A Silicon Inner Tracker for the LHCb Experimentversitat Z¨ urich auf Antrag von Prof.Dr. Ulrich Straumann und Prof.Dr. Peter Tru¨ ol als Disser-¨ tation angenommen. Wenn man ein

A Silicon Inner Trackerfor the LHCb Experiment

Dissertationzur

Erlangung der naturwissenschaftlichen Doktorwurde(Dr. sc. nat.)

vorgelegt derMathematisch-naturwissenschaftlichen Fakultat

der

Universitat Zurich

von

Phillip Sieversaus

Deutschland

Begutachtet vonProf. Dr. Ulrich Straumann

Priv.-Doz. Dr. Michael Schmelling

Zurich 2002

CE

RN

-TH

ESI

S-20

04-0

0531

/12

/20

02

Die vorliegende Arbeit wurde von der Mathematisch-naturwissenschaftlichen Fakultat der Uni-versitat Zurich auf Antrag von Prof. Dr. Ulrich Straumann und Prof. Dr. Peter Truol als Disser-tation angenommen.

Wenn man ein 0:2 kassiert, dann ist ein 1:1 nicht mehr moglich

Aleksander Ristic

Abstract

The future LHCb experiment operated at the Large Hadron Collider (LHC) will perform pre-cision measurements of CP violation parameters and rare decays in theB system. A siliconstrip detector is being developed for the inner part of the LHCb tracking system covering the re-gion near to the beam pipe. Different prototype silicon sensors with a large strip pitch between198µm and 240µm were tested for the LHCb Inner Tracker. The electrical characteristics ofthe sensors are presented. Laboratory and test beam results on resolution, signal-to-noise andefficiency are discussed. Fast readout electronics have been used in order to meet the LHCboperational requirements. It has been found that the efficiency, especially in the inter-strip gap,is very sensitive to different tested geometries. The results demonstrate that sensors with a strippitch of about 200µm and a large ratio of strip width over pitch comply with the requirementsof the LHCb Inner Tracker and ensure a reliable operation of the detector. Studies on differentreadout chips were performed in order to identify the optimal front-end design for the final chip.

Zusammenfassung

Das LHCb Experiment, das am LHC Beschleuniger in Betrieb gehen wird, wird mit hoherGenauigkeit CP verletzende Grossen und seltene Zerfalle im System derB-Mesonen messen.Fur den inneren Teil des Spurkammersystems von LHCb, das den Bereich nahe des Strahlrohresabdeckt, wird ein Siliziumstreifendetektor entwickelt. Verschiedene Prototypen von Silizium-sensoren mit einem grossem Streifenabstand zwischen 198µm und 240µm wurden fur dasinnere Spursystem von LHCb getestet. Die elektrischen Eigenschaften der Sensoren wer-den vorgestellt. Die Auflosung, das Signal-zu-Rauschen-Verhaltnis und die Effizienz wurdenim Labor und verschiedenen Teststrahlmessungen untersucht und die Ergebnisse werden indieser Arbeit dargestellt. Um den betriebsbedingten Anforderungen des LHCb Experimentsgerecht zu werden, wurde schnelle Ausleseelektronik verwendet. Es hat sich erwiesen, dass dieEffizienz besonders in der Region zwischen zwei Auslesestreifen besonders empfindlich aufdie unterschiedlichen Geometrien ist, die getestet wurden. Die Ergebnisse zeigen, dass Sen-soren mit einem Streifenabstand von 200µm und einem grossen Verhaltnis von Streifenbreitezu Streifenabstand die Voraussetzungen des inneren Spurkammersystem von LHCb erfullenund einen zuverlassigen Betrieb des Detektors sicherstellen. Um die Architektur des endgulti-gen Auslesechips zu bestimmen, wurden Untersuchungen an verschiedenen Prototypen vonAuslesechips durchgefuhrt.

iv

Contents

1 CP Violation and the LHCb Experiment 2

1.1 Theoretical Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.1 CP Violation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.2 RareB Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2 The LHCb Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.1 LHCb Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Semiconductor Detectors 7

2.1 Basic Properties of Semiconductors . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.1 Charge Carrier Generation . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.2 Doped Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.3 The Energy Loss Distribution . . . . . . . . . . . . . . . . . . . . . . 9

2.2 The Semiconductor Junction . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.1 The Electric Field and the Depletion Depth . . . . . . . . . . . . . . . 10

2.2.2 The Reversed-Bias Junction . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.3 Signal Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Silicon Strip Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.4 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4.1 Thermal Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4.2 Shot Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4.3 Low-Frequency Voltage Noise . . . . . . . . . . . . . . . . . . . . . . 15

2.5 Radiation Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

i

3 The LHCb Inner Tracker 17

3.1 Requirements and Constraints on Design . . . . . . . . . . . . . . . . . . . . . 18

3.2 Detector Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.3 Silicon Ladders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.4 Readout Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4 Prototype Silicon Sensors 23

4.1 Characterisation of SPA sensors . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.1.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.1.2 Irradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.1.3 Leakage Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.1.4 Total Strip Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.1.5 Second Batch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.2 Evaluation of HPK Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.2.1 Tests Performed by the Manufacturer . . . . . . . . . . . . . . . . . . 35

4.2.2 Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2.3 Leakage Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2.4 Total Strip Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.2.5 Tests with Automatic Probe Station . . . . . . . . . . . . . . . . . . . 38

4.2.6 Metrological Measurements on Sensors . . . . . . . . . . . . . . . . . 42

4.3 Source and Laser Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.3.1 Experimental Setup and Electronics . . . . . . . . . . . . . . . . . . . 46

4.3.2 Analysis Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.3.3 Laser Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.3.4 Measurements with a106Ruβ-Source . . . . . . . . . . . . . . . . . . 49

5 Readout with the Beetle Chip 56

5.1 BeetleFE Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.1.1 BeetleFE 1.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.1.2 BeetleFE 1.1 and BeetleFE 1.2 . . . . . . . . . . . . . . . . . . . . . . 57

5.1.3 Implications on Signal-to-Noise . . . . . . . . . . . . . . . . . . . . . 59

5.2 Pulse Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

ii

6 Test Beam Results 64

6.1 Test Beam with HELIX Readout . . . . . . . . . . . . . . . . . . . . . . . . . 64

6.1.1 Test Beam Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

6.1.2 Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

6.1.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

6.2 First Measurements Using the Beetle Readout Chip . . . . . . . . . . . . . . . 80

6.2.1 Readout Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.2.2 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.2.3 Analysis and Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6.2.4 Charge, Noise and Signal-to-Noise . . . . . . . . . . . . . . . . . . . . 85

6.2.5 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

6.3 Test Beam with Full Size Prototype Sensors . . . . . . . . . . . . . . . . . . . 90

6.3.1 Readout Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

6.3.2 Test Beam Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

6.3.3 Data Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

6.3.4 Analysis Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

6.3.5 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

6.3.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

iii

Introduction

The observations of astronomers imply that the Universe is still expanding from an infinitelydense and energetic state, after an initial “hot big bang” some 15 billion years ago. One of themajor questions that modern research in particle physics seeks to answer is why did the matterin our Universe not annihilate with antimatter immediately after its creation. The phenomenonof CP violation may be the clue to this fundamental question.

High energy collisions of subatomic particles can take us back in time to the forms of matter thatprobably existed in the first fraction of a second after the big bang. In this way studying matterat the smallest of scales (subatomic particles) has become inextricably linked with research atthe largest of scales (the cosmos).

LHCb is a future experiment dedicated to investigate CP violation in theB system with highprecision. It is one of the four experiments at the LHC collider at CERN and is scheduled tostart its operation in 2007.

An important component of the LHCb detector is the tracking system which allows the deter-mination of the trajectories of charged particles that traverse its sensitive area. The trackingsystem consists of two subsystems, the Outer Tracker and the silicon Inner Tracker that is thesubject of this thesis.

The aim of this thesis is to evaluate the performance of a LHCb silicon Inner Tracker and anoptimisation of the silicon sensor geometry in order to match the LHCb Inner Tracker require-ments.

Chapter 1 gives an overview of CP violation and its formalism in the Standard Model followed,by a brief introduction to the LHCb experiment.

After the presentation of the basic properties of semiconductors and the functionality of siliconstrip sensors in chapter 2, the LHCb silicon Inner Tracker is described in detail in chapter 3.

Chapter 4 gives a description of the different prototypes of silicon sensors that were designedand produced for the LHCb Inner Tracker. The electrical properties of different prototype sili-con sensors are presented. Furthermore results of laboratory measurements are discussed.

Chapter 5 is devoted to the readout chip that is used for the LHCb Inner Tracker. The perfor-mance of several prototype chips and simulation results on the pulse shape are described.

In chapter 6 data from beam tests of silicon prototype ladders are analysed. The presentedresults provided the basis for the decision on the geometry that is implemented in the finalsensors.

A summary of the results obtained in the previous chapters concludes the thesis.

1

Chapter 1

CP Violation and the LHCb Experiment

The Standard Model (SM) is the theoretical framework of modern particle physics. It tiestogether three of the four fundamental forces known to exist, the strong force, the electromag-netic force and the weak force. Gravity, the fourth force, has not yet been incorporated into themodel. The validity of the SM is experimentally confirmed to a level that was unexpected in thebeginning. In present data no significant deviation from SM predictions is observed.

Despite the model’s excellent track record, there are strong conceptual indications for physicsbeyond the SM, like the proliferation of parameters and the intriguing pattern of fermion masses.For testing the SM, the exploration of physics withb flavoured hadrons appears to be verypromising. Measurements of CP violation in theB meson systems are particularly exciting asthey provide a powerful tool to probe physics beyond the SM. Another main topic is the studyof rare decays which are also sensitive to new-physics effects.

The LHCb experiment at the Large Hadron Collider (LHC) at CERN will perform precisionstudies of CP violating parameters in theBsystems. The copious production ofB mesons,Bu,Bd, Bs andBc at the LHC, together with the unique particle identification capabilities of theLHCb detector, will allow the experiment to measure CP violating asymmetries in a variety ofchannels that are beyond the reach of the current generation of CP violation experiments.

1.1 Theoretical Overview

1.1.1 CP Violation

Although CP violation was already discovered in 1964 by Christenson, Cronin, Fitch and Turlayin the neutral kaon system [1], it is still one of the experimentally least constrained phenomenain present particle physics.

CP is the combined transformation of charge conjugation C and parity transformation P. Theparity transformation P changes a space coordinate~x in −~x, which is equivalent to a mirrorreflection followed by a 180 rotation. Charge conjugation C transforms a particle into its

2

1.1. THEORETICAL OVERVIEW 3

antiparticle. It turns out that nature is largely, but not entirely, invariant under these transforma-tions. The violation of CP invariance implies that matter and antimatter can be distinguished inan absolute, convention-independent way. It is therefore a necessary condition for the excessof baryons over antibaryons that is observed in the universe [2]. However, CP violation withinthe SM seems to be too small to explain this imbalance, giving a hint for the presence of CPviolation beyond the SM. Many extensions of the SM have additional sources of CP violationor affect SM relations among CP violating observable. This explains the tremendous activity inpresent particle physics to study CP violation in all its facets.

The SM Description of CP Violation

CP violation enters the SM through the Cabibbo-Kobayashi-Maskawa (CKM) matrix, that con-nects the electroweak eigenstates (d’, s’, b’) of the down, strange and bottom quarks with theirphysical (i.e. mass) eigenstates (d, s, b):

d′

s′

b′

=

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

·d

s

b

≡ VCKM ·

d

s

b

. (1.1)

The elements of the CKM matrix describe charge-current (flavour changing) couplings. It canbe shown, that, in the case of three generations, three real parameters and one irreducible com-plex phase are needed to parameterise the CKM matrix. The complex phase represents a gen-uine CP violation within the SM as pointed out by Kobayashi and Maskawa in 1973 [3].

Experimentally, it is found that the transition amplitudes between different quark generationsfollow a clear hierarchy and get smaller the more they are away from the diagonal. To accom-modate this hierarchy Wolfenstein [4] proposed a parameterisation of the CKM matrix as anexpansion in powers ofλ ≡ |Vus| = sin θC , whereθC is the Cabibbo mixing angle for twoquark families [5]:

VCKM =

1− λ2/2 λ Aλ3 (ρ− i η)

−λ 1− λ2/2 Aλ2

Aλ3 (1− ρ− i η) −Aλ2 1

+O(λ4). (1.2)

Up toO(λ4) the only complex elements in the Wolfenstein parametrisation areVtd andVub.

The unitarity of the CKM matrix leads to a set of 12 equations. Six of them can be displayedas triangles in the complex plane, which are of very different shape but all of the same size.If there is no CP violation the triangles all degenerate to lines. Only two of the triangles havesides that are of the same order, namelyO(λ3). The equations describing these non-squashedtriangles are given as follows:

VudV∗

ub + VcdV∗

cb + VtdV∗

tb = 0 (1.3)

V ∗udVtd + V ∗usVts + V ∗ubVtb = 0. (1.4)

4 CHAPTER 1. CP VIOLATION AND THE LHCB EXPERIMENT

Both triangles are related to quantities that can be experimentally determined inB meson de-cays. Up toO(λ3) the two triangles coincide and the triangle corresponding to equation 1.3 isusually referred to as “the” unitarity triangle of the CKM matrix.

However, at LHC, the experimental accuracy will be so high that terms of the orderλ4 have tobe taken into account, which allows to distinguish between the unitarity triangles described byequation 1.3 and 1.4, which are shown in figure 1.1. Here,ρ andη are related to the Wolfenstein

Re

Im

(ρ,η)

0 1

γ

α

β

R

(a)

R tb

Re

Im

0 1

γ

(ρ,η)

δγ

(b)

Figure 1.1: The two non-squashed unitarity triangles. (a) and (b) correspond to the equations 1.3and 1.4, respectively.

parametersρ andη through

ρ ≡ 1− λ2/2

ρ, η ≡ 1− λ2/2

η. (1.5)

CP Violation in the B system

The measurement of CP violation is in particular simple whenB0q and 0

qB (q ∈ d, s) candecay into the same final statef wheref is a CP eigenstate. To determine CP violation, it isthen sufficient to measure the time-dependent decay asymmetry:

ACP =Γ(B0

q → f)− Γ( 0qB → f)

Γ(B0q → f) + Γ( 0

qB → f), (1.6)

whereA is related to an angle in the unitarity triangle, e.g. the CKM angleβ is measured inthe “gold-plated” modeBd→J/ψKS. Recent measurements of this angle by the BaBar andBelle collaborations established CP violation in theBd system [6, 7]. Both measurements areconsistent with SM expectations.

The measurement of otherB decays and their interpretation is more complex [8]. The aim ofthe LHCb experiment is to measure all three angles and to study if the unitarity relation

α + β + γ = 180 (1.7)

is fulfilled as expected in the SM.

1.2. THE LHCB EXPERIMENT 5

New physics could show up in several ways [9], e.g. through the violation of the unitarityrelation. Also when the unitarity relation is satisfied, it is possible that the measured angles ofthe unitarity triangle disagree with the SM predictions. Therefore, it is the utmost interest ofall futureB physics experiments to overconstrain the unitarity triangle by performing as manyindependent CP violating measurements as possible. For this purpose an important ingredientis the exploration of theBs system that is not accessible for e+-e− B-factories operating at theΥ(4S) resonance.

1.1.2 RareB Decays

By rare decays one commonly understands heavily Cabibbo-suppressedb→u transitions orflavour-changing neutral currentsb→s or b→d which, in the Standard Model, occur at smallbranching ratios∼ O(10−5) or smaller. Rare decays proceed via internal loops in whichbeyond-the-SM particles may participate. Hence, rareB decays are an important testing groundof the Standard Model and offer a strategy in the search for new physics complementary to thatof direct searches by probing the indirect effects of new physics.

The LHC will significantly enhance the statistics of rareB decays that are in principle alsoaccessible at theB factories or the Tevatron.

1.2 The LHCb Experiment

LHCb [10] is an experiment dedicated toB physics, which will be operated at the LHC atCERN. Operating with an average luminosity of 2×1032 cm−2s−1 about 1012 bb pairs are ex-pected to be produced in one year of data taking. This will allow to perform unprecedentedprecision measurements of CP violation and rare decays in theB meson system.

As bb pairs are predominantly produced at small angles with respect to the beam axis, the LHCbdetector has been designed as a single-arm forward magnetic spectrometer. Its acceptance ex-tends from approximately 10 mrad to 300 (250) mrad in the bending (non-bending) plane of the4 Tm dipole magnet.

A side view of the LHCb detector is shown in figure 1.2. Starting from the interaction point,the detector comprises a vertex detector system, a first RICH counter and a tracking system; thetracking system is followed by a second RICH counter, electromagnetic and hadronic calorime-ters and by a muon system. The vertex detector, which is located inside the beam pipe, alsoincludes a pile-up veto counter to reject events with multiple primary pp interactions. The maintracking system consists of four planar tracking stations: three stations (“T1-T3”) are locatedbetween the magnet and RICH2, the fourth station (“TT”) is situated in between RICH1 andthe magnet.

Stations T1-T3 are split into an inner and outer subsystem. The Outer Tracker will be realisedin a straw-tube drift chamber technology [11] and a silicon microstrip detector will cover theinner region around the beam pipe. This part of the detector is the Silicon Inner Tracker.

The TT station will be entirely covered by silicon strip detectors. However, the final TT layoutis still subject to further optimisation [12].

6 CHAPTER 1. CP VIOLATION AND THE LHCB EXPERIMENT

250mrad

100mrad

M1

M3M2

M4 M5

RICH2

HCALECAL

SPD/PS

SideView

MagnetT1-T3

TT

VertexLocator

RICH1

Figure 1.2: Sideview of the LHCb spectrometer. Tracking stations are labelled ”TT” and ”T1-T3”.

1.2.1 LHCb Performance

The design of the LHCb experiment is optimised to exploit the wide range ofB physics.

For this purpose, it has a high-performance trigger based on single leptons, hadrons and photonswith large transverse momentum and originating from displaced decay vertices. LHCb will inparticular benefit from its hadron trigger, since this allows the collection of many events indecay channels without leptons, e.g. the decayBs→DsK, which is one of the most promisingchannels for the determination of the angleγ of the unitarity triangle.

The detector provides excellent particle identification for charged particles which plays an im-portant role in manyB decay channels as the separation ofπ/K is crucial in hadronicB decays.Therefore LHCb has a dedicated system consisting of two RICH detectors [13].

A key element of the detector is the reconstruction of theB decay vertex with very good reso-lution. The excellent resolution of the LHCb Vertex Locator (VELO) [14] allows the studyingof the rapidly oscillatingBs mesons and to measure their CP asymmetries.

An efficient and precise track reconstruction provided by the LHCb tracking system is of utmostimportance in view of the high rates of charged particles in the detector.

Chapter 2

Semiconductor Detectors

Semiconductors combine a number of unique properties that make them very attractive for theapplication in high-energy physics experiments. For charged particle detection, silicon is themost widely used semiconductor material and silicon strip and pixel detectors are presently themost precise tracking devices. In addition, these detectors are radiation hard and fast-respondingwhich allows for applications with high counting rates. This chapter describes the basic semi-conductor properties and presents the functionality of a silicon strip detector, followed by ashort discussion of noise sources and the radiation damage in silicon detectors.

2.1 Basic Properties of Semiconductors

2.1.1 Charge Carrier Generation

In a semiconductor, the excitation of an electron from the valence band to the conduction bandalso leaves a vacancy (a hole) in its original position. The current in the semiconductor thusarises from the movement of electrons in the conduction band as well as the movement of holesin the valence band.

At any nonzero temperature, thermal energy leads to a constant generation of electron-holepairs. For semiconductor radiation detectors this intrinsic generation of charge carriers is usu-ally tried to be kept to a minimum since it contributes to the noise superimposed onto the signals.The probability per unit time that an electron-hole pair is thermally generated is given by

p(T ) = CT 3/2e−Eg2kT , (2.1)

whereT is the absolute temperature,Eg the band-gap energy,k the Boltzmann constant andC acharacteristic constant of the semiconductor material. In absence of an external electric field, anequilibrium concentration of electron-hole pairs is established. As reflected in the exponentialterm of equation 2.1 this equilibrium concentration critically depends on the temperature anddecreases drastically if the semiconductor is cooled.

7

8 CHAPTER 2. SEMICONDUCTOR DETECTORS

Another important mechanism of free carrier generation is radiation. Depending on the typeof radiation, the generation processes are highly diverse. High-energy charged particles willproduce a uniform electron-hole density along their path since they traverse the semiconductorwith almost constant velocity, whereas visible and ultraviolet light will produce single electron-hole pairs. A detailed description of charge carrier generation can be found in standard litera-ture [15].

In silicon the average energy needed to create an electron-hole pair is 3.62 eV1 which is threetimes larger than the energy gap of 1.12 eV. Hence, only part of the energy deposited by radia-tion is used for the creation of charge carriers. Two thirds of the energy go into the excitation oflattice vibrations. Note, that semiconductor radiation detectors have no built-in charge multipli-cation2, that is, the maximal output charge is equal to the charge created by the radiation. Forminimum ionising particles this charge depends on the specific energy loss in the semiconductormaterial, about 270 eV/µm in silicon, and its thickness.

If an external electric field is applied to the semiconductor, both electrons and holes will undergoa net migration. The drift velocity of the electrons and holes can be written as

ve(x) = −µeE(x)

vh(x) = µhE(x),(2.2)

whereE is the electric field strength andµe andµh are the mobilities of the electrons andholes respectively. The mobilities depend onE and the temperature. For moderate values ofthe electric field (E < 103 V/cm) and normal temperaturesµe andµh are constant, while athigher fields the drift velocities are no longer proportional to the applied field and approach asaturation value of107 cm/s atE > 104 V/cm. There is also diffusion due to random thermalmotion that inclines to smear the intrinsically concentrated charge cloud of either electrons orholes. For a typical semiconductor detector operated with an electrical field sufficiently highto reach saturated drift velocities the time to collect all charge carriers is in the order of a fewnanoseconds (see also discussion in section 2.1.3 below).

2.1.2 Doped Semiconductors

In a process called doping, small amounts of impurities are added to pure semiconductors caus-ing large changes in the conductivity of the material. A distinction is drawn whether the im-purities have a valence electron more (donor impurity) or less (acceptor impurity) than thesemiconductor material. In the first case, electrons are the majority charge carriers in the semi-conductor which is then called a n-type semiconductor. In the second case, holes dominatethe conductivity of the material and the semiconductor is referred to as p-type semiconductor.Donor impurities in silicon are phosphorous and arsenic, while gallium, boron and indium areused as acceptors. Typical impurity concentrations are between 1012 cm−3 and 1017 cm−3.

1The energy needed to create a electron-hole pair slightly depends on the temperature.2There are, however applications for semiconductors like avalanche diodes, that make use of a multiplication

process.

2.1. BASIC PROPERTIES OF SEMICONDUCTORS 9

2.1.3 The Energy Loss Distribution

The detection of charged particles by measuring their energy loss in semiconductor detectorshas led to thorough studies of the corresponding energy loss distribution [16]. Charged parti-cles traversing material lose part of their energy through elastic collisions with electrons. Theaverage energy loss in a material of finite thickness can be calculated from the Bethe-Blochformula [17, 18] by integration. There are in addition, however, statistical fluctuations aboutthis value, which have to be taken into account. For thin sensors the energy loss distributionis given, to a first approximation, by the Landau [19] and Vavilov [20] theories, which bothtreat electrons as free in the scattering process. The distinguishing parameter in both theories isthe ratio between the mean energy loss∆ and the maximum energy transferWmax in a singlecollision

κ =∆

Wmax

. (2.3)

Landau’s calculation treats the case of very thin sensors, that isκ < 0.01. The distribution canbe approximated by [21]

f(ξ(x),∆) =1

ξφ

(λ =

∆−∆′

ξ

)φ(λ) =

1√2π

exp(−1

2λ+ eλ

),

(2.4)

where∆′ is the most probable energy loss andx the thickness of the absorber. The quantityξcan be numerically expressed as

ξ = 0.1536z2

β2

Z

A· xρ [keV], (2.5)

wherez is the charge of the incident particle,Z,A andρ are the atomic number, atomic weight,and density of the semiconductor material, andx is the distance traversed through the material.Note, that due to the asymmetric shape of the Landau distribution there is a difference betweenthe most probable and the mean value of the energy loss.

The Vavilov theory covers the region of moderateκ and reduces to the Landau distribution inthe limit κ→ 0.

Most Probable Charge Deposition

Whereas experimental results show that the average energy loss increases with the momentumof the incident particle as expected from the Bethe-Bloch formula, no relativistic rise of themost probable energy loss is observed forβγ >50 [22, 23]. Forβγ >50 the most probablecharge deposition is measured to be in the order of 24000 electrons for 300µm thick silicon.However, a small decrease of the most probable energy loss is measured towards small momenta(βγ <50). This behaviour is also in good agreement with model calculations [16, 24].

The most probable charge deposition is commonly quoted for minimum ionising particles,which have a lowβγ '2-3. For 300µm thick silicon sensors this charge deposition is ap-proximately 22000 electrons [25]. Since particle momenta in the performed test beams (seechapter 6) are well aboveβγ=50, the higher value of 24000 electrons is taken as the mostprobable charge deposition in 300µm thick silicon in the context of the test beam analysis.


Extensions of the Landau and Vavilov Theories

Extensions of the calculations of Landau and Vavilov take into account the electron binding en-ergy. The modified energy loss spectrum can then be expressed as the convolution of a Gaussianfunction with a Landau or Vavilov distribution, respectively:

f(∆, x) =1

σtot√

2π

∫ ∞−∞

fL,V (∆′, x) · e−(∆−∆′)2

2σ2tot d∆′, (2.6)

wherefL,V (∆′, x) is either the Landau or Vavilov distribution and∆ is the actual energy loss.

Electronic and detector noise can be incorporated with

σ2tot = σ2

ab + σ2noise, (2.7)

whereσnoise is the standard deviation of the Gaussian noise distribution andσab describes theeffect of the atomic binding.

2.2 The Semiconductor Junction

Most semiconductor detectors are based on the formation of a p-n junction, which exhibitsa diode characteristic. Such a structure is obtained by bringing semiconductors of oppositedoping in good thermodynamical contact. Then, due to the difference in the concentrationof electrons and holes between the semiconductors, electrons diffuse into the p region andholes into the n region where they recombine. As a consequence, an electric field gradientis created which eventually stops the diffusion process and establishes thermal equilibrium.Because of the electric field there is a potential difference across the junction. The region ofchanging potential is known as depletion zone since it is almost fully depleted of all mobilecharge carriers. This characteristic can be utilised for radiation detectors. Electron-hole pairs,that are generated in the depletion zone by ionising radiation, will be separated by the electricfield and can be detected if electrical contacts are connected to the device.

2.2.1 The Electric Field and the Depletion Depth

The electric field across the junction and the width of the depletion zone depend on the donorand acceptor impurity concentration. If the charge density distributionρ(x) in the depletionzone is known, the electric field and the depletion zone width can be derived from Poisson’sequation,

∇2V =ρ(x)

ε, (2.8)

whereε is the dielectric constant (ε = 11.9ε0 in silicon). An exact analytical solution of thisequation is in most cases not possible. However, approximations such as the assumption of anabrupt change between a neutral and a completely depleted space-charge region lead to simpleexpressions [26, 27]. For example, if the acceptor impurity concentration is much higher than

2.2. THE SEMICONDUCTOR JUNCTION 11

the donor impurity concentrationNA ND, which is usually the case, the total width of thedepletion zone can be expressed as

d ' xn '(

2εV0

qND

)1/2

, (2.9)

whereq is the charge of the electron andV0 the contact potential which is in the order of 1 V.The electric field can then be found

−dV

dx= E(x) = −2V0

d2(d− x). (2.10)

Semiconductor p-n junctions to which no external voltage is applied are not used for radiationdetectors since the intrinsic electric field is too low to provide efficient charge collection. Fur-thermore, the small thickness of the depletion zone presents a large capacitance to the readoutelectronics and increases the noise.

2.2.2 The Reversed-Bias Junction

To enlarge the depletion zone a reverse-bias voltage (negative voltage to the p-side) is appliedto the junction. It is possible to obtain full depletion of the junction which can then be usedas an effective radiation detector. When applying reverse bias, equation 2.9 and 2.10 must beslightly modified by replacingV0 with VB + V0, whereVB is the bias voltage. In generalV0 canbe neglected sinceV0 VB. The electric field and therefore the carrier drift velocity decreaseslinearly (see equation 2.10), towards zero at the end of the depletion region, leading to longcharge collection times.

A more uniform field distribution and reduced collection times can be achieved by applying abias voltage higher than that required for full depletion of the junction (overbiasing) [28].

The maximum bias voltage applied to the diode is given by the resistance of the semiconductor.The current of a reverse-biased diode is called leakage current. This current has several sources(see e.g. [27]) and can increase dramatically with irradiation of the diode.

With increasing bias voltage the capacitance of the diode decreases withC ∝ V 1/2 until itreaches at full depletionV = Vdep a value of

C = εA

d, (2.11)

whered is the thickness of the diode andA its area. Hence, from a C-V-curve one can determinethe full depletion voltage of a sensor.

2.2.3 Signal Shape

Charges generated in a fully depleted detector move to the electrodes due to the applied fieldand to diffusion. Before the arrival of the moving charges at the electrodes, electrons and holes


will both induce a signal current [29]. If the applied bias voltage is higher than the minimumvoltageVdep that is needed for full depletion, the total current can be written as [15]

i(t) = ie(t) + ih(t) =q

d

(−dxe

dt+

dxhdt

)

=q(V + Vdep)

d2

(1− x0

d

2VdepV + Vdep

)

×[µee−2µe

Vdepd2 tΘ(te − t) + µhe

−2µhVdepd2 tΘ(th − t)

](2.12)

with Θ(x) =1 for x ≥ 0

0 for x < 0,

whered is the detector thickness,V the bias voltage andte andth denote the total drift time ofthe electrons and holes respectively. For 300µm thick silicon the drift time is of the order of10 ns and 25 ns for electrons and holes, respectively. The above expression strictly holds onlyfor a single electron-hole pair created atx0 and disregards diffusion. A full treatment of thepulse shape due to ionising radiation taking into account diffusion and electric field distributionis a complex issue and subject to computer simulations (see e.g. [61]). It is clear that the signalshape and its rise time strongly depend on the location of the generated charges with respect tothe electrodes and on the bias voltage.

2.3 Silicon Strip Detectors

To obtain a high-resolution spatial detector one can divide a large-area diode into many smallregions [30] (strips or pixels) and read them out separately. This section restricts to the descrip-tion of silicon strip detectors, in particular single-sided p+n (p-type strips on n-type substrate)detectors, that are most widely used in high-energy physics. The cross-section of such a deviceis shown in figure 2.1.

Most silicon strip sensors are fabricated using high-ohmic n-type silicon wafers as the bulkmaterial [31]. The implanted p strip (collecting holes) in the n bulk represent a junction whilethe backside (collecting electrons) of the detector is ohmic. The readout electronics can bedirectly connected to the p strips (DC-coupling) or to AC-coupled aluminum strips in order todecouple the front-end electronics from the the DC leakage current. A typical choice for thecoupling capacitor consists of a multilayer structure of SiO2 and Si3N4. Typical dimensionsfor silicon strip detectors are strip pitches (distance between strip centres) from 20µm up to250µm and a thickness of the order of 300µm which implies a full depletion voltage of 70 V(using equation 2.9 withND = 1012 cm−3).

The intrinsic and physical properties of silicon used in the context of this work are summarisedin table 2.1.

Depending on the application, requirements on the silicon detector can be entirely different.The detector performance can not be optimised without considering the readout electronics.

2.3. SILICON STRIP DETECTORS 13

width

Readout electronics

pitch

n

SiO

p+

Aluminum

Aluminum

+

2n

Figure 2.1: Layout of a silicon strip detector.

Atomic number 14

Average atomic mass 28.09

Dielectrical constant [ε0] 11.9

Radiation length [cm] 9.36

[g/cm2] 21.82

Band gap [eV] 1.12

indirect

Intrinsic carrier concentration [cm−3] 1.4×1010

Mean energy to create e-h pair [eV] 3.62

Drift mobility µ [cm2/V·s]Electronsµe 1450

Holesµp 450

Saturation field [V/cm] 2×104

Table 2.1: Selected properties of silicon.

The achievable spatial resolution, as an example, depends on the pitch of the strips but alsoon the readout method. For a digital readout it can be shown that the measurement precision3

can not exceed a value ofp/√

12 where p is the pitch of strips that are read out. For analoguereadout the precision can be improved by calculating the centre of gravity of the signal or otherinterpolation techniques, if the charge is distributed over several strips.

Another crucial specification of the detector is the ratio signal-to-noise which directly translatesinto a hit finding efficiency. As described in the next section, the signal-to-noise ratio criticallydepends on the detector capacitive load, which is a function of the sensor geometry. Furtherconstraints, in particular for applications in high energy physics, may arise from the require-

3The measurement precision is defined as the root-mean-square distance of the measured coordinate to the truehit position.


ments of a fast readout and of radiation hardness. For a tracking detector, radiation length isan important issue and therefore sensors should be as thin as possible. The sensor geometryhas thus to be carefully chosen in order to optimise its performance for these often somewhatcontradictory requirements.

2.4 Noise

Since there is no intrinsic signal amplification in semiconductor detectors, particular care mustbe taken to minimise the noise in the readout electronics. The noise referred to the readoutamplifier input is usually expressed in terms of equivalent noise charge (ENC) and quoted inroot-mean-square (rms) electrons. A distinction is drawn between three different sources ofnoise: thermal noise, shot noise and low-frequency voltage noise.

2.4.1 Thermal Noise

This noise is generated by thermal agitation of electrons in a conductor. Considering a conduc-tor with a resistanceR the variance of the noise voltage can be expressed as

< U2n >= 4kTR∆f, (2.13)

where∆f is the observing bandwidth,k the Boltzmann constant andT the absolute tempera-ture. Thermal noise is present in the absence of an external voltage and a flowing current. Anyphysical resistor can be described as an idealised noiseless resistor with a noise voltage sourceU2n in series. Connected to a charge-sensitive amplifier this noise voltage results in a signal

charge−Qn = CTUn, (2.14)

with CT the total capacitance, or expressed in ENC

ENC = CT eUnw, (2.15)

wherew is the average energy required to create an electron-hole pair. From equation 2.15it is obvious that minimising the noise requires minimising the total input capacitance to theamplifier. Another way to reduce the noise is to make the signal response slower. In doing sothe accepted bandwidth is decreased and thus the thermal noise.

2.4.2 Shot Noise

Shot noise originates in the quantisation of charge and the subsequent statistical fluctuations ofthe charge carrier number in a chargeQ = Nq or a current∆Q = I∆t. These fluctuations canbe represented as a noise current sourceIn flowing into the amplifier input

< I2n >= 2Ie∆f. (2.16)

Thus the current of a reversed-bias sensor contributes to the shot noise in the amplifier.

2.5. RADIATION DAMAGE 15

2.4.3 Low-Frequency Voltage Noise

Frequency dependent noise is common in most electronic systems. The1/f dependence ofthe power spectrum is a generic term for a wide range of phenomena which are possibly notalways related. An explanation of the1/f noise in transistors are crystal defects, which causetrapping of charge carriers. These traps have a certain lifetime to retain the charge leading tomodulations of the transistor current.

2.5 Radiation Damage

Radiation damage in silicon can be divided into surface damage and bulk damage. Ionisingradiation deposits charge on the surface of the silicon which changes the electric properties,like inter-strip and bias resistance, of the sensor. As a consequence sensors with punch-throughresistors are not appropriate in a high radiation environment while polysilicon or implantedresistors are radiation hard [32, 33]. The bulk is mainly damaged by displacement of the latticeatoms. Hence hadrons and heavy ions cause more damage than electrons and photons. This“Non-Ionising Energy Loss” (NIEL) is usually expressed in units of 1 MeV-neutron equivalentfluence [34].

The interaction of the radiation with the silicon lattice leads to permanent material changessuch as the creation of trapping centres [35]. Signal charge may be trapped and released too latefor detection causing a degradation of the signal and charge collection efficiency. In addition,the bulk damage leads to an increase of the leakage current which is proportional to the activesilicon volumeV and the irradiation fluenceΦ:

∆I = α · Φ · V. (2.17)

Here,α denotes the damage constant which is typically 4·10−17 A/cm for 1 MeV neutrons [36].The damage constant depends on the type and energy of the irradiation. In addition, all radiationinduced changes are initially not stable, but show strong annealing which is temperature depen-dent [37, 38]. This makes the damage constant also time-dependent. It is found that damagecan also become worse [39]. Due to the long time constant of this reverse annealing, however,its effects can be completely suppressed when operating the detector below 0C.

Radiation also changes the effective charge density in the silicon bulk thus requiring an in-creased bias voltage to ensure full depletion of the sensor [40]. In figure 2.2 the effective chargedensity and the corresponding depletion voltage for a 300µm thick silicon sensor are shown asfunction of the irradiation expressed in 1 MeV-neutron fluence. The effective doping decreaseswith the irradiation fluence and the silicon becomes intrinsic at an irradiation fluence of approx-imately 2×1012 cm−2. Above this value the silicon becomes effectively p-type. This behaviouris referred to as type inversion [41].


Fig. 4. Change in the bulk material as measured immediately

after irradiation [20].

with respect to 20°C is +200, has proven to be

quite useful. A moderately short annealing of e.g.

80 min at that temperature (equivalent to about

10 days at room temperature) has hence been pro-

posed to be used as an intrinsic way of monitoring

the irradiation fluence employing a universal a-

value [16]

a80@60

"4.0]10~17 A cm~1$5%. (7)

4.3. Effective doping concentration and depletion

voltage

For a given detector thickness d with pad area

A and an effective doping concentration N%&&

the

voltage necessary to extend the electric field

through a depth w is given by

C(»)"ee0

A

w(»)(8)

with

w(»)"S2ee

0»

q0N

%&&

(9)

and hence the depletion voltage (necessary for

reaching w"d ) is related to N%&&

by

DN%&&

D"2ee

0q0

»$%1-d2

. (10)

A measurement of »$%1-

, easily obtainable from

a capacitance voltage characteristic is therefore the

normal method to investigate the radiation induced

change in N%&&

. Again, a proper determination of

the electric field geometry (by use of a guard ring,

see above) is very important. Also the used fre-

quency and temperature at which the measurement

is performed plays a role especially in the case of

damaged silicon diodes in which deep levels are

affecting the C/» behavior. This has recently be

shown again in Ref. [22] and a thorough discussion

can be found in Ref. [23]. Finally it should be

mentioned that the detector could be either looked

at as a parallel or serial circuit of a capacitance and

a resistor. All these different methods could result

in slightly different values for the depletion voltage

resp. the effective doping concentration. In addition

what really counts is the full sensitivity of the de-

tector thickness to ionizing radiation and hence

instead of relying on C/» measurements one could

extract the full depletion voltage as that for which

a saturation of charge collection can be obtained

[21,24,25]. Most measurements have however been

done with the normal C/» method and at a fre-

quency of 10 kHz. The whole matter had been the

subject of several papers with somewhat slightly

different approaches for parameterization of the

results. The following description uses mainly

the results of the Hamburg group. Their findings

are not only based on very systematic investiga-

tions but have also included a number of other

results in a universal comparison and modeling

[21,26,27].

The observed change in the effective doping con-

centration N%&&

of the bulk material as measured

immediately after irradiation, is displayed in

Fig. 4 [20].

For the starting n-type material an exponential

decrease of the effective impurity concentration

N%&&

had been observed at lower fluences as obvious

also in Fig. 4 and this behavior had been inter-

preted as an apparent “donor removal”. Alterna-

tively the low fluence reduction of N%&&

had been

accounted for by a compensation model, which

however would not explain the observed exponen-

tial decrease [28]. There is so far no clear under-

standing of the underlying physics. On top of the

“donor removal part” acceptor-like states are being

generated leading finally to inversion of the con-

duction type and a further fluence proportional

increase of N%&&

.

6 G. Lindstro( m et al. / Nuclear Instruments and Methods in Physics Research A 426 (1999) 1—15

Figure 2.2: Effective doping concentration and the depletion voltage of an initiallyn-type sili-con sensor (300µm thick) as function of the irradiation fluence (from [38]).

Chapter 3

The LHCb Inner Tracker

A silicon strip detector has been adopted as baseline technology for the LHCb Inner Tracker. Itconsists of three stations covering a cross-shaped area around the LHCb beam pipe. Each stationhas four detection layers. Major design criteria are low material budget, fast shaping time anda moderate spatial resolution. After a discussion of the requirements for the Inner Tracker,the layout of the detector and the silicon ladders is presented, followed by a description of theInner Tracker readout scheme. An isometric view of the sensitive elements of one Inner TrackerStation is shown in figure 3.1.

Figure 3.1: Isometric view of the sensitive elements in one station of the Inner Tracker.

17

18 CHAPTER 3. THE LHCB INNER TRACKER

3.1 Requirements and Constraints on Design

The primary task of the tracking system in LHCb is to provide efficient reconstruction ofcharged particle trajectories and precise measurements of their momenta.

Single track efficiencies above 95% are required to ensure high reconstruction efficiencies forB meson decays which usually comprise multiple charged particle tracks. Taking the decaymodeB0

s→D−s (K+K−π−)K+ as an example, the trajectories of five particles, namely thosefrom theB0

s decay plus a tagging particle from the “other”b particle, have to be reconstructed.

In order to measure the invariant mass ofB decay candidates and separate the signal from back-ground an excellent momentum resolution is essential. Simulations show that in the LHCbdetector design, the momentum resolution is dominated by multiple scattering for momentaup to 100 GeV [42]. Thus, the minimisation of material budget is a major design criterionand the choice of material for building the Inner Tracker is severely constrained. On the otherhand a spatial resolution of 70µm is adequate for the Inner Tracker. In the case of the decayB0

s→D−s K+, it can be shown that the relative precision ofδp/p = 0.4% and the error of thetrack angles as measured by the vertex detector equally contribute to the invariant mass resolu-tion [43].

Charged particle rates of up to 5×105 cm−2s−1 are expected in the innermost region of the InnerTracker [44]. Primary pp interactions occur at the LHC bunch crossing frequency of 25 ns. Suchhigh rates can lead to a pile-up of events and increased dead time. For the front-end electronicsthis implies the use of much shorter shaping times than one would use to optimise the powerconsumption and the signal-to-noise ratio. However a high charge collection efficiency (CCE)over the full surface of the detector has to be reached in order to ensure an efficient trackingperformance. In addition, the layout and granularity of the detector has to be matched to theexpected particle rates to ensure low occupancies and good pattern recognition.

Radiation damage is a problem for both sensors and front-end electronics. The silicon sen-sors have to withstand a maximum radiation fluence of 9×1012 cm−2 1 MeV equivalent neu-trons and approximately 1 Mrad, after 10 years of operation at the nominal luminosity ofL=2×1032 cm−2s−1. Hence it follows that the projected maximum operation voltage for sil-icon sensors deployed in the Inner Tracker is below 200 V (see figure 2.2). Compared to othersilicon detectors at LHC [45, 46], these are moderate radiation levels. Front-end electronics,however, have to be radiation qualified since they are located close to the detector and suffersimilar radiation doses.

3.2 Detector Layout

The Inner Tracker covers a cross-shaped area around the LHC beam pipe and is surrounded bythe straw-tube Outer Tracker. The layout and the outer dimensions of the Inner Tracker weredetermined by the following requirements

• average occupancies in the innermost modules of the Outer Tracker should not exceed alevel of 10% at the nominal LHCb luminosity ofL=2×1032 cm−2s−1;

3.2. DETECTOR LAYOUT 19

21.8

41.4

52.9

125.6

36.35 36.35

19.8

Figure 3.2: 90 layer of the second station. Dimensions are given in cm and refer to the sensitivesurface covered by the Inner Tracker.

• the sensitive areas of Inner and Outer Tracker should overlap by about 1 cm;

• the area covered by the expensive silicon microstrip detectors should be kept as small aspossible;

• the modularity of standard detectors used in Inner and Outer Tracker should be respected.

The three Inner Tracker stations are each assembled from four separate detector boxes, above,below and to the two sides of the beam pipe. Each detector box contains four detection lay-ers with either vertical or near-vertical readout strips (strip orientation of 90, 85, 95 and90). Detection layers are assembled from seven detector ladders: one-sensor ladders in thetop/bottom boxes, two-sensor ladders in the left/right boxes.

The layout of a 90 layer of the second Inner Tracker station is shown in figure 3.2. Since thebeam pipe in the experiment is conical, the boxes are adjusted accordingly so that the outerdimensions slightly differ for the three stations.

Each detector box contains 28 silicon ladders, arranged in four detection layers. In order toguarantee full acceptance, ladders within a detection layer are pairwise staggered. An isometricview of a detector box is shown in figure 3.3. The box enclosure consists of thin sheets ofPIR foam that are cladded with a Kapton tape and a thin aluminum foil in order to providemechanical stiffness and electrical insulation [47]. The enclosure is light tight and guarantees agood thermal insulation.

All ladders are individually attached to a common cooling plate. To efficiently remove the heatdissipated by the front-end chips the cooling plate is operated at a temperature of -10C. Mea-surements show that the ambient temperature in the box is then around 5C [47]. Liquid C6F14,running through a cooling pipe attached to the plate, is used as cooling agent [48]. Ladders are


Figure 3.3: Isometric view od a detector box. The box enclosure is shown partially removedsuch that silicon ladders and support mechanics are visible.

mounted on the cooling plate using L-shaped ”balconies”. Leakage current calculations usingthe estimated particle fluences [44] (see equation 2.17) show, that the shot noise contribution tothe total noise can be kept below 5%, if the silicon sensor temperature is below 5C.

The choice of material for the cooling plate and the balconies has been the subject of intenseR&D program [49]. Both have to be precisely machined pieces, must exhibit excellent thermalconductivity, and need to be made from lightweight materials.

3.3 Silicon Ladders

The Inner Tracker is a silicon microstrip detector using 320µm thick single-sided sensors witha strip pitch of around 200µm. A p+n technology has been chosen to keep production costsat a tolerable level as it is the most common production method. Sensors are produced from6” wafers, 11.0 cm long and 7.8 cm wide, and are arranged in 11.0 cm (one sensor) and 22.0 cm(two sensors) ladders mounted on a U-shaped support shelf.

The support is made from high thermal conductive carbon fibre to provide cooling for the sen-sors and to give mechanical stiffness to the ladders [50]. The shelf itself is mounted directlyonto the balcony that is also produced from a highly thermal conductive material to ensuregood thermal contact to the cooling plate. The balcony also acts as a heat sink for the front-end electronics. The readout hybrid housing the front-end chips is mounted on the balcony.Thus, a direct thermal contact between the hybrid and the support shelf is avoided, preventingpossible heat flow from the readout electronics to the silicon sensors. In order to match the

3.4. READOUT ELECTRONICS 21

Silicon Sensors

Support shelf

Readout ChipPitch Adaptor

Balcony

Readout Hybrid

Balcony

Support shelf

Figure 3.4: Sketch of a two sensor silicon ladder.

BEETLE

FADC

FADC

FADC

FADC

GO

L

VSCL

copperanalogue

8

8

8

8

1 of 12

Service box on station frames

fibre transmitter

40 MHz

~5 m

L1 trigger

DAQ

Detector box

L1 electronicsboard

Electronics trailer

de−multiplexerfibre receiver

digitaloptical

19.6 Gbit/s

~100 m

Figure 3.5: Sketch of readout scheme.

different pitches of readout chips and silicon sensors, a pitch adapter made of thin film ceramicsis designed.

3.4 Readout Electronics

A sketch of the readout scheme is shown in figure 3.5. Each sensor ladder is connected to areadout hybrid carrying three Beetle front-end chips [51]. The Beetle chip is described in detail


in chapter 5. Upon a level-0 trigger accept, 32-fold multiplexed analog signals are transmittedfrom the Beetle output ports via approximately 5 m long twisted pair cable to a service box.This service box is located on the frames of the tracking station outside the acceptance ofthe experiment. In the service box, the analogue signals are digitised using four parallel 8 bitFADC channels and then serialised by a CERN GOL chip [53]. The output of 12 GOL chips,corresponding to four silicon ladders, are transmitted via 100 m long 12-fibre optical cableto the Level-1 electronics located in the LHCb electronics hut. Each Level-1 electronics boardreceives the data from four optical cables, corresponding to the data from 16 ladders. A detaileddescription of the data readout system is given in [52].

The complete Inner Tracker comprises 336 silicon ladders with 384 channels each. This addsup to approximately 129000 detector channels or 4032 Beetle output channels.

Chapter 4

Prototype Silicon Sensors

The large surface to be covered by the Inner Tracker, together with the moderate requirementson spatial resolution and radiation hardness, calls for a simple and robust design of the siliconsensors. Single-sided, AC-coupled p+n strip detectors were selected as sensor technology forthe Inner Tracker.

The combined requirements of fast shaping time, thin sensors and long readout-strips with ac-cordingly high capacitive load seen by the front-end electronics restrict the attainable signal-to-noise performance of the sensor ladders. A sensor thickness of 320µm was chosen because it isthe minimum thickness that can be expected to give an acceptable signal-to-noise performancefor the long silicon ladders employed in the Inner Tracker.

The sensor R&D program has concentrated mainly on the optimisation of the strip geometry.A strip pitch of approximately 200-240µm is suggested by the required spatial resolution, thedetector geometry, and the readout chip granularity. In addition, the pitch of the sensors shouldbe as large as possible in order to reduce costs of the readout electronics. Another importantparameter is the width of the strip implants. For a given pitchp, the total strip capacitanceincreases with increasing implant widthw. Thus, small values of the width-over-pitch ratio,w/p, are in principle favoured since reducing strip capacitance also reduces preamplifier noise.On the other hand, a high charge collection efficiency over the full sensor has to be reached.In the first test beam (see section 6.1) it was observed that the charge collection efficiency inthe region in between the strips deteriorates significantly for smallw/p values if fast readoutelectronics are used.

A careful optimisation of strip geometry is thus necessary in order to optimise the single-hitefficiency of the detector. For this purpose, different strip geometries, using pitches between198µm and 240µm and implant widths corresponding tow/p values between 0.2 and 0.35were implemented and investigated on prototype sensors.

Two generations of prototype sensors were developed and tested. In this chapter, technologyand geometry specifications of the sensors will be described, as well as their characterisation inthe laboratory.

23

24 CHAPTER 4. PROTOTYPE SILICON SENSORS

Bulk material n-type silicon, oxygenated

Crystal orientation <100>

Resistivity 4-6 kΩ·cm

Thickness 300µm

Wafer size 4” diameter

Table 4.1: Characteristics of silicon wafers.

Implant type p+

Implant depth 1µm

Breakdown protection strip side n+ guard rings, 15 rings

Strip biasing polysilicon resistors

Breakdown protection backplanenone

Backplane biasing edge contact

readout coupling AC, SiO2/Si3N4 multilayer

Coupling capacitance >100 pF/cm

Breakthrough voltage >500 V

Leakage current at full depletion<2µA

Table 4.2: Specifications of sensor technology.

4.1 Characterisation of SPA sensors

A first batch of 22 multi-geometry prototype sensors for the LHCb Inner Tracker were designedand produced by the company SPA Detector, Kiev, in November 2000. The sensors were pro-duced on oxygenated 4” wafers, purchased from SINTEF and CNM Barcelona and providedto SPA Detector by the Inner Tracker group. Oxygenation is expected to improve the radia-tion hardness of the sensors [54]. Four of these prototype sensors were irradiated with 24 GeVprotons to a peak fluence of about 1014 particles per cm2.

The main characteristics of the wafers and the sensor technology specifications are summarisedin tables 4.1 and 4.2. Two sensors with a strip length of 66.6 mm and 64 readout strips each,were produced from each wafer. The active area is surrounded by a guard ring design consistingof 15 rings in order to enable high voltage operation and long term stability of the sensor. Thegeometry specifications of the sensors are summarised in table 4.3.

Overall, six different strip geometries were implemented on two types of sensors. The strip pitchis 240µm everywhere. Each sensor has three regions with implant widths of 48µm, 60µm, and72µm, respectively. In addition, the readout metal is 8µm wider than the implant width on oneof the two sensors produced on a wafer, whereas on the second sensor it is 2µm narrower thanthe implant width.

Different strip geometries were implemented in order to study their influence on strip capac-itance, charge collection efficiency, and high-voltage performance. The width of the readout

4.1. CHARACTERISATION OF SPA SENSORS 25

Overall dimensions 21.040 mm× 71.930 mm

Active area 15.192 mm× 66.60 mm

Strip length 66.60 mm

Number of strips 64

Strip pitch 240µm

readout pitch 240µm

Implant width, strips 1-21 48µm (w/p = 0.20 )



Metal strip width, sensor type 1implant width +8µm

Metal strip width, sensor type 2implant width -2µm

Table 4.3: Sensor geometry.

metal strip is normally chosen slightly narrower than the width of the implant. Simulations andmeasurements by the CMS tracking group have however indicated that a metal strip wider thanthe implant (so-called “over-metallisation”) can improve high-voltage stability, while increas-ing the strip capacitance only marginally [55]. The bias resistors were measured to be around3 MΩ. At this value the contributed additional noise of the resistor is negligible compared tothe total sensor noise that is dominated by the capacitive load [33].

The layout of the corner of a sensor is shown in figure 4.1. The guard-ring structure, the biasingring and bias resistors, the readout strips with two AC pads and a DC pad, as well as varioustest pads and markers are clearly visible.

The sensors are numbered according to the following scheme, wherexx is the wafer number:

SINTEF wafers CNM wafers

under-metallised 4820-xx-p–2 4821-xx-p–2

over-metallised 4820-xx-p+8 4821-xx-p+8

A number of tests were performed at SPA Detector, on 0.42 cm2 small test structures that wereimplemented on the wafers, in addition to the sensors. The main results of these tests are:

SINTEF wafers CNM wafers

full depletion voltage 70 V 74 V

leakage current 10-15 nA <10 nA

Typical breakdown voltages of 300-800 V were measured on these test structures. However,it was found that leakage currents on the sensors already started to grow significantly for biasvoltages above typically 120 V.


Figure 4.1: Layout detail of the corner of a sensor.

4.1.1 Setup

Overall, 13 sensors produced on SINTEF wafers and two irradiated sensors produced on CNMwafers were tested. In order to characterise the sensors two measurements have been performedas function of the bias voltage:

• leakage current

• total strip capacitance

The measurement of the leakage current is a first and simple quality check of the sensor. Thecurrent was measured between the back plane and the strip biasing pad at room temperature.

From the voltage dependence of the capacitance one can extract the full depletion voltage ofthe sensor. The total capacitance is also the limiting factor for building long sensor modulesbecause signal-to-noise performance deteriorates with increasing capacitance.

The capacitance measurements have been performed with a HP 4192A LCR meter connectedto a PC via GPIB bus. To determine the total capacitance seen by one strip, the two closestneighbouring strips were AC-coupled to the back plane during the measurements (couplingcapacitance of 1µF). A scheme of the setup is shown figure 4.2. The effect of all remainingstrips is neglected in view of the large pitch of the sensors. The total strip capacitance is thenthe sum of the body capacitance and the capacitance to the closest neighbouring strips. Thetotal strip capacitance shows a strong frequency dependence above 1 MHz (see figure 4.3), dueto the complex impedance of the sensor. The sensors are not “pure” capacitances. A measuringfrequency of 1 MHz and an amplitude of 1 V were used for all following tests.


PC

LCR

−M

eter

R=1M

C=1

Sensor

−+

C=1

C=1µ

Ω

µµ

F

F F

Power Supply

GPIB

RS232

Prober Chuck

Figure 4.2: Schematic view of the setup for the four-wire measurement of the total strip capac-itance.

Frequency [Hz]

Cto

t [pF

]

10

105

106

Figure 4.3: Total capacitance as function of frequency. During the measurement the sensor wasbiased with 75 V.


4.1.2 Irradiation

Four sensors (two under-metallised and two over-metallised) were exposed to a peak fluence ofabout 1.7×1014 24 GeV protons cm−2, corresponding to more than 10 years of LHCb operation.The damage factor of this beam is 0.5 to 0.6 [56], i.e. the equivalent 1 MeV-neutron fluence isabout half of the 24 GeV proton fluence. The fluence is significantly higher than the maximalfluence of 9×1012 cm−2 1 MeV equivalent neutrons expected for the Inner Tracker, since at thetime the irradiation was carried out simulations predicted much higher radiation levels [57]. Theirradiation was performed at the CERN IRRAD1 facility and the received fluence on the sensorswas monitored by measuring the activation of aluminum foils after the irradiation. It was foundthat the irradiation was non-uniform over the surface of the sensors. For the under-metallisedsensor only the outer part of the sensor towards the highest strip numbers was exposed to themaximal fluence, whereas for the over-metallised sensor the irradiation profile was reversed.The irradiation profile as function of the strip number for the over-metallised sensors is shownin figure 4.4. During irradiation the sensors were not biased. After irradiation the sensors were

strip

fluen

ce [1

014cm

-2]

0.5

1

1.5

2

0 20 40 60

Figure 4.4: Irradiation profile for the over-metallised sensors. The fluence of the under-metallised is obtained by replacing the strip numbers→ 65− s.

annealed for four days at room temperature. More details on the irradiation can be found in [58].

4.1.3 Leakage Current

Figure 4.5 shows the leakage current as function of the bias voltage for two sensors beforeirradiation. An ideal sensor should exhibit the typical characteristic curve of a diode and havea plateau in the I-V-curve. A deviation indicates a problem of the sensor, although it does notmean that the sensor is useless. Two of the 15 analysed sensors do not show a plateau in the


characteristic curve. All results are in agreement with measurements performed on the samesensors done by our collaborating group at the University of Lausanne [59].

bias voltage [V]

leak

age

curr

ent [

nA]

0

500

1000

1500

2000

2500

3000

0 20 40 60 80 100 120bias voltage [V]

leak

age

curr

ent [

nA]

0

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60

Figure 4.5: Leakage current as function of the bias voltage for two sensors before irradiation.Left: well working sensor, the characteristic curve is diode-like. Right: sensor with continuousincrease of the current. The characteristic curve shows no plateau. Both sensors are over-metallised.

As mentioned in section 2.5, one of the main changes due to irradiation is the increase of theleakage current, which rises linearly with the exposed fluence. In figure 4.6 the leakage currentas function of the bias voltage is illustrated for an irradiated sensor. Due to the large leakagecurrent the bias voltage was not increased above 150 V.

Furthermore, strip leakage currents on an irradiated sensor have been measured at room tem-perature. Due to the inhomogeneous irradiation the strip currents decrease continously towardshigher strip number, as figure 4.7 demonstrates. Shown are measurements on eight differentstrips equally distributed across the sensor and at various bias voltages. They are in reasonableagreement with the strip currents expected from the received fluence and beam profile (see fig-ure 4.4). The reasonable agreement between the calculation and the measurements suggests thatthe assumed irradiation profile during the exposure has indeed been applied on the detector.

4.1.4 Total Strip Capacitance

The knowledge of the total strip capacitance is of utmost interest since it limits the lengthof sensor ladders. The signal-to-noise performance of the detector degrades with increasingload capacitances resulting from longer sensor ladders. The measurement of the total stripcapacitance is also used to estimate the full depletion voltage of the sensors where the C-V-curve is expected to become flat. To be precise, it is the capacitance to the back plane that issensitive the depletion voltage (see section 2.2.2). But since the inter-strip capacitance is almostindependent of the bias voltage, it is adequate to use the total strip capacitance. Figure 4.8 showsthe total strip capacitance as function of the bias voltage for one sensor before irradiation. The


bias voltage [V]

leak

age

curr

ent [

µA]

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120 140 160

Figure 4.6: Leakage current as function of the bias voltage of an irradiated sensor (4820-17-P+8). The measurement was performed at room temperature.

strip number

strip

cur

rent

[µA

]

bias=100Vbias=120Vbias=140Vbias=160Vcalc

0

2

4

6

0 10 20 30 40 50 60 70

Figure 4.7: Strip leakage current on an irradiated sensor (4821-14-P-2) for different bias volt-ages as function of the strip number. The two solid lines indicate the expected strip currentsfrom the beam profile (see figure 4.4), and using radiation damage constants of 2·10−17 A/cmand 3·10−17 A/cm respectively corresponding to 24 GeV protons.

C-V-curves look similar for all sensors, indicating that the full depletion voltage is reached atabout 50 V to 70 V consistent with expectation.

The total strip capacitance depends on the ratio of strip width to strip pitch (w/p) and can beparametrised as a linear function [60]. A linear fit to measured capacitances on differentw/p-


w/p=0.3

w/p=0.25

w/p=0.2

w/p=0.3

w/p=0.25

w/p=0.2

w/p=0.3

w/p=0.25

w/p=0.2

bias voltage [V]

capa

cita

nce

[pF

/cm

]

0

1

2

3

4

5

6

7

0 20 40 60 80 100

Figure 4.8: Total capacitance per unit length as function of the bias voltage. The figure alsoshows the effect of the different values of the parameterw/p on the capacitance.

regions yields

Ctot = (1.08 + 1.55 · wp

) [pF/cm] (4.1)

for the under-metallised and

Ctot = (1.15 + 1.51 · wp

) [pF/cm] (4.2)

for the over-metallised sensors (see figure 4.9). The systematic dependence onw/p can be ob-served individually for every sensor, however the variation from sensor to sensor is of the samemagnitude. These results are in fair agreement with electrostatic simulations [61] and measure-ments by other groups [46]. Table 4.4 summarises the capacitance measurements performedwith sensors before irradiation.

Changes of the material properties induced by irradiation also affect the behaviour of the sensorswith respect to the capacitance. Figure 4.10 shows the total measured strip capacitance asfunction of the bias voltage after irradiation.

Due to the very inhomogeneous irradiation profile, different areas of the sensor are expectedto fully deplete at different bias voltages, making a detailed interpretation of the measuredcurve difficult. However, the measurement clearly demonstrates that a higher bias voltage isneeded to fully deplete the sensor. At 150 V the measured capacitance is still significantly largerthan before irradiation, but it seems to still decrease with increasing bias voltage. Higher biasvoltages were not applied because the leakage current started to grow significantly. Table 4.5presents the results of the capacitance measurements of the irradiated sensors.


w/p

C[p

f/cm

]

Ctot=1.01+1.55*w/p

11.11.21.31.41.51.61.71.8

0 0.1 0.2 0.3 0.4 0.5w/p

C[p

f/cm

]

Ctot=1.15+1.51*w/p

11.11.21.31.41.51.61.71.8

0 0.1 0.2 0.3 0.4 0.5

Figure 4.9: Total strip capacitance per unit length as function of the ratio strip width to pitch(w/p) for under-metallised (left) and over-metallised sensors (right). Different markers refer todifferent sensors. During the measurement the sensors were biased with 75 V.

capacitance in pF

Sensor w/p =0.2 0.25 0.3

4820-08-P-2 9.570 9.865 10.36

4820-11-P-2 9.659 9.792 10.59

4820-12-P-2 9.109 9.763 9.934

4820-13-p-2 9.011 9.690 9.969

4820-06-P-2 9.853 10.32 11.08

4820-14-P-2 8.981 9.631 10.21

4820-08-P+8 9.735 10.31 10.59

4820-12-P+8 9.580 10.23 10.68

4820-13-P+8 9.673 10.22 10.49

4820-16-P+8 10.07 10.60 10.98

4820-05-P+8 9.798 10.07 11.18

Table 4.4: List of measured capacitances for not irradiated sensors. A frequency of 1 MHz anda bias voltage of 75 V was used.

4.1.5 Second Batch

For further tests, a second batch of prototype sensors were ordered from SPA Detector. Allof the 20 delivered sensors exhibited a slightly improved I-V-characteristic compared to thesensors of the first batch. The leakage current was measured to be of the order of 100 nA. Inaddition a bias voltage of 110-125 V could now be applied without significant enhancement ofthe leakage current (see figure 4.11). However, the breakdown voltage of the new sensors alsodoes not match the requirements of the LHCb Inner Tracker.


w/p=0.3

w/p=0.25

w/p=0.2

w/p=0.3

w/p=0.25

w/p=0.2

w/p=0.3

w/p=0.25

w/p=0.2

bias voltage [V]

capa

cita

nce

[pF

/cm

]

0

1

2

3

4

5

0 50 100 150

Figure 4.10: Total capacitance per unit length as function of the bias voltage after irradiation.

capacitance in pF

Sensor w/p = 0.2 0.25 0.3

4820-17-P-2 12.75 14.28 12.75

4821-14-P-2 12.54 13.64 13.70

4820-17-P+8 14.17 15.06 15.64

4821-13-P+8 14.11 14.99 15.03

Table 4.5: List of measured capacitances for irradiated sensors. A frequency of 1 MHz and abias voltage of 120 V was used.


bias voltage [V]

leak

age

curr

ent [

nA]

0

200

400

600

800

1000

0 50 100

Figure 4.11: Leakage current as function of the bias voltage for a SPA sensor of the secondbatch.

4.2. EVALUATION OF HPK SENSORS 35

Wafer size 6”

Wafer thickness (320±20)µm

Bulk material n-type

Resistivity (3-8) kΩ·cm

Crystal orientation < 100 >

Implant p+-type

Strip biasing resistors (1.5±0.5) MΩ, polysilicon

Readout coupling AC

Coupling capacitance > 125 pF/mm2

Table 4.6: Wafer characteristics and specifications of the sensor technology.

4.2 Evaluation of HPK Sensors

Based on the first test beam results on the SPA prototype sensors presented in section 6.1 thesensor specifications for the Inner Tracker were reviewed. New full-sized prototype sensorswere then ordered from HPK Hamamatsu. In February 2002 Hamamatsu delivered 15 prototypesensors. A summary of the sensor technology specifications and the wafer characteristics isgiven in table 4.6. The single-sided and AC-coupled sensors were produced from 6” wafers,have a physical dimension of 110 mm×78 mm and a thickness of 320µm of the n-type substrate.The overall dimensions and the technology are identical to the foreseen final sensor design asdescribed in section 3.3.

The sensors consist of five regions of different strip geometry. Two different pitches of p+

strips, 198µm and 237.5µm respectively, are implemented on the sensor. Additionally, thewidth of the p+ strips is varied. The 198µm region has implant widths of 50µm, 60µm and70µm, whereas the width of the strips in the 237.5µm region is 70µm and 85µm, respectively.This design results in five different values (two almost are the same) of the ratio strip widthto strip pitch,w/p, which is the scaling parameter of the sensor capacitance. The width ofthe aluminium strip is 8µm wider than the implant width. Table 4.7 summarises the geometryparameters of the prototype sensors.

It is intended to implement one of these strip geometries in the final design for the siliconsensors of the LHCb Inner Tracker. The decision will be based upon performance tests on theprototype sensors described in section 6.3.

4.2.1 Tests Performed by the Manufacturer

The quality acceptance criteria are summarised in table 4.8. Before delivery, the leakage currentand the capacitance as function of the bias voltage (I-V and C-V-curves), the sensor thicknessand the breakdown voltage were measured by the manufacturer for all sensors. Additionally, thesize of the polysilicon resistors was estimated and the quality of every strip was checked. Strips


Overall dimensions 110 mm× 78 mm

Active area 108 mm× 75.6 mm

region strip No. pitch [µm] number of strips p+ width [µm] AC Al width [µm] w/p

A 1-64 198 64 50 58 0.252

B 65-128 198 64 60 68 0.303

C 129-192 198 64 70 78 0.354

D 193-272 237.5 80 70 78 0.295

E 273-352 237.5 80 85 93 0.358

Table 4.7: Sensor geometry.

Figure 4.12: Photographs of one prototype sensor. The five different geometries implementedon a sensor are clearly visible (left). The close-up (right) shows details of the sensor edge likethe single-guard ring structure, the bias ring, polysilicon bias resistors and DC- and AC-contactpads.

with a coupling capacitor short at 100 V, a current above 10 nA at 80 V or a broken polysiliconresistor were flagged as “not good” strip by the manufacturer. These strips are listed in table 4.9.

Seven of the 15 delivered sensors have more than three bad channels and therefore in fact donot pass the quality acceptance test. Nevertheless these sensors were accepted, in view of thetight production schedule imposed by an upcoming test beam period. Hamamatsu said that theycould not produce replacement sensors within the short time between receiving the specificationand the requested delivery date. They assured that, given an appropriate time for production, itwill not be a problem for them to fulfil the given specification. From the C-V-measurements thefull depletion voltage of the sensors was estimated to be between 65 V and 75 V.

4.2.2 Measurement Setup

The experimental setup used to characterise the HPK prototype sensors was identical to thatused for the measurements on the SPA sensors. For every sensor, the leakage current was mea-sured as function of the bias voltage. The total strip capacitance was determined also as function


Wafer planarity <50µm

Dicing tolerance ±20µm

Dicing parallelity ±10µm

Depletion voltage 40-100 V

Breakdown voltage >300 V

Inter-strip resistance >1 GΩ

Total leakage current <1µA at 80 V

Breakthrough voltage AC coupling >100 V

Number of bad strips per sensor <4

Table 4.8: Quality acceptance criteria.

No. of bad strip with

sensor coupling short enhanced leakage current

0001 / /

0002 / 153

0003 59 /

0004 / /

0006 58, 60 53, 93, 100, 106, 147, 148, 150, 160

0008 33 17, 22, 32

0009 139, 205 70, 163

0010 / /

0011 223, 235, 245 213, 214, 215, 218, 219, 227, 242

0012 261, 330 232, 244, 245, 248, 249, 255, 256, 260, 263, 275

0013 217, 232 227, 231, 236, 237

0014 / /

0015 / /

0016 54, 70, 76, 77, 132 45, 60, 81, 82,151

0018 / /

Table 4.9: Number of strips flagged as bad by the manufacturer.

of the bias voltage, once for every region on every sensor. All measurements were performed atroom temperature. For the determination of the capacitance, a measuring frequency of 1 MHzand an amplitude of 1 V were applied.

4.2.3 Leakage Current

Figure 4.13 shows the leakage currents as function of the bias voltage, for all 15 prototype sen-sors. In this test, the bias voltage was not increased above 300 V. Up to 300 V, all except one of


the sensors show no evidence of breakdown and for six of the sensors the leakage current is stillbelow 200 nA at 300 V. Three sensors (0006, 0008 and 0012) generally show a somewhat higherleakage current and sensor 0018 exhibits a breakdown at 280 V. All our leakage current mea-surements are consistent within 20 % with the measurements performed by the manufacturer,apart from the breakdown of sensor 0018 that was not observed by the manufacturer.

Moreover, a few sensors have been biased up to 500 V without showing any indication of ajunction breakdown. This demonstrates that the single guard ring design by Hamamatsu ensuresan excellent protection for single-sided devices against breakdown effects. The current stabilityof two sensors was investigated and verified in a∼20 h long biasing test. No significant increaseof the leakage current was observed over the duration of the test.

4.2.4 Total Strip Capacitance

As for the measurements on the SPA sensors, the total strip capacitance was measured as thesum of the capacitance to the backplane and the capacitance to the adjacent strips, measuredat 1 MHz. Figure 4.14 shows the total strip capacitance per unit length as function of the biasvoltage.

C-V-curves were measured for all sensors, indicating a full depletion voltage of the order of60 V, which is consistent with the value quoted by the manufacturer. The measured values ofthe total strip capacitances at a bias voltage of 80 V (which is above full depletion voltage) aresummarised in table 4.10.

The total capacitance can be expressed as a linear function of the ratio strip widthw to strippitch p. Figure 4.15 shows the total capacitance as function ofw/p. A linear fit results in theparametrisation:

Ctot = (1.02 + 1.65 · wp

) [pF/cm]. (4.3)

This result is in agreement at a 15 % level with the previous measurements on the SPA sensors.

4.2.5 Tests with Automatic Probe Station

An automatic wafer probe station setup has been commissioned, consisting of an Electroglas1034XA6 probe station with a 6” chuck1, a probe card for contacting DC- and AC-pads on thesensor and an HP 4192A LCR meter . The probe station and the LCR meter were controlled viaGPIB bus and a LabVIEW program running on a PC.

The automatic probe station has been used to carry out coupling capacitor scans on all deliveredsensors. The measurement of the coupling capacitances for each individual strip allowed todetect certain classes of bad strips, which are characterised by a metal open, a metal short or apinhole in the dielectric substrate of the coupling capacitor.

1The Electroglas 1034XA6 wafer prober has air bearings, so that the chuck holding the sensor under vacuumruns frictionless on a linear electro motor plate without any mechanical wear. After an alignment of the sensor onthe prober chuck, a fast and fully automatised scan of the sensor can therefore be performed.


bias voltage [V]

leak

age

curr

ent [

nA]

sensor 0001

0

500

1000

1500

2000

0 100 200 300bias voltage [V]

leak

age

curr

ent [

nA]

sensor 0002

0

500

1000

1500

2000


leak

age

curr

ent [

nA]

sensor 0003

0

500

1000

1500

2000

0 100 200 300

bias voltage [V]

leak

age

curr

ent [

nA]

sensor 0004

0

500

1000

1500

2000


leak

age

curr

ent [

nA]

sensor 0006

0

500

1000

1500

2000


leak

age

curr

ent [

nA]

sensor 0008

0

500

1000

1500

2000

0 100 200 300

bias voltage [V]

leak

age

curr

ent [

nA]

sensor 0009

0

500

1000

1500

2000


leak

age

curr

ent [

nA]

sensor 0010

0

500

1000

1500

2000


leak

age

curr

ent [

nA]

sensor 0011

0

500

1000

1500

2000

0 100 200 300

bias voltage [V]

leak

age

curr

ent [

nA]

sensor 0012

0

500

1000

1500

2000


leak

age

curr

ent [

nA]

sensor 0013

0

500

1000

1500

2000


leak

age

curr

ent [

nA]

sensor 0014

0

500

1000

1500

2000

0 100 200 300

bias voltage [V]

leak

age

curr

ent [

nA]

sensor 0015

0

500

1000

1500

2000


leak

age

curr

ent [

nA]

sensor 0016

0

500

1000

1500

2000


leak

age

curr

ent [

nA]

sensor 0018

0

500

1000

1500

2000

0 100 200 300

Figure 4.13: Leakage current as function of the bias voltage. The measurement was performedat room temperature.


Region A B C D E

Region A B C D E

Region A B C D E

Region A B C D E

Region A B C D E

bias voltage [V]

capa

cita

nce

[pF

/cm

]

0

1

2

0 25 50 75 100

Figure 4.14: Total capacitance per unit length as function of the bias voltage. This measurementwas performed on sensor 0001.

capacitance in pF

Sensor Region A B C D E

0001 15.12 16.33 16.32 15.26 16.63

0002 15.65 16.21 17.38 15.91 17.37

0003 15.60 16.20 17.38 16.13 17.62

0004 15.51 16.12 17.38 15.86 17.59

0006 15.45 16.38 17.16 16.10 17.53

0008 15.74 16.42 17.66 16.52 18.00

0009 15.82 16.29 17.71 16.22 17.71

0010 15.82 16.53 17.52 16.48 18.28

0011 15.51 16.28 17.55 16.02 17.53

0012 14.81 16.43 17.22 16.37 18.73

0013 15.38 16.14 17.31 15.82 17.57

0014 15.32 16.25 17.61 16.16 17.68

0015 16.04 15.97 16.81 15.61 17.18

0016 15.32 15.93 17.21 15.96 17.64

0018 15.84 16.41 17.73 16.44 17.96

Table 4.10: List of measured capacitances at 80 V bias voltage. A frequency of 1 MHz wasused.

The bad channels observed in our coupling capacitor scans were used as a cross check of Hama-matsu’s results. In addition, the specified value of the coupling capacitors was verified, which


w/p

capa

cita

nce

[pf/c

m]

w/p

capa

cita

nce

[pf/c

m]

w/p

capa

cita

nce

[pf/c

m]

w/p

capa

cita

nce

[pf/c

m]

w/p

capa

cita

nce

[pf/c

m]

w/p

capa

cita

nce

[pf/c

m]

w/p

capa

cita

nce

[pf/c

m]

w/p

capa

cita

nce

[pf/c

m]

w/p

capa

cita

nce

[pf/c

m]

w/p

capa

cita

nce

[pf/c

m]

w/p

capa

cita

nce

[pf/c

m]

Ctot=1.02+1.65*w/p

1.4

1.5

1.6

1.7

0.2 0.25 0.3 0.35 0.4

Figure 4.15: Total strip capacitance per unit length as function of the ratio strip width to strippitch (w/p). Different markers refer to different sensors. The line is an averaged linear fit.

was requested to be larger than 125 pF/mm2.

The coupling capacitor measurements were performed by simultaneously contacting the AC-and DC-pads of one strip of the sensors swith the probe card, in order to determine the couplingcapacitance of the strip with the LCR meter. This setup can be modelled as an impedancenetwork, consisting of a coupling capacitance between implant and metal (aluminium) layer,and a finite resistance represented by the metal and the implant itself. Since this network acts asa low-pass filter, the measured capacitance value becomes frequency-dependent. This frequencydependence, as obtained with the LCR meter at an oscillator amplitude of 1 V, is shown infigure 4.16, where the coupling capacitor values are plotted for the five geometrical strip regionsA-E (compare table 4.7). Note, that the coupling capacitor values depend on the implant widthand hence differ from region to region, except for regions D and C, which have the same implantwidth.

The roll over frequency in figure 4.16 occurs at around 10 kHz, so that a safe coupling capacitorvalue can be extracted in the low-frequency limit at frequencies of 1 kHz or less. Therefore,we have chosen to perform the coupling capacitor scan of the silicon sensors at a frequency of1 kHz. One of the resulting coupling capacitor profiles across the five geometrical regions A-Eas function of strip number for sensor Ham-0012 is shown in figure 4.17. Two particular chan-nels in this plot have coupling capacitors out of specifications, due to pinholes in the oxide. Inoder to detect pinholes in the dielectric the leakage current through the capacitor was measuredwhile a voltage was being applied across the dielectric. Overall, the capacitor profile is veryuniform and has an rms value of less than 1%. The obtained mean capacitance values for theregions A-E are presented in table 4.11. The values are well within specifications.


0

500

1000

10-1

1 10 102

freq [kHz]

capa

cita

nce

[pF

]

region Aregion Bregion Cregion Dregion E

Figure 4.16: The frequency dependent value for the coupling capacitor in regions A-E.

500

750

1000

1250

1500

0 100 200 300strip

capa

cita

nce

[pF

]

Figure 4.17: Coupling Capacitor scan of HAM-0012. The capacitor measurement was per-formed at a frequency of 1 kHz and a voltage amplitude of 1 V.

4.2.6 Metrological Measurements on Sensors

The proposed assembly procedure for Inner Tracker ladders [62] makes use of the cut edges ofthe sensors for alignment purposes. In a fixture or assembly template, the sensors are pushedwith their cut edge against posts in order to align two sensors with respect to each other andwith respect to alignment pins in the ladder support. This procedure has the advantage of beingsimple and fast, but relies on the quality of the cutting line of the wafer. In the specifications,


region width [µm] mean capacitance (pF/cm)specification (pF/cm)

A 50 76.8 62.5

B 60 90.7 75

C 70 104.4 87.5

D 70 104.2 87.5

E 85 123.8 106.25

Table 4.11: Average coupling capacitor values in different regions.

we requested that the cutting line has to be parallel within±10µm with respect to a datum linedefined by the silicon targets. Furthermore, the dicing tolerance should be within±20µm ofthis datum line. Another specification is the flatness or planarity of the sensor itself, which wasrequested to be within±25µm.

In order to verify these mechanical specifications, four silicon sensors were characterised on aprecise optical metrology machine2. The profile of the sensors has been determined by mea-suring the surface height of the sensors in a free state. Different focusing techniques, namelya laser focus and a LCD grid-projector, have been applied to determine the heightz, and themeasurement uncertainty is below 2µm. On each sensor,z-coordinates have been recorded onan equidistant grid of 10×10 points covering the full surface of the sensor. A typical example ofthe resulting profiles is shown in figure 4.18. It shows a characteristic sensor deflection of80µmover the full length of 110 mm and width of 78 mm. Similar to the surface curvature studies forthe LHCb VELO sensors [63], the shape has been fit by a five parameter 2D parabolic curve:

z = A+Bx+ Cx2 +Dy + Ey2 (4.4)

The values obtained forC andE are in between 2.2·10−5 mm−1 and 2.9·10−5 mm−1. These re-sults can be compared to the shape parameters for the 300µm thick Hamamatsu VELO sensors3,which have been determined to be in the range between 2.6·10−5 mm−1 and 4.4·10−5 mm−1 inx and 3.4·10−5 mm−1 and 8.1·10−5 mm−1 in y. The curvature of the Inner Tracker sensorsseems to be in general smaller than that of the VELO ones, which can probably be attributedto the different aspect ratios of sensors and the double-metal layer on the VELO sensors. Themore square or circular they are, the less warp is expected due to tension either during pro-cessing or during dicing. Although a sensor flatness of±25µm was specified for the prototypesensors, none of the measured sensors reached this criterion. They all had planarities between±(40− 50)µm.

The accuracy and parallelity of the cut lines have been determined by scanning along bothsensor edges of all four measured sensors. A total of 100 points with respect to the nominalaxis defined by the silicon targets have been recorded. A typical edge contour scan is shown infigure 4.19. The nominal dicing line is supposed to be atx = −0.300 mm with respect to thesilicon targets. The parallelity of the cut line on all the measured four silicon sensors was foundto be better than±4µm over the length of the sensor. The accuracy of the cutting, as measuredby the average deflection from the nominal line was determined to be better than 3.5µm. Hence,the measured numbers on the silicon edges are significantly better than what was specified.

2Optische Messtechnik Stein, Hunzenschwil, Switzerland3These sensors have been produced in 4”-technology


2040

60

0

50

100

-0.04

-0.02

0

0.02

0.04

0.06

x [mm]y [mm]

z [m

m]

Figure 4.18: Thez-Profile of a sensor is shown. The measured points are connected by surfacegrid lines. The parabolic fit (grey surface) is also drawn. The flatness of the sensor is within±40µm.

x [mm]

y [m

m]

0

50

100

-0.302 -0.301 -0.3 -0.299 -0.298

Figure 4.19: The results of an edge scan along the dicing line of a sensor. The nominal cut lineis indicated by the vertical line. The parallelity of the measured points is better than±4µm.


Finally, the width and the parallelism of the visible aluminium traces for some strips in allfive geometrical regions were measured and checked for misalignment and uniformity. Themeasurements were performed by scanning automatically along a strip and recording up to 15equidistant data points. No misalignment of the strips could be found during the scans, and theparallelism of the measured traces with respect to the silicon targets was better than±1µm. Thetrace width of the aluminium on top of the implant was uniform within better than 0.3µm (rms-value). The measurements, however, yielded consistently a thinner trace width everywhere thanthe design values given in table 4.7. The resulting difference was found to be between 1.4µmfor region A, and 1.8µm for the region E. It is not clear, however, if this is due to a smallermetal overhang or not, since the implant strip itself could not be measured.


Al

Si strip-detector module LHCb - ITR

m(240 µ pitch)

Al(22 , 20 , 22 chnls)

Coolingblock

48 60 72 µµµ( )

implant width)(

Detector

ChipsHelix 128.2.2 Chips

Hybrid

KaptonCable

Detector

Kapton

Hybrid

(Kiev-prototype + HELIX 128-2.2)

KaptonCable

Figure 4.20: Layout of sensor and HELIX hybrid glued to the support Al frame (not to scale).

4.3 Source and Laser Measurements

SPA sensors were connected to the HELIX128-2.2 readout chip and evaluated in the labora-tory. In order to investigate the charge sharing between two adjacent strips, measurements witha 1083 nm laser were performed. Minimum ionising electrons from a106Ru β-source wereused to study the signal-to-noise (S/N ) performance of the silicon sensors. TheS/N measure-ments were also performed on sensors after irradiation with 24 GeV protons up to a fluence of1.7×1014 cm−2 (equivalent fluence of 0.9×1014 1 MeV neutrons), corresponding to more than10 years of LHCb Inner Tracker operation in the most irradiated zones.

4.3.1 Experimental Setup and Electronics

Figure 4.20 illustrates schematically the layout of the test module. The silicon sensor is attachedto an aluminum support frame using the silicone-based glue NEE0014. The choice of this gluewas motivated by results of the MPI HERA-B VDS group that had tested several adhesivesand found out that using the silicone-based adhesive does not affect the detectors at all whereasthere was a severe increase of dark currents if “hard” or ceramic powder loaded adhesiveswere used [64]. The 64 readout strips of the sensor were directly bonded to the input pads ofthree HELIX chips [65]. The HELIX chip provides a low-noise charge sensitive preamplifieron each of its 128 channels, followed by a shaper with an adjustable shaping time of about50 ns to 150 ns (FWHM) and an analogue pipeline with a maximum latency of 128 samplingintervals. The front-end bias voltages and currents of the HELIX chip can be adjusted via

4Dr. Neumann Peltier-Technik, Utting Germany

4.3. SOURCE AND LASER MEASUREMENTS 47

programmable DAC registers. In particular, the pulse width can be varied within certain limitsvia the programmable shaper parameters (Vfs andIpre). The fastest shaping time that can beobtained with the HELIX chip is slightly slower than operation at LHCb requires. However, thenoise performance of the HELIX is quite similar to that of the Beetle chip.

In order to match the different pitches of the chip and the sensor (41.4µm and 240µm, re-spectively) only every 6th input channel of the HELIX chips was used. The support frame wasattached to a cooling block, that used water at 10-20C as coolant. The whole setup was placedin a vacuum vessel. Two irradiated sensors, one over-metallised (4820-17-P+8) and one under-metallised (4820-17-P-2), and an unirradiated sensor with under-metallisation (4820-13-P-2)were tested. In addition, measurements with the106Ru β-source were performed on a 20 cmlong ladder assembled from three unirradiated sensors with over-metallisation (4820-08-P+8,4820-12-P+8 and 4820-05-P+8). For all measurements a complete readout chain developed forthe vertex detector of the HERA-B experiment was used [66].

4.3.2 Analysis Procedure

A hit finding algorithm developed for the HERA-B vertex detector was adopted. In a first step,pedestals from an N-event sliding average of the raw pulse height are subtracted from the FADCvalues of each strip. Event-by-event common mode fluctuations are estimated by a first orderspline fit with three knots to the pedestal subtracted data, using a 2-step iterative procedurewith outlier rejection. The final hit finding is performed on the pedestal and common modesubtracted datad and their rms-noise valuesn =

√〈d2〉, where the average is again a sliding

average over N events. Hit candidates are identified as clusters of consecutive strips, if the singlestrip significanced2/n2 is larger than a given cut parameter (seed-cut). A cluster is accepted,if the sum of the single strip significances is above a second cut value (χ2-cut). Typical valuesused in the analysis are N=50, seed-cut=4 andχ2-cut=20. The hit position is estimated bythe centre-of-gravity of the cluster. To avoid hit-related biases, only strips withd2/n2 smallerthan the seed-cut contribute in the pedestal and noise following. The signal-to-noise ratio for acluster ofW strips was defined asS/N = Q/σ, whereQ is the total cluster charge andσ the

rms-noise from all contributing strips,σ =√∑

n2/W . Assuming that the noise is the same for

all strips, the factor√W normalises theS/N ratio to an equivalent value, corresponding to the

case that all charge is deposited on one strip.

4.3.3 Laser Measurements

Measurements to study the charge division and the depletion voltage of the unirradiated sensorwere carried out using a 1083 nm laser beam with a spot size of 7µm and a repetition rate of200 Hz. At this wavelength infrared light completely penetrates the silicon sensor. The intensityof the laser has been tuned to produce a charge equivalent to that of a minimum ionising particlecrossing the sensor. The laser beam enters the sensor perpendicular to the silicon surface.

Figure 4.21 shows the amplitude of the analogue output signal of the HELIX chip as functionof the bias voltage. The beginning of the plateau of the curve indicates that maximal charge


0

100

200

300

400

0 20 40 60 80 100 120 140bias voltage [V]

sign

al a

mpl

itude

[m

V]

Figure 4.21: Amplitude of the analog output of the HELIX chip as function of the bias voltage.

x [µm]

η

0

0.2

0.4

0.6

0.8

1

20 40 60 80 100 120 140 160

Figure 4.22:η-function obtained from the laser measurements.

collection efficiency is reached at about 90 V. This result is in good agreement with full depletionvoltage of 60 V determined from the C-V-measurements.

The charge sharing between two adjacent strips is measured by moving the laser beam acrossthe strips in steps of 10µm. At each position 1000 laser pulses are collected. The charge sharingamong two adjacent strips is described by anη-function [68]

η(x0) =CR(x0)

CR(x0) + CL(x0)(4.5)


0

50

100

150

200

0 50 100 150 200signal left strip [mV]

sign

al r

ight

str

ip [m

V]

Figure 4.23: Correlation between signals on two neighbouring strips. The laser was moved in20µm steps across the inter-strip gap. Points refer to measured data. The solid line displaysthe expected results if no charge loss would occur. The measurement was performed at a biasvoltage of 80 V.

where CR and CL denote the charge collected on the R(ight) and L(eft) strips, andx0 is the centreof the laser beam measured from the edge of one strip. Theη-function cannot be measured forthe positions where the laser is right above the strip because of the metallisation. Aluminumhas a very high reflectance for the light of the laser and accordingly a very low penetrationdepth. Figure 4.22 shows theη-function obtained from measurements in between two strips inthe middle of the sensor (strip 30 and 31).

Figure 4.23 shows the measured correlation between the signals on two adjacent strips, wherethe laser was moved between the strips in steps of 20µm. The experimental points deviatefrom a straight line in the middle of the inter-strip region indicating a charge loss of 20-30 %in this region. However, a final interpretation is difficult, since internal reflections in the regionof the readout strips may lead to an excess of the signal [67]. A charge loss in the inter-stripregion may impact the efficiency of hit reconstruction and has been investigated further in thetest beams. It is expected that by increasing the bias voltage the CCE can be improved. TheCCE as function of the bias voltage has been measured in the test beams described in chapter 6.

4.3.4 Measurements with a106Ru β-Source

To study theS/N performance of the sensors, a106Ruβ-source setup was used. Measurementswere performed at a bias voltage of 80 V and a temperature of 20C. The peaking time of theHELIX chip was set to 50 ns and the chip was operated with a readout frequency of 10 MHz.


delay [ns]

S/N w/p=0.2

0

5

10

15

0 20 40 60 80 100delay [ns]

S/N w/p=0.25

0

5

10

15

0 20 40 60 80 100delay [ns]

S/N w/p=0.3

0

5

10

15

0 20 40 60 80 100

Figure 4.24: RatioS/N as function of the trigger delay for the different regions ofw/p. Thelatency of the HELIX was kept constant.

In a first step the correct trigger delay had to be found. While the latency of the HELIX was keptfixed, the trigger delay was varied in steps of 10 ns, scanning the shape of the HELIX signal. Infigure 4.24 the delay curve for an irradiated sensor is illustrated (for the unirradiated sensor itlooks similar). The maximum of the curve is shifted towards larger delay times with increasingw/p due to the higher corresponding capacitive load at the input of the preamplifier. For thefurther measurements, the delay was accordingly adjusted to the maximum of the curve.

Results for Unirradiated Sensors

Figure 4.25 shows the overall cluster charge, noise, cluster width and theS/N ratio, averagedover the full surface of the sensor. In general, theS/N performance degrades with increasingload capacitance at the input of the pre-amplifier and thus scales with the ratio strip width tostrip pitch (w/p) and the length of the strip. The results presented in this section refer to singlesensors with a strip length of 6.66 cm, whereas in the design of the LHCb Inner Tracker thesilicon ladders are 22 cm long. Source measurements on a 20 cm long ladder are presented laterin this section. In figure 4.26 theS/N distributions are shown for the differentw/p-regionsof the sensor. From a Landau function fitted to the distributions, one obtains aS/N value ofabout 21, 19.5 and 18.5, for aw/p of 0.2, 0.25 and 0.3, respectively. TheS/N value is heredefined as the most probable value of the Landau function. Using the peak-position of theLandau to characterise theS/N performance has the advantage that it is less affected than thesimple average by cutoffs induced by the hit finding algorithm. It is, however, less robust thanthe average, in particular if only the upper tail of the distribution is available for the fit, and,because of the Landau tail towards large values, it is also smaller than the average.

Clusters with a width of two strips mainly occur in the central region in between two stripswhere theS/N value can be affected by a potential charge loss between the strips. In figure 4.27theS/N distributions are shown for the differentw/p-regions, only for clusters with a width oftwo strips. Here, theS/N value forw/p = 0.3 is higher than forw/p = 0.2, indicating thatthere is in fact a charge loss between the strips and that this effect is more pronounced for thesensor region withw/p = 0.2. This charge loss is apparently larger than the reduction in noisedue the smaller capacitive load and may lead to a reduced hit finding efficiency in the inter-stripgap.


charge [ADC]

N

0

500

1000

0 20 40 60Noise/√width [ADC]

N

0

200

400

600

0.6 0.7 0.8 0.9 1

width [strips]

N

0

2000

4000

6000

8000

0 1 2 3 4 5S/N

N

0

250

500

750

0 20 40 60 80 100

Figure 4.25: Overall cluster charge, noise, width andS/N distributions for the sensor 4820-13-p-2.

Results for Irradiated Sensors

As described in section 4.1.2 a set of prototype sensors was irradiated with an equivalent fluenceof 0.9×1014 1 MeV neutrons corresponding to more than 10 years of LHCb operation. Damageinduced defects can act as trapping centres that deteriorate the CCE. Measurements by othergroups have shown that the charge loss by trapping is in the order of 10-15 % for a minimumionising particle at highest LHC fluences considered [69, 70].

Figure 4.28 shows theS/N ratio at room temperature (19C) as function of the bias voltagefor the differentw/p-regions of the irradiated sensors. Deviations in the ratioS/N betweenfigure 4.24 and figure 4.28 may be due to different HELIX settings.

For all regions of the sensors aS/N value above 12 can still be observed. The extent of thedecrease in theS/N ratio with higherw/p for the under-metallised sensor is mainly due to the


P1 650.6P2 21.27P3 -3.200

S/N

N

w/p=0.2

0

200

400

600

0 20 40 60

P1 696.1P2 19.47P3 -3.331

S/N

N

w/p=0.25

0

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600

0 20 40 60

P1 360.7P2 18.58P3 -3.061

S/N

N

w/p=0.3

0

100

200

300

0 20 40 60

Figure 4.26:S/N distributions for different regions of the sensor 4820-13-P-2. TheS/N dis-tributions are described by a Landau function (solid line).

irradiation profile and not due to the higher capacitive load. The measurement also demonstratesthat after irradiation a higher bias voltage of more than 100 V is needed to reach maximumCCE. At highest bias voltages the determination of theS/N value from a Landau fit is notvery precise due to the broadening of the corresponding pulse height spectra. For the followingmeasurements a bias voltage of 110 V was applied. At this voltage a leakage current of afew µA per strip was measured (the total leakage current of sensor 4820-17-P-2 was about100µA). Figure 4.29 illustrates theS/N ratio as function of the accumulated fluence for theover-metallised sensor. TheS/N ratio as function of the strip number is shown in the samefigure (for the irradiation profile see figure 4.4.

106Ru-Source Measurements on a 20 cm Long Ladder

Measurements using the106Ru-source were also performed on a 20 cm long ladder, assembledfrom three unirradiated, over-metallised sensors. This ladder was constructed for test beammeasurements described in the following chapter.

Figure 4.30 shows the measuredS/N values as function of the trigger delay for different HE-LIX settings, corresponding to peaking times of about 50, 60, 70, and 100 ns, respectively. All


P1 254.1P2 14.69P3 -4.214

S/N

N

w/p=0.2

0

100

200

0 20 40 60

P1 199.9P2 14.26P3 -3.485

S/N

N

w/p=0.25

0

50

100

150

0 20 40 60

P1 47.03P2 15.40P3 -4.271

S/N

N

w/p=0.3

0

10

20

30

0 20 40 60

Figure 4.27:S/N distributions for different regions of the sensor 4820-13-P-2, only for clusterswith a width of two strips.

measurements were carried out at a bias voltage of 100 V and the source was focused on the sec-ond sensor on the ladder (4820-12-P+8). The distributions show that theS/N values decreasesignificantly with faster shaping time. For the slowest shaping time, aS/N value of around 18can be reached. The best obtainable value for the fastest shaping time is around 12. Figure 4.31shows theS/N value as function of the bias voltage. The three sets of measurements correspondto the source being focused on the third (4820-05-P+8), second (4820-12-P+8) and first sensor(4820-08-P+8) on the ladder, respectively. The first two measurements were performed at a“slow” shaping of about 100 ns (peaking time), the third one for “fast” peaking time of about50 ns. For each measurement, the trigger delay was adjusted to the maximum of the pulse-shapedistribution. Whereas theS/N value saturates at about 100 V for slow shaping time, for fastshaping time it keeps growing up to the highest measured bias voltage of 120 V. Higher biasvoltages could not be applied because of detector breakdowns.


voltage [V]

S/N wp=0.2

5

10

15

20

50 100 150voltage [V]

S/N wp=0.25

5

10

15

20

50 100 150voltage [V]

S/N wp=0.3

5

10

15

20

50 100 150

voltage [V]

S/N wp=0.2

5

10

15

20

50 100 150voltage [V]

S/N wp=0.25

5

10

15

20

50 100 150voltage [V]

S/N wp=0.3

5

10

15

20

50 100 150

Figure 4.28: S/N of the irradiated sensor as function of the bias voltage for the differentw/p-regions: sensor 4820-17-P-2 with under-metallisation (top) and 4820-17-P+8 with over-metallisation (bottom). Due to the very inhomogeneous irradiation profile, only the outer partof the under-metallised sensor towards the highest strip numbers was exposed to the maximalparticle flux, for the over-metallised sensor the irradiation profile was vice versa.

strip

S/N

10

15

20

0 20 40 60fluence [1014cm-2]

S/N

10

15

20

0.5 1 1.5 2

Figure 4.29:S/N ratio of the irradiated sensor 4820-17-P-2 as function of the strip number(left plot). TheS/N ratio as function of the accumulated fluence is illustrated in the right plot.Due to the collimation of the source and restrictions of the setup there are no events for stripnumbers higher than 50.


S/N

trigger delay (ns)

Figure 4.30:S/N ratio (top) and cluster charge (bottom) as function of trigger delay for the20 cm long ladder, at 100 V bias voltage and for different HELIX shaping times.

sqrt (V )bias

S/N

Figure 4.31:S/N ratio as function of bias voltage for three different source positions along the20 cm long ladder. Two measurements with slow, the third one (black circles) with fast HELIXshaping time.

Chapter 5

Readout with the Beetle Chip

In order to fulfil the special requirements of the LHCb trigger and readout scheme, a radia-tion hard readout chip in 0.25µm CMOS technology, called Beetle, is custom developed forthe Inner Tracker, the VELO and pile-up veto [71]. It implements the basic RD-20 front-endelectronics architecture. The chip integrates 128 channels. Each channel consists of a low-noise charge-sensitive preamplifier and an active CR-RC pulse shaper [72]. The rise time of thepulse is in the order of 25 ns pursuant to the requirements of LHC. A comparator per channelprovides the operation of the chip in binary mode. Either the comparator or the shaper outputis sampled with the LHC bunch-crossing frequency of 40 MHz into an analogue pipeline witha programmable latency of max. 160 sampling intervals and a 16 stages deep derandomisingbuffer. For analogue readout, which is used for the Inner Tracker, data is multiplexed with40 MHz in up to 4 ports. In addition, the Beetle chip is equipped with a test channel, that isdirectly connected to the output of the pipeline amplifier and allows to monitor the analoguesignal on an oscilloscope. The bias settings and other parameters of the Beetle can be con-trolled via a standard I2C-interface [73]. The pulse width can be tuned on a limited scale byprogramming shaper parameters.

5.1 BeetleFE Tests

The noise performance and pulse shape of the Beetle were investigated on several prototypechips. Some of these test chips without full functionality contained different sets of analogueinput stages with different shaping times and noise behaviour. The noise referred to the am-plifier input is usually expressed in terms of equivalent noise charge (ENC) and quoted in rmselectrons. Extensive tests on the test chips were performed in order to identify an optimal front-end for the final chip. In terms of the pulse width,Vfs is the most important programmableparameter.Vfs controls the value of the shaper feedback resistance and determines the timeconstant of the discharge of the shaper feedback capacitor and thus the width of the output sig-nal. The impact of all other parameters on the pulse width turns out to be marginal. The noise,however, depends on the preamplifier bias currentIpre. Increasing this current reduces the noiseat the cost of power consumption, however. A precise description of all programmable DACregisters can be found in [65].

56

5.1. BEETLEFE TESTS 57

Figure 5.1: Transient response of the BeetleFE 1.0 to a signal of 50000 electrons at a capacitiveinput of 22 pF and 33 pF.

5.1.1 BeetleFE 1.0

Before the first submission of the complete readout chip, the front-end BeetleFE 1.0 [74] wasdeveloped and tested. The chip contains three different front-end designs, of which two use aPMOS transistor as input device and the third a NMOS transistor. Figure 5.1 shows the transientresponse of the NMOS front-end to an input signal of 50000 electrons at a capacitive load of22 pF and 33 pF respectively.

The ENC for the NMOS front-end has been measured to 303 e−+33.6·Ctot e−/pF at a bias cur-rent of Ipre = 600µA [75]. This front-end chip is implemented in the first complete readoutchip, the Beetle 1.0, and the improved version, the Beetle 1.1. Unfortunately, an error in thelayout of the Beetle 1.0 control circuitry prevented its programming. The Beetle 1.1 is fullyfunctional, but does not contain SEU (Single Event Upset) resistant logic and its front-end wasnot yet optimised for the large input capacitances of the Inner Tracker sensor ladders. The ENCof the Beetle 1.1 as function of the total input has been measured [76] to

ENC = 870 e− + 41.5 · Ctot e−/pF. (5.1)

This significantly differs from the measurement on the BeetleFE front-end chip. No explanationfor this discrepancy has been found so far.

Several Beetle 1.1 were connected to Inner Tracker silicon prototype sensors and operated suc-cessfully during two test beams at the CERN-X7 facility in October 2001 and May 2002.

5.1.2 BeetleFE 1.1 and BeetleFE 1.2

In May 2001 two new prototype front-end chips were submitted. The BeetleFE 1.1 and BeetleFE 1.2chips contain 12 different sets of analogue input stages [77]. Tests of these chips were performed

58 CHAPTER 5. READOUT WITH THE BEETLE CHIP

2a2c2e

C[pF]

Noi

se[e

- ]

0

2000

4000

0 20 40 60

Figure 5.2: ENC as function of the total input capacitance for three different front-ends ofBeetleFE 1.1. The measurement was performed withVfs = 0 V. Front-end 2c was selected forthe Beetle 1.2 chip.

at NIKHEF, in Heidelberg and in Zurich. All results obtained by the three groups were compati-ble and a front-end for the next generation Beetle was selected based upon these measurements.The signal shape and the noise behaviour of the different front-ends were studied in detail forload capacitances up to 50 pF. In addition, the impact on the pulse width was investigated byvarying the shaper parameterVfs. For all other parameters nominal values were chosen, in par-ticular a bias current ofIpre = 600µA was used. The nominal values for all registers are listedin [71].

Figure 5.2 shows the ENC for three different input stages of the BeetleFE 1.1 as function ofthe total input capacitance. These three front-ends (2a, 2b and 2c) were shortlisted as candi-dates for implementation in the next version of the readout chip, Beetle 1.2. Although front-end 2c exhibits a slightly worse noise performance than 2a, it was selected for the Beetle 1.2,since front-end 2a saturates in case of high strip rates (for a detailed discussion of this problemsee [78]).

A linear fit to the data of the front-end 2c yields

ENC = 430 e− + 47 · Ctot e−/pF. (5.2)

However, this result is only valid for a certain set of parameters of the Beetle chip (in this setVfs = 0 mV). The noise of the chip can be reduced at the expense of the pulse width which isthen getting larger (see section 2.4.1), and with a value ofVfs = 1000 mV an ENC of

ENC = 382 e− + 35.5 · Ctot e−/pF. (5.3)

can be obtained. The ENC and the pulse width for different values ofVfs are shown in figure 5.3.

5.2. PULSE SHAPE 59

Vfs=0 mV

Vfs=1600 mV

pulse width [ns]

Noi

se[e

- ]

0

1000

2000

40 60 80 100 120

Figure 5.3: ENC and pulse width for different values ofVfs fromVfs = 0 mV toVfs = 1600 mVin steps of 200 mV.

The output signal of the front-end 2c for various load capacitances, the rise time and the signalremainder after 25 ns, the time of the next LHC bunch crossing, are shown in figure 5.4. Theremainder determines the probability of reconstructing a “ghost” hit in the triggered event whilethe signal originates from the previous bunch crossing. Measurements were performed withVfs = 0 mV and the output signal of the front-end is the response to a delta-like input pulse.With this settings a rise time below 13 ns and a signal remainder less than 40 % after 25 ns wereobtained for capacitances up to 50 pF.

First measurements on the fully functional Beetle 1.2 chip confirm the results that have beenobtained for the BeetleFE 1.1 [79].

5.1.3 Implications on Signal-to-Noise

The total strip capacitance is the main contribution to the noise of the front-end amplifier. Inequation 4.3 the total strip capacitance is expressed as function of the ratio strip width to strippitch w/p. Using this expression and the ENC parametrisations as in equation 5.2 and 5.3,theS/N ratio can easily be derived as function ofw/p and for a silicon ladder consisting of acertain length. In figure 5.5 the computedS/N ratio for a two sensor long ladder (22 cm) asfunction ofw/p is shown. A signal of 3.5 fC, corresponding to 22000 e−, is assumed.

5.2 Pulse Shape

In section 2.2.3 the signal form generated by s single electron-hole pair, e.g. created by aphoton, was derived. To calculate the pulse shape due to ionisation from charged particles,


00

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itude

[mV

]

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rise

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[ns]

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101112131415

0 10 20 30 40 50 60

ZurichNIKHEFHeidelberg

C[pF]

rem

aind

er [%

]

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1015202530354045

0 10 20 30 40 50 60

Figure 5.4: Measured signal shape, rise time and signal remainder after 25 ns for the front-end2c. Output signals are the response to a delta-like input signal.

one basically has to integrate equation 2.13. This integral can be numerically approximatedby a sum of discrete charge depositions in the sensor. The duration of the signals created byelectrons and holes is determined by the time required to traverse the sensors, which dependson the full depletion voltage, the applied voltage and of course the thickness of the sensor.

Figure 5.6 shows the result of a calculation that uses 20 equidistant charge depositions of equalvalues for a sensor of 300µm thickness. The total signal is normalised to 22000 electron-holepairs, i.e. every charge deposition consists of 1100 electron-hole pairs. For the full depletionvoltage 70 V and for the applied voltage 80 V were assumed. The rising edge of the signal wassmeared in the calculation to simulate a rise time in the order of 1-2 ns due to diffusion [61, 80].Without diffusion the rise time of the signal is zero.

5.2. PULSE SHAPE 61

w/p

S/N

Vfs=1000 mVVfs=0 mV

11

12

13

14

15

16

0.25 0.3 0.35

Figure 5.5:S/N ratio as function ofw/p. The noise is calculated from the ENC parametrisationof the Beetle chip assuming a capacitive load corresponding to two HPK sensors. The signalcorresponds to a minimum ionising particle. The lines are fits to the computed values andrefer to two different Beetle parameter settings (solid lineVfs = 0 mV and dashed lineVfs =1000 mV, see text). For the fit the averaged capacitance value of all sensors was taken andthe shaded bands indicate the variation of theS/N ratio due to the spread of the individuallymeasured capacitances.

totalholeselectrons

time [ns]

curr

ent [

µA]

0

0.2

0.4

0.6

0.8

0 10 20 30

Figure 5.6: Calculation of the current pulse generated by an ionising particle traversing a300µm thick sensor. The sensor is biased with 80 V and has a full depletion voltage of 70 V.


time [ns]

arbi

trar

y un

its

Vfs=0mVoverbias 10V

0

1

2

3

4

0 20 40 60 80time [ns]

arbi

trar

y un

its overbias 10VVfs=1000mV

0

1

2

3

4

0 20 40 60 80

time [ns]

arbi

trar

y un


0

1

2

3

4

0 20 40 60 80time [ns]

arbi

trar

y un


0

1

2

3

4

0 20 40 60 80

Figure 5.7: BeetleFE responses to a delta-like (solid line) and a calculated (dashed line) currentsignal. Results are shown for two values ofVfs and two different bias voltages and correspondto a 300µm thick sensor with a depletion voltage of 70 V. A capacitive load of 40 pF (corre-sponding a two sensor ladder) for the front-end was assumed.

The result of this calculation can be used as input for the simulation of the BeetleFE. Thecalculation does not take into account exact diffusion, the particle trajectory, the density ofionisation and the electric field distribution between strips. Nevertheless, it is an appropriateinput for the simulation of the Beetle signal. A more elaborated electrostatic simulation for theInner Tracker silicon sensors using a finite element analysis can be found in [81].

Since the rise time of the Beetle front-end shaper is comparable to the charge collection timein silicon of 300µm thickness, the observed output signal is lower compared to the outputfor a delta-like current signal. The difference in pulse height is referred to as ballistic deficit,meaning that the full charge is not collected in time. As a result of the ballistic deficit theS/N ratio will increase with sensor bias voltage beyond the full depletion voltage (overbiasing)for charge collection times not significantly smaller than the rise time of the amplifier. Due tothe saturation of the velocity of the charge carriers, theS/N ratio reaches a constant value atsufficiently high over depletion. In addition, a non-delta-like input signal leads to an increaseof the rise time of the Beetle response.

In figure 5.7 the BeetleFE response to a delta-like input is compared to the output of a calculated

5.2. PULSE SHAPE 63

current signal for two values ofVfs and two different bias voltages of a 300µm thick sensor.Results are shown for a capacitive load of 40 pF. A small ballistic deficit is visible in the case ofVfs = 0 mV and overbiasing of 10 V, whereas it is otherwise negligible.

Chapter 6

Test Beam Results

In this chapter the results of three test beams are presented. The test beams in May 2001and October 2001 were performed on silicon ladders of SPA prototype sensors. For the firsttest beam sensors were connected to HELIX chips, whereas in the October test beam the SPAprototype sensors were read out using for the first time the Beetle 1.1 chip.

In May 2002 a third test beam was carried out on HPK prototype sensors, that were connectedto Beetle 1.1 chips.

6.1 Test Beam with HELIX Readout

Data of this first test beam were taken at a T7 test beam at CERN in May 2001. The signal-to-noise ratio, resolution, efficiency and noise rate were measured. Particular importance wasattached to the determination of the efficiency in the inter-strip region of the SPA prototypesensors. The sensors performance was studied at various bias voltages and for different valuesof the ratio strip width to strip pitch.

SPA prototype sensors were read out using the HELIX128-2.2 chip that was operated at a read-out frequency of 10.4 MHz. Runs with two different settings of the shaper parameters weretaken, that are in the following denoted by “fast” (DAC valuesVfs = 225 andIpre = 80) and“slow” (Vfs = 160 andIpre = 200) shaping. The pulse shape for fast shaping is illustrated infigure 6.2. For slow shaping the pulse is approximately twice as wide. Runs with slow shapingwere used to study the optimal sensor performance, whereas runs with fast shaping time weretaken to come as close as possible to the situation at LHC.

6.1.1 Test Beam Setup

The test beam was performed in the T7 beam line of the SPS accelerator at CERN, using a9 GeVπ− beam. Two ladders of prototype sensors were installed in the beam. One ladder wasequipped with one sensor (“short” ladder), the other with three sensors (“long” ladder). The

64

6.1. TEST BEAM WITH HELIX READOUT 65

Figure 6.1: Test beam setup. The test sensors were assembled on Stesalit support structures. Apair of double sided telescope sensors were placed upstream and downstream of the two ladders.

total strip length of the long ladder was thus 20 cm, which is close to the design of the LHCbInner Tracker that uses ladders of 22 cm length. The ladders were mounted on G10 frames thathad cutouts underneath the sensors in order to minimise multiple scattering and were tested forfunctionality before being installed in the beam.

Four double-sided silicon strip detectors provided by the HERA-B vertex detector group [66]served as a beam telescope. The sensors have a strip pitch of 54.6µm on the n-side and 51.7µmon the p-side. The active area of the telescope sensors is 50 mm×70 mm. The test ladderswere installed, with the strips horizontal, inside an aluminum box that also housed the beamtelescope. The strips faced the beam for the short ladder, whereas the backplane faced the beamfor the long ladder. The telescope and the ladders were mounted individually on horizontalrails, for easy adjustment of their relative positions in order to allow measurements on all threesensors of the long ladder. Telescope and test ladders were attached to cooling blocks in order toremove the heat generated by the readout chips. Water at about 10C was used as coolant. Thecomplete readout chain of the HERA-B vertex detector was used, both for the beam telescopeand for the test ladders. A photograph of the test beam setup is shown in figure 6.1.

The trigger for this setup was defined by a threefold coincidence of a large 10 cm×10 cm scin-tillator and two 1.5 cm×1.5 cm scintillators, all placed upstream of the silicon sensors. Theacceptance of the trigger covered all strips of the test ladders. To determine the correct trig-ger delay, the HELIX signal was scanned varying the trigger delay in steps of 10 ns while thelatency of the HELIX was kept constant. The delay scan for the test ladders is illustrated in fig-ure 6.2 for fast shaping. Because of the higher capacitive load, the maximum of the delay curvefor the long ladder is shifted towards larger delay times and the gain of the HELIX is reduced.Different runs were taken with the delay adjusted to the maximum of either of the curves.

The first runs were taken with the first sensor of the long ladder and the short ladder simul-

66 CHAPTER 6. TEST BEAM RESULTS

small ladder

long ladder

trigger delay [ns]

Clu

ster

Cha

rge

[AD

C]

0

10

20

30

0 100 200

Figure 6.2: Trigger delay curve showing the cluster charge as function of the scintillator triggerdelay for the long (open dots) and short (filled dots) ladder.

taneously in the beam. Later, a position scan of the long ladder was performed such that thebeam was focused successively on the third and the second sensor and on the transition regionbetween these two sensors. During this scan, the short ladder was not in the beam. In eachposition, runs with “fast” and “slow” shaping of the HELIX chip were taken. Furthermore,the bias voltage was varied when the second sensor of the long ladder was in the beam. Thesame cluster finding procedure as for the laboratory measurements was used (see section 4.3.2).However, various combinations of the seed-cut and theχ2-cut were studied.

6.1.2 Tracking

For a detailed study of the Inner Tracker prototype sensors, the precise impact point of a trackon the sensor has to be known. With the test beam setup described above, straight tracks werereconstructed using the beam telescope which, including multiple scattering, provided an ef-fective single hit resolution of typically 14µm. This value is close to the naive expectationσhit = p(itch)/

√12 for the beam telescope.

Since most of the recorded events had exactly one track passing through the setup, a simplemanual procedure could be employed to determine the precise alignment of the sensors. Keep-ing the positions of the first and the last telescope station fixed, the other sensors were shiftedlaterally, requiring the average residual of a hit measured in the sensor from the track definedby the fixed stations to be zero.

After this procedure, the track residuals on all telescope sensors already matched the expectedsingle hit resolution. This implies an impact point resolution better than 20µm on the InnerTracker prototype sensors, good enough for a detailed study of the 240µm inter-strip region.


There was thus no need to adjust the additional rotational degrees of freedom, i.e. the orienta-tions of all sensors were kept at their nominal values.

Since the track multiplicities per event were low, a simple combinatorial approach was usedto reconstruct all tracks in an event. In a first step, tracks were searched that had hits in allviews of the telescope. All combinations satisfying this requirement were scrutinised and theone with the bestχ2-value in the track fit was accepted if theχ2 confidence level was largerthanclcut = 0.001. The hits associated to this track were removed from the sample and theprocedure iterated. Thus, hit sharing between tracks was not permitted. If no further trackscould be found with hits in all layers, the required number of hits per track was reduced by oneand the search started over. This procedure was iterated down to a minimum of 5 hits per track,i.e. one hit more than needed to define a straight track in 3-d space.

6.1.3 Results

Figure 6.3 shows the number of reconstructed tracks per event for a typical run. For all inves-tigations on signal-to-noise, resolution, efficiency and noise rate of the test ladders, only eventswith exactly one reconstructed track were analysed. Furthermore, all distributions (of coursewith exception of the efficiency) were plotted only for clusters that could be associated to atrack. A cluster was assigned to a track if its residual to the track impact point was the smallestof all clusters and smaller than 1.5 strip pitches. Unless explicitly stated otherwise, the biasvoltage of the test sensors was 90 V.

Different combinations of the clustering parameters were studied in order to determine theoptimal set of cuts with respect to hit finding efficiency and noise rate. These investigationsare presented in the following section, followed by the performance measurements of the shortand long ladders. Results for the long ladder are shown as function of beam position and biasvoltage.

Choice of Clustering Parameters

Table 6.4 lists the different combinations of clustering parameters that were tested. For technicalreasons of the analysis program, the cuts were changed for the telescope sensors at the sametime as for the test ladders. This results in slightly different track samples for the differentcombinations of cuts. However, the effect on the event sample is less than 1% when only eventswith exactly one reconstructed track are selected.

The clustering parameters must be optimised to give highest possible efficiency also for hitswhere not the full charge is collected, while retaining low noise hit rates. Efficiency and noisehit rate are obviously correlated and both depend on the choice of the clustering parameters.Figure 6.4 shows the reconstructed efficiency for the second sensor on the long ladder as func-tion of the track position, for the different tested sets of parameters. A significant efficiencyloss can be observed in the region in between two strips for the parameter sets rp01, rp02 andrp04. The plots also demonstrate that lowering the seed-cut does not improve the situationconsiderably.


Number of Tracks

N

0

10000

20000

30000

40000

50000

0 2 4 6

Figure 6.3: Number of tracks per event for a typical run.

parameter set seed-cut χ2-cut

rp01 4 20

rp02 4 16

rp03 4 9

rp04 3 16

rp05 3 9

rp06 2 9

Table 6.1: List of the tested combinations of the clustering parameters.

The corresponding noise rates for the different sets of parameters are summarised in table 6.2.The noise rate per strip is here defined as the number of clusters that are not assigned to a track,normalised to the total number of clusters and to the number of active strips. The noise rates forthe different parameter sets vary from 0.1% to 0.25%. It should be mentioned here, that due tothe slightly different track samples the reconstructed noise rate is higher for rp03 than for rp05and rp06 although the corresponding cut is tighter.

To ensure an efficient operation at LHC, the noise rate has to be small compared to the expectedtrack occupancy, which is in the order of a few % [82]. This is the case for all sets of parameters.The parameter set rp03 was selected for all following studies.

Results for the Short Ladder

All measurements for the short ladder were performed at a bias voltage of 90 V. A hitmap andthe cluster width distribution are illustrated in figure 6.5. No “dead” strip was observed for theshort ladder.


strip

effic

ienc

y

rp01

0.95

1

1.05

0 0.2 0.4 0.6 0.8 1strip

effic

ienc

y

rp02

0.95

1

1.05

0 0.2 0.4 0.6 0.8 1

strip

effic

ienc

y

rp03

0.95

1

1.05

0 0.2 0.4 0.6 0.8 1strip

effic

ienc

y

rp04

0.95

1

1.05

0 0.2 0.4 0.6 0.8 1

strip

effic

ienc

y

rp05

0.95

1

1.05

0 0.2 0.4 0.6 0.8 1strip

effic

ienc

y

rp06

0.95

1

1.05

0 0.2 0.4 0.6 0.8 1

Figure 6.4: Efficiency as function of the track position in between two strips, for the secondsensor on the long ladder. The data from all strips belonging to the region withw/p = 0.3 weresuperimposed.


dataset noise rate per strip

rp01 0.112%

rp02 0.126%

rp03 0.247%

rp04 0.124%

rp05 0.224%

rp06 0.231%

Table 6.2: Noise hit rates for the different combinations of clustering parameters, for the secondsensor on the long ladder.

strip number

N

0

100

200

0 20 40 60cluster width [strips]

N

0

20000

40000

60000

0 1 2 3 4 5

Figure 6.5: Hitmap (left) and cluster width in number of strips (right) for the short ladder.

Figure 6.6 shows the spatial resolution obtained for the short ladder. The residual distributionis fitted well by a single Gaussian. Using the sigma of the Gaussian as definition of the detectorresolution, a value of 50µm is obtained, which is better than the design value of the LHCb InnerTracker. It is also better than the digital resolution of the sensor given byσhit = p(itch)/

√12 =

70µm, demonstrating that some charge sharing between adjacent strips occurs and contributesto enhance the resolution.

The measured distributions of theS/N ratio were fitted by a Landau function folded with aGaussian. The maximum of the Landau was used to define the most probable value of theS/Nratio. Figure 6.7 shows theS/N distributions, separately for reconstructed clusters widths ofone and two strips, derived from runs with fast and slow shaping. With slow (fast) shaping,S/N values of 25.2 (17.4) and 20.4 (15.0) are obtained for one-strip and two-strip clusters,respectively.

Due to the normalisation of theS/N value to the cluster width (as described in section 4.3.2),the S/N distributions for one-strip and two-strip clusters should have their maximum at thesame value if there was full charge collection efficiency everywhere. In figure 6.8, theS/Nratios for one-strip and two-strip clusters are illustrated as function of the track position. Thedifference in the population is clearly visible: one-strip clusters predominantly occur close toa strip, whereas two-strip clusters are mostly found in the inter-strip regions. The lowerS/N


Constant 4870.

Mean -0.2990E-02

Sigma 0.1959

∆ [strips]

N

0

2000

4000

6000

-2 -1 0 1 2

Figure 6.6: Residual distribution for the short ladder. The distribution is well described by asingle Gaussian with a sigma of 0.196 strips, corresponding to 50µm.

cluster width=1 most probable 25.2cluster width=2 most probable 20.4

S/N

N

0

500

1000

0 20 40 60

cluster width=1 most probable 17.4cluster width=2 most probable 15.0

S/N

N

0

500

1000

0 20 40 60

Figure 6.7:S/N ratio for clusters of one and two strips for slow (left) and fast (right) shaping.

value for two-strip clusters thus indicates a charge loss in the inter-strip region of the sensor.The difference in theS/N between fast and slow shaping is due to the better noise performanceof the readout chip for slower shaping. In addition, incomplete charge collection can occur thatis more pronounced for the fast shaping.

In general, a poorS/N value leads to a degradation of the hit reconstruction efficiency. Infigure 6.9, the efficiency in the inter-strip region is shown for the differentw/p regions and forfast and slow shaping. Only in thew/p = 0.2 region, a small efficiency loss can be observedfor fast shaping. In the region withw/p = 0.25 andw/p = 0.3, theS/N value is high enoughto reach full efficiency in the inter-strip region.

The charge sharing between two adjacent strips can be studied using theη-function (see sec-


strip number

S/N

0

20

40

60

30 31 32 33 34 35strip number

S/N

0

20

40

60

30 31 32 33 34 35

Figure 6.8:S/N ratio as function of the strip number for clusters of one (left) and two (right)strips.

w/p=0.2

track position

effic

ienc

y

0.95

0.975

1

0 0.2 0.4 0.6 0.8 1

w/p=0.25

track position

effic

ienc

y

0.95

0.975

1

0 0.2 0.4 0.6 0.8 1

w/p=0.3

track position

effic

ienc

y

0.95

0.975

1

0 0.2 0.4 0.6 0.8 1

Figure 6.9: Efficiency as function of the track position, for the differentw/p-regions and forslow (open squares) and fast (filled dots) shaping.

tion 4.3.3). Since no access of raw data was possible in this analysis (only cluster propertieswere stored) theη-function is in this context only meaningful for tracks in the inter-strip region,because only here significant charge sharing occurs and clusters are expected to consist of twostrips. Theη-functions for the differentw/p-regions are illustrated in figure 6.10. No signifi-cant difference between the curves can be observed. As expected, the charge sharing dependslinearly on the track position in the middle of the inter-strip region. Taking into account thenon-linearity of theη-function towards the edges of the strips, it should be possible to furtherimprove the position resolution using a non-linear hit reconstruction algorithm.

Results for the Long Ladder

Most probably due to a bad bond connection, one strip on the first sensor on the long laddershowed no signal (first sensor on the ladder denotes to the sensor that is directly bonded theHELIX chip). For the second and third sensors, one additional strip was “bad”. These badchannels were excluded from the analysis.

The cluster width distributions for the three sensors on the long ladder are shown in figure 6.11.


w/p=0.2

strip

ηw/p=0.3w/p=0.25

0

0.25

0.5

0.75

1

0.2 0.4 0.6 0.8

Figure 6.10:η-function as defined in the text for the differentw/p-regions on the short ladder.

cluster width [strips]

N

sensor 1

0

20000

40000

0 1 2 3 4 5cluster width [strips]

N

sensor 2

0

10000

20000

0 1 2 3 4 5cluster width [strips]

N

sensor 3

0

20000

40000

0 1 2 3 4 5

Figure 6.11: Cluster width in strips for the three sensors on the long ladder.

The number of clusters with two strips is significantly smaller for the first sensor than for thetwo other sensors. A different behaviour of the first sensor is also seen in the measuredS/Nratios. Figure 6.12 shows theS/N distributions for each sensor on the long ladder, measuredfor slow shaping and plotted separately for one-strip and two-strip clusters.S/N values aresignificantly lower than for the short ladder as expected from the higher load capacitance. Aclear double peak structure can be observed in all plots. It is noticeable that for the first sensorthe first peak is almost entirely suppressed in the distribution for two-strip clusters, whereasfor the two other sensors it is more prominent than the second peak. No explanation for thisdifferent behaviour of the first sensor has been found so far and it cannot be excluded that itmay also have affected the results obtained from the other sensors on the long ladder.

According to the results obtained from the short ladder, one would expect that the peak at lowerS/N values in theS/N distributions belongs to clusters of two strips and the second peak toclusters of one strip. The double peak structure can indeed be resolved when theS/N ratiois plotted separately for hits associated to tracks that extrapolate directly to the readout stripor to the middle of the inter-strip region, as is shown in figure 6.13. The maxima of the two


S/N

1/N

dn/

d(S

/N)

sensor 1

0

0.05

0.1

0 20 40 60S/N

1/N

dn/

d(S

/N)

sensor 2

0

0.05

0.1

0 20 40 60S/N

1/N

dn/

d(S

/N)

sensor 3

0

0.025

0.05

0.075

0 20 40 60

Figure 6.12:S/N distributions for the three sensors on the long ladder. The dashed (solid) linerefers to clusters of two (one) strips. The distributions were normalised to compensate for thedifferent rate of occurrence of one- and two-strip clusters.

most probable 7.7

S/N

N

0

50

100

150

0 20 40 60

most probable 13.8

S/N

N

0

100

200

300

0 20 40 60

Figure 6.13:S/N distributions for clusters where the track extrapolates to the middle of theinter-strip region (left) or directly to the read out strip (right).

distributions respectively match the positions of the first and second peaks in figure 6.12. Thatthe double-peak structure is still present in the separate distributions for one-strip and two-strip clusters indicates that at the smallS/N values obtained for the long ladder, the clusteringalgorithm partially failed and assigned clusters to the wrong category.

For fast shaping, the maxima of theS/N distributions are shifted towards smaller values, butthe double peak structure is retained for all sensors. TheS/N values for the three sensors onthe long ladder are summarised in table 6.3.

In figure 6.14, theS/N distributions for two-strip clusters are plotted as function of the trackposition. In contrast to the second and third sensors, the positions of the two-strip clusters arefor the first sensor are smeared out over the full surface of the sensor and the typical curvingstructure of the distribution is almost not visible. The deficient charge sharing influences alsothe spatial resolution of the sensor. A value of 75µm is obtained for the first sensor, comparedto 60µm for the second and the third sensors.

However, the observed peculiarity of the first sensor has no obvious impact on its efficiency,since no significant difference in the efficiency performance of the three sensors on the long


strip number

S/N sensor 1

0

10

20

30

30 31 32 33 34 35strip number

S/N sensor 2

0

10

20

30

30 31 32 33 34 35strip number

S/N sensor 3

0

10

20

30

30 31 32 33 34 35

Figure 6.14:S/N ratio as function of the track position for the three sensors on the long ladderand for slow (open squares) and fast (filled dots) shaping.

fast shaping slow shaping

sensor first peak second peak first peak second peak

first 6.6 8.3 9.0 11.8

second 6.9 9.0 9.0 13.2

third 7.0 7.8 9.0 13.7

Table 6.3:S/N values for the three sensors on the long ladder. First (second) peak refers to thefirst (second) peak in theS/N distribution for clusters with two (one) strips.

ladder can be observed. In figure 6.15, the efficiency in the inter-strip region is shown for allsensors on the long ladder, for the differentw/p-regions, and for slow and fast shaping. Inaddition, also the efficiencies measured in the transition region between the second and thethird sensor are shown. The obtained results do not vary considerably for the different sensors.For slow shaping, a small efficiency drop in the middle of the inter-strip region can only beobserved for the region withw/p = 0.2. For fast shaping, however, the efficiency loss in theinter-strip region is very pronounced for the regions withw/p = 0.2 andw/p = 0.25, and isstill visible for the region withw/p = 0.3 for the second and third sensor. The inactive area(due to guard-ring structure etc.) at the edges of the sensors causes an efficiency loss in thetransition region between two connected sensors. For the transition region between the secondand the third sensor, the overall efficiency is of the order of 65%. This is comparable to the ratioof the active sensor area in this region to the surface of the small trigger scintillators.

TheS/N ratio, efficiency and noise rate were studied as function of the bias voltage for thesecond sensor on the long ladder. Data for this voltage scan were only taken with slow shapingtime. Prior to these measurements, a second trigger delay scan was performed that resultedin an increase of the trigger delay by 10 ns. Bias voltages higher than 110 V were not appliedbecause the leakage current of the sensors started to grow significantly.

In figure 6.16, overall distributions of theS/N ratio are shown for the different bias voltages.The double peak structure is again visible in all distributions. At 80 V, theS/N distributionsfor clusters with one and two strips are very similar, whereas towards higher bias voltages thefirst (second) peak becomes more pronounced for clusters with two (one) strips. This indicatesthat the clustering improves with increasing bias voltage. The positions of the two peaks for


sensor 1 w/p=0.2

track position

effic

ienc

y

0.9

1

0 0.2 0.4 0.6 0.8 1

sensor 1 w/p=0.25

track position

effic

ienc

y

0.9

1

0 0.2 0.4 0.6 0.8 1

sensor 1 w/p=0.3

track position

effic

ienc

y

0.9

1

0 0.2 0.4 0.6 0.8 1

sensor 2 w/p=0.2

track position

effic

ienc

y

0.9

1

0 0.2 0.4 0.6 0.8 1

sensor 2 w/p=0.25

track position

effic

ienc

y

0.9

1

0 0.2 0.4 0.6 0.8 1

sensor 2 w/p=0.3

track positionef

ficie

ncy

0.9

1

0 0.2 0.4 0.6 0.8 1

sensor 3 w/p=0.2

track position

effic

ienc

y

0.9

1

0 0.2 0.4 0.6 0.8 1

sensor 3 w/p=0.25

track position

effic

ienc

y

0.9

1

0 0.2 0.4 0.6 0.8 1

sensor 3 w/p=0.3

track position

effic

ienc

y

0.9

1

0 0.2 0.4 0.6 0.8 1

transition w/p=0.2

track position

effic

ienc

y

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

transition w/p=0.25

track position

effic

ienc

y

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

transition w/p=0.3

track position

effic

ienc

y

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Figure 6.15: Efficiencies for the three sensors on the long ladder and for the transition regionbetween the second and the third sensor, for the differentw/p-regions. The efficiencies areshown as function of the track position for fast (filled dots) and slow (open squares) shaping. Ineach plot, data from the inter-strip regions of several strips belonging to the same region ofw/pwere superimposed.


S/N

1/N

dn/

d(S

/N)

80 V

0

0.05

0.1

0 20 40 60S/N

1/N

dn/

d(S

/N)

90 V

0

0.05

0.1

0 20 40 60

S/N

1/N

dn/

d(S

/N)

100 V

0

0.05

0.1

0 20 40 60S/N

1/N

dn/

d(S

/N)

110 V

0

0.05

0.1

0 20 40 60

Figure 6.16:S/N distributions for different bias voltages. The dashed (solid) line refers toclusters of two (one) strips. The distributions were normalised to compensate for the differentrate of occurrence of one- and two-strip clusters.

bias voltage first peak second peak

80 V 7.4 12.3

90 V 8.5 13.0

100 V 8.5 13.4

110 V 8.9 13.7

Table 6.4:S/N values of the second sensors on the long ladder for different bias voltages. First(second) peak refers to the first (second) peak in theS/N distribution for clusters with two (one)strip.

the different bias voltages are summarised in table 6.4. The difference between the resultsquoted in tables 6.3 and 6.4 for 90 V may be due to the different trigger delays used for the twomeasurements.

The efficiency of the ladder improves with increasing bias voltage. The efficiencies as functionof track position for the different bias voltages andw/p-ratios are shown in figure 6.17. The


80 V w/p=0.2

track position

effic

ienc

y

0.94

0.96

0.98

1

1.02

0 0.2 0.4 0.6 0.8 1

80 V w/p=0.25

track position

effic

ienc

y

0.94

0.96

0.98

1

1.02

0 0.2 0.4 0.6 0.8 1

80 V w/p=0.3

track position

effic

ienc

y

0.94

0.96

0.98

1

1.02

0 0.2 0.4 0.6 0.8 1

90 V w/p=0.2

track position

effic

ienc

y

0.94

0.96

0.98

1

1.02

0 0.2 0.4 0.6 0.8 1

90 V w/p=0.25

track position

effic

ienc

y

0.94

0.96

0.98

1

1.02

0 0.2 0.4 0.6 0.8 1

90 V w/p=0.3

track position

effic

ienc

y0.94

0.96

0.98

1

1.02

0 0.2 0.4 0.6 0.8 1

100 V w/p=0.2

track position

effic

ienc

y

0.94

0.96

0.98

1

1.02

0 0.2 0.4 0.6 0.8 1

100 V w/p=0.25

track position

effic

ienc

y

0.94

0.96

0.98

1

1.02

0 0.2 0.4 0.6 0.8 1

100 V w/p=0.3

track position

effic

ienc

y

0.94

0.96

0.98

1

1.02

0 0.2 0.4 0.6 0.8 1

110 V w/p=0.2

track position

effic

ienc

y

0.94

0.96

0.98

1

1.02

0 0.2 0.4 0.6 0.8 1

110 V w/p=0.25

track position

effic

ienc

y

0.94

0.96

0.98

1

1.02

0 0.2 0.4 0.6 0.8 1

110 V w/p=0.3

track position

effic

ienc

y

0.94

0.96

0.98

1

1.02

0 0.2 0.4 0.6 0.8 1

Figure 6.17: Efficiency as function of the track position for the differentw/p-regions and fordifferent bias voltages.


voltage [V]

nois

e ra

te/s

trip

10-5

10-4

10-3

10-2

10-1

80 90 100 110

Figure 6.18: Noise rate per strip as function of the bias voltage for the second sensor on thelong ladder.

efficiency loss in the middle of the inter-strip region decreases for higher bias voltages. Forall bias voltages, the best efficiency is again found for the region ofw/p = 0.3 and an overallefficiency above 99 % is obtained in this region. However, a slight decrease of the efficiency forthe regionw/p = 0.3 is observed at a bias voltage of 110 V, close to the break-down voltage ofthe sensors. For new prototype sensors with a higher breakdown voltage, the hope is that theefficiency performance can be further improved by increasing the bias voltage.

The noise rate per strip as function of the bias voltage is shown in figure 6.18. The noise rate isdefined as described above. It is in the order of 0.2 % for all bias voltages, which is significantlybelow the track occupancy expected at the LHC.


6.2 First Measurements Using the Beetle Readout Chip

In October 2001 SPA silicon prototype sensors were connected to the Beetle 1.1 readout chipand evaluated in a test beam, performed at the X7 facility at CERN. The main goal of this testwas to integrate for the first time different components (Beetle chip, ODE prototype board)of the LHCb readout chain into a running system. Noise characteristics and pulse shape wereinvestigated in the test beam and in a laboratory test setup. Measurements of theS/N ratio andefficiency are presented.

6.2.1 Readout Electronics

The sensors were connected to the Beetle 1.1 readout chip. The Beetle was used at a clockfrequency of 40 MHz, corresponding to a sampling interval length of 25 ns. As mentioned inchapter 5, the pulse width can be tuned on a limited scale by programming the shaper parameterVfs. Data were recorded with slow (Vfs = 1252 mV) and fast (Vfs = 315 mV) shaping time,with the main focus on the ladder performance using the fast shaping time.

A readout PCB was designed to house two Beetle chips. The design of this PCB was based on anexisting board that had been developed for functionality tests of the Beetle chip. Modificationscomprised a re-routing of some traces and an extension of the PCB in such a way that it servedalso as support frame for the sensors. The 64 readout strips of the sensors were directly bondedto the two Beetle chips. In order to approximately match the different pitches of chip and sensor(40.24µm and 240µm respectively.), only every 4th input channel of the Beetle was used. Onereadout strip was connected to the test channel of one of the two chips.

To interface the analog output signals of the Beetle to the prototype ODE (Off Detector Elec-tronics) board [83], the current output signals of the Beetle had to be converted into voltagesignals, which were then amplified in a second stage. This staged approach using two oper-ational amplifiers was chosen in order to obtain a high bandwidth and high slew rate for theoverall amplifier chain. To drive the approximately 7 m long cable to the electronics area, thecable driver described in [84] was used. It has a gain factor of +2 and contains a series resistorfor impedance matching. As the Beetle output is differential, the cable driver has been designedwith two parallel paths in order to minimise its sensitivity to external noise. The schematic ofthe cable driver is illustrated in figure 6.19.

6.2.2 Setup

The test beam was performed in the X7 beam line of the SPS accelerator at CERN, using a120 GeV muon beam.

Two ladders of prototype sensors were built. One ladder was equipped with one sensor (“short”ladder), the other with three sensors (“long” ladder). The total strip length of the long ladderwas thus 20 cm.

The existing test beam telescope of the LHCb VELO group was used [85] to reconstruct chargedparticle tracks. It is equipped with the VA2 chip with a shaping time of 2µs [86].

6.2. FIRST MEASUREMENTS USING THE BEETLE READOUT CHIP 81

CLC400

+

-

CLC400

+

-100

270

120

270

HFA1212

G= +2

CLC400

+

-

CLC400

+

-100

270

120

270

HFA1212

G= +2

50

50

Twisted Pair

(Z=100 )W

1 k

W

4700

100

-5 V

common modeoffset adjust

differential analogBEETLE signal

A0

A0

Figure 6.19: Schematics of the used cable driver. Power supply lines are not shown. All powersupply pins of the amplifiers are blocked to ground with 100 nF and 100 pF in parallel.

One test ladder at a time was installed inside an aluminum box, together with a ladder built bythe Inner Tracker group of Lausanne. Initially, data were taken with the short ladder, then thiswas dismantled and the long ladder was installed for the remainder of the test beam time. Thetest ladders were installed with the strips horizontal and the beam focused on the first sensor(nearest to the readout chips). Neither the sensors nor the electronics were cooled. The biasvoltage for the short ladder was 90 V. For the long ladder, data were taken with different biasvoltages. The I2C programming of the Beetle chip was done via the serial interface of a PC,controlled by LabVIEW.

The ladder of the Lausanne group was equipped with two prototype sensors of the same kindas the ones described here, read out by the SCTA chip [87]. The analog output signals fromboth the SCTA and the Beetle were received and digitised by the ODE-board. Simultaneous toour test, two further boxes with test sensors of the VELO group were installed in the beam. Aphotograph of the test beam setup is shown in figure 6.20.

The coincidence of two scintillators, covering the full width of the test ladder, served as triggerfor the DAQ system. The determination of the correct trigger delay turned out to be cumber-some, since the different components were integrated for the first time and due to time pressureand lack of manpower in the preparation of the test beam no well-engineered analysis code ex-isted at the time. A coarse adjustment of the trigger latency could be performed searching forcorrelations between extrapolated tracks from the beam telescope and hits in the test ladder (seefigure 6.21). Such correlations could be observed for several consecutive sampling intervals,reflecting the total width of the Beetle output signal. The latency before the last for which a cor-relation could be observed was used for data taking (the latency is defined such that the risingedge of the signal was at large values). Since the rise time of the Beetle chip of approximately25 ns corresponds roughly to the length of one sampling interval, this setting should be close tothe maximum of the pulse.

The latency scans for the short test ladder for slow and fast shaping are illustrated in figure 6.22.For these plots, refined algorithms for hit finding and determination of theS/N ratio were used


Figure 6.20: Test beam setup. The long test ladder equipped with three sensors can be seen infront of the ladder of the Lausanne group.

y [cm]

strip

num

ber

0

20

40

60

-1 -0.75-0.5-0.25 0 0.25 0.5

Figure 6.21: Correlation between extrapolated tracks from the beam telescope and hits in thelong test ladder. The bias voltage was 90 V. Strips that were broken or masked out in the analysisare clearly visible.


slow shaping short ladderfast shaping short ladder

fast shapinglong ladder

latency [BX]

S/N

0

2

4

6

8

10

12

14

16

18

150 152 154 156 158

Figure 6.22: Latency scan for the short ladder.S/N is shown as function of the latency for slow(filled dots) and fast (open squares) shaping. The Beetle signal was scanned in steps of 25 ns forslow shaping. For fast shaping additional points were taken close to the maximum of the signal.Lines are intended to guide the eyes. For the long ladder, only the rising part of the signal wasscanned (filled triangles). The arrow indicates the latency that was used for data taking with fastshaping time, for both the short and the long ladders.

that were available only after the test beam. The rise time of the signal is about 25 ns for bothslow and fast shaping, but the different shaping times are clearly reflected in the falling edge ofthe pulse (towards small values of the latency). The time offset between the latency curves forfast and slow shaping is due to a change in the cabling of the setup that was necessary in orderto reduce the width of the trigger gate from 25 ns for slow shaping to 5 ns for data taking withfast shaping. For data taking with fast shaping time, the same latency was used for the shortand the long ladder. The data shown in figure 6.22 suggest that the chosen latency for the longladder did not correspond to the maximum of the pulse.

The amplitude is significantly smaller for fast shaping than for slow shaping.

6.2.3 Analysis and Tracking

In contrast to the analysis of the May-2001 test beam data (previous section), pedestals andnoise values for the individual channels were determined globally for each run rather than byan adaptive pedestal and noise following algorithm.

To obtain a robust estimate of the pedestal for a given channel, the average of the central 50 %of all ADC values from the analysed run were taken as the pedestal for that channel (”50 %trimmed average”).

After pedestal subtraction, events were rejected if the rms scatter of the corrected ADC valueswas larger thanvarcut =14 counts. Next, an iterative procedure was used to subtract the


Residual [cm]-0.04 -0.02 0 0.02 0.04

0

5

10

15

20

25

30

35

40

45Sigma = 0.006211 Sigma = 0.006211

Figure 6.23: Residual distribution for the short ladder. The distribution is well described by aGaussian with a sigma of 62µm.

baseline. In a first step, a constant offset was subtracted for each event such that the averagepulse height was centred around zero.

A robust estimate for the pedestal- and common-mode corrected noise for each channel wasthen obtained as the half width of the central 68 % CL interval of the pedestal- and baseline-subtracted ADC values. If this “subtracted noise” exceeded a value ofdcut =5 ADC counts, itwas set to zero, effectively flagging the channel as dead.

Using the estimates of subtracted noise, refined baselines for all accepted events were deter-mined from a 5th-order polynomial, fitted to all bonded channels that were not flagged dead.In order to safeguard against biases from hits, the two strips with the most significant devia-tion form zero were excluded from the fit. The baseline fit was done separately for the twoBeetle chips. This procedure was performed twice in order to converge. Finally, the subtractednoise was again determined for each strip and used as the relevant strip noise for the hit finding,which used the same algorithm as for the May-2001 data. The cuts for single strip- and cluster-significance were set to seed-cut=2 andχ2-cut=6, respectively, to achieve optimal hit findingefficiency. Strips with a “subtracted noise” value below 1 ADC count (e.g. bad bonding) orabove 2 ADC counts (excessive noise) were excluded from the hit finding procedure.

In order to study cluster properties, clusters were selected that could be correlated to particletracks from the VELO telescope. The track information was provided by the VELO group [88].In order to obtain a clean sample, tracks were required to point inside the fiducial region ofthe sensor, defined to be at least two strips away from the sensor boundary, a boundary be-tween differentw/p regions, or a dead strip. The closest cluster found within 2 strips from theextrapolated impact point was used in the analysis.

Figure 6.23 shows the distribution of track residuals on the test sensors after the final alignment.Using the sigma of a Gaussian fitted to the distribution as definition of the spatial resolution, avalue of 62µm is obtained. This is consistent with the result obtained in the previous test beam.

The signal-over-noise of a cluster,S/N , was defined as described in section 4.3.2. The most


channel number

pede

stal

s [A

DC

]

0

20

40

0 20 40 60 80 100 120channel number

raw

noi

se [A

DC

]

0

1

2

3

4

0 20 40 60 80 100 120

Figure 6.24: Pedestals (left) and raw noise (right) for the first Beetle chip of the short ladder.The bonded channels can be easily identified by the enhanced noise.

probableS/N value of the distribution was estimated from a maximum-likelihood fit of a Lan-dau function, folded with a Gaussian.

6.2.4 Charge, Noise and Signal-to-Noise

Figure 6.24 shows the reconstructed pedestals and the raw noise for one Beetle chip on the shortladder. The shape of the Beetle baseline depends on the settings of programmable parametersand the parameters used in the test beam resulted in the “S”-shaped baseline shown in the figure.

After the test beam, some further investigations, including a charge calibration, were performedon the two test ladders in a laboratory setup. A different DAQ system was used in this setup (noODE board, digitisation by an oscilloscope) but the amplitude of the “S”-shape, obtained usingthe same Beetle parameters, could be used to relate the measured ADC values in the laboratorysetup and the test beam:

ADCbeam = f · ADClab (6.1)

f =ADCmax

beam − ADCminbeam

ADCmaxlab − ADCmin

lab

(6.2)

Here,ADCbeam andADClab denote the ADC values in test beam and laboratory, respectively.The indicesmax andmin denote the corresponding maxima and minima of the “S”-shapedbaseline.

The gain of the four used Beetle chips was determined in the laboratory, coupling a well definedcharge to a readout strip of the corresponding test ladder. The gain of the individual chips variedbetween 2.5 and 2.65µV/ e− (see figure 6.25). In general, the gain of a readout chip decreaseswith higher load capacitance, while its noise increases with the load capacitance. However,within the precision of our laboratory measurements, no significant difference could be ob-served between the gain of the chips connected to the long ladder and those connected to theshort ladder. For a charge of 22000 e−, corresponding to the most probable signal from a min-imum ionising particle in a silicon sensor of 300µm thickness, output signals of 18.5 ADClab


electrons

beet

le r

espo

nse

[mV

]

0

100

200

300

400

0 1000 2000 3000

x 102

Figure 6.25: Gain calibration of a Beetle chip, coupling a well defined charge to a readout stripof the test ladder and measuring the output of the Beetle chip. The arrow indicates the signal ofa minimum ionising particle in a silicon sensor of 300µm thickness, corresponding to 22000 e−.

counts and 17.5 ADClab counts were measured for the Beetle chips connected to the short lad-der and the long ladder, respectively. The quoted values are averaged between the two chips oneach ladder.

The measured noise for the long ladder (1.5 ADClab counts) was 20 % higher than that for theshort one, but this enhancement is much smaller than expected from the difference of the totalstrip capacitances of the two ladders. The noise contribution of the laboratory DAQ setup wasevaluated disconnecting the Beetle from the cable driver and replacing it by a 200Ω resistor tosimulate the output impedance of the Beetle chip. With this setup, a noise of 1.1 ADClab countswas measured, indicating that the DAQ setup contributed significantly to the total noise.

The signals in e− obtained in the test beam were estimated using equations 6.1 and 6.2 and theADC values measured in the test beam taking into account 24000 e− as the most probable valuefor the charge deposited in 300µm thick silicon by a 120 GeV muon. Most probable signalsof 15900 e− (10.6 ADCbeam counts) and of 11300 e− (6.5 ADCbeam counts) were obtained inthis way for the short and the long ladders, respectively (see figure 6.26). These results wereboth obtained for a bias voltage of 90 V. For the long ladder, also the cluster charge distributionobtained at a bias voltage of 115 V is shown in figure 6.26. The most probable value increasedto 7.8 ADCbeam counts, corresponding to 13400 e−. To obtain these distributions, only thoseclusters were taken into account that could be associated to a track, as described above.

Any attempt at an interpretation of these results must take into account that they were obtainedin a rather indirect fashion and are based upon measurements that were taken under far fromperfect conditions. Thus, no final conclusions should be drawn from these results, but a roughand qualitative attempt at an interpretation may nonetheless be interesting and useful.


charge [ADC]

N

most probable 10.6

0

200

400

0 20 40 60 80 100charge [ADC]

N

most probable 6.5

0

200

400

600

0 20 40 60 80 100charge [ADC]

N

most probable 7.8

0

100

200

300

0 20 40 60 80 100

Figure 6.26: Cluster charge distribution of the short (left) and the long (middle) ladder at a biasvoltage of 90 V. The right plot shows the distribution for the long ladder at a bias voltage of115 V.

long ladder short ladder

bias voltage charge noise S/N charge noise S/N

80 V 6.2 1.3 4.7 / / /

90 V 6.5 1.3 5.3 10.6 1.3 7.4

100 V 7.2 1.2 5.7 / / /

105 V 7.0 1.3 5.6 / / /

115 V 7.8 1.3 6.1 / / /

120 V 7.1 1.3 5.7 / / /

Table 6.5: Peak values of the charge, noise andS/N ratio for the long and the short ladder,measured in the test beam. For the short ladder, no bias voltage scan was performed.

In the previous measurements, a charge loss in the inter-strip gaps of the sensor had been ob-served that could partially explain a certain loss of signal with respect to the expected 24000 e−.The observation, for the long ladder, of an increase of the most probable signal with the biasvoltage would be consistent with this interpretation.

However, this effect could not explain the large observed difference between the collected sig-nals for the long and short ladders. There is no reason why a charge loss in the inter-strip gapshould be more pronounced for the long ladder. The most likely explanation for this differenceis that the latency of the chips was not correctly adjusted to the maximum of the signal pulsefor the measurements on the long ladder, as indicated in figure 6.22.

The strip noise levels of the short and the long ladders were measured to 1.3 ADCbeam counts,corresponding to about 2000 e−, for both ladders (see figure 6.27). For the long ladder, thenoise was independent of the bias voltage. The peak of the cluster noise distribution was also at1.3 ADCbeam counts in every configuration.

The peak values of all measured charge, noise andS/N distributions are summarised in table 6.5and the most probableS/N ratio as function of the bias voltage is also shown in figure 6.28.


channel number

subs

trac

ted

nois

e [A

DC

]

0

1

2

3

4

0 10 20 30 40 50 60

Figure 6.27: Subtracted noise as function of the strip number, for the long ladder. The first 31readout channels were bonded to the first Beetle chip and the last 33 channels to the second chip.Noisy channels were masked out in the analysis (subtracted noise above 2 ADCbeam counts orbelow 1 ADCbeam count).

long laddershort ladder

bias voltage [V]

S/N

3

4

5

6

7

8

80 100 120

Figure 6.28:S/N ratio as function of the bias voltage for the short (open circles) and long(filled circles) ladder.


w/p=0.2

w/p=0.25

w/p=0.30

bias voltage [V]

effic

ienc

y

open symbols = short ladder

filled symbols = long ladder

00.10.20.30.40.50.60.70.80.9

1

80 100 120

Figure 6.29: Efficiency as function of the bias voltage for the differentw/p-regions and for theshort and the long ladder.

6.2.5 Efficiency

The particle detection efficiencies for the long and the short ladder, and for the differentw/p-regions, are illustrated in figure 6.29. For the long ladder, efficiencies are shown as function ofthe bias voltage. The efficiency improves with increasing bias voltage, and for all bias voltageson the long ladder the highest efficiencies are obtained for the sensor region withw/p = 0.3.Qualitatively, this behaviour is consistent with the results from the previous test beam. However,the absolute value of the efficiencies (about 90 % for the long and 96 % for the short ladder)reached in this test beam are unsatisfactory.

The main limitation of this testbeam was the extremely tight schedule during its preparation,dictated by the availability of on the one hand the first equipped Beetle PCBs and on the otherhand the test beams at CERN. As a consequence, measurements suffered from a not ideal setupand an unstable software environment that made a lot of R&D work necessary during the testbeam. The measured performance was therefore limited by the setup and our understanding ofit.


6.3 Test Beam with Full Size Prototype Sensors

The HPK multi-geometry silicon prototype sensors were studied in a test beam performed in theX7 beam line at CERN in May 2002. Measurements were carried out using the the Beetle 1.1analogue front-end chip. In this section results on resolution, signal-to-noise, noise rates andefficiencies are presented as function of the bias voltage and for different shaping times. Basedon the results the decision will be made which readout strip geometry will be implemented inthe final sensors for the LHCb Inner Tracker. The sensors evaluated in the test beam were the6” multi-geometry prototype sensors described in detail in section 4.2.

6.3.1 Readout Electronics

The prototype sensors were connected to the Beetle 1.1 readout chip. The test sensor datawere sampled at 40 MHz, corresponding to a sampling interval length of 25 ns . However,the whole readout chain was operated at a frequency of 10 MHz1. The bias settings and otherparameters of the Beetle chip were programmed by an I2C-interface. Standard settings of theBeetle parameters were used for the data taking, apart from the preamplifier currentIpre whichwas set toIpre = 800µA and the parameterVfs controlling the shaper feedback resistance. Thelatter was varied during data taking, as described below.

A front-end hybrid in a four layer copper on polyimid technology was designed to house threeBeetle 1.1 chips. In order to match the different pitches of readout chip and prototype sensor apitch adapter produced in thin-film technology on a ceramic substrate [51].

6.3.2 Test Beam Setup

In total three test ladders were assembled. Two ladders were equipped with two sensors (longladder) and one ladder with one sensor (short ladder). Ladders of exactly these sizes will beused for the LHCb Inner Tracker. The large surface of the sensors allowed a functionalitytest of the ladders in a cosmic ray setup. In May 2002 a long and a short ladder were theninstalled at the X7-CERN test facility and operated in a 120 GeV charged pion beam. As forthe May test beam in 2001, four double-sided silicon strip detectors provided by the HERA-Bvertex group [66] served as beam telescope. The telescope and the test ladders were installed inseparate boxes. To remove the heat generated by the Beetle chips the test ladders were attachedto cooling blocks. Water at about 10C was used as coolant. A photograph of the test beamsetup is shown in figure 6.30.

The readout was triggered by a coincidence of two scintillators placed upstream of the beamtelescope and the test ladders. Trigger delay scans were performed to determine the optimalBeetle sampling time. The delay between the trigger signal and the sampling time was varied insteps of 5 ns and the most probable cluster charge signal was determined for each of the delaysettings. In order to study the total width of the Beetle output signal the scans were performed

1The Beetle chip contains a programmable readout clock divider.

6.3. TEST BEAM WITH FULL SIZE PROTOTYPE SENSORS 91

Figure 6.30: Test beam setup. Test ladders were mounted on rails for easy adjustment of theirrelative positions.

trigger delay [ns]

char

ge [A

DC

]

short ladderlong ladder

Vfs=400 mV

0

5

10

15

20

25

20 40 60 80trigger delay [ns]

char

ge [A

DC

]

short ladderlong ladder

Vfs=1000 mV

0

5

10

15

20

25

20 40 60 80

Figure 6.31: Pulse shape scans showing the cluster charge of the long (open squares) and short(filled dots) ladder as function of the trigger delay for two Beetle settings (Vfs = 400 mV andVfs = 1000 mV). The curves correspond to simulation results.

over several consecutive sampling intervals. The results of the delay scans for different Beetlesettings are shown in figure 6.31 and reflect the signal shape of the Beetle chip. The measureddata is compared to simulation results (see section 5.2) of the Beetle front-end and is found tobe well described. The deviation between data and simulation at the falling edge of the signalfor the short ladder is due to a lower capacitance used in the simulation (10 pF) compared to themeasured capacitance of'16 pF.


To ensure a correct timing over the entire data taking period the delay scans were repeatedperiodically. For all recorded runs the trigger delay was adjusted to the maximum of the corre-sponding curve.

6.3.3 Data Samples

In the May 2001 test beam it had been found that the efficiency, especially in the inter-stripregion, was very sensitive to the bias voltage and the shaping time of the read-out chip. Datataking was thus focused on the variation of the bias voltage. In addition, for each bias voltagepoint data was recorded with two Beetle settings corresponding to different shaping times. Inthe following, these two shaping times will be referred to as “fast” (Vfs = 400 mV) and “slow”(Vfs = 1000 mV) shaping.

The HERA-B telescope had a limited active area of 50 mm×70 mm. Therefore in order toachieve full illumination of all readout strip geometries on the prototype sensors, different runswere taken adjusting the position of the test ladders to the telescope active area. At least 200Ktriggers were recorded for each data set. However, due to the beam profile the number of usefulevents varies between the different strip geometry regions of the test sensors.

6.3.4 Analysis Procedure

Tracking

The tracking procedure is based on that from the May 2001 test beam as described in section 6.1.The single hit resolution of the beam telescope is found to be 17µm in this setup well suitedfor a precise scan of the inter-strip region in the order of 200µm for the test sensors. In theanalysis software the test ladders were aligned with respect to the fixed beam telescope for eachrun using lateral shifts and rotations such that the average hit residual distribution is centred atzero. The width of the cluster to track position residual versus theχ2 of the track fit is shown infigure 6.32. Theχ2 of the track fit is calculated from hits in the telescope only. The dependenceof the residual of the cluster position on theχ2 of the track fit is due to a degradation of thetracking resolution. The width of the residual distribution increases continuously for largerχ2

of the track fit and a maximum value of 10 was chosen as a quality cut. Furthermore, a minimumnumber of 7 hits in the telescope was demanded and the analysis was restricted to events withexactly one reconstructed track. The large fraction of events with zero reconstructed tracks infigure 6.32 is due to the fact that the spatial coverage of the trigger scintillators and the testladders is larger than that of the tracking telescope.

Clustering

Pedestals and noise are determined from the raw pulse heights for each stripi in an iterativeprocedure using a statistical method. The ADC valuex of a strip (x : adc[i]) is composed of


2χtrack 0 10 20 30

resi

dual

[mm

]

-0.2-0.15-0.1

-0.05-0

0.050.1

0.15

number of tracks0 1 2 3

num

ber

of e

vent

s

0

50000

100000

150000

Figure 6.32: The width of the cluster to track position residual versus theχ2 of the track fit(left) and the distribution of the number of tracks per event.

three different parts: pedestal (p), noise (σx) and common mode (c), where noise and commonmode are assumed to be uncorrelated.

x = p+ axσx + bc (6.3)

The distributions ofax andb are normalised to have an rms equal to one. Similarly, one canwrite for the mean ADC valuey of its neighbouring strips (y : (adc[i− 1] + acd[i+ 1])/2):

y = q + ayσy + bc (6.4)

From the distribution ofy versusx (see figure 6.33, top), one can determine

〈x〉 = p, (6.5)

〈y〉 = q, (6.6)⟨x2⟩

= p2 + σ2x + c2, (6.7)

〈xy〉 = pq + c2. (6.8)

All other terms cancel ifax, ay andb are assumed to be uncorrelated. Therefore, the “averagecommon mode”c can be extracted from the correlation ofx andy,

〈xy〉 − 〈x〉〈y〉 = c2, (6.9)

and the noiseσx from ⟨x2⟩− 〈x〉2 = σ2

x + c2. (6.10)

In this way, pedestals and noise are determined (almost) without any assumptions about theshape of the baseline. The central area of the distribution ofy versusx in figure 6.33 showsa 2-dimensional Gaussian density a demonstrated by the projections. While the outliers corre-spond to hits, the noise and common mode are Gaussian distributed. For the pedestal and noisedetermination, a window of two rms around the mean was used in order to reject the outliers.


adc[i]120 130 140 150 160 170

(adc

[i-1]

+ a

dc[i+

1]) /

2

120

130

140

150

160

170

(adc[i-1] + adc[i+1]) / 2120 130 140 150 160 1700

200

400

600

800

1000

1200

1400

1600

Chi2 / ndf = 52.33 / 28 23.2 ±Constant = 1613

0.02126 ±Mean = 141.6 0.01545 ±Sigma = 1.827

Chi2 / ndf = 52.33 / 28 23.2 ±Constant = 1613

0.02126 ±Mean = 141.6 0.01545 ±Sigma = 1.827

adc[i]120 130 140 150 160 170

0

200

400

600

800

1000

1200

1400

Chi2 / ndf = 61.36 / 31 20.15 ±Constant = 1392

0.02464 ±Mean = 139.6 0.0182 ±Sigma = 2.115

Chi2 / ndf = 61.36 / 31 20.15 ±Constant = 1392

0.02464 ±Mean = 139.6 0.0182 ±Sigma = 2.115

Figure 6.33: Illustration of the statistical method for pedestal and noise determination. Thedistribution ofx andy (see text) and their correlation (top plot).

In figure 6.34, the pedestals of the short and the long ladder are shown. Their shapes reflect thebaseline of the Beetle.

Event-by-event common mode fluctuations were estimated by a third order polynomial fittedto the pedestal subtracted data. The common mode has been determined separately for regionsof different strip geometry. Region D has further been split into two groups of readout stripsaccording to the readout chip boundary. Channels at region or chip boundaries were excludedfrom the analysis. As a cross-check, one can compare the rms of the data after common modesubtraction with the average noise. For a random sample (200V, short ladder, region A), therms of the data was 1.588 whilst the average noise was 1.522. Thus, a third order polynomialmodels well the shape of the baseline.

For the clustering, the same algorithm as for the previous test beam and laboratory data wasused. The signal-to-noise ratio for clusters was also defined as for the previous data and isdescribed in section 4.3.2.

The two parameters in the clustering algorithm have to be optimised to give a maximum ef-ficiency maintaining a tolerable rate of noise clusters per strip. With an estimated averageoccupancy in the Inner Tracker silicon sensors of 0.6 % per strip [82], a noise hit rate of up to


strip number0 50 100 150 200 250 300 350

pede

stal

0

20

40

60

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100

120

140

160

180

strip number0 50 100 150 200 250 300 350

pede

stal

0

20

40

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80

100

120

140

160

Figure 6.34: Pedestals of the short (left) and the long ladder (right).

0.1 % seems tolerable. Theχ2-cut value has been scanned from 5 to 20 in order to find the opti-mal setting, as shown in figure 6.35. The influence of the seed-cut on the performance is foundto be very small. The noise rate and the corresponding performance of the clustering algorithmin terms of the resulting product of efficiency and purity is also shown in figure 6.35 as functionof the clustering parameters. Parameters seed-cut=3 andχ2-cut=13 have been chosen for the

χ2 cut

nois

e ra

te%

seed cut=3seed cut=4seed cut=5

0

0.2

0.4

0.6

5 10 15 20χ2 cut

effic

ienc

y*(1

-noi

se r

ate)

seed cut=3seed cut=4seed cut=5

0.96

0.98

1

5 10 15 20

Figure 6.35: The noise rate and the product of efficiency and purity for various values of thetwo clustering parameters. The results shown here are for region C of the long ladder with 90Vbias voltage and fast shaping.

analysis. A breakdown of the noise rates that are observed in the different regions for 90V biasvoltage and fast shaping is given in table 6.6. Region E of the short ladder exhibits a very largenoise. This can obviously not be attributed to the strip geometry of the region, and nothingsimilar is observed for the long ladder. It is either an anomaly in the sensor or can be related tothe readout chip/chain. However, the readout chip covering region E also covers a small part ofregion D and it does not seem that the last part of region D is also affected.


Also given in the table is an estimate of the “fake noise” rate, which is of the order of'15 %. As “fake noise” clusters are classified that are not attributed to a reconstructed particletrack, but have an associated cluster in the other test ladder. Having correlated clusters in bothladders suggests, that the clusters indeed result from a real particle, whose track failed thereconstruction.

short ladder

Region A B C D E

Noise Rate 0.083 % 0.073 % 0.083 % 0.059 % 0.430 %

Fake Noise 0.016 % 0.007 % 0.018 % 0.012 % 0.026 %

Relative 18.9 % 9.1 % 21.6 % 20.3 % 6.0 %

long ladder

Region A B C D E

Noise Rate 0.057 % 0.077 % 0.093 % 0.090 % 0.070 %

Fake Noise 0.016 % 0.007 % 0.016 % 0.014 % 0.021 %

Relative 28.6 % 8.7 % 17.6 % 15.6 % 30.5 %

Table 6.6: The noise rate split for the different regions for the long and the short ladder at 90Vbias voltage and fast shaping. Here the final cluster algorithm cuts have been chosen.

In figure 6.36 the correlation of clusters not associated to a track in the long and short ladderis shown. One can clearly see a strong correlation in the position of these clusters resultingfrom particle clusters where the track failed to be reconstructed, either because of inefficiencyin the telescope or because of its spatial dimensions. Given that this “fake noise” rate shouldbe subtracted from the quoted noise hit rate, the resulting noise occupancy is well below 0.1 %.The distributions of noise clusters for the short and the long ladder are shown in figure 6.37.The large noise in region E of the short ladder mentioned already in table 6.6 is clearly visiblein the plot. There is also a slightly increased noise level in the last part of region D, which isparticularly visible for the long ladder. The latter is most likely due to the fact that in this smallregion the common mode correction, calculated on a small number of channels, is performingworse than elsewhere.

6.3.5 Analysis

Data Quality

The spatial distribution of clusters for both test ladders is displayed in figure 6.38, showing thata full illumination of all regions has been achieved. Again, it is clearly seen that region E ofthe short ladder exhibits a large noise. There is one noisy channel in the long ladder. No deadchannels are observed neither in the short nor in the long ladder.

The residual distribution for reconstructed clusters is shown in figure 6.39, separately for regionC with 198µm strip pitch and for region E with the larger pitch of 237.5µm. The distributions


channel number (short ladder)0 100 200 300

chan

nel n

umbe

r (lo

ng la

dder

)

0

100

200

300

Figure 6.36: The correlation between the noise clusters observed in the short and the longladder. The correlation is due to fake noise clusters, where the track has not been reconstructed.

channel number0 100 200 300

entr

ies

0

2000

4000

6000

channel number0 100 200 300

entr

ies

0

1000

2000

Figure 6.37: The distribution of noise clusters over the sensors for the short ladder (left) and thelong ladder (right).


strip number0 100 200 300

num

ber

of h

its

0

10000

20000

30000

40000

strip number0 100 200 300

num

ber

of h

its

0

20000

40000

60000

80000

Figure 6.38: Reconstructed clusters as function of the strip position of the short ladder (left)and the long ladder (right).

are reasonably well described by a single Gaussian. Deviations from Gaussian shape are dueto the contributions from one and two-strip clusters. The resolution, defined as the one-sigmawidth of a Gaussian fit to the residual distribution, is 52µm and 59µm for region C and regionE, respectively. These resolutions are both better than the required resolution for the LHCbInner Tracker [10]. They are also slightly better than the digital resolutions of 56.9µm and68.6µm expected for the respective regions C and E, demonstrating that some charge sharingoccurs and enhances the resolution.

residual [mm]-0.4 -0.2 0 0.2 0.4

entr

ies

0

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2000

3000

4000

5000

6000

sigma:

0.052 mm

residual [mm]-0.4 -0.2 0 0.2 0.4

entr

ies

0

2000

4000

6000

8000

10000

sigma:

0.059 mm

Figure 6.39: Residual distribution of the region C (198µm pitch) and region E (237.5µm pitch)of the long ladder. A single Gaussian is fitted to the distributions in order to determine theresolution.

A detailed investigation of all individual regions revealed a problem in region A and B of the


long ladder. In contrast to the other regions, mainly two- and three-strip clusters are observedhere. In addition, a strong asymmetry of the charge on the strips of the two-strip clusters ispresent. Figure 6.40 shows the relative fraction of the total cluster charge seen on the stripwith the lower strip number,chargei/(chargei + chargei+1). In average, more charge is seenon the first strip, although a symmetric distribution is expected. This is due to the fact, thatthese clusters are reconstructed as two-strip clusters only because some charge of the stripi isalso seen in the next readout stripi + 1. The effect could not be reproduced in a laboratorysetup, using the same ladder as in the test beam. Several possible mechanisms generatingsuch an asymmetry have been investigated aiming to correct for this effect in the raw data.For example an incorrect timing of the ADC sampling of the serial Beetle output signal wasstudied. However, the best results in terms of the cluster width and residual distributions wereobtained for a simple subtraction of 31 % of the ADC counts in channeli from channeli + 1.This disfavours the assumption of an ADC timing problem. However the average cluster chargeafter the subtraction suggested that the correction procedure does not correctly recover the truesignal. Therefore these regions are excluded from most of the further investigations.

charge[i]/(charge[i]+charge[i+1])0 0.2 0.4 0.6 0.8 1

entr

ies

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1000


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ies

0

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1200

1400

1600


entr

ies

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300

400

500

600

700

Figure 6.40: The relative fraction of the cluster charge on the strip with the lower strip number,for region A, B and C (from left to right).

Cluster Properties

In the following section cluster properties are studied taking a bias voltage of 90 V and fastshaping time as an example. The charge sharing between adjacent strips is characterised by theη-function shown in figure 6.41 and defined in equation 4.5. Theη-function shows a clear non-linear behaviour of the charge sharing between the strips. Significant charge sharing is observedonly in the central region between the two strips. In spite of the fact that this charge sharingseems to occur only in a limited region, a significant amount of charge is always depositedin the neighbouring strips. This is reflected by the fact that the value of theη-function doesnot approach zero or one for tracks extrapolating right onto a readout strip. The average eventcluster shapes for the short and the long ladder are shown in figure 6.42 for tracks from particlesthat pass the detector close to a strip. For these clusters, most of the charge is deposited on thecentral strip, but shoulders resulting from charge induced on the neighbouring strips are clearly


track position0 0.5 1

η

0

0.1

0.2

0.3

0.4

0.5

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0.8

0.9

region C

region E

track position0 0.5 1

η0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

region C

region E

Figure 6.41: Charge sharing between two strips as function of the relative track position inregion C and E for the short ladder (left) and the long ladder (right) in two strip clusters.

-20 -15 -10 -5 0 5 10 15 200

5000

10000

15000

20000

relative strip number

entr

ies

-20 -15 -10 -5 0 5 10 15 200

2000

6000

10000

14000

relative strip number

entr

ies

Figure 6.42: The average event cluster shape is shown as the distribution of the charge signalmeasured in the strip hit centrally by the particle and the neighbouring strips for the short ladder(left) and the long ladder (right).

visible. These shoulders are about two times larger for the long ladder than for the short ladder.This suggests that the charge seen in the neighbouring strips is induced by capacitive couplingof the strips in the sensor itself and not due to cross talk in the readout chain.

Figure 6.43 shows measured signal distributions for strip geometry region C on the long ladder.In order to investigate possible charge loss in the inter-strip region, distributions are shownseparately for tracks that extrapolate directly to a readout strip and for tracks that point to theregion in between two readout strips. In both cases, the signals of the four adjacent stripsclosest to the track were summed in order to include all the charge deposited in the detector


charge [ADC counts]0 20 40 60

entr

ies

0

500

1000

1500

Width (scale of landau) 1.093

MPV 15.7

area 2.031e+04

Width Gaussian 3.067


entr

ies

0

500

1000

1500


MPV 13.08

area 1.929e+04


Figure 6.43: Measured signal distributions for region C of the long ladder at a bias voltageof 90 V for tracks extrapolating directly to a readout strip (left) and to the region in betweentwo readout strips (right). The signal is determined as the sum of the signals on the four stripsclosest to track.

and to avoid possible missing of charge in a clustering algorithm2. The distributions are fittedwith a Landau distribution convolved with a Gaussian. For tracks close to a readout strip, thefit yields a most probable value of 15.7 ADC counts, whereas one obtains 13.1 ADC counts inthe inter-strip region, indicating that there is a significant charge loss in the region between tworeadout strips. With a measured average noise amplitude of 1.27 ADC counts a most probableS/N value of 12.3 is obtained for tracks close to a strip and a value of 10.3 is found in the inter-strip region. The charge losses and the measured S/N values for clusters on top of a readoutstrip are summarised in table 6.7 for all different bias voltages and ladders.

These numbers can be compared to a predictedS/N ratio derived from the measured Beetle 1.1noise dependence on its load capacitance, and the knowledge of the most probable charge depo-sition for a 120 GeV pion in a 320µm thick silicon sensor. The expected noise can be calculatedusing equation 5.1 and the measured total capacitance of the sensors (see section 4.2). Witha capacitance of 34.5 pF for the long ladder a noise of 2300 e− is obtained, while the noise is1580 e− for the short ladder (17 pF). The most probable energy loss in silicon sensors of 320µmthickness is about 91 keV [16](see section 2.1.3). With the average energy of 3.62 eV needed tocreate a electron-hole pair this translates into a most probable charge deposition of' 25100 e−

in our test sensors.

Taking into account all these numbers, the predicted S/N ratios are 10.9 and 15.9 for the long

2Due to the cut on the minimum significance for a strip in a clustering algorithm, it is possible to miss smallcontributions to a cluster and thus artificially generate a charge loss. This is more probable in the inter-strip regionwhere charge is distributed over at least two strips.


short ladder long ladderbias voltage

fast shaping fast shaping

S/N charge loss S/N charge loss

60 V 15.4 18.0 % 11.8 17.2 %

70 V 15.7 18.1 % 12.1 16.1 %

80 V 15.8 19.0 % 12.2 16.1 %

90 V 15.7 19.1 % 12.3 16.6 %

100 V 15.7 19.1 % 12.5 17.0 %

110 V 15.6 19.2 % 12.5 17.0 %

120 V 15.1 19.4 % 11.9 16.0 %

140 V 15.0 18.6 % 12.0 14.6 %

170 V 15.0 19.5 % 12.0 13.4 %

200 V 15.0 18.5 % 11.9 12.8 %

Table 6.7: TheS/N measured for clusters where the particles track passed close to a readoutstrip and the relative charge loss between the readout strips. These results were obtained fromthe strip geometry of region C.

σ [ADC]

noise per strip 1.27

channel-to-channel gain variations 0.62

atomic binding in silicon 1.045

total: 2.82

Table 6.8: Contributions to the width of the Gaussian part in the convolution of a Landaudistribution and a Gaussian function that is used to represent the signal distributions. Note thatthe strip noise enters for each strip in the cluster in the total noise.

and the short ladder, respectively. These values are in good agreement with the values obtainedfor tracks close to a strip and demonstrate that a significant charge loss in between the strips isencountered.

The one-sigma widths of the Gaussians of 3.07 ADC and 3.09 ADC counts from a fit to therespective distributions are in agreement with the expected width of 2.82 ADC counts that iscalculated taking into account noise per strip, channel-to-channel gain variations and atomicbinding effects in silicon (see section 2.1.3). The various contributions to the width of theGaussian are listed in table 6.8. The strip noise and channel-to-channel gain variations are themeasured values. The effect of the atomic binding in silicon is taken from reference [22]. Notethat in the quadratic sum of the individual contributions the strip noise has to be multiplied bya factor of

√4 since the result is compared to the signal of four strips.

Figure 6.44 shows the signal distributions for tracks close to a strip and between strips, afterapplying the cluster finding algorithm. The measured cluster charge is approximately 10 %



entr

ies

0

500

1000

1500


MPV 14.15

area 2.027e+04



entr

ies

0

500

1000

1500


MPV 11.96

area 1.928e+04


Figure 6.44: Measured cluster charge distribution for region C of the long ladder at a biasvoltage of 90 V for tracks extrapolating directly to a readout strip (left) and to the region inbetween two readout strips (right).

smaller than the summed signal shown in figure 6.43. This is due to the fact that the shouldersseen in figure 6.42 are typically missed by the clustering algorithm. Since no precise chargecalibration is available, we cannot say with certainty whether the shoulders should be consideredas signal or not. The relative size of the charge loss in the inter-strip region is however notaffected by the clustering algorithm.

cluster width [strips]1 2 3 4 5

num

ber

of e

vent

s

0

10000

20000

30000

cluster width [strips]1 2 3 4 5

num

ber

of e

vent

s

0

10000

20000

30000

Figure 6.45: Distribution of the size of the clusters reconstructed in the short ladder (left) andthe long ladder (right) at 90V depletion voltage.

In the following all results and distributions are shown for reconstructed clusters. The cluster


size distributions for the short and the long ladder are displayed in figure 6.45. As mentionedbefore, the small shoulders are not included in the typical cluster and hence most clusters consistof one or two strips only.

S/N0 10 20 30 40

entr

ies

0

200

400

600

800

1000

1200

1400

1600 1 strip clusters: MPV= 9.6

2 strip clusters: MPV=11.0

Figure 6.46:S/N measured for reconstructed one-strip (filled circles) and two-strip (open cir-cles) clusters in region C of the long ladder.

In figure 6.46S/N distributions are shown for reconstructed cluster widths of one and two stripsfor region C.S/N ratios of 9.6 for one-strip clusters and 11.0 for two-strip clusters are derivedfrom fits (Landau folded with Gaussian) to the corresponding distributions. Considering thatthe clustering algorithm mostly misses the shoulders one would typically expect that two-stripclusters are found in the inter-strip region where significant charge loss is observed. Therefore,they should have a smaller charge and henceS/N than one-strip clusters expected close to astrip. In figure 6.47 theS/N ratio is shown as function of the track position. It is clearly visiblethat a significant fraction of reconstructed two-strip clusters with an increasedS/N ratio occurclose to a strip. In addition, also one-strip clusters are found in between the strips, where asignificant amount of charge is then missed. This explains the largerS/N observed for thetwo-strip clusters compared to the one-strip clusters in figure 6.46.

The tendency of the clustering algorithm to include either one of the shoulders or neither ofthem, degrades the spatial resolution. Taking into account only one shoulder for clusters closeto a strip spoils the residual distribution and is partially responsible for its non Gaussian shape.It is conceivable to increase the resolution by suppressing the shoulders all together. On theother hand, one can consider a better clustering algorithm taking into account both shouldersusing the knowledge of the cluster shape.


strip number140 141 142 143 144 145

S/N

0

5

10

15

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25

301 strip clusters1 strip clusters

strip number140 141 142 143 144 145

S/N

0

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10

15

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302 strip clusters2 strip clusters

Figure 6.47:S/N as function of the strip number for clusters of one (left) and two (right) strips.

The most probable value of theS/N for clusters as function of the relative position in betweenstrips is shown in figure 6.48. Results are shown for all five regions of the long ladder and forthe two different shaping times. The slow shaping generally results in a largerS