1.1

Market development of RF-MEMS as forecasted in [1]

2002 2003 2004 2005 2006 2007

Tur

nove

r (U

S $

mil

lion

)

1200

1000

800

600

400

200

0

Year

Source: WTC (Wicht Technology Consulting)

1.1 High frequency requirements of modern electronic systems

11

personal and ground telecommunications require very low weight, small volumeand very low power. Furthermore, in order to transmit/receive the maximumamount of information, communication systems are moving up in frequency to X,K and Ka-bands (see Figure 1.2). The convergence of the Internet with wirelessaccess requires microwave techniques to provide advances to key function sys-tems of power amplification, sensitive receivers and smart antennas.

One can observe that modern electronic systems are using higher and higher fre-quencies, in part for size considerations and in part for bandwidth. Commercialand military satellites, some commercial, terrestrial, and space–borne communi-cation systems are operating in or being designed for frequency bands in the mil-limeter-wave region. To fabricate such systems, it is important to consider theavailable technology, in terms of production maturity. High frequency circuitrycan be divided into a passive and an active part. The passive part is comprised oftransmission lines, switchers, lumped inductors and capacitors, couplers, filtersand very important the circuitry package. The transistor, as a representative ofactive components, can be considered as highly developed, in terms of workingfrequency. In fact, always the performance of active components has been pursuedto higher frequencies and passive components were adapted to the new environ-ment dictated by the active devices. As transistors moved from silicon to com-pound wafers (e.g. GaAs), new factors were taken into consideration for lumpedelements and transmission line components (e.g. couplers, filters). And as operat-

Figure 1.2

Microwave frequency spectrum with associated wavelength in free-space (a) and frequency band designation according to IEEE (b).

frequency [GHz]

wavelength [m]

0.3 3 30 300

10-2 10-310-11

L S C X Ku K Ka V W

1 2 4 8 12.4 18 26 40 75 110

band designation

frequency [GHz]

a)

b)

1 Introduction

12

ing frequencies of transistors reached higher bands, investigations on coplanarlines for Monolithic Microwave IC (MMIC) gained more significance.

In the last years transistors with operating frequencies in the upper edge of the mil-limeter-wave range have been reported. The production maturity of these activedevices will dictate the available technology for next generations of modern elec-tronic systems. In microwave engineering, due to the shift from military applica-tions to those in the commercial and consumer sector, the focus has shifted fromdesign for performance to design for manufacturability. This means that minimumcost at acceptable performance has become more important than high perfor-mance without regarding the cost; having the objective of mass production for thecommercial market. In this sense, MEMS micromachining techniques will play avery important role.

1.2 State-of-the-art MEMS micromachining

Advances in the process technology for MEMS permits an extension from planartechnology towards vertical processing in order to fabricate three–dimensional(3D) structures. There are 3 predominant MEMS fabrication processes whichhave to be mentioned; bulk micromachining, surface micromachining and high-aspect-ratio-micromachining (HARM), which includes technologies such asLIGA.

1.2.1 Bulk micromachining

This involves the removal of part of the bulk substrate by using wet or dry etchingmethods. With the former, the substrate is immersed in a liquid bath of a chemicaletchant, which can be isotropic or anisotropic. As isotropic etchants etch the mate-rial at the same rate in all directions, they consequently also remove part of thematerial under the etch mask (undercutting). Particularly, the geometry of thestructure affects the isotropic etch process. The most popular isotropic etchant forsilicon is HNA, which consists of a mixture of hydrofluoric acid (HF), nitric acid(HN0

3

) and acetic acid (CH

3

COOH). Anisotropic etchants etch faster in a pre-ferred crystallographic direction. Consequently, the structures formed in the sub-strate are dependent on the crystal orientation of the substrate. Most of the aniso-tropic etchants etch much faster in the direction perpendicular to the (100) plane.

1.2 State-of-the-art MEMS micromachining

13

In the direction perpendicular to the (111) plane they etch very slowly if at all. Themost common anisotropic etchants for silicon substrates are potassium hydroxide(KOH), ethylene diamine pyrochatechol (EDP) and tetramethylammoniumhydroxide (TMAH). The use of anisotropic etchants in conjunction with highdopant levels (e.g. Boron) within the substrate enables selective etching of thesubstrate, in that high dopant levels stop the etching of KOH.

Dry etching relies on vapor phase or plasma-based etch methods using convenientreactive gases or vapors usually at high temperatures (> ). The most popu-lar method for MEMS is Reactive Ion Etching (RIE) which additionally uses radiofrequency (RF) power to activate the chemical reaction, so that the etching canoccur at much lower temperature ( ). During RIE, the gas ions areaccelerated towards the material to be etched within a plasma phase supplying theadditional energy needed for the reaction. Based on this feature RIE is not limitedby the crystal orientation of the substrate and consequently arbitrary shapes withvertical walls can be fabricated independently of the crystal plane. A furtherimprovement of RIE in terms of higher aspect ratio is Deep Reactive Ion Etching(DRIE). Its process is comprised of a high–density plasma etching, as in RIE, andthe use of a protective polymer film to achieve better aspect ratios. Etch ratesdepend on a variety of parameters like time, temperature, concentration and mate-rial to be etched, so that until now no universally accepted recipe could be found.

1.2.2 Surface micromachining

With the surface micromachining technique, in contrast to bulk micromachining,the structuring process takes place above the substrate, mainly using it as a baselayer on which to build. The process consists of the deposition of different mate-rials in the form of thin films, which can be structural or sacrificial layers. Pattern-ing of the structural layer consists of lithography and dry etching. The sacrificiallayer is then removed, in order to create either an open area or a free–standingmechanical structure made of the structural layer. Commonly used structurallayers are polysilicon, silicon nitride and aluminum, whereas silicon oxide is themost popular material used as a sacrificial layer. To achieve complex MEMSstructures more levels of structural layers can be included into the process. Nev-ertheless this increases the level of complexity and makes the fabrication moredifficult. Foundry services that offer multi-level surface micromachining are the

100°C

150° 250– °C

1 Introduction

14

Multi-User MEMS Process (MUMPS) and the Sandia Ultra-Planar Multi-LevelTechnology (SUMMiT). The success of the surface micromachining processdepends on the ability to remove completely all of the sacrificial layers so that thestructural elements can be released perfectly. In this step the phenomenon knownas stiction plays an important role. Due to capillary forces from rinsing liquids,structural elements can stick either to the substrate or to the adjacent elements, andcan then remain attached after the drying process.

1.2.3 High-aspect-ratio micromachining (HARM)

A very popular technique for HARM is the Lithographie-Galvano-Abformung(LIGA) technique. It is an important method for extraordinary high-aspect-ratiomicrostructures. With the LIGA technique a thick acrylic resist of PMMA isdeposited on a metal layer, then the resist is patterned lithographically using X-raysynchrotron radiation. After removing the exposed area of the resist, a metal moldis formed by electroplating the metal layer not covered by the resist. This moldcan be used to reproduce very finely (in the order of micrometers) defined micro-structures up to high. A limitation for the use of LIGA is the access to an X-ray synchrotron facility.

Table 1.1

Comparison of basic MEMS micromachining techniques [2].

Criterion Bulk Surface LIGA

Maximum structural thickness

Wafer thickness <

Planar geometry Wet: rectangularDRIE: unrestricted

Unrestricted Unrestricted

Minimumplanar size

Side wall feature Wet: 54.74° slope on (100) siliconDRIE: depending on dry etchant

Dry etchant dependence

Excellent

Surface and edge quality

Excellent Mostly adequate Very good

1mm

50µm 1000µm

2 depth⋅ 1µm 3µm

1.3 State-of-the-art transmission lines and waveguides

15

Mostly Bulk and surface micromachining, in contrast to the LIGA technique, havebeen used to fabricate RF-MEMS.

A very attractive alternative with which one can build more complex and largerstructures is the process known as wafer bonding, which refers to the permanentbonding of two or more micromachined wafers in order to achieve a completedevice. Wafer bonding can be classified in fusion, anodic and eutectic bonding.Fusion bonding happens when pressure is applied to very flat, clean and hydratedsurfaces, resulting in a silicon-to-silicon bond with a water by-product. After asubsequent annealing step at about the resulting bond strength reachesthe bond strength of crystalline silicon: 10 to 20 MPa. With anodic bonding anelectrostatic potential (200 to 1000 volts) is applied across a glass-to-silicon inter-face at to . The resulting bond strength is 2 to 3 MPa. In the case ofeutectic bonding an eutectic film must be deposited on one wafer, then pressureand the eutectic temperature ( for Au-Si) are applied to the two wafers in avacuum chamber. An eutectic bond is formed between the two substrates and thebond strength can achieve values of 148 MPa [2].

With the inclusion of thick resist SU-8 into the working tools for MEMS fabrica-tion, new capabilities are made possible. A more detailed treatment of SU-8 isgiven in section 3.1.


At high frequencies the electronic signal to be transmitted must be conceived asan electromagnetic wave and new concepts must be considered in order to trans-

Material properties Very well controlled Mostly adequate Very good

Integration with electronics

Demonstrated Demonstrated Difficult

Costs Low Moderate High

Published knowledge Very high High Moderate

Table 1.1 Comparison of basic MEMS micromachining techniques [2].

Criterion Bulk Surface LIGA

1000°C

200 500°C

363°C

1 Introduction

16

mit the electronic signal in the best possible way. Characteristic impedance of thetransmission line and wave propagation mode for example become importantwhen transmission lines have to be designed. Most practical wave guiding struc-tures rely on single-mode propagation, which can be Transversal-Electro-Mag-netic (TEM), Transversal-Electric (TE) or Transversal-Magnetic (TM) accordingto their wave polarization properties. Figure 1.3 gives an overview of the mostpopular transmission lines or waveguides.

The coaxial cable (Figure 1.3a) is a good representative for TEM transmissionlines. Although its fabrication as a cable means no challenge at all, its microelec-tronic fabrication can achieve such levels of difficulty, that its realization does notseem to be convenient. The rectangular version of the coaxial cable (Figure 1.3b)appears to be convenient for microelectronic fabrication using MEMS technol-ogy. It is the same case for the strip line and the shielded strip line(Figure 1.3c and d), which, as they are TEM transmission lines, seem to be goodcandidates for microelectronic fabrication in RF applications. Planar guidingstructures are the microstrip line (Figure 1.3e), the coplanar waveguide (CPW)

Figure 1.3 Cross-section of most popular transmission lines. coaxial cable (a), rectangular coaxial cable (b), strip line (c), shielded strip line (d), microstrip line (e), coplanar waveguide (f) and slot line (g).

a) b) c) d)

e) f) g)

conductor dielectric


17

(Figure 1.3f) and the slot line (Figure 1.3g). The fundamental mode of propaga-tion for this type of planar waveguide is often referred to as quasi-TEM, becauseof its similarity to pure TEM modes. These transmission lines are conceptuallysuitable for planar technology used in microelectronic fabrication. In the micros-trip line the ground metallization is made by metal deposition of substrate’s back-side, whereas the signal conductor is made by photolithography techniques.Microstrip is the most common type of planar transmission line used in micro-wave and millimeter-wave circuits, nevertheless because of vias for groundingand of dispersion phenomena (frequency dependency of line parameters) thecoplanar waveguide represents a good choice for high frequency operation.Having its three terminals on the same level, the CPW represents an uniplanartransmission line with better performance than the microstrip. When the twoground terminals of the CPW are kept at the same potential, then only the CPW-mode propagates. For this reason air bridges connecting the ground terminalsmust be included in the design.

With the availability of micromachining techniques, the next step in improvingtransmission lines concentrated on reducing dielectric and radiation losses. Theformer was addressed by removing a part of the substrate where the electromag-netic field is confined. The latter was solved with the shielding approach. Theimprovements of CPW based on MEMS techniques will be reviewed next. Thereason is that most publications deal with CPW.

Definitely MEMS techniques have been applied to transmission lines based onSilicon rather than on GaAs-substrate, in part because of the need to compensatethe lower resistivity of Si-substrates. Improvements of the performance of CPWusing MEMS techniques relied on the improvements of propagation characteris-tics. Removing part of the substrate, which forms part of the CPW, is the simpleway to reduce the attenuation constant and dispersive characteristics of lineparameters. In fact, having air rather than the lossy substrate as the dielectric, theattenuation of the CPW can be reduced considerably. Using bulk micromachiningthe substrate in-between the metal terminals can be removed, in [3] Herrick et alapplied anisotropic wet etching to remove the substrate material between the ter-minals of a finite-ground coplanar (FGC) line, when comparing the measuredattenuation constant of the micromachined FGC line with the conventional FGCa decrease of about to was determined. Herrick used ethyl-0.5dB 0.115dB mm⁄

1 Introduction

18

enediamene pyrocatechol (EDP) as anisotropic etchant, which etches selectivelyalong the crystal planes, forming the pyramidal grooves as is shown inFigure 1.4a. Another way to reduce the amount of the substrate in the wave prop-agation region is to fabricate the transmission line on a suspended thin dielectricmembrane (~ ). The dielectric membrane can consist of SiO2/Si3N4/SiO2[4], [5], of SiO2 [6] or of polymide [7]. The membrane is obtained by removingthe substrate from the backside using anisotropic wet etching (Figure 1.4b) [5] orfrom the top side using apertures on the SiO2-membrane [6]. These aperturespermit the etchant to remove the substrate material from beneath the transmissionlines, leaving only the desired metal structure encapsulated in SiO2 (Figure 1.4c).At this point the so–called microshield line has to be mentioned [8], [9], [10](Figure 1.4d). It combines the membrane approach with wafer bonding in order tofabricate a half or complete shielded line. The line geometry resembles that of acoplanar structure, which is situated on a thin dielectric membrane above a metal-lized, air filled cavity forming the half shielded version. For the complete shieldedversion a third micromachined wafer is positioned above the half shielded one. Asimilar approach was also applied to the microstrip line and reported in [11], [12]as a shielded membrane microstrip. Also the LIGA-technique was utilized in thefabrication of transmission line components as is reported in [13], Willke et al fab-ricated filters for the X-band frequency range and proposed geometries for the W-band.

The above presented micromachined transmission lines can be classified to thegroup which used only the substrate material for micromachining as opposed to anew group which incorporates organic material to fabricate transmission lines bymicromachining [14],[15], [16]. In [14] SU-8 is used to fabricate membrane sup-ported structures like in [12], but using SU-8 instead of the Si-substrate in themicromachining process (Figure 1.4f). In [15] the SU-8 replaces not only themicromachined material but also the membrane material. SU-8 is a negative pho-toresist, therefore it can be processed by simple standard photolithography. Thefabricated structures can have significant thickness with high aspect ratio.

In [16] Ponchak et al used a 20.15 thick polymide instead of the substrate asthe material to be removed from the top side. This approach is similar to the onein [3] (Figure 1.4a) but has the advantage that the process is simple and is inde-pendent of the crystallographic orientation of the used substrate. The process con-

111( )

1.5µm

µm


19

sists mainly of polymide deposition followed by a lithography step for metalliza-tion and at the end reactive ion etching (RIE) to remove the polymide not pro-tected by CPW metallization (Figure 1.4e). In Table 1.2 signal attenuation andsome parameters of selected transmission lines are listed.

Figure 1.4 Cross sections of reported micromachined transmission lines.a) Micromachined coplanar waveguide (CPW) by anisotropic Si–etching between conductor strips [3]. b) Membrane–supported CPW by back–side anisotropic etching [4], [5] and [7]. c) Partly membrane–supported CPW by front–side anisotropic etching [6]. d) Membrane–supported, shielded CPW by back–side anisotropic etching and wafer bonding [10]. e) Micromachined CPW by applying organic material [16]. f) Membrane–supported, full-shielded CPW by micromachining of organic material [14].

Silicon

<111>

GroundConductor

Signal Conductor

GroundConductor

<111>DielectricMembrane

Signal GroundGround

a) b)

open areaSiO

Silicon

2c)

<111>

<100>

<100><100>

Silicon

Signal GroundGround

Silicon

Silicon

Lower Shielding Cavity(100)

DielectricMembraned)

Signal GroundGround

Silicon

Polymide

f)

SU-8

SU-8

SU-8PolymideMembraneMetal

Signal GroundGround

e)

1 Introduction

20

Table 1.2 Comparison of reported signal attenuation with selected transmission lines. With as central conductor width and as conductor space.

Transmission lineW S Z Attenuation

Conventional FGC on Si [3]

5.5@

CPW on GaAs ( ) calculated with HFSS [17]

6.20.32@

Micromachined FGC [3] on Si ( undercut), Figure 1.4a

2.9@

CPW on SiO2-membrane [6], Figure 1.4b

~2.4@

CPW on polymide membrane, GaAs substrate [7]

~1@

CPW on Si (1 )with etched polymide interface (20 )[16], Figure 1.4e

1.3@

Microshield (Figure 1.4d), [10]

1.00.06

@

190 55 1.00.03

@

W S

µm[ ] µm[ ] Ω[ ] εεεεr,eff dB mm⁄[ ]

500 µm40 80 64

0.16560GHz

106Ωcm6 22 70

30GHz

12µm40 80 87.6

0.115 60GHz

24 30 500.4

40GHz

18 16 1150.1425GHz

Ωcmµm 10 9 106

0.27540GHz

250 25 7540GHz

10040GHz

1.4 Organization of the thesis

21

1.4 Organization of the thesis

In Chapter 2 a basic theoretical background of wave propagation in transmissionlines is given. Starting from the Maxwell equations, the Helmholtz and the Teleg-rapher equations are derived and the similarity to their derivation from circuittheory is shown. Chapter 2 also describes the numerical calculation of the charac-teristic impedance of the strip line, using a program implemented for this thesis.Full-wave calculations, obtained from a commercial simulator showing the fre-quency behavior of line parameters, are also included in Chapter 2. The completefabrication sequence of the micromachined strip line is described in detail inChapter 3. In particular, special attention is paid to the processing of the thick pho-toresist SU–8 as the dielectric in the strip line. Difficulties concerning the fabrica-tion and their solutions are documented in this chapter. Mask layouts are includedin Chapter 3. Finally, the exhaustive characterization of the strip lines based onon–wafer measurements is reported in Chapter 4. S-parameters with frequenciesof up to are measured on strip lines with different strip widths. Chapter 4shows how the S-parameters are used to extract line parameters and build anequivalent circuit model for the line. Finally, the results are discussed.

1.5 Major Results

FINITE ELEMENT PROGRAM FOR QUASI-STATIC CALCULATION

The Finite Element Method(FEM) was programmed inMathematica in order to calculatethe quasi-static potential distribu-tion and characteristic impedanceof the strip line. The program canbe applied to strip lines withnon–symmetrical cross sections, which represent a great challenge to analyticalsolutions. The program, with results, is described in chapter 2.

48GHz

1 Introduction

22

STRIP LINE WITH SU-8 AS THE DIELECTRIC

In chapter 3 the SU–8, which hasexcellent micromachinable prop-erties, was applied to the fabrica-tion of strip lines. The process,additionally also consists of elec-trodeposition of copper as theconductors in strip lines. Thecomplete process was improvedleading to fabricated SU–8 layerswhich show neither cracking nor interlayer adhesion problems between the SU–8and the copper layers. Strip lines with different strip widths and lengths were fab-ricated successfully.

MICROWAVE CHARACTERIZATION OF STRIP LINES AND SU-8

Microwave characterization ofthe strip lines was performed byon–wafer measurements. Trans-mission line models based onlumped elements were extractedfor the strip lines. The measure-ment of the dielectric constantand the loss tangent of the SU–8directly with microwave signalswas accomplished in this work,which represents a great contri-bution to the microwave charac-terization of this new micromachinable material. The results are presented inchapter 4.

MICROWAVE DIELECTRIC DATA OF SU-8

dielectric constant loss tangent

3.2 0.043@

εr δtan

10GHz

TRANSMISSION LINE MODEL OF STRIP LINE

R L

G C

2.1 Maxwell’ s Equations

23

2 Simulation

When transmission lines are involved, wave propagation phenomena should beunderstood. This chapter starts with the Maxwell equations and derivates theHelmholtz equation from them, which is important in describing wave propaga-tion in transmission lines. The Telegrapher equation which also describes the lossin the line, due to lossy conductors and dielectric, is derived using both, the Max-well equation and the elementary circuit theory. The latter is useful when anequivalent circuit model must be given for transmission lines and their wave prop-agating characteristics including loss properties must be fully described in a cir-cuit simulator environment. In this chapter, a program, which was implementedfor this thesis, is use to calculate the characteristic impedance of the strip line. Itapplies the Finite Element Method (FEM) to, first calculate the potential distribu-tion along the line’s cross-section and then from it the characteristic impedance.Some results from a commercial full-wave simulator are also presented. Theseresults show the frequency behavior of transmission line parameters, in particularthe line attenuation.


Electromagnetic-wave phenomena may be described by the 4 Maxwell equations

(2.1)

(2.2)

(2.3)

(2.4)

∇∇∇∇ E× t∂

∂B–=

∇∇∇∇ H× It∂

∂D+=

∇∇∇∇ D• ρ v=

∇∇∇∇ B• 0=

2 Simulation

24

and the material or constitutive equations

(2.5)

(2.6)

, (2.7)

where is the electric field intensity vector, is the magnetic field intensity vec-tor, is the electric flux density or electric displacement vector, is the mag-netic flux density vector, is the current density vector and is the volumecharge density. In the constitutive equations, is the electrical permittivity ordielectric constant, is the magnetic permeability and is the electric conduc-tivity of the medium where Maxwell’s equations apply.

All vectors in (2.1)-(2.7) are functions of time and have three components in Car-tesian coordinates, each of which is additionally a function of the coor-dinates:

(2.8)

with

Time Harmonic Fields

In this work we consider with time-harmonic fields, that is, fields which vary at asinusoidal frequency . In this case it is useful to apply the phasor notation

(2.9)

to represent the field quantity by its phasor form , which is ingeneral complex valued.

Since any other arbitrary time-dependent field can be represented as the superpo-sition of their harmonic Fourier components, the solution to Maxwell’s equationsfor a nonsinusoidal field can be obtained by adding up all the Fourier components

over [20]:

D εE=

B µH=

I σE=

E HD B

I ρvε

µ σ

x y z, ,( )

V x y z t, , ,( ) exV x x y z t, , ,( ) eyV y x y z t, , ,( ) ezV z x y z t, , ,( )+ +=

V E H D B I, , , , ∈

ω

V x y z t, , ,( ) V r t,( ) Re V p r( ) e jωt⋅[ ]= =

V r t,( ) V p r t,( )

V p r ω,( ) ω


25

. (2.10)

In this work we will imply phasor notation even when the subscript in isdropped. Maxwell’s equations in phasor form are given by the following equa-tions, where the common factor is suppressed

(2.11)

(2.12)

(2.13)

. (2.14)

They represent coupled first-order partial differential equations, which are diffi-cult to apply directly to wave-guiding problems. Therefore, in the next sections,the Maxwell equations will be decoupled in order to obtain second-order equa-tions: the Helmholtz and the Telegrapher equations.

2.1.1 Helmholtz Equation

in order to obtain the generalized Helmholtz equations we allow the permittivityand permeability of the medium to be a general tensor but the medium itself issource-free ( ) and current-free ( ). Then the set of Maxwell’s equa-tions (2.11)-(2.14) together with the constitutive equations reduces to

(2.15)

(2.16)

(2.17)

. (2.18)

V r t,( ) Re V p r ω,( ) e jωt ωd⋅∞–

+∞∫=

p V p

e jωt

∇∇∇∇ E× jωB–=

∇∇∇∇ H× I jωD+=

∇∇∇∇ D• ρ v=

∇∇∇∇ B• 0=

ρv 0= I 0=

∇∇∇∇ E× jωµH–=

∇∇∇∇ H× jωεE=

∇∇∇∇ εE• 0=

∇∇∇∇ µH• 0=

2 Simulation

26

In principle, for time varying fields ( ), equations (2.17) and (2.18) can beobtained from equations (2.15) and (2.16), when the divergence is applied as fol-lows:

(2.19)

. (2.20)

Therefore, applying the curl equations to and to solve the problem, we applythe divergence equations to the vector fields.

In order to derive the Helmholtz equation for the electric field vector , we mul-tiply Equation (2.15) by and then take the curl of the expression to get

. (2.21)

With (2.16) in (2.21) follows

. (2.22)

This is the generalized Helmholtz equation for the electric field. By using a similarprocedure starting with (2.16), we obtain the generalized Helmholtz equation forthe magnetic field

. (2.23)

The equations (2.22) and (2.23) can be further simplified, when we assume thatthe permittivity and permeability of the medium are constant. Applying thevector identity , the generalized Helmholtzequations reduce to

(2.24)

, (2.25)

ω 0≠

∇∇∇∇ E×( )∇• 0≡ jω µH∇•–=

∇∇∇∇ H×( )∇• 0≡ jω εE∇•=

E H

Eµ 1–

∇∇∇∇ µ 1– ∇∇∇∇ E×( )× jω∇∇∇∇ H×–=

∇∇∇∇ µ 1– ∇∇∇∇ E×( )× ω2εE=

∇∇∇∇ ε 1– ∇∇∇∇ H×( )× µω2H=

ε µ∇∇∇∇ ∇∇∇∇ E×( )× ∇∇∇∇ ∇∇∇∇ E⋅( )⋅ ∇∇∇∇ 2E–=

∇∇∇∇ 2E ω2εµE+ 0=

∇∇∇∇ 2H ω2εµH+ 0=


27

which are also simply called wave equations. These equations, together with prop-erly boundary conditions for the vector fields at the interface between differentmedia, are generally used to solve waveguiding problems.

TEM Waves

When we deal with waveguides or transmission lines we deal with several fieldconfigurations, called modes of propagation, which satisfy the Helmholtz equa-tion or in general Maxwell equations in the presence of transverse boundary con-dition of the line. Every mode possesses its own propagation characteristics: anattenuation per unit length, phase velocity and cutoff frequency. The modes forma discrete set when the structure is surrounded by a metal boundary, like in hollowwaveguides.

Different propagating modes travel at different velocities, so the signal excited bya source gets distorted. By Selecting one signal frequency, which is low enough,only one mode will propagate on the line (the dominant mode), and thus multi-mode distortion is prevented. The excitation of higher-order modes sets an upperlimit to the operating frequency of transmission lines.

Two-conductor transmission lines, like coaxial lines, have no cutoff frequency, soa signal at any frequency can propagate along the line. When the structure is alsohomogeneous and the conductor lossless, the signal is not attenuated or distorted.Then, both its electric and magnetic fields are transverse to direction of propaga-tion, and the mode is called commonly transverse electromagnetic (TEM).

Wave solution for TEM transmission lines

Since the fields of a TEM wave are both transverse to the direction of propagation,then the longitudinal components of the fields vanish everywhere. Assuming thatthe wave is propagating in the direction, then we have

and . (2.26)

The only nonzero components are transverse to the direction of propagation, andthus

z

Ez 0= Hz 0=

2 Simulation

28

and . (2.27)

For further analysis the differential operator is separated into a transversal anda longitudinal part:

. (2.28)

We apply (2.28) to the Maxwell’s curl equations (2.15) and (2.16) to obtain

(2.29)

. (2.30)

The two expressions are separated into their transverse and longitudinal parts,yielding the transverse parts

and (2.31)

and the longitudinal parts

and . (2.32)

The transverse parts are transformed to give

and , (2.33)

which are combined, yielding the wave equations

and . (2.34)

E Et= H Ht=

∇∇∇∇

∇∇∇∇ ∇∇∇∇ t ez z∂∂

+=

∇∇∇∇ t ez z∂∂

+ E× ∇∇∇∇ t E× ez z∂

∂E×+ j– ωµH= =

∇∇∇∇ t ez z∂∂

+ H× ∇∇∇∇ t H× ez z∂

∂H×+ jωεE= =

ez z∂∂

E× j– ωµH= ez z∂∂

H× jωεE=

∇∇∇∇ t E× 0= ∇∇∇∇ t H× 0=

z∂∂

E jωµez H×=z∂

∂H j– ωµez E×=

z2

2

∂∂

E ω2εµE+ 0=z2

2

∂∂

H ω2εµH+ 0=


29

The solutions are exponentials having the general form for the electric fieldvector

, (2.35)

where the first term on the right hand side denotes a wave propagating in the direction, whereas the second term represents a wave propagating in the direc-tion. and are phasor vectors, whose amplitude and phase are specified bythe boundaries at the ends of the line (generator and load). The phase constant for TEM waves is

. (2.36)

It determines the propagation characteristic of the wave. The propagation velocity with (2.36) yields the following expression for TEM mode:

. (2.37)

Its value is determined by the material parameters of the medium where the TEMwave propagates.

Another parameter of electromagnetic wave propagation is the characteristicimpedance , which is given by the quotient of the magnetic to the electric fieldintensity vector. To find , we just consider the simple case of having only a

-component and propagating in the -direction. By differentiating it with respectto , and substituting the result in the first equation of (2.31), we get

. (2.38)

With (2.36) the factor in (2.38) can be rewritten as

, (2.39)

E

E E+e jβz– E-e+ jβz+=

zz–

E+ E-β

β ω εµ=

c ω β⁄=

c1

εµ----------=

Z0Z0 E

y zz

Hxβ

ωµ-------Eye jβz–=

βωµ------- ε

µ---=

2 Simulation

30

which is the reciprocal of the intrinsic impedance

. (2.40)

In this case of loss-free wave propagation the intrinsic impedance is constant, onlydetermined by the material properties and of real value. For plane waves propa-gating in air, the characteristic impedance, popularly called the intrinsic imped-ance, is .

With (2.35) we have the dependency of the TEM wave on the coordinate. To getthe dependency from the transverse coordinates ( and ), we can take the Helm-holtz equation (2.24), which reduces to the Laplace equation for the transverseelectric field vector

(2.41)

with and .

It should be noted that in (2.41) no angular frequency appears, thus the trans-verse field configuration can be solved from electrostatic calculation.

The propagating wave in a transmission line can be found by solving of (2.41),nevertheless for TEM-waves the calculation based on electrostatic and the corre-sponding electrical potential is more elegant and simpler.

Electrostatic calculation for TEM waves

Since the transverse electrical field in (2.32) is curl-free, it can be represented bya potential field as follows

Z0µε---=

Z0 µ0 ε0⁄ 370Ω= =

zx y

∆tEtx2

2

∂

∂ Ex

y2

2

∂

∂ Ex+

x2

2

∂

∂ Ey

y2

2

∂

∂ Ey+

0= =

∆t x2

2

∂∂

y2

2

∂∂+= Et Exex Eyey+=

ω

Ψ

ψ


31

. (2.42)

Applying (2.42) in the divergence equation results in

, (2.43)

the Laplace equation for the electrical potential .

The transverse electric field of a propagating TEM-wave can be calculated in asimple way like in the static case by solving the Laplace equation (2.43). That willbe performed in section 2.3 for the strip line. The propagation property in the -direction is given by the phase constant .

2.1.2 Telegrapher Equation

The Telegrapher equation is a more general equation which treats wave propaga-tion in media which are not current free ( ), like metals. In particular, theTelegrapher equation is used to characterize wave propagation in transmissionlines, which contain lossy conductors and lossy dielectrics, due to electric currentand displacement current . For a derivation of the Telegrapher equation westart with the Maxwell equations for a source-free medium which are linear andisotropic:

(2.44)

(2.45)

(2.46)

. (2.47)

With the vector identity and the curl ofEquation (2.45) follows

. (2.48)

Et ∇ t– ψ=

∇∇∇∇ t Et⋅ ∇∇∇∇ t ∇∇∇∇– t ψ⋅( )⋅ ∇∇∇∇ t2– ψ 0= = =

ψ

zβ

σ 0≠

∂D ∂t⁄

∇∇∇∇ E× jωµH–=

∇∇∇∇ H× σE jωεE+=

∇∇∇∇ E• 0=

∇∇∇∇ H• 0=

∇∇∇∇ ∇∇∇∇ H×( )× ∇∇∇∇ ∇∇∇∇ H⋅( )⋅ ∇∇∇∇ 2H–=

∇∇∇∇ ∇∇∇∇ H⋅( )⋅ ∇∇∇∇ 2H– σ∇∇∇∇ E× jωε∇∇∇∇ E×+=

2 Simulation

32

Considering equation (2.44) in (2.48) and with (2.47) we get the Telegrapherequation for

. (2.49)

In analogous form we get the Telegrapher equation for

. (2.50)

Equations (2.49) and (2.50) are again second-order partial differential equations,which in contrast to Maxwell equations are not coupled. The solutions of theTelegrapher equation for are exponentials having the general form

, (2.51)

which represent a superposition of forward and backward propagating waves.They are characterized by the propagation constant , containing the attenuationconstant and the phase constant , in the following form

. (2.52)

The characteristic impedance of the medium, where the wave propagates, can bedetermined in an analogous manner as it was done for (2.38), when the forwardpropagating wave of (2.51) is considered and substituted in (2.44) yielding

. (2.53)

Where and are orthogonal to each other. With (2.52), we get

, (2.54)

the reciprocal of the characteristic impedance. It is complex and a function of theoperating frequency.

H

∇∇∇∇ 2H jωσµH ωεµH–=

E

∇∇∇∇ 2E jσµωE ωεµE–=

E

E E+e γz– E-e+γz+=

γα β

γ α jβ+ jωµ σ jωε+( )= =

Hγ

jωµ----------Ee γz–=

H E

αjωµ---------- σ jωε+( )

jωµ------------------------ 1

Z0------= =

2.2 Telegrapher equation in circuit theory

33

Skin depth

For the case of a good conducting media like metals we have . Then (2.52)can be expanded in series as follows

(2.55)

The skin depth represents the distance traveled by a wave into a materialuntil its amplitude decreases by the factor .


In this section the Telegrapher equation for a transmission line will be derivedusing circuit theory. Circuit theory offers the advantages of lumped elementsapproach to model physical behavior. We consider the equivalent circuit inFigure 2.1 for a small portion of the transmission line with a resistance per unitlength , a conductance per unit length , a inductance per unit length and acapacitance per unit length of the line.

Applying both Kirchhoff’s voltage and current law to the circuit in Figure 2.1, weget a system of first-order coupled differential Equation for the transmission line

(2.56)

. (2.57)

δ

σ ωε»

α jβ+ jωµσ 1 jωε2σ---------+=

jωµσ 1 jωε2σ---------+

≈

ωµσ2

----------- 1 ωε2σ-------–

jωµσ

2----------- 1 ωε

2σ-------+

+≈

ωµσ2

----------- 1 j+( ) 1 j+( )δ

----------------.≈ ≈

δ 1 α⁄≈e 2.718≅

R G LC

z∂∂V

RI Lt∂

∂I+

–=

z∂∂I

GV Ct∂

∂V+

–=

2 Simulation

34

After some algebraic manipulation we get the following decoupled second-orderdifferential equations for the transmission line of Figure 2.1

. (2.58)

These are also called the one-dimensional Telegrapher equations for the voltageand current of the transmission line. They describe one-dimensional physicalpropagation phenomena in a generalized form. Applying (2.58) in order to modelother propagation phenomena, and will have different meaning, as well as theparameters , and in some cases one or two of these parameters maybe zero. Therefore, the transmission line model represents a generalized model forpropagation phenomena [19]. Its modeling capabilities are completely exploitedin the Transmission-line-matrix Method [20], a numerical technique used for solv-ing electromagnetic field problems.

Figure 2.1 Equivalent circuit for a length of transmission line.

R dz⋅ L dz⋅

C dz⋅dz⋅V z( )

I z( )

z z dz+

I z dz+( )

V z dz+( )

dz

z2

2

∂∂ V

RGV RC GL+( )t∂

∂VLC

t2

2

∂∂ V

+ +=

z2

2

∂∂ I

RGI RC GL+( )t∂

∂ILC

t2

2

∂∂ I

+ +=

V IR G L and C, ,


35

Equivalent circuit modeling

The equivalent circuit for the transmission line can be used to model problemsinvolving different partial differential equations. To show this, equation (2.58)may be written in general as

, (2.59)

where represents either , or any other field quantity.

• With equation (2.59) becomes

, (2.60)

which is the one-dimensional Poisson equation.

• With , it follows for equation (2.59) that

, (2.61)

which has the same mathematical form as the Telegrapher equation in (2.49)and (2.50), but for one-dimension.

• With either and or and equation (2.59) becomes

, (2.62)

with being or respectively. It represents the diffusion (or heat)equation.

• Finally, with (lossless line) we get

z2

2

∂∂ Φ

RGΦ RC GL+( )t∂

∂ΦLC

t2

2

∂∂ Φ

+ +=

Φ V I

C L 0= =

z2

2

∂∂ Φ

RGΦ=

R 0=

z2

2

∂∂ Φ

GLt∂

∂ΦLC

t2

2

∂∂ Φ

+=

R 0= C 0= G 0= L 0=

z2

2

∂∂ Φ

Constt∂

∂Φ⋅=

Const GL RC

R G 0= =

2 Simulation

36

, (2.63)

the Helmholtz equation (or simply wave equation) of (2.24) and (2.25), in one-dimension. The wave velocity in (2.63) in terms of line parameters is

. (2.64)

Sinusoidal steady state solution

In phasor form equation (2.58) can be written as follows

, (2.65)

which can be simplified to

(2.66)

in order to get an expression similar to the wave equation of the transmission line.

The solution of (2.66) is again based on exponentials of the general form

, (2.67)

with

(2.68)

The first term on the right side of (2.67) represents a wave propagating in the -direction, the second term a wave propagating in the -direction. The propaga-tion constant , like in the solution for the Telegrapher equation for electromag-

z2

2

∂∂ Φ

LCt2

2

∂∂ Φ

=

c1

LC------------=

z2

2

∂∂ V

RGV RC GL+( ) jωV L– Cω2V+=

z2

2

∂∂ V

R jωL+( ) G jωC+( )V=

V z( ) V1e γ– z V2eγz+=

γ R jωL+( ) G jωC+( )=

zz–

γ


37

netic fields, is complex and consists of the attenuation constant and phase con-stant as follows

(2.69)

For a loss-less line the phase constant can be given as

(2.70)

In Figure 2.2 a wave propagating in the -direction is depicted showing the mean-ing of attenuation and phase constant.

By applying (2.67) in (2.56), it follows that

. (2.71)

From (2.71) the equation of the characteristic impedance of the transmissionline in terms of the line parameters is given as

Figure 2.2 Propagating wave with depicted propagation parameters.

αβ

γ α jβ+=

β ω2LCω2

c2------ 2π

λ------= = =

z

2 4 6 8 10

- 1

- 0.5

0

0.5

1

Propagation coordinate z

Am

plitu

de o

f E

e αz–

e j ωt βz–( )

λ 2πβ

------=

Iγ

R jωL+( )-------------------------V

G jωC+( )R jωL+( )

--------------------------V= =

Z0

2 Simulation

38

. (2.72)

It is the quotient of the series impedance per unit length to shunt admittance perunit length. It is therefore complex and dependent on frequency. For a lossless linethe characteristic impedance has a real and constant value. In terms of transmis-sion line concepts, is defined as “the input impedance of an infinitely long sec-tion of the line in question”. Since an infinite line cannot give rise to any reflectionof energy, it is in effect a “perfectly matched” line. For the lossless ( )case or at very high frequencies ( , ), (2.72) reduces to

, (2.73)

or with (2.64) in (2.73) to

, (2.74)

where the characteristic impedance depends on wave velocity and capacitanceper unit length ; this result will be used in Section 2.3.

2.3 Quasi-static Simulation and Modeling

In subsection 2.1.1 transverse electromagnetic (TEM) wave propagation was dis-cussed. The important feature of this mode propagation is that the transverse fieldconfiguration of the electric field within the transmission line can be determinedby solving the Laplace equation for the electric potential . Furthermore, thecapacitance is identical with the electrostatic capacitance of the structure, andhence, the real physical three-dimensional problem can be reduced to the simplertwo-dimensional mathematical problem of calculating the electrostatic capaci-tance of the line cross-section. This can usually be solved by the use of conformaltransformation techniques. In other cases approximate, semi-empirical, or numer-ical techniques can be used when a closed-form exact solution cannot be obtained.

Z0R jωL+( )G jωC+( )

--------------------------=

Z0

R G 0= =R jωL« G jωC«

Z0LC----=

Z01

cC-------=

cC

ΨC


39

Exact solution and empirical solution

For a nonzero strip thickness of the strip line in Figure 2.3 an exact analysis canbe carried out using conformal transformation techniques but with considerabledifficulty yielding very complicated expressions for the characteristic impedance,as can be seen in the results of Waldron [21].

, (2.75)

where is related to the geometrical parameters of the line via the followingexpressions

. (2.76)

Figure 2.3 Cross-section of the strip line with geometrical parameters.

wth

strip thickness

strip width

height of dielectric

t

w

h

t

Z059.952

εr

----------------π2---K ' 1 θ⁄( )

K 1 θ⁄( )-------------------=

θ

th---

K υ'( ) RΠ R' υ',( )+

R Π R' υ,( ) Π 1 θ2– υ',( ) K υ'( )–+( )---------------------------------------------------------------------------------------–=

wb---- K υ( ) 1 υ2 θ2⁄–( )Π υ 2 θ2⁄ υ,( )–

R Π R' υ,( ) Π 1 θ2– υ',( ) K υ'( )–+( )---------------------------------------------------------------------------------------=

Rθ2 υ2–

θ2 1–------------------ R', 1 υ2–

1 θ2–--------------- υ', 1 υ2–= = =

2 Simulation

40

and are, respectively, complete elliptic integrals of the first and third kinds,whereas is the associated complementary function to defined as

with .

The above expressions are very complex. However, Cohn [22] and Chen [23]inde-pendently developed approximate expressions which are both simple and accu-rate. These expressions are in fact identical [24] and can be written as

, (2.77)

where

(2.78)

and

. (2.79)

The accuracy of (2.77) is stated to be within 1%, when the following requirementsare fulfilled:

and (2.80)

. (2.81)

The strip lines fabricated in this work have a strip thickness of and a dielec-tric thickness of and with these parameters fulfill equation (2.81). Thelimit of the strip width in (2.80) is . In Figure 2.4 the characteristicimpedance for the strip line calculated using (2.77) is shown. The geometricalparameters used are those which have been used in strip line fabrication.

K ΠK ′ K

K ′ x( ) K x ′( )= x ′ 1 x2–=

Z01

ε------ 94.172

x w h⁄( ) 1 π⁄( ) Fln x( )+---------------------------------------------------------=

F x( ) x 1+( )x 1+

x 1–( )x 1–---------------------------=

x1

1 t h⁄–-----------------=

wh---- 0.35 1 t

h---–

≥

th--- 0.25≤

t 3µmh 30µm

w 9.45µm


41

Numerical Solution

The excellent computational resources available nowadays make numericalapproaches very convenient. Numerical methods, like the Finite Difference (FD),Finite Element (FE) or the Finite Volume (FV) Method to discretize the Laplaceequation can be programmed in a simple way and the resulting matrix equationcan be solved by using available numerical libraries. The advantage of a numericalmethod is that it is more flexible than the exact solution. For example, the exactsolution in (2.75) is restricted to a symmetrical cross section of the line. For thenon symmetrical case the whole equation has to be reviewed which in turn willcost a lot of time and effort. With the numerical approach, once the solution is pro-grammed, the result can be determined as a function of any geometrical parame-ter. Of course, the result is an approximate solution, but the accuracy depends onthe mesh and on the available computational resources. With modern resourcesgood accuracy can be achieved within a reasonable time frame.

In this work the Finite Element Method was used to calculate the electric potentialdistribution along the cross section of the line. It was programmed inMathematica [26] and in the following a brief description of the calculation pro-cedure will be given.

Figure 2.4 calculated using the approximate formula in (2.77). , .

5 10 15 20 25 30 35

20

40

60

80

100

120

140

εr 1=

3

5

10

Strip width w µm[ ]

Cha

ract

eris

tic I

mpe

danc

e Z

0

Ω[]

Z0 t 3µm=h 30µm=

ψ

2 Simulation

42

Since the calculation is restricted to the two-dimensional case the governing equa-tion (2.43) can be rewritten as

, (2.82)

where the nabla operator is used instead of the transverse operator .

In Figure 2.5 the calculation domain is shown. It is the cross section of the striplines produced in this work. The new geometrical parameter denotes the dis-tance between the vertical ground walls.

The problem that needs to be solved is a boundary–value problem with prescribedpotentials at the inner and outer conductors. The first step in the discretization ofthe governing equation is done by applying the Galerkin weighted residual [25] to(2.82) yielding

. (2.83)

represents the weighting function. Applying the Green-Gauss theorem to(2.83) one obtains the weak form of (2.83).

Figure 2.5 Cross section of the shielded strip line used for numerical calculation. New geometrical parameter, width of outer conductor , is also shown.

∇ 2ψ 0=

∇ ∇ t

wg

wth

ε

wg

wg

∇ 2ψNi Ωd

Ω∫ 0=

Ni


43

. (2.84)

The second term in (2.84) calculates the total flux at the boundaries of the element.Due to the nature of the boundary–value problem this term is equal zero. Whatremains of (2.84) is

. (2.85)

The weighting function was chosen to be sthe ame as the shape function usedto represent the electric potential . Then and are given by

and (2.86)

. (2.87)

With (2.87) in (2.85) one gets

, (2.88)

which can be written in matrix form as follows

. (2.89)

Here is the unknown vector of the potential at all nodes in the domain and isthe stiffness matrix. Each matrix element is related to the shape or weightingfunctions as follows

. (2.90)

Ni∇ ψ∇⋅ Ωd

Ω∫– Ni ψ∇ n⋅ ∂Ωd

∂Ω∫+ 0=

Ni∇ ψ∇⋅ Ωd

Ω∫ 0=

Niψ ψ ∇ψ

ψ ψkNkk∑=

ψ∇ ψ k∇ Nkk∑=

Ni∇ ψ k∇ Nkk∑⋅ Ωd

Ω∫ 0=

K ψψψψ⋅ 0=

ψψψψ KKi k,

Ki k, Ni∇ Nk∇ ΩdΩ∫=

2 Simulation

44

Since we have a boundary–value problem with prescribed potentials at somenodes, equation (2.89) can be further simplified which results in a non-zero right-hand-side.

Equation (2.89) represents a system of algebraic equations which is solved byusing built–in functions in Mathematica. The meshing of the whole computationalspace, which is the complete dielectric medium of the line, was performed by theprogram Easymesh [27] which is started from within the Mathematica program.The output data of Easymesh, which consists of the elements, their nodes andcoordinates, are read into the Mathematica program. A meshing sample for thestrip line visualized by Mathematica is shown in Figure 2.6.

Dirichlet boundary conditions were applied to the boundaries of the dielectricwhich are also the boundaries of the metal electrodes. The outer conductor has theprescribed potential and the inner conductor the prescribed potential . Thecalculated electrical potential is shown Figure 2.7.

The program also calculates the electrical energy per unit length of the linewhich is used to calculate the characteristic impedance of the strip line.

Figure 2.6 Finite Element Model of the shielded strip line using 1066 triangular elements. Strip width and thickness are and respectively, whereas a dielectric thickness of and dielec-tric width of were assumed.

Outer conductor

Inner conductor

ψ1 0=

ψ2 1=

w 20µm= t 3µm=h 30µm=

wg 98µm=

ψ1 ψ2

W


45

The electrical energy per unit length is

. (2.91)

With (2.87) in (2.91) the energy per unit length for the strip line can be calculatedfrom its stiffness matrix by using

. (2.92)

The capacitance per unit length for the strip line is related to the stored energy and applied voltage through the following expression

. (2.93)

And finally, the characteristic impedance of the line is calculated using the follow-ing expression

Figure 2.7 Electrical potential distribution along cross section of the strip line in Figure 2.6. It was computed by the FEM Mathematica program.

ψψψψ1

ψψψψ2

W12--- ε E 2 Ωd

Ω∫ 1

2--- ε ψ∇ 2 Ωd

Ω∫= =

W12---εψψψψT Kψψψψ=

CW Vappl ψ2 ψ1–=

W12---CVappl=

2 Simulation

46

, (2.94)

where is the wave propagation in air.

The characteristic impedance calculated with the FEM Mathematica program asa function of the strip width is shown in Figure 2.8, where all other parametersare kept fixed. In the same graph the comparison with the approximate expressionin (2.77) is also given.

2.4 Full-Wave Simulation

The full-wave simulation was performed with the program written and distributedby the Computer Simulation Technology (CST) GmbH [28]. The program is calledMicrowave Studio and it applies the Finite Integral (FI) Method to discretize thefollowing integral form of Maxwell’s equations.

Figure 2.8 Characteristic impedance from Finite Element Simulation of a strip line with , and . Comparison with the approximate expression (2.77) results in a deviation of about 1%.

Z0

εr

c0C---------=

c0

w

10 20 30 40

10

20

30

40

50

60

70

80

1

2

3

4

5

6

7

8

Cha

ract

eris

tic I

mpe

danc

e Z

0

Strip width w µm[ ]D

evia

tion

[%]

FEMwith (2.77)

h 30µm= wg 98µm= εr 3=


47

(2.95)

(2.96)

(2.97)

. (2.98)

In order to solve these equations numerically the whole calculation domain is splitup into small grid cells according to the meshing procedure. Equations (2.95)-(2.98) are then solved numerically on these grid cells according to the proceduredescribed in [29].

The solver tool of this software comprises four different solvers: the transientsolver, the frequency domain solver, the eigenmode solver, and the modal analysissolver. The transient solver is most suitable for simulations of transmission linesbecause from only one time domain calculation the entire broadband frequencyinformation of the device can be obtained. Moreover, the frequency dependent S-parameters are calculated from the Fourier-transformed transient signals.

The geometrical structure of the transmission line can be entered by using theStructure Modeling Tool. It offers a full parameterization of the structure whichmakes simulation very comfortable when geometrical parameters of transmissionlines are varied. The meshing procedure of the calculation domain is performed inan automatic way according to certain criteria, for example the smallest wave-length. Furthermore, adaptive mesh refinement in 3D is included in the software.

E ds⋅A∂∫° t∂

∂BdA⋅

A∫°=

H ds⋅A∂∫° t∂

∂D J+ dA⋅

A∫°=

D dA⋅V∂∫° ρ dV⋅

V∫°=

B dA⋅V∂∫° 0=

2 Simulation

48

2.4.1 Strip Line Simulation

Transient simulation was performed on the strip line to obtain the S–Parametersin the frequency range from 0 to . The material data in Table 2.1 was usedin simulations of the strip line.

In the entered structure model of the strip line, the strip width and strip length were parameterized, whereas dielectric thickness , strip thickness and were

fixed to , and respectively.

Table 2.1 Material data and their properties used in full-wave simulation with Microwave Studio.

Material Conductivity

Copper 1 - 1

Nickel 1 - 1

SU-8 - 3 and 4 0.01-0.05 1

Silicon - 11.9 - 1

Figure 2.9 Structure model of the strip line in Microwave Studio, where the dielectric’s visibility is turned-off. It shows the bounding box of the simulation domain and the reduced simulated region (meshed part) due symmetry of the line.

50GHz

εεεεr δδδδtan µµµµr

5.8E7 S/m

1.39E7 S/m

wl h wg

30µm 3µm 98µm


49

In Figure 2.9 the entered structure model of the strip line within Microwave Studiois shown. The visibility of the dielectric material is turned off to make the 3Dstructure more visible. The metal material chosen in this case is copper and thestrip width is . The whole structure is surrounded by air( ) and the boundary conditions of the bounding box were deter-mined by selecting the transversal electric intensity vector in such a way that itvanishes ( ).

The symmetry property of the strip line offers the possibility of reducing the needfor computational resources. By defining two symmetry planes, on which thetransversal magnetic intensity vector vanishes ( ), only a quarter of thestrip line’s cross-section was taken into account. In Figure 2.9 this meshed part isalso shown.

The transient simulation was performed and as a result one also obtains theS–parameters of the strip line in the frequency domain. The S-parameters (seeappendix A.1) are used to characterize devices at microwave frequencies by mea-suring the reflection and transmission coefficients at their ports. Here we use themto compute the characteristic impedance and propagation constant of the lines ina post processing step. The detailed calculation is discussed in section 4.2, wherethe manufactured strip lines are characterized by the measured S–parameters.

Characteristic Impedance

Strip lines with strip width of , and were simulated, whilea dielectric thickness of and a strip thickness of were kept the samefor all strip lines. The metal layers were assumed to be copper whereas the dielec-tric material was assumed to be lossless ( ) SU-8 with a dielectric con-stant of 3.

The characteristic impedance of the three strip lines are shown in Figure 2.10. Athigh frequencies tends towards the constant value , only depen-dent on the capacitance and inductance p.u.l. of the line.

w 20µm=εr 1 µr, 1= =

Et 0=

Ht 0=

w 5µm 15µm 32µmh 30µm 3µm

δtan 0=εr

Z0 Z0 L C⁄=C L

2 Simulation

50

In Table 2.2 the values of the characteristic impedance calculated from full-wavesimulations are compared with the results obtained from Quasi-static calculationsof the previous subsection.

Attenuation

In general, the electrical signal propagating in the transmission line is attenuateddue to the fact that the metal conductors are not infinitely conductive ( ) andthe dielectric is lossy.

Figure 2.10 Characteristic impedance of the strip line, calculated from full-wave simulations with Microwave Studio.

Table 2.2 Characteristic impedance from full-wave simulations compared with Quasi-static calculations from previous subsection. Strip line dimen-sions (in ): , and .

Strip width in Microwave Studio FEM Equation(2.76)

5 70.9 71.0 71.0

15 47.2 47.2 47.8

32 30.5 30.5 30.8

0 10 20 30 40 50

20

30

40

50

60

70

80

90

Cha

ract

eris

tic I

mpe

danc

e Z

0 [

]Ω

Frequency [GHz]

w 5µm=

w 15µm=

w 32µm=

Z0

µm h 30= t 3= wg 98=

µµµµm

σ ∞→


51

At microwave frequencies the skin–effect must be considered when metal relatedloss is described. 97% of the current density flowing through the metal is concen-trated within a thickness three times the skin–depth.

The skin-depth is defined as follows

. (2.99)

In Table 2.3 the calculated skin-depths for copper and nickel are listed.

The metal thickness used in the strip lines is , ensuring that the skindepth is much smaller than the metal thickness and that the skin effect dominateswithin the considered frequency range. In that case, the conductor loss can bedescribed by the surface resistance

. (2.100)

With (2.99) in (2.100) the surface resistance can be rewritten in terms of frequencyand conductivity, yielding

. (2.101)

It can be observed that it increases with the square root of the frequency and thatit is inversely proportional to the square root of the conductivity of the metal.

S-parameters were simulated for three different strip widths and two differentmetals of strip lines. The attenuation constants which were extracted from simu-lated S-parameters are shown in Figure 2.11.

Table 2.3 Skin depth for copper and nickel.

Frequency Copper Nickel

δ 1

πfµσ-----------------=

δ

20GHz 0.47µm 0.95µm

50GHz 0.29µm 0.6µm

t 3µm=

Rs1

σδ------=

Rsµω2σ-------=

w

2 Simulation

52

As expected from (2.101), with increasing strip width , the attenuation constant of the strip line decreases since the total cross-sectional area for the current den-

sity also increases, regardless of the actual skin-depth. The attenuation for the striplines made of nickel is nearly twice that of ones made of copper since the squareroot of their conductivities also yields the same factor ( ).

In a subsequent set of simulations the metal was assumed to be a PEC (perfectelectrical conductor) with and the dielectric to be lossy with the loss tan-gent . In this case, only the loss related to the dielectric material willappear in the attenuation constant. Three simulations for a strip width of were performed with three loss tangents: , and . Again, the attenu-ation constants were extracted from the simulated S-parameters, which aredepicted in Figure 2.12.

The dependency of the dielectric loss with respect to the frequency and loss tan-gent was described in [30] by using the following analytical expression

Figure 2.11 Attenuation constants of the strip line due to skin-effect for different strip widths and metals. Results from full-wave simulations (Microwave Studio).

10 20 30 40 50 60

0.1

0.2

0.3

0.4

0.5

0.6

Frequency [GHz]

Ni

Cu

w 5µm=

w 15µm=

w 32µm=

Atte

nuat

ion

[]

αd

Bm

m⁄

w

wα

σCu σNi⁄ 2.04=

σ ∞→δtan 0≠

15µm0.01 0.02 0.04


53

, (2.102)

where is the free wave velocity. It shows that the dielectric loss is directly pro-portional to the frequency and the loss tangent, which can also be observed inFigure 2.12. Furthermore, the dielectric loss obtained from full-wave simulationsand calculated with (2.102) is nearly the same, as can be observed in Table 2.4.

Figure 2.12 From full-wave simulations, the calculated attenuation constant of a strip line, due to dielectric loss, for different . Strip width is

.

Table 2.4 Dielectric loss in at , calculated analytically and from full-wave simulations.

from Microwave Studio from equation (2.102)

0.078 0.078

0.157 0.157

0.320 0.315

10 20 30 40 50 60

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Frequency [GHz]

Atte

nuat

ion

[]

αd

Bm

m⁄

δtan 0.04=

0.02

0.01

δtanw 15µm=

αd 27.3εr f δtan

c0------------------------=

c0

dB mm⁄ 50GHz

δδδδtan

0.01

0.02

0.04

2 Simulation

54

Finally, one simulation was performed for a strip line having both dielectric andconductor loss. For this, copper was chosen as the metal, and a value of waschosen for the loss tangent of the dielectric. As expected, the resulting attenuationconstant was the same as the addition of the independently calculated attenuation,due to both lossy dielectric and skin-effect (Figure 2.13).

2.4.2 Contact pad

On-wafer measurements to characterize the manufactured strip lines were neces-sary therefore, the design of the contact pads as interface between the strip line andmicrowave probes had to be taken into consideration. The tip of the designatedmicrowave probes has a coplanar configuration with 3 contacts pads and a contactpitch of . For this reason, the contact pads on the wafer also have to be ofcoplanar configuration. Furthermore, when they were designed, the geometryparameters were chosen to match the contact pitch and the port impedance of of the microwave probe. On the other side a smooth transition to the strip line hadto be ensured. In Section 3.3 two types of transitions from the strip line to the con-tact pads were discussed and in the end, the one shown in Figure 2.14 was chosen.By turning-off the visibility of the dielectric in Figure 2.14b, the three-dimen-

Figure 2.13 Attenuation constant calculated from full-wave simulations for a strip line having both lossy dielectric ( ) and loss due to skin-effect.

0.02

10 20 30 40 50 60

0.1

0.2

0.3

0.4

0.5

Frequency [GHz]

Atte

nuat

ion

[]

αd

Bm

m⁄

both effects

skin-effect

dielectric loss

δtan 0.02=

100µm

50Ω


55

sional illustration of the contact pads and their transition to the strip line can bemore easily recognized.

The geometrical dimensions of the contact pads are shown in Figure 2.15 whichincludes a top and a front view. The coplanar configuration can be readily recog-nized containing two ground electrodes and one signal electrode which is themiddle electrode. The gap between the two ground electrodes was fixed at so that it also matches , the total width of the strip line. In this way a smoothtransition for the ground electrode is ensured. More critical is the transition fromthe signal electrode of the strip line to the signal pad of the contact pads. There-fore, in order to avoid any disturbance of the measurement signals, the width of the signal pad (about ) was first reduced to and then to the width

of the strip line, e.g. . The transition takes place in a length of which is electrically short compared to the wavelengths, which also come intoconsideration. Finally, the pitch specification from the microwave probeis fulfilled.

Figure 2.14 Contact pads and strip line schematically depicted. In a) both dielec-tric and metal parts are visible, in b) the visibility of the dielectric is turned off.

a)

b)

98µmwg

wcp50µm 30µm

w 15µm 20µm

100µm

2 Simulation

56

The signal pad width and the dielectric constant of SU-8 are the parameterswhich have to be considered when the characteristic impedance of the contactpads are adjusted to the port impedance of the measurement system. Simu-lations with Microwave Studio were carried out in order to find the best value of

to attain the . Due to the fact that the of SU-8 found in literature,ranges between 3 and 4 these values were also considered for the optimization ofthe signal pad width . The coplanar line shown in Figure 2.16, which consti-tutes longer contact pads, was used for S-parameter simulations and consecutiveimpedance calculations. Part of the silicon substrate wafer is also shown whichwas also taken into consideration in the simulation.

The simulation results are listed in Table 2.5. The characteristic impedance of thecontact pads depending on the ground slot is given for a dielectric constant of 3 and 4. A ground slot of was found to be the best choice in order to geta value near when any of the dielectric constants (3 or 4) applies for

Figure 2.15 Geometrical dimensions of the contact pads, which are used in on-wafer measurements of the strip line. Top view and front view are shown.

126126 wcp

50

100

98

20

stri

p lin

eco

ntac

t pad

s

s

signal groundground

100µm pitch100µm pitch

t

h

top view

front view

wcp

50Ω

wcp 50Ω εr

wcp

s εr24µm

50Ω εr


57

SU–8. This value was used in the design for the fabrication of the contact pads,being part of the strip lines for on-wafer measurements.

From the simulated S-parameters the reflection coefficient for a stripline with contact pads is shown in Figure 2.17. The signal pad width is and the strip line width is , whereas an of 3 for the dielectric wasassumed. Lossless material (PEC for metal and for the dielectric) wasalso assumed in order to restrict the amount of the reflection coefficient only totransition effects between contact pads and strip lines. From Figure 2.17 a reflec-tion coefficient better than can be observed.

Figure 2.16 Longer contact pads, representing a coplanar line, which were used for the simulation with Microwave Studio and the calculation of the characteristic impedance.

Table 2.5 Simulated characteristic impedance of longer contact pads shown in Figure 2.16. Values are listed as a function of the ground slot and the dielectric constant of SU8.

Ground slot 18 21 24 27 30

in for 50.6 53.2 53.5 55 56

in for 46 47.5 48.7 50.2 51.1

SU-8

Metal

Substrate

s

s µµµµm[ ]

Z0 Ω[ ] εεεεr 3=

Z0 Ω[ ] εεεεr 4=

S11 500mms 24µm=

w 15µm= εrδtan 0=

24– dB

2 Simulation

58

Figure 2.17 Simulated reflection coefficient for a strip line with contact pads. better than can be achieved for the whole frequency

range.

10 20 30 40 50

-40

-30

-20

-10

0

Frequency [GHz]

Ref

lect

ion

coef

fici

ent

S 11d

B[

]

S11S11 24– dB

3.1 SU-8 as dielectric and micromachined material

59

3 Technology and Fabrication

The SU-8 as the dielectric and as a versatile micromachinable material is intro-duced and its complete process recipe is included. Technology considerationsconcerning strip line fabrication are discussed.They address metallization layersand the transition from the strip line to the contact pads. These transitions are alsoapplicable as an interface between the strip line and the coplanar line. The com-plete fabrication sequence of the strip line is then given. After that mask layout isdescribed. It includes the design of various test structures and strip lines, whichare used for characterization purposes. Finally, the fabricated strip lines are shownand discussed.


Some of the requirements for the dielectric material to be used in the strip line’sfabrication are that its deposition process should be as simple as possible and thatit should also be micromachinable by simple process steps. Nowadays, a largenumber of organic dielectric materials is available which can be spin-coated ontothe wafer. Benzocyclobutene (BCB) is one of these materials which is very pop-ular as an interlayer dielectric, however, it is not used in micromachiningapproaches. As opposed to this, SU-8 is a very promising micromachining mate-rial which as the same time has not yet been characterized in the microwaveregion. In this work, we will use SU–8 as the dielectric and micromachined mate-rial in the strip line’s fabrication.


60

3.1.1 SU-8 for micromachining

SU-8 is the name of an epoxy-based negative photoresist originally developed[31] and patented [32] by IBM-Watson Research Center (Yorktown Height-USA)in 1998. It consists of three basic components:

• The epoxy EPON SU8 (Shell Chemicals).

• The organic solvent gamma-Butyrolactone (GBL).

• The photoinitiator taken from the family of the triarylium-sulfonium salts.

For MEMS-Applications, where large aspect ratios are also required, one attrac-tive feature of SU-8 is the fact that, using standard UV-lithography, layer thick-ness of about with aspect ratios up to 25 can be achieved. The fact that dep-osition can be accomplished by spin-coating just like a conventional resist hasincreased the popularity of SU-8 in low-cost MEMS applications [33]-[42]. It rap-idly became very popular in MEMS applications because of the outstanding qual-ity of the fabricated vertical structures and also of its excellent mechanical andchemical properties. In Figure 3.1 the reported papers related to SU-8 in MEMSare depicted for the last 6 years. One can easily see the growing tendency.

The following companies supply SU-8:

Figure 3.1

Reported papers related to SU-8 in MEMS.

2mm

0

5

10

15

20

200220012000199919981997

Source: Web of Science

Year of publication

Num

ber

of p

ublis

hed

pape

rs


61

• MicroChem Inc. (www.microchem.com) and

• SOTEC MICROSYSTEM (www.somisys.ch)

The SU–8 used in this work was purchased from MicroChem. In particular theseries SU–8–2000 was used. It consists of the faster drying solvent cyclopentatoneinstead of GBL. According to the manufacturer’s specifications, improved coat-ing properties are expected when using SU–8–2000.

3.1.2 Spin-curve

SU–8 is delivered with different viscosities depending on the desired thickness.For a particular viscosity the achieved thickness plotted as a function of the spinspeed is called the spin–curve. SU–8–2010 from MicroChem used in this workhas a viscosity corresponding to a nominal thickness of at a nominal spinspeed of . However, it is recommended to measure the spin curve of thedelivered SU-8 again.

For this purpose 6 wafers, each with 4 inch diameter, were processed. The processsequence is detailed in Table 3.1. First, they were cleaned in acetone, isopropanol,and DI-water before they were spin-coated. Approximately of SU–8–2010was delivered statically onto each wafer which is sufficient to completely coverthe wafer. Using the Suss Spincoat CT62 each wafer was spun at a different speed

Table 3.1

Process parameters applied for measuring spin–curve of SU-8-2010.

Process step Process parameters

SU-8 dispense

Spread acc. and @

Spin acc. and @ to

Softbake @ and @

Expose

Post Exposure Bake @ and @

Develop SU-8 developer and isopropanol

10µm3000rpm

4ml

100rpm s⁄ 5s 500rpm

300rpm s⁄ 30s 1000 2250rpm

60s 65°C 120s 95°C

230mJ cm2⁄

60s 65°C 120s 95°C

180s 120s

4ml


62

in order to obtain different film thicknesses. Prior to exposure the wafers werethen baked on a BLE hot plate with the cover closed for the purpose of completeevaporation of the solvent (Sofbake).The SU-8 films were then patterned by pho-tolithography using the Karl Suss MA6/BA6 mask-aligner with UV illuminationand a photomask containing the patterns. Post exposure bake (PEB), again on theclosed BLE hot plate, was then performed for ultimate crosslinking of the resist.The wafers were then developed by immerging them in SU-8 developer and iso-propanol.

* outlier, will be not considered.

The Tencor P-11 profilometer was used for measuring the thickness of the result-ing SU-8 film on each wafer. To get a representative mean value of film thickness,8 measurement points, uniformly distributed on the wafers, were chosen. Themeasured thicknesses, the mean values, and deviations are listed in Table 3.2. InFigure 3.2 the mean values of the thicknesses versus spin–speed are depicted. Thespin–curve contains error–bars denoting measured minimum and maximum val-ues.

Table 3.2

Thickness of spun SU-8-2010 films for extracting spin–curve.

spin speed [rpm]

Film thickness in at measurement point mean value [ ]

stand. dev. [ ]1 2 3 4 5 6 7 8

1000 15.41 15.78 15.63 15.47 15.56 15.70 15.62 15.57 15.59 0.11

1250 13.48 17.06* 12.84 12.60 12.17 12.22 12.44 12.71 12.64 0.41

1500 10.86 11.11 10.51 10.43 11.77 10.64 11.05 10.88 10.91 0.40

1750 8.79 9.07 9.50 10.06 10.08 10.13 9.55 9.07 9.53 0.49

2000 7.92 8.20 8.85 9.20 9.50 8.48 8.14 7.93 8.53 0.56

2250 8.10 7.73 8.11 7.80 7.34 8.16 7.50 8.05 7.85 0.29

µm

µm µm


63

3.1.3 SU-8 dielectric in microwave applications

SU-8 has aroused great interest in the microwave community. Thorpe et al [43]used SU-8 as dielectric material for a microstrip transmission line. In his paper theattenuation and phase constant were measured in the range from 20 to .Unfortunately, no specifications have been made as to the contributions to thetotal attenuation through conductor and dielectric loss, although the dielectric lossin the microwave range is an important parameter. Thorpe reported a value of 4for the dielectric constant of SU–8. In another contribution Arscott et al [44]used terahertz time–domain spectroscopy to make measurements of the refractiveindex and the attenuation constant of SU-8 films. They reported 1.7 for ,which is equivalent to a dielectric constant of 3. Their reported value of

for the loss tangent at was corrected to 0.14 in a comment[45] by Lucyszyn. At the time of this work no specification about the attenuationconstant of SU-8 extracted directly from microwave measurements could befound. Obviously one needs to include such measurements in the treatment of thiswork (Chapter 4).

Besides the application of SU-8 as a substrate material other applications wereshown such as micromachinable packaging material for a microwave membrane

Figure 3.2

The experimentally determined spin-curve of MicroChem SU–8–2010. Each sample point represents 8 measurements.

1000 1200 1400 1600 1800 2000 2200 2400

2.5

5

7.5

10

12.5

15

17.5

20

Spin peed [rpm]

Film

thic

knes

s [µ

m]

40GHz

εr

n α nεr

6.3 10 6–× δtan 1THz


64

resonator [46]. In [47] SU-8 is used for the fabrication of membrane-supportedcoplanar waveguides, showing measurements with frequencies of up to the milli-meter-wave region. Hesler et al [48] demonstrated the advantageous applicationof SU-8 in the fabrication of micromachined horn antennas for the submillimeter-wave region.

3.2 SU-8 process recipe

Although processing of SU–8 may lead to satisfactory results even for “begin-ners”, the user has to optimize the process in order to get structures of best qualityor to overcome certain problems. These problems include adhesion to other mate-rials and cracks in the structured layer. To overcome these difficulties the processof SU–8–2010 for layer thickness was optimized. In the end, structuredSU–8 layers with very good adhesion to copper were achieved showing almost nocracking. The complete lithography process of SU–8 for layers is describednext.

P1 Coating of SU–8–2010.

P1.1 Static dispense of SU–8.

P1.2 Spread @ . acc.

P2 Wait longer than .

P3 Softbake: @ , @ .

P4 Edge bead removal with acetone @ ( ).


P6 Expose with light source ( ). Soft–contact.

P7 Post exposure bake: @ , @ .


15µm

15µm

5ml

5s 500rpm 100rpm s⁄

12h

60s 65°C 120s 95°C

500rpm 60s

10min

19s 10mW cm2⁄ 190mJ cm2⁄=

60s 65°C 120s 95°C

2h

3.3 Technology considerations

65

P9 Develop with SU–8 developer.

P10Rinse with isopropanol ( ) and spin dry.


When thinking about how to fabricate a shielded strip line, we first have to con-sider its principal structure. In Figure 3.3 one can see that the shielded strip linesimply consists of a signal metal layer completely embedded in a dielectric mate-rial which is itself surrounded by ground metal.

From this we conclude that the shielded strip line simply consists of alternatelayers of metal and dielectric material. Furthermore, only 3 masks are neededusing IC-technology as is shown in Figure 3.4, one for the ground metal, thesecond for the dielectric, and the third for the signal metal layer.

Nevertheless, more masks are needed when, for example, the transmission linesare to be connected to some devices on the wafer or, as in our case, it has to beconnected to contact pads for on-wafer measurements. In both cases some vias inthe dielectric layers have to be considered in the design with the consequence thateach dielectric and metal layer needs its own mask, which makes altogether 5masks.

Figure 3.3 Simple shielded strip line

180s

120s

signal metal

ground metal

dielectric


66

3.3.1 Transition to contact pads.

In this work two concepts for the transition of the strip line to the contact padswere pursued, considering their vertical positions:

• Contact pads on the same vertical position as the signal metal layer(Transition A).

• Contact pads on the same vertical position as the top ground metal(Transition B).

Transition A

In Figure 3.5 a detailed description of the fabrication process of Transition A isshown. A cross-section of both the strip line and the contact pad is shown. A three-dimensional representation is also given.

The bottom ground metal consists of a sputtered and electroplated layer with anopen area in the place where the signal pad of the contact pads is designated (a).The reason of this open area in the ground metal is to avoid a parasitic capacitancebetween signal pad and ground metal. The first SU-8 layer is then deposited on the

Figure 3.4 Fabrication steps of a shielded strip line using 3 masks.

Bottom ground metal

Lower dielectric layer

Signal metal

Upper dielectric layer

Top ground metal

Substrate

Substrate

Substrate

Substrate

Substrate

mask No. 1

mask No. 2

mask No. 3


67

whole wafer on which some vias are opened by photolithography (b). The bottomground metal is then electroplated through the SU-8 vias to achieve a full pla-narization of the wafer (c). With this step one half of strip line’s side walls is real-ized and connection of the ground pads to the ground metal is ensured. With thesecond metallization the contact pads, the signal metal of the strip line, and itstransition are fabricated (d). The second SU-8 layer is needed only for the stripline (e) and finally, the metallization of the top ground metal of the strip line isperformed (f).

Transition B

We will now consider the fabrication sequence of the strip line with transition B.The description of this sequence is depicted in Figure 3.6. In this case, open areasin the bottom ground metal are also provided (a) and vias in the first SU-8 layerfollowed by wafer planarization are also ensured. The difference to Transition A

Figure 3.5 Schematic description of the strip line fabrication process with Transition A to the contact pads. Cross sections are not to scale.

bottom ground metal

lower SU-8 layer

upper SU-8 layer

top ground metal

signal metal

planarization

cross section of linecross section of contact pad

(a)

(b)

(c)

(d)

(e)

(f)

3-Dprocess step


68

is that after signal metallization (e) and deposition of the second SU-8 layer (f),some vias are designated to perform a second planarization (f). At this stage, con-nections are provided for both ground and signal metal to the last metallization. Inthe last step metallization of the top ground metal of the strip line as well as thecontact pads is performed (g).

Transition A between the strip line and contact pads was preferred because itenables a vias–free transition from the signal pad of the contact pads to the signalmetal of the strip line. Hence, with Transition A, in contrast to Transition B, lessdisturbance of signal propagation is ensured.

Figure 3.6 Schematic description of the strip line fabrication process with Transition B to the contact pads. Cross sections are not to scale.

bottom ground metal

lower SU-8 layer

upper SU-8 layer

2nd planarization

signal metal

1st planarization

cross section of linecross section of contact pad

top ground metal

(a)

(b)

(c)

(d)

(e)

(f)

(g)

3-Dprocess step

3.4 Technology of metallization

69

Nevertheless, in the fabrication of the top ground metal with Transition A onemain difficulty will be encountered, namely the metallization of the side walls ofthe upper SU-8 layer. The thickness of this SU-8 layer represents a problem forthe subsequent photolithography step in building the top ground metal, especiallywith regard to the resist material and its exposure parameters (see 3.4.3).

With a thickness of for the SU-8 layer a trade-off was found between mod-erate thickness and achievable impedance of the strip lines. In fact with total dielectric thickness and a conductor width ranging from 5 to animpedance from 70 to can be obtained.


The metallization used in building the strip line is performed by the electroplatingof sputtered seed layers. Two concepts of metallization were applied in the fabri-cation process of the strip line. They are depicted in Figure 3.7.

Figure 3.7 Photolithography processes for fabrication of electroplated metal lay-ers. See text for explanation of their use.

15µm30µm

h w 30µm30Ω

a)

b)

c)

d)

e)

sputtering of seed layer

deposition and exposure of resist

development of resist

etching of seed layer electroplating

stripping of resist andelectroplating

stripping of resist andetch of seed layer

metallization #1 metallization #2, #3


70

One concept (left) consists of electroplating the seed layer when it is already struc-tured by a photolithography and etching process. With the other concept (right)the seed layer is electroplated through vias in the resist, which afterwards isstripped. The open seed layer (not electroplated) is subsequently etched by usinga selective etchant.

The former was used for the bottom ground metallization and the latter for boththe signal and the top ground metallization. Due to the fact that the signal and topground metallization are isolated metal structures on the wafer, the concept ofetching the seed layer after the electroplating step is indispensable. The carefullyselection of convenient materials for the seed and electroplating material as wellas the selective etchant. represents one difficulty.

Several tests were performed in order to find out the best material and etchant sys-tem. A very important criterion which was also considered was the adhesion ofSU-8 to metallic materials.

In this thesis the adhesion of SU–8 to copper and nickel was found to be best incontrast to gold, showing poor adhesion to SU–8.

3.4.1 Seed layer

The seed layers in all three metallizations involved in the strip line fabricationhave the same composition: titan-tungsten (TiW) and nickel (Ni), which are sput-tered subsequently by Physical-Vapor-Deposition (PVD) using TiW andNi targets respectively.

The TiW layer is sputtered to a thickness of from a target with 90% tung-sten by RF-power. Deposition time is about and . The Ni layer is sputtered with DC-power for about . Table 3.3 summa-rizes seed layer deposition.

Table 3.3 PVD sputtering of seed layer for electroplating in strip line fabrica-tion.

Process step # Material Thickness Power Time

1 TiW RF-power ,

2 Ni DC-power

50nm200W 3min 3s 100nm

120W 5min

50nm 200W 3min 3s

100nm 120W 5min


71

3.4.2 Electroplating

The metals which were available for electroplating with our equipment are the fol-lowing: nickel (Ni), copper (Cu) and gold (Au). These materials are also suitablefor the subsequent selective etching process of the seed layer as is the case for onekind of metallization applied here and discussed before.

More experimental know-how was accessible when nickel or copper were chosenas the electroplating materials, as it was not the case for gold. Another drawbackof using gold concerns its adhesion to SU-8. From experimental tests carried outduring this thesis, a poor adhesion between gold and SU-8 was observed.

Another important aspect in qualifying these materials is their electrical conduc-tivity. The higher the conductivity of the metal the lower the attenuation of thefabricated strip line. Nickel, which has a conductivity almost three times lowerthan the other two, also represents a bad candidate.

Table 3.4 summarizes the above discussion. The three electroplating approacheswhich consider nickel, copper and gold were pursued but in the end only electro-plating with copper has lead to good fabrication results and electrical performanceof the strip line. Therefore, only electroplating with copper is reported in the scopeof this thesis.

3.4.3 Top ground metallization

As mentioned before, one difficulty was encountered after the second SU-8 layerprocess step, namely when the top ground metal was to be fabricated. The resistdeposited on the seed layer has non-uniform thickness on the wafer. The resist isthicker at the steps built by the structures of the second SU–8 layer

Table 3.4 Some relevant properties of metals used in the electroplating process.

Metal Adhesion to SU8 electrical conductivity (at 300K)

Nickel good

Copper good

Gold bad

1.39 107× S m⁄

5.8 107× S m⁄

4.4 107× S m⁄

15µm


72

(Figure 3.8a) with the consequence that the optimum exposure doses and time arenot the same for the complete resist area to be exposed.

In one experiment the standard resist AZ4533 was utilized. Spin-coating parame-ters were set to achieve a thick resist. Exposure and developing parametersfor this thickness were used with the result that part of the thicker resist at theSU–8 steps still remained as is shown in Figure 3.8b. This remaining resist avoidsthe subsequent electroplating of the seed layer of the line (Figure 3.8c) with theconsequence that during the next etch step this part of the seed layer will beremoved (Figure 3.8d).

To overcome this obstacle a thick photoresist AZ9260 [49] was used, which isdesigned for film thicknesses of between and using standard expo-sure tools. It was spun-on to achieve a resist thickness of thus avoiding thatthe thickness at the SU-8 steps becomes significant compared with the rest. InFigure 3.9 a SEM- photograph of a successfully metallized SU-8 structure usingAZ9260 is shown. The SU-8 structure is thick which is not an obstacle for

Figure 3.8 Photolithography/Electroplating problem using standard resist AZ4533 for the top ground metal.Schematically shown and with a SEM–photograph of a test structure.

3µm

SU-8

SU-8

SU-8

seed layer resist

metal

a) Resist deposition and exposure

b) Resist developement

c) Electroplating

d) Stripping and etching of seed layer

not completelyexposed resist

unwanted etchedseed layer

not completely exposed resist after developement electroplated metal

4µm 24µm10µm

15µm


73

the metallization process. The metalization is very conform, even at the stepsformed by the substrate and the SU-8 structure.

The complete lithography process of the AZ9260 photoresist to achieve film thickness will be described next

Process of thick photoresist AZ9260

P1 Coating of photoresist

P1.1 Static dispense of resist

P1.2 Spin-on 1 min at . , .


P3 Edge bead removal with acetone at ( ). , .

Figure 3.9 Test wafer (wlz02033ni) with SU-8 structure and metallization. The thick photoresist AZ9260 was used as electroplating mask. A confor-mal metallization of the SU-8 steps was achieved.

SU-8

Metallization

Si-wafer

15µm

10µm

2.5ml

2400rpm tacc 600ms= tbreak 2s=

60s

500rpm 10s tacc 400ms=tbreak 2s=


74


P5 Softbake at .


P7 Multiple exposure to get . With a light source: 5 cycles with exposure and waiting time.

P8 Develop of resist with AZ400K (1:4). > min.

3.5 Fabrication sequence of the strip line

The complete fabrication sequence consists of the process steps discussed in theprevious sections. The process is described in detail in this section. In order toavoid that it becomes unnecessarily long, process description for the photoresistsSU-8 and AZ9260 are rather mentioned than described. The full process descrip-tion for these photoresists can be found in sections 3.1 and 3.4 respectively.

P1 Bottom ground metal

P1.1 Sputtering of TiW by PVD with a TiW-target (90% W). Parameters: RF-power, (Ar), 3 min and 3 s.

P1.2 Sputtering of Nickel by PVD. Parameters: DC-power, 5 min.

P1.3 Photolithography of AZ5214E (image reverse photoresist).

P1.3.1 Spin-on of to thick layer.

P1.3.2 Softbake at .

P1.3.3 Exposure, at , proximity with , with mask M1 (Metal 1).

1min

200s 95°C

7h

500 mJ cm2⁄ 10 mW cm2⁄10s 10s

t

50nm200W 7 mbar

100nm 120W

1.8µm

10s 110 °C

0.8s 10 mW cm2⁄ 10µm

3.5 Fabrication sequence of the strip line

75

P1.3.4 Reversal bake at .

P1.3.5 Exposure flood type, at .

P1.4 Development of AZ5214E with AZ726 MIF, and rinse with DI-water.

P1.5 Etching of nickel with AZ5214E as etch mask. , .Etchant: of and of .

P1.6 Resist strip with acetone. Rinse with isopropanol and DI-water.

P1.7 Etching of TiW with nickel as etch mask. Etchant: at .

P1.8 Electroplating of copper, thick. Current density: .Electrolyte solution: of Cu, of and of

.

P2 First SU-8 layer.

P2.1 Photolithography of a SU-8 layer as described in section 3.1 and with mask D1 (Dielectric 1).

P3 Wafer planarization by electroplating.

P3.1 Electroplating of copper with the same electrolyte solution as in P1.8 and current density.

P4 Signal metallization.

P4.1 PVD-sputter of TiW. Same parameters as in P1.1.

P4.2 PVD-sputter of Ni. Same parameters as in P1.2.

P4.3 Photolithography of AZ4533.

2min 115 °C

20s 10 mW cm2⁄

30s

T 40°C= 60s100g l⁄ N H4( )

2S2O8 250ml l⁄ H2SO4

K3 Fe CN( )6[ ] 40°C

3µm 0.5A dm2⁄20g l⁄ 150g l⁄ H2SO4 50g l⁄

Cl

15µm

15µm0.3A dm2⁄

50nm

100nm


76

P4.3.1 Spin-on of thick layer. Parameters: spread at , and spin at .

P4.3.2 Softbake at .

P4.3.3 Exposure, at , proximity with and M2 (Metal 2) mask.

P4.4 Development of AZ4533 with AZ400K, and rinse with DI-water.

P4.5 Hardbake of AZ4533, at .

P4.6 Electroplating of copper, thick. Same electroplating parameters as in P3.1.

P4.7 Resist strip with acetone. Rinse with isopropanol and DI-water.

P4.8 Selective etching of nickel with copper as etch mask. Etchant contains nitrobenzene, sulfonic acid, sulfuric acid and a etch-inhibitor for copper.

P4.9 Etching of TiW with copper as etch mask as described in P1.7.

P5 Second SU-8 layer.

P5.1 Photolithography of a SU-8 layer as described in section 3.1.

P6 Top ground metallization.

P6.1 PVD-sputter of TiW. Same parameters as in P1.1.

P6.2 PVD-sputter of Ni. Same parameters as in P1.2.

P6.3 Photolithography and development of AZ9260 as described 3.4.

P6.4 Electroplating of copper, thick. Same electroplating parameters as in P3.1.

5µm 5s 800rpm30s 2300rpm

50s 100 °C

3.4s 10 mW cm2⁄ 10µm

4min

50s 115°C

3µm

15µm

50nm

100nm

3µm

3.6 Layout

77

P6.5 Stripping of resist AZ9260 with acetone and rinse with DI-water.

P6.6 Selective etching of nickel with copper as etch mask as described in P4.8.

P6.7 Etching of TiW with copper as etch mask as described in P1.7.

3.6 Layout

In the previous section the technology to be applied in strip line fabrication wasdetermined. In this section the layout of the strip lines and part of the different teststructures will be described.

The complete layout comprises the layouts for the five required masks, threemasks for the metal layers and two masks for the dielectric layers. The layoutswere designed with the layout editor IC station of Mentor Graphics [50]. Thelayout layers were named: Metal 1, Dielectric 1, Metal 2, Dielectric 2 andMetal 3.

The following factors have to be noted regarding the shapes in the layout layers:

• Shapes in the Metal 1 layer denote areas which are not intended for metalli-zation. Most of these shapes appear in the layout of the contact pads. Al-though they are not necessary in the strip line layout, they are included in itto have an area which overlaps the Metal 1 layer in the layout of the contactpads.

• Shapes in the Dielectric 1 layer represent vias in the SU-8 dielectric.Through these vias electroplating of the first metallization will be performedachieving wafer planarization.

• Shapes in the Metal 2 layer determine the places on which metallization willbe performed. With this metallization, primarily the signal metal of the stripline and the contact pads are made.


78

• Shapes in the Dielectric 2 layer denote areas on which the SU-8 structureswill be kept on the wafer. These SU-8 structures are only necessary in thelayout of the strip line.

• Shapes in the Metal 3 layer represent places where metallization will be per-formed. This metallization is needed to form the top ground metal of the stripline. It was also included in the contact pad layout in order to reinforce padsmetallization, already fabricated with Metal 2.

In the following, the layout of some structures will be shown and commented. Thelayout and the dimensions of the contact pads are shown in Figure 3.10. Thedimensions are compatible with Ground-Signal-Ground (G-S-G) coplanar micro-wave probes with pitch. Dimensions of the contact pads were also chosento match the impedance of the probes. Note that in the layout of the contactpads the Dielectric 2 layer is not included.

In Figure 3.11 the layout of a long strip line without contact pads isshown. It contains all layers, but shapes of layer Metal 1 are placed only in theoverlapping areas, when the layout of the strip line and contact pads are puttogether.

In Figure 3.12 the layout of a set of long strip lines is shown. They arecomposed of several contact pads from Figure 3.10 and strip lines fromFigure 3.11. The strip lines differ in their strip widths which vary from to

. An open and shorted line are also included in this set. In Figure 3.12 a partof the layout is enlarged showing the intersection between contact pads and stripline. Similar sets of strip lines but with different strip lengths were included in thefinal layout.

Some strip line configurations are also shown in Figure 3.13. In this layout theDielectric 2 and Metal 3 layers are missed, intentionally, in order to characterizeoptically the signal metal of the strip lines after fabrication. Therefore, this set oftest structures consists of strip lines with different strip widths.

Another set of test structures is shown in Figure 3.14. It concerns the contact pads.These test structures represent longer contact pads with a different space between signal and ground pads.

100µm50Ω

500µm

500µm

4µm30µm

s

3.6 Layout

79

On the left of Figure 3.15 the layout of some strip line filters are shown. They con-sist of -stub resonators and long connecting lines. On the right the cor-responding layouts of test structures are included. The dimensions of the filterswere taken from standard filter design literature. Filters with , and

long –stubs were designed, assuming a dielectric constant of for SU–8. The ones in Figure 3.15 consist of –stubs. In the

test structures of Figure 3.15 (right) the Dielectric 2 and Metal 3 layers are notincluded, allowing optical inspection of the signal metallization.

The layouts of the structures described above are included in the main-cell shownin Figure 3.16. It comprises an area of and contains differentdesign sets of strip lines, filters and test structures. The strip lines in the main-celldiffer in length and width.

Finally, the main-cell is instantiated times to cover an area which correspondsto a 4-inch wafer. In Figure 3.17 the layout for one mask is shown, where the viewhierarchy is turned off to recognize the 70 main cells along the wafer area. InFigure 3.17 the position of the align marks is also shown.

The complete design was converted to a file with GDSII-format [51] and sent toDelta Mask (Netherlands) [52] as an order for five chrome-glass masks. Withthese masks the fabrication of the strip lines and several test structures was per-formed.

λ 4⁄ λ 4⁄

300 600900µm λ 4⁄εr 3.8= 300µm λ 4⁄

7.5 7.5×( ) mm2

70


80

Figure 3.10 Layout of coplanar contact pads.

Figure 3.11 Layout of a strip line with a strip width of .

100

126

5098

126

30

Metal 1

Dielectric 1

Metal 2

Metal 3

500

98

15

Metal 1

Dielectric 1

Metal 2

Dielectric 2

Metal 3

500µm w 15µm

3.6 Layout

81

Figure 3.12 Layout of a set of long strip lines with variation of strip width .

Figure 3.13 Layout of test structures for strip lines with different strip width .

Metal 1

Dielectric 1

Metal 2

Dielectric 2

Metal 3

Strip width: 15 µm

Strip width: 20 µm

Strip width: 25 µm

Strip width: 30 µm

Strip width: 10 µm

Strip width: 8 µm

Strip width: 6 µm

Strip width: 4 µm

Short circuited line

Open line

500µmw

Metal 1

Dielectric 1

Metal 2

Metal 3

Strip width: 15 µm

Strip width: 10 µm

Strip width: 6 µm

Strip width: 4 µm

Strip width: 2 µm

w


82

Figure 3.14 Layout of test structures for coplanar contact pads with different space between ground and signal pads.

Metal 1

Dielectric 1

Metal 2

Metal 3

s = 40 µm

s = 35 µm

s = 30 µm

s = 24 µm

s = 20 µm

s = 15 µm

s = 10 µm

s

3.6 Layout

83

Figure 3.15 Layout of strip line filters with –stubs and connecting lines. The filter configurations on the right are test structures, which do not include the last two layers, second dielectric (Dielectric 2), and third metal (Metal 3) layer.

Metal 2

Dielectric 2

Metal 1

Dielectric 1

Metal 3

300µm λ 4⁄


84

Figure 3.16 Layout of the main-cell. Specification of cell parti-tion is given.

A: Filters with -stubs.

B: Filters and test structures with , and -stubs.

C: Test structures for strip lines.

D: Test structures for coplanar contact pads.

E: strip lines with different strip width.

F: strip lines with different strip width.

G: strip lines with different strip width.

H: strip lines with different strip width.

600µm λ 4⁄

300 600 900µm λ 4⁄

3mm

2mm

1mm

0.5mm

Metal 1 Dielectric 1 Metal 2 Dielectric 2 Metal 3

A B

C

D

E F G H

7.5 7.5×( ) mm2

3.6 Layout

85

Figure 3.17 Layout of one design mask for a 4-inch Si-wafer. It consists of 70 main–cells (grey rectangles) and aligning marks (filled shapes). The circle denotes the wafer boundary.


86

3.7 Fabrication results

With the design and technology described in the previous sections, fabricationwas carried out at the Reinraum Service Center (RSC) [53] at IMTEK. 4-inch Sil-icon-wafers were processed, but any substrate can be used with the only restrictionthat adhesion between the substrate and the first TiW metallization layer must beensured.

In Figure 3.18 the photograph of a processed Si-wafer is shown. The main-cellsalong the wafer can easily be identified.

In the photograph of Figure 3.19 several fabricated strip lines are shown. Thesestrip lines belong to the set of strip lines which are long with a variation ofsignal strip width. The contact pads can be clearly seen as opposed to the signalstrips of the strip lines. Since signal strips are embedded in a dielectric and ground

Figure 3.18 Photograph of the 4-inch wafer containing the main-cell with strip lines and test structures.

7.5 7.5×( )mm2

1mm


87

metal, their optical inspection is not possible. For this purpose the included teststructures for strip lines are very useful.

The photographs of those test structures are shown in Figure 3.20. As discussed inthe last section these test structures do not include the second dielectric and topmetal layer. Thus, the signal metal is on the top and can be evaluated optically.

Strip line test structures with a strip widths of 15, 10, 6 and are shown. Onthe top is the line with the widest strip. The magnified view of the transition of thesignal pad of the contact pads to the signal strip of the line is also shown. The illus-tration of the transition of the line with is also magnified.

The wide strip in the test structures of Figure 3.20 is missing, which statesthat metalization of all narrow signal strips in the strip lines also failed. This wasconfirmed by electrical measurements of the strip lines. As discussed during tech-nology description, the metallization process consists of seed layer deposition,photolithography of the resist, electroplating through vias in the resist, strippingof resist, and etching of seed layer. One reason for metallization failure is that theelectroplating step cannot be successfully processed when the strip width is nar-rower than , with the consequence that at the subsequent etching step of the

Figure 3.19 Photograph of a set of strip lines.1mm

4µm

6µm

4µm

6µm


88

seed layer the narrow strips that have not been plated are also etched. Anotherreason is that even if the electroplating step was successful the subsequent seedlayer etching step produces an undercut underneath the electroplating layer whichis critical for narrow strips. That is more critical if the etching time is prolongedcausing in the extreme case that the strip line is not at all supported by the seedlayer. These hanging plating strips can be damaged by the subsequent dielectricdeposition and metallization steps.

In Figure 3.21 the photograph of a -stubs strip line filter (left) and its corre-sponding test structure (right) are shown. Again, with this test structure opticalinspection of the fabricated signal strips is possible.

Finally, the SEM-photograph of Figure 3.22 shows a strip line with contact pads.This perspective allows a view of the second SU-8 dielectric layer of the strip line,which is thick.

Figure 3.20 Set of test structures for the strip line. Their fabrication did not include the second SU-8 layer and third metal.The lines are long.

w 15µm=

w 10µm=

w 6µm=

w 4µm=

500µm

λ 4⁄

15µm


89

Figure 3.21 -stub filter structure (left) and a test structure for the filter which allows optical inspection of the second metallization.

Figure 3.22 SEM photograph of a strip line with coplanar contact pads.

λ 4⁄

contact pads

upper SU-8 layer

top groundmetal


90

4.1 On-wafer microwave measurements

91

4 C

HARACTERIZATION

AND

MODELING

This chapter deals with the characterization of the fabricated strip lines and withthe extraction of the transmission line models for these lines. This characterizationis based on microwave measurements with an on-wafer probe station in a fre-quency range of up to . Measured S-parameters are the basic data onwhich microwave characterizations of the strip lines were based. The characteris-tic impedance and the propagation constant for the strip lines with different stripwidth will be determined as well as the dielectric constant for the SU–8. Fur-thermore, the transmission line model for the strip lines will be extracted. Fromthe lumped element per unit length (p.u.l.) in the models the loss tangent of theSU–8 can be determined and the resistance p.u.l. can be expressed by the combi-nation of both the d.c. and the high-frequency resistance p.u.l. of the strip line. Thelatter is related to the skin-effect in the conductive strip. In the end, a comparisonof measured and modeled characteristic impedance and attenuation constant forthe strip lines with different strip widths will be given.

4.1 On-wafer microwave measurements

With on-wafer measurements it is possible to characterize the DUTs (device undertest) directly on the wafer, without having to slice the DUT, put it on a carrier andbond it to the connectors, which are used to connect the DUT with the measure-ment system. This measurement procedure implies numerous sources of signalreflection, which in the end modify the measured signal considerably. With theproperties of on-wafer measurements, signal reflections are minimized and thereference plane can be defined more exactly. On the other hand, design and tech-nology must be adapted to include the contact pads as part of the DUT. The tran-sition from the contact pads to the DUT must be as smooth as possible and thecharacteristic impedance of the contact pads must match the port impedance

48GHz

w

50Ω

4 Characterization and modeling

92

of the measurement system. All these design criteria were considered in the pre-vious chapters.

For this thesis the measurement system of the

Fraunhofer Institute of AppliedSolid State Physics

(IAF) was used. With this equipment on-wafer measurementsin a frequency range of up to are possible. A photograph of the system isshown in Figure 4.1. The measurement system was calibrated using the Line-Reflect-Match (LRM) technique [54].

Figure 4.1

Photograph of the on-wafer microwave measurement system at the Fraunhofer IAF for a frequency range of up to . On the left is a vector network analyzer (HP8510C) which is connected to a pair of microwave probes which are aligned through the microscope to the DUT on the substrate. The PC that runs the calibration and measure-ment software is not shown.

48GHz

Vector networkanalyzer HP8510C

Probe station

microwave probes

48GHz

4.2 Line parameters from S-parameters

93

4.2 Line parameters from S-parameters

A simple way to extract transmission line parameters from measured S-parame-ters is to transform them to ABCD-parameters. The ABCD matrix of a transmis-sion line section, with the characteristic impedance , is

. (4.1)

The S-parameters are related to the ABCD-parameters as follows

, (4.2)

where is the source and load impedance. From (4.1) the characteristic imped-ance and the propagation constant are given by

(4.3)

, (4.4)

where is the length of the transmission line. In (4.4) matrix element insteadof can also be used.

Then the following expressions for the characteristic impedance and the propaga-tion constant in terms of S-parameters can be given:

Z0

A B

C D

γl( )cosh Z0 γl( )sinh

γl( )sinhZ0

-------------------- γl( )cosh=

A B

C D

1 S11+( ) 1 S22+( ) S12S21+

2S21---------------------------------------------------------------------

Zr 1 S11+( ) 1 S22+( ) S12– S212S21

------------------------------------------------------------------------

1 S11–( ) 1 S22–( ) S12– S21Zr2S21

-----------------------------------------------------------------1 S11–( ) 1 S22+( ) S12S21+

2S21--------------------------------------------------------------------

=

Zr

Z0BC----=

γ 1l--- A( )acosh=

l DA


94

(4.5)

. (4.6)

The described line parameters extraction procedure starting from S-parameterswas applied by Kizologlu et al [55].

4.3 Line parameters of strip lines

First, the phase constant will be characterized. From equation (2.36) for TEMtransmission lines we expect that is linear dependent on the angular frequency

with as the linear factor. In Figure 4.2 the measured phaseconstants for strip lines with different strip widths are shown. As expected, thephase constant is independent of strip width and depends linearly on the fre-quency. The calculated phase velocity which is also shown in Figure 4.2 dem-onstrates this linearity.

When the SU-8 is used as the dielectric in the strip lines, its dielectric constant canthen be extracted from the phase constant when (2.36) is transformed, yielding:

. (4.7)

In Figure 4.3 the dielectric constants for SU-8, extracted from measurements onthe strip lines with different strip widths, are shown. A value of forSU–8 can be computed from the microwave measurements performed in this the-sis.

Z0 Zr

1 S11+( ) 1 S22+( ) S12– S211 S11–( ) 1 S22–( ) S12– S21

------------------------------------------------------------------=

γ 1l---

1 S11+( ) 1 S22+( ) S12S21+

2S21---------------------------------------------------------------------

acosh=

ββ

ω 2πf= εµ c=w

β wc

β

εrβ

ω ε0µ0

-------------------- 2 βc0

ω---------

2

= =

εr 3.2=


95

Figure 4.2 Measured phase constant and phase velocity vs. frequency for strip lines with different strip width . , and

.

Figure 4.3 Dielectric constant of SU-8 extracted from measurements on strip lines with different strip widths . , and

.

10 20 30 40 50

500

1000

1500

2000

75

150

225

300

Frequency GHz[ ]

Phas

e co

nsta

nt β

m1–

[]

Phas

e ve

loci

ty c

106m

s⁄[

]

w µm[ ] 6 8 10 15 20 30, , , , ,=

h

w

t

wg

w wg 98µm= h 30µm=t 3µm=

0 10 20 30 40

2.5

3

3.5

4

4.5

5

Frequency GHz[ ]

Die

lect

ric

cons

tant

εr

h

w

t

wg

w µm[ ] 6 8 10 15 20 30, , , , ,=

εrw wg 98µm= h 30µm=

t 3µm=


96

4.3.1 Characteristic impedance

The characteristic impedance is extracted from measured S-parameters byapplying equation (4.5). In section 2.2 the relation between and the line ele-ments was given in equation (2.72). For low frequency values ( ,

) (2.72) yields the following expression

. (4.8)

Then, the real and imaginary part of the characteristic impedance at low frequen-cies behaves as follows

. (4.9)

In Figure 4.4 the real and imaginary part of the measured characteristic impedanceof a strip line are shown. The low frequency behavior is described by (4.9). As thefrequency increases, and can be assumed and the curve tends tothe frequency range, where the imaginary part of vanishes and the real partdecreases towards the value of

. (4.10)

In Figure 4.4 this is the case for frequencies higher than . One can alsoobserve that near the measurement becomes instable. The reason for thisis that the measured strip line, which is long, represents half of the signal’swavelength at this frequency. Considering also that the contact pads are notwell-matched to the strip line, resonance effects occur in the line.

The real part of the characteristic impedance, extracted from the S-parameter mea-surements performed on strip lines with different strip width , are shown inFigure 4.5. The longest available strip lines with were chosen to mini-mize the error caused by the contact pads. The frequency is limited to ,which is a sufficient frequency range to get reliable values of .

Z0Z0

R L G C, , , R L»G 0→

Z0R

jωC-----------=

Re Z0[ ] I– m Z0[ ] R2ωC-----------≅ ≅

R ωL« G ωC«Z0

Re Z0[ ] LC----=

20GHz26GHz

3mmλ

wl 3mm=

20GHzZ0


97

Figure 4.4 Frequency behavior of the real and imaginary part of the characteris-tic impedance extracted from S-parameter measurements on strip lines with different strip width .

Figure 4.5 Real part of the measured characteristic impedance of long strip lines with different strip width in a frequency range limited to

.

10 20 30 40 50

-40

-20

0

20

40

60

80

100

Frequency GHz[ ]

Im

peda

nce

Z0

Ω[]

w µm[ ] 6=

810152030

resonance effects

Re

Im

3mmw

2.5 5 7.5 10 12.5 15 17.5 20

30

40

50

60

70

80

90

100

Frequency GHz[ ]

Re

Z0

[]

Ω[]

w µm[ ] 6=

8

10

15

20

30

3mmw

20GHz


98

The measured characteristic impedances at for the strip line with differentwidths are listed in Table 4.1. The measured values can be compared with thecharacteristic impedances calculated with the approximate expression in (2.77),which are also listed in Table 4.1. The measured dielectric constant of for SU-8 was used in (2.77). Furthermore, a conductor thickness of was assumed which, together with a thickness of for each SU-8 layer,makes a total thickness of . The deviation between measured andcalculated values is small for wide strip widths (4%) but large for narrow stripwidths (16%). Certainly one of the reasons is the tolerance of the strip width which has a stronger effect on strip lines with narrow strip widths. For example,when all the strip widths are reduced by then for the strip lines with nominalstrip widths of and characteristic impedances of and respectively will be obtained which are more closer to the calculated values. Interms of deviation, it will be reduced to 12% for the strip line with the nominal

and to 0.4% for the strip line with the nominal .

From the measured strip lines, the one with a strip width of has acharacteristic impedance near and matches the port impedance of themeasurement system best.

Table 4.1 Measured characteristic impedance at extracted.

strip width measured calculated deviation

16%

13%

12%

7%

5%

4%

10GHzw

εr 3.2=t 2.5µm=

16.5µmh 35.5µm=

w

1µm6µm 30µm 75.6Ω 36.9Ω

w 6µm= w 30µm=

w 20µm=50Ω 50Ω

Z0 10GHz

w Z0 Z0

6µm 86.0Ω 72.4Ω

8µm 76.68Ω 66.9Ω

10µm 70.3Ω 62.0Ω

15µm 56.67Ω 52.7Ω

20µm 48.21Ω 45.7Ω

30µm 37.73Ω 36.2Ω


99

4.3.2 Propagation characteristic

The propagation constant for the strip lines was extracted from mea-sured S-parameters by using (4.6). Again, the longest lines with werechosen for evaluation, since at this length the influence of the contact pads is min-imized. In Figure 4.6 the attenuation constant of the strip line for different stripwidths is shown.

One can observe that the attenuation constant increases when the strip width ofthe lines is decreased. That was expected from the full-wave simulations made insection 2.4. The fact that the attenuation increases with increasing frequency isdue to both, the conductor loss (skin-effect) and dielectric loss. The dielectric lossis related to the dielectric’s loss tangent . For a first estimation of the loss tan-gent of SU–8 one may also consider the full–wave simulations in section 2.4,where conductor and dielectric losses were calculated separately. For a strip linewith a strip width of and copper as conductor material a conductor loss ofabout at was calculated. For the same strip line a total atten-uation of at the same frequency was measured which leads to an

Figure 4.6 Attenuation constant for strip lines with different strip widths . Values were extracted from S-parameter measured on long strip lines. , and .

γ α jβ+=l 3mm=

αw

10 20 30 40 50

0.2

0.4

0.6

0.8

Frequency GHz[ ]

Atte

nuat

ion

cons

tant

d

Bm

m⁄

[]

w µm[ ] 6 8 10 15 20 30, , , , ,=

h

w

t

wg

α w3mm

wg 98µm= h 30µm= t 3µm=

w

δtan

15µm0.20dB mm⁄ 48GHz

0.62dB mm⁄


100

estimation of attenuation due to dielectric loss. From simulationsthis value corresponds to a loss tangent of about for the SU–8. However, theloss tangent of SU–8 will be computed more exactly and reliably in the next sec-tion.

4.4 Equivalent circuit model for the strip line

In section 2.2 the transmission line model in terms of lumped elements for a sec-tion of the line was discussed. The model consists of the resistance per unit length(p.u.l.) , the conductance p.u.l. , the inductance p.u.l. , and the capacitancep.u.l. as is shown in Figure 4.7.

The relation between circuit elements p.u.l., characteristic impedance andattenuation constant was also derived, which is as follows:

(4.11)

(4.12)

Figure 4.7 Equivalent circuit for a length of transmission line with the per unit length circuit elements: Resistance , inductance , conduc-tance and capacitance .

0.42dB mm⁄0.05

R G LC

R dz⋅ L dz⋅

C dz⋅dz⋅V z( )

I z( )

z z dz+

I z dz+( )

V z dz+( )

dzR L

G C

Z0α

Z0R jωL+( )G jωC+( )

--------------------------=

γ R jωL+( ) G jωC+( )=


101

4.4.1 Model extraction

In this section the circuit elements p.u.l. will be calculated from the S-parametermeasurements made on the strip lines. The characteristic impedance and attenua-tion constant of the strip lines were already calculated in the previous section.From these, the circuit element p.u.l. will be calculated by transforming equations(4.11) and (4.12) which yields:

(4.13)

For strip lines with a different strip width the extracted capacitance and induc-tance p.u.l. are shown Figure 4.8 and Figure 4.9, respectively.

Figure 4.8 Measured capacitance p.u.l. vs. frequency extracted from S-parame-ter measurements on strip lines with a different strip width .

R Re γ Z0⋅[ ]= L Im γ Z0⋅[ ]=

G Reγ

Z0------ = C Im

γZ0------=

w

2.5 5 7.5 10 12.5 15 17.5 20

50

100

150

200

Frequency GHz[ ]

Cap

acita

nce

p.u.

l. p

Fm⁄

[]

w µm[ ] 6 8 10 15 20 30, , , , ,=

w


102

With increasing frequency both circuit elements tend toward a constant value.These values are listed in Table 4.2.

The extracted conductance p.u.l. as a function of frequency is shown inFigure 4.10. It is related to both the capacitance p.u.l. and the loss tangent by the following expression:

. (4.14)

In Figure 4.10 the strip line with the narrowest strip width of has the lowestconductance p.u.l. which corresponds to the lowest capacitance p.u.l. of this stripline.

Figure 4.9 Measured inductance p.u.l. vs. frequency extracted from S-parameter measurements on strip lines with a different strip width .

Table 4.2 Measured per-unit-length capacitance and inductance at for strip lines with different strip widths .

6 8 10 15 20 30

71.7 80.4.4 87.5 108.3 127.1 162.7

528 471 431 347 295 231

2.5 5 7.5 10 12.5 15 17.5 20

100

200

300

400

500

600

700

Frequency GHz[ ]

Indu

ctan

ce p

.u.l.

n

Hm⁄

[]

w µm[ ] 6 8 10 15 20 30, , , , ,=

w

C L10GHz w

w µm[ ],

C pF m⁄[ ],

L nH m⁄[ ],

GC δtan

G ωC δtan=

6µm


103

The conductance p.u.l. is strongly related to the loss properties of the dielectricmaterial, which is SU-8. The loss tangent of SU-8 can be calculated when (4.14)is transformed yielding:

. (4.15)

In Figure 4.11 the loss tangent for SU-8 is shown. The different curves correspondto the measured strip lines with different strip widths . The extracted values aredepicted as a function of frequency of up to . Beginning from allcurves tend towards a constant value and at the effects of line resonanceare visible. At an average value of was extracted.

The resistance p.u.l. for all strip lines is shown in Figure 4.12. In the low fre-quency region is related to the d.c. resistance p.u.l. of the metal strip of the lineas follows

, (4.16)

Figure 4.10 Measured conductance p.u.l. vs. frequency extracted from S-parame-ter measurements on strip lines with different strip widths .

2.5 5 7.5 10 12.5 15 17.5 20

0.25

0.5

0.75

1

1.25

1.5

1.75

Frequency GHz[ ]

Con

duct

ance

p.u

.l.Ω

m(

)1–

[]

w µm[ ] 6 8 10 15 20 30, , , , ,=

w

G

δtan GωC--------=

w20GHz 3GHz

15GHz10GHz δtan 0.0429=

RR

Rdc Ω m⁄[ ] 1σtw----------=


104

with , and being the conductivity, the thickness, and width of the striprespectively.

Figure 4.11 Loss tangent of the SU-8 dielectric extracted from measurements on a strip line with .

Figure 4.12 Measured resistance p.u.l. vs. frequency extracted from S-parameter measurements on strip lines with different strip width .

2.5 5 7.5 10 12.5 15 17.5 20

0.05

0.1

0.15

0.2

0.25

Frequency GHz[ ]

Los

s ta

ngen

t δ

tan

w µm[ ] 6 8 10 15 20 30, , , , ,=

w 20µm=

σ t w

2.5 5 7.5 10 12.5 15 17.5 20

1000

2000

3000

4000

5000

6000

7000

Frequency GHz[ ]

Res

ista

nce

p.u.

l. Ω

m⁄[

]

w µm[ ] 6 8 10 15 20 30, , , , ,=

w


105

With increasing frequency the skin-effect starts to dominate forcing the signal toflow within a thickness smaller than which corresponds to the skin depth . Theskin-effect dominated resistance is

. (4.17)

The calculated for different strip widths as a function of frequency is shownin Figure 4.13.

With decreasing frequency the curves also decrease and are equal to zero atzero frequency. The d.c. resistance of the metal strips has to be included in themodel in order to accurately reproduce the resistance p.u.l. of the strip lines. Thatwas accomplished with expression (4.18).

(4.18)

The modeled for the same strip lines is also shown in Figure 4.13. andare calculated with (4.16) and (4.17) respectively.

With the model for , the transmission line model for the strip line is completed.It comprises the p.u.l. circuit elements. The capacitance and inductance p.u.l. wereextracted directly from measurements whereas the resistance and conductance

p.u.l. are based on a standard loss model. The model for includes the losstangent of SU-8, which was extracted from measurements. The dielectricconstant of SU-8 was extracted from the measured phase velocity.

t δ

Rskin Ω m⁄[ ] 1σδw-----------

πf µ0

σw-----------------= =

Rskin

Rskin

RRdc , Rdc Rskin>

Rskin

=

R RdcRskin

R

RG G

δtanεr


106

4.4.2 Verification of model

The transmission line model for the strip lines will be verified by comparing cer-tain line parameters with measured data. The circuit model with the per unit length(p.u.l.) lumped elements was shown in Figure 4.7. The capacitance and induc-tance p.u.l. for the strip lines with different strip widths were taken fromTable 4.2. The values of the conductance p.u.l. were calculated from the losstangent and the corresponding capacitances by applying (4.15). The resis-tances p.u.l. were modeled by the expression (4.18), which takes both thed.c. resistance and the increasing resistance due the skin–effect into consideration.

Characteristic impedance

The characteristic impedance for the strip lines with different strip widths was calculated from the model. In Figure 4.14 the real parts of are comparedwith measurements showing a very good agreement. The imaginary part of themodeled strip line also agrees well with the measured data as is shown inFigure 4.15.

Figure 4.13 Calculated resistance due to skin-effect and modeled for strip lines with different strip width .

2.5 5 7.5 10 12.5 15 17.5 20

1000

2000

3000

4000

5000

6000

7000

R

Rskin

Frequency GHz[ ]

Res

ista

nce

p.u.

l. Ω

m[

] w µm[ ] 6=

8

10

1520

30

Rskin Rw

CL w

Gδtan

Z0 wZ0


107

Figure 4.14 Measured (symbols) and modeled (lines) real part of the characteris-tic impedance vs. frequency for strip lines with different strip widths .

Figure 4.15 Measured (symbols) and modeled (lines) imaginary part of the char-acteristic impedance vs. frequency for strip lines with different strip widths .

2.5 5 7.5 10 12.5 15 17.5 20

20

40

60

80

100

120

Frequency GHz[ ]

Re

Z0

[]

Ω[]

w µm[ ] 6=

810

1520

30

w

2.5 5 7.5 10 12.5 15 17.5 20

-60

-50

-40

-30

-20

-10

0

Frequency GHz[ ]

ImZ

0[

] Ω[

]

w µm[ ] 6 8 10 15 20 30, , , , ,=

w


108

Attenuation constant

The modeled attenuation is compared with data measured on strip lines with dif-ferent strip widths in Figure 4.16. For the whole frequency range the transmissionline model reproduces nearly the same measured signal attenuation for all striplines with different strip widths.Therefore, both the dielectric loss of the SU–8 andthe loss of the metal conductors are well modeled. In particular, as is expectedfrom measurements, the model shows non-zero attenuation when the frequencytends to zero. This was accomplished by the inclusion of the d.c. resistance of themetal conductors. Otherwise, when the resistance due to the skin–effect and theconductance in the dielectric are solely considered, the model will show zeroattenuation at zero frequency.

In [56] fabrication and microwave characterization of the strip lines werereported.

Figure 4.16 Comparison of modeled with measured attenuation vs. frequency for strip lines with different strip widths .

10 20 30 40 50

0.2

0.4

0.6

0.8

10 20 30 40 50

0.2

0.4

0.6

0.8

Frequency GHz[ ]Frequency GHz[ ]

Measured Attenuation dB mm⁄[ ] Modeled Attenuation dB mm⁄[ ]

w µm[ ] 6 8 10 15 20 30, , , , ,= w µm[ ] 6 8 10 15 20 30, , , , ,=

w

4.5 Strip line filters

109

4.5 Strip line filters

In the wafer layout some filter structures were included (Figure 3.15) which con-sist of strip lines with different strip widths and therefore with different character-istic impedances. They were designed to work as degree 3 Chebyshev filtersassuming an of 3.8 for the SU–8 which is quite different from the value of 3.2which was later measured. Therefore, the characteristic impedances of the striplines in the fabricated filters are expected to be different from the designed values.Furthermore, it is expected that measurements of the filter characteristics willshow the poor performance of the design when an of 3.2 is assumed. That iswhy microwave characterization of the filters was not performed, even thoughthey were fabricated successfully (Figure 3.21).

However, with the characterization values of the strip lines obtained from thiswork a new design of the strip line filters can be accomplished.

εr

εr


110

5.1 Summary

111

5 Final remarks

5.1 Summary

In this thesis a technological process was developed which applies micromachin-ing techniques to the manufacturing of strip lines, which have a cross section sim-ilar to that of a rectangular coaxial line and therefore represent a three–dimen-sional transmission line. The process consists of the patterning of a photosensitivepolymer with variable thickness and the electroplating of copper. Many succes-sive layers of polymer dielectric and metallization layers can be processed, with adielectric thickness of between a few micrometers and several hundred microme-ters and thus with excellent micromachining properties.

The feasibility of SU-8 as the micromachinable dielectric material in the stripline’s fabrication was demonstrated. Several tests were necessary to improve met-allization processing steps, interlayer adhesion, and cracking in SU-8. In the end,a reliable process was achieved which makes the technological realization of striplines with a total dielectric thickness of and variations of strip widthsbetween and possible, thus achieving values for the characteristicimpedance of between and . The pitch contact pads for on-wafermeasurements of the strip lines as well as their transition to the lines were fabri-cated together with the strip lines.

The determination of the layout parameters was carefully carried out by using aself-written program based on the Finite Element Method (FEM), which was usedto calculate the characteristic impedance of the strip lines from their cross sec-tions. Additional simulations with a commercial full-wave simulator were alsoperformed.

The manufactured strip lines were characterized on-wafer by S-parameter mea-surements in a frequency range of up to . Based on these data the charac-teristic impedances and the propagation constants were determined. Furthermore,transmission line models with per unit length lumped elements were extracted

30µm6µm 30µm

37 86Ω 100µm

48GHz

5 Final remarks

112

from the microwave measurements. Additionally, from the measurements per-formed on the strip lines the electrical properties of SU-8 in the microwave fre-quency range were determined. Measurements of the dielectric constant and theloss tangent of SU-8 produced a value of 3.2 and respectively. To theauthor’s best knowledge, these values were determined for the first time directlyfrom microwave measurements. This approach makes more sense when the appli-cation of SU-8 in the microwave frequency range has to be evaluated.

5.2 Conclusion

Firstly, it has to be noted that the elaborated process in this thesis represents amajor contribution to micromachining techniques. With SU-8 as the microma-chinable material structures with a height of several hundred micrometers andhigh aspect ratios can be fabricated. Due to the fact that these structures are pro-cessed by common UV-photolithography of SU–8 instead of the expensive Syn-chrotron X–ray approach, this process, which is now called UV-LIGA, is low-costand simple.

The improved process shows nearly no cracking in the SU–8, good interlayeradhesion between SU–8 and the metallization layers, and electroplating of nickeland copper with excellent selective etching of the sputtered seed layers. The man-ufactured strip lines with contact pads showed good technological performance.

When using SU-8 the dimensions of the strip lines are not limited to those of thestrip lines fabricated in this thesis. In the following we only consider striplines to get an idea of feasible dimensions with SU-8 . With the narrowest stripwidth of realized in this work a dielectric thickness of about would benecessary. On the other hand, dielectric thickness is only limited by the feasiblelayer thickness of SU–8, which can be up to .

The value of 0.043 for the loss tangent ( ) of SU-8 is much higher than otherorganic dielectrics like Benzocyclobutene

(

BCB) and teflon. The dielectric loss isa linear function of the frequency as opposed to the conductor loss (skin-effect),which is proportional to the square root of the frequency. Therefore, it is not rec-ommendable to use SU–8 as the sole dielectric in high–frequency low-loss appli-cations. To illustrate this one should consider the strip line with strip

0.043

50Ω

6µm 9µm

500µm

δtan

50Ω 20µm

5.3 Outlook

113

width. This line has an attenuation of about at which is rela-tively high. However, in the X-frequency band, which is around , the sameline has about which is more useful. Nevertheless, SU–8 can be usedin high-frequency and at the same time low-loss applications, where the advan-tages of its micromachining properties are exploited to the full rather than simplyusing it as the sole dielectric.

5.3 Outlook

The micromachining process elaborated in this thesis can be seen as a basis fornew impulses of MEMS in microwave applications (RF-MEMS). This could leadto the improvement of already existing passive microwave components, for exam-ple transmission lines and filters based on them. Also, new RF-MEMS compo-nents can be manufactured and new packaging approaches devised.

In the following, some examples will be discussed to illustrate the aforemen-tioned. Bulk–micromachining in the fabrication of membrane–supported planartransmission lines (coplanar, microstrip) can be replaced by using SU–8 as themembrane and supporting material. In fact, thin (~ ) and thick (~ )SU–8 layers can be combined in order to build up transmission lines which requirefewer process steps than the strip lines shown here. Membrane–supported linesshow very low signal attenuation due to the air which serves as the main dielectric.With the process from this thesis low-loss, low-dispersive, and low-cost transmis-sion line filters for the mm–wave region can be fabricated. In the same way theSU-8 based UV-LIGA process can be applied to replace the LIGA-technique infabricating a kind of low-loss microstrip lines.

The potential applications of the process in packaging should also be investigated.SU-8 can be further be examined as a carrier or as packaging material. Then activeas well as passive components can be combined with wafer-level-packaging toproduce system solutions.

However, future work can also be focused on combined application areas, forexample high-frequency electronics and medicine, since SU–8 is also biocompat-ible. The different areas of sensor technology, where high-frequency componentsare indispensable, should also be considered for future work.

0.6dB mm⁄ 48GHz10GHz

0.2dB mm⁄

5µm 500µm

5 Final remarks

114

115

A

PPENDIX

A.1 Scattering (S)-parameter

Basic concepts

In traditional analysis of electrical networks such as the one shown in Figure A.1,one is quite used to applying the , or -parameter sets. All of these networkparameters relate total voltages and total currents at each of the ports, which arethe network variables, in the following manner

(A.1)

(A.2)

(A.3)

Figure A.1

A two-port device, representing any electrical network.

Z Y H

V1

V2 Z11 Z12

Z21 Z22 I1

I2

=

I1

I2 Y11 Y12

Y21 Y22 V1

V2

=

V1

I2 H11 H12

H21 H22 I1

U2

=

2-Port

NetworkV1V2

I1 I2

116

From (A.1)-(A.3) we can see that the only difference in the parameter sets is thechoice of the independent and dependent variables. The parameters themselvesare the constants used to relate these variables.

In order to determine any parameter in (A.1) from measurements, both open andshort circuit at network ports must be ensured. For example, to measure parame-ters for and of a two-port network, the following factors have to be con-sidered:

(A.4)

When the frequency of measurement signals is increased in such a way that thedimensions of the network are no longer large compared with the signal’s wave-length, then some problems arise:

• Equipment is not readily available to measure total voltage and total currentat the ports of the network.

• Short and open circuits are difficult to achieve over a broad band of frequen-cies.

• Active devices, such as transistors, very often will not be short or open stable.

Other methods of characterization are necessary to overcome these problems.Consequently, traveling waves rather than total voltages and currents will bedefined as variables to be used at these frequencies.

Definition

Without making any restriction, assume that the two-port network to be analyzedrepresents a transmission line with a characteristic impedance (Figure A.2).Voltages and currents can be assumed to be in the form of waves traveling in bothdirections along this transmission line.

H11 H12

H11

V1I1------

V 2 0=

=

H12

V1V2------

I2 0=

=

Z0

117

In the general case when either the source impedance nor the load impedance match the line impedance , a standing wave will form in the line and the

voltages and currents at the ports can then be expressed in terms of incident and reflected voltage waves at the respective ports

(A.5)

The incident and reflected voltage waves at the ports divided by the square of thecharacteristic impedance represent the new wave variables of the two-port net-work:

(A.6)

Figure A.2

Definition of incident and reflected wave signals at the ports of a transmission line (with ) connected to a load impedance and a source with source impedance .

2-Port

Network

Ei2

Er2

Ei1

Er1

ZL

Zs

Z0 ZLZs

ZsZL Z0

EiEr

V1 Ei1 Er1+= V2 Ei2 Er2+=

I1

Ei1 Er1+

Z0-----------------------= I2

Ei2 Er2+

Z0-----------------------=

a1

Ei1

Z0

----------= a2

Ei2

Z0

----------=

b1

Er1

Z0

----------= b2

Er2

Z0

----------=

118

The square of these new variables has the dimension of power. Therefore thesenew variables can be called traveling power waves rather than traveling voltagewaves.

The scattering parameters relate those waves scattered or reflected from the net-work to those waves incident upon the network:

(A.7)

These scattering parameters are commonly referred to as S-parameters. InFigure A.3 a two-port network with the wave variables is shown. In the micro-wave community has been accepted as the universal reference impedance,thus in S-parameter measurements, was adopted for , and .

To measure the S-parameters of a network only matching conditions at the corre-sponding port have to be ensured. For example, terminating the output port of thenetwork in an impedance equal to the characteristic impedance of the transmissionline is equivalent to setting , since a traveling wave incident on this loadwill be totally absorbed. In this case is determined by measuring the ratio to :

Figure A.3

b1 S11a1 S12a2+=

b2 S21a1 S22a2+=

50Ω50Ω ZS ZL Z0

2-Port

NetworkZL 50Ω=

Zs 50Ω=

a1

b1

a2

b2Z0 50Ω=

a2 0=S11 b1

a1

119

(A.8)

Even though only two-port networks were considered, these concepts can beexpanded to multiple-port networks. For an n-port network the following relationcan be given in matrix form:

(A.9)

Some typical networks can be represented in terms of S-parameters:

• A reciprocal network is defined as having identical transmission characteris-tics from port one to port two or from port two to port one. This implies thatthe S-parameter matrix is equal to its transpose. In the case of a two-port net-work, .

• For a lossless network, in which no power dissipates, one has. It states that the power incident must be equal to the

power reflected. This implies that the S-matrix is unitary: ,where is the identity matrix and is the complex conjugate of the trans-pose of .

• For a lossy network, the net power reflected is less than the net incident pow-er. The difference is the power dissipated in the network. This implies thatthe matrix is positive definite.

Change of reference plane

Another useful relationship is the equation for changing the reference plane.When the network to be measured is embedded in the transmission line structuresshown in Figure A.4, we can then measure the S-parameters at these two planes.

S11

b1a1-----

a2 0=

=

b1

b2

.

.

.bn

S11 S12 . . . S1n

S21 S22 . . . S2n

. . .

. . .

. . .Sn1 Sn2 . . . Snn

a1

a2

.

.

.an

=

S12 S21=

an2∑ bn

2∑=I S*S– 0=

I S*

S

I S*S–

120

We have added a length of line to port one of the network and another length to port two. Since lossless lines only influence the phase of the propagating sig-

nal, their lengths can be expressed in terms of phase. For example for :

, (A.10)

where is the phase constant of the traveling wave. The S-parameter matrix, ,measured at these two planes is then related to the S-parameter matrix of thenetwork as follows

(A.11)

The S-parameters of the network can be determined from the measured S-parameters by the following relationship:

(A.12)

Smith chart

The smith chart was created in the thirties by Phillip Smith, a Bell Lab engineer.He was looking for a method to solve the often repeated equations appearing inmicrowave theory, in particular the reflection coefficient at one port, which is

Figure A.4 Illustration of the changing reference plane of S-parameters.

l1l2

l1

φ1 βl12πλ

------l1= =

β S ′S

S ′ φSφ= with φ e jφ1– 0

0 e jφ2–=

2-Port

Networka1

b1

a2

b2

MeasurementPlane 2

MeasurementPlane 1

, l2 φ2, l1 φ1

SS ′

S φ 1– S ′φ 1–=

Γ

121

defined by the impedance of the port normalized to the reference impedance as follows

(A.13)

It contains numbers of complex values. The tedious work of solving such equa-tions was reduced by applying Smith’s graphical techniques.

The chart is essentially a mapping between two planes, the or impedance planeand the or reflection coefficient plane as is depicted in Figure A.5.

Figure A.5 Mapping of the impedance plane to the reflection coefficient plane by (A.13). The impedance plane is normalized to the characteristic impedance .

Z Z0

ΓZ Z0⁄ 1–

Z Z0⁄ 1+-----------------------=

ZΓ

-planeZ -planeΓΓΓΓ

∞

∞–

0

Re Z Z0⁄

Im Z Z0⁄

Im Z Z0⁄

Re Z Z0⁄

1 ∞ 1 ∞–∞

0

Z0

122

123

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[43] J. Thorpe, D. Steenson, and R. Miles, High frequency transmission line using micromachined polymer dielectric, Electron. Lett. 34 (1998), pp. 1237-1238.

[44] S. Arscott, F. Garet, P. Mounaix, L. Duvillaret, J.-L. Coutaz, and D. Lip-pens, Terahertz time-domain spectroscopy of films fabricated from SU-8, Electron. Lett.34 (1999), pp. 243-244.

[45] S. Lucyszyn, Comment : Terahertz time-domain spectroscopy of films fabri-cated from SU-8, Electron. Lett. 35, (2001), pp. 1267.

[46] E. Harris, L. W. Pearson, X. Wang, C. H. Barron, Jr., and A.-V. Pham, Mem-brane-Supported Ka Band Resonator Employing Organic Micromachined Packaging, IEEE MTT-S International Microwave Symposium Digest, Boston, MA, USA, 2000.

[47] W. Y. Liu, D. P. Steenson, and M. B. Steer, Membrane-Supported CPW with Mounted Active Devices, IEEE Microwave and Wireless Components Let-ters 11 (2001), pp. 167-169.

[48] Hesler, K. Hui, R. K. Dahlstrom, R. M. Weikle, T. W. Crowe, C. M. Mann, and H. B. Wallace, Analysis of an Octagonal Micromachined Horn Antenna for Submillimeter-Wave Applications, IEEE Transactions on Antennas and Propagation 49 (2001), pp. 997-1001.

[49] Clariant, AZ9200 Photoresist, Product Data Sheet.[50] Mentor Graphics Corp, Wilsonville, OR USA. http://www.mentor.com/.[51] http://www.xs4all.nl/~kholwerd/interface/bnf/gdsformat.html.[52] Delta mask V.O.F. (Netherland). http://www.deltamask.nl/.[53] Reinraum Service Center. http://www.imtek.de/rsc/.[54] On-Wafer Vector Network Calibration and Measurements, Application

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[56] R. Osorio, M. Klein, H. Massler, J. G. Korvink, Micromachined Strip Line with SU–8 as the Dielectric, accepted paper at the 11th Gallium Arsenide Application Symposium 2003, Munich (DE), 6-7 Oct. 2003.

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128

Ricardo Osorio

IMTEK at the Albert-Ludwigs-University of Freiburg im Breisgau

Fakultät für Angewandte Wissenschaften

Georges-Köhler-Allee 103

D-79085 Freiburg i. Br., Germany

[email protected]

129

ACKNOWLEDGMENTS

First of all, I wish to express my gratitude to Prof. Dr. Jan G. Korvink for givingme the possibility of carrying out this work at the IMTEK, with the simulationgroup. In particular, I wish to thank him for his encouragement and support duringthis period and for his personal commitment in creating and maintaining a friendlyand warm atmosphere in the simulation group. This has contributed a lot to thesuccess of this work. I enjoyed this time very much.

I am very grateful to Prof. Dr. Jürgen Wilde for agreeing to be co-examiner andfor his careful reviewing of the manuscript.

Furthermore, I wish to thank the people at the Cleanroom Service Center (RCS)at the IMTEK for their cooperation in manufacturing the strip lines. Technologicaldiscussions with Dr. M. Wandt and M. Reichel were instrumental in making thiswork a success. My thanks goes also to Kay Steffen for his engagement in all thework related to electroplating.

The microwave measurements were performed at the Fraunhofer Institute forApplied Solid State Physics (IAF). It is a pleasure to thank Dr. MichaelSchlechtweg and Hermann Massler for their valuable cooperation.

I would like to thank the staff members of the simulation group for very interestingdiscussions and for helping to maintain a pleasant and harmonious working atmo-sphere. Special thanks go to Dr. A. Greiner, Dr. Jens Müller, Darius Koziol, Dr.E. Rudnyi, Oliver Rübenkönig, and Jan Lienemann.

My gratitude goes to Anne Rottler for her efficient work and help in the adminis-tration, and to the system administrator Bruno Welsch.

I have gotten to know people in other working groups at the IMTEK who werealways there as I needed their help. I would like to thank Dr. P. Ruther, MichaelEhmann, Achim Trautmann, Josef Joos, Julian Bartholomeyczik, Christoph Blat-tert, Dr. Claas Müller and all the people of the group for micro-optics.

130

I wish to thank the students I supervised, Mona Klein and Dario Mager for theircontribution to SU–8 processing and for the implementation of the FEM–code.

Finally, my deepest feelings of thankfulness go to my parents, my relatives andfriends for their support. Specially, I wish to thank my wife and my children fortheir patience during the last months and for their love.

131

CURRICULUM VITAE

Ricardo Osorio

Born March 7, 1961

1982-1986 Studies in electrical engineering, Fachhochschule Ulm. Obtainingthe grade of Diplom -Ingenieur (FH).

1987-1991 Working for the Fraunhofer Institute for Applied Solid-State Physics in Freiburg, in the area of design and characterization of MSM-Photodiodes.

1990-1995 Studies in electrical engineering, (High-frequency electronics), Uni-versity of Karlsruhe. Diplom -Ingenieur (TH).

1995-1998 Working on large signal modeling of high electron mobility transis-tor (HEMT) at the Fraunhofer Institute for Applied Solid-State Phys-ics in Freiburg.

since 1998 Working at the IMTEK-department at the Freiburg University pursu-ing the doctoral degree under the supervision of Prof. Dr. J.G. Korv-ink.

132

133

ABBREVIATIONS AND SYMBOLS

Complex normalized wave, entering a device at port .

At port outgoing complex normalized wave.

3D Three-dimensional.

Magnetic flux density vector.

Phase constant.

Wave propagation velocity.

CH3COOH Acetic acid.

CPW Coplanar waveguide.

Electric flux density or electric displacement vector.

Skin depth.

Resistance per unit length.

Conductance per unit length.

Inductance per unit length.

Capacitance per unit length.

DRIE Deep reactive ion etching.

Electric field intensity vector.

EDP Ethylene diamine pyrochatechol.

Electrical permittivity or dielectric constant.

Electric constant of vacuum.

aii

W[ ]

bii W[ ]

B Vs m2⁄[ ]

β rad m⁄[ ]

c m s⁄[ ]

D As m2⁄[ ]

δ m[ ]

R Ω m⁄[ ]

G S m⁄[ ]

L H m⁄[ ]

C F m⁄[ ]

E V m⁄[ ]

ε As Vm⁄[ ]

ε0 As Vm⁄[ ]

134

Relative permittivity.

FEM Finite element method.

FGC Finite-ground coplanar.

GaAs Gallium-Arsenide compound.

Propagation constant

GPS Global positioning system.

Magnetic field intensity vector.

HARM High-aspect-ratio-micromachining.

HF Hydrofluoric acid.

HFSS High frequency structure simulator

HN03 Nitric acid.

HNA Isotropic etchant for silicon, consisting of a mix-ture of HF, HN03 and CH3COOH.

Current density vector.

IC Integrated circuit.

Imaginary part.

KOH Potassium hydroxide.

LAN Local area network.

LIGA Lithographie-Galvanotechnik-Abformung.

MEMS Micro-electro-mechanical systems.

Magnetic permeability.

Magnetic constant of vacuum.

Relative permeability.

MUMPS Multi-user MEMS process.

Angular frequency ( ).

Electrical potential field.

εr

γ m 1–[ ]

H A m⁄[ ]

I A m2⁄[ ]

Im

µ Vs Am⁄[ ]

µ0 Vs Am⁄[ ]

µr

ω 2πf s 1–[ ]

ψ V[ ]

135

Real part.

RF Radio frequency.

RF-MEMS MEMS for radio frequency applications.

RIE Reactive ion etching.

Volume charge density.

Electric conductivity.

SUMMiT Sandia ultra-planar multi-level technology.

TE Transversal-electric.

TEM Transversal-electro-magnetic.

TM Transversal-magnetic.

TMAH Tetramethylammonium hydroxide.

Characteristic impedance.

Re

ρv As m3⁄[ ]

σ S m⁄[ ]

Z0 Ω[ ]

136

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Micromachined Transmission Lines for Microwave Applications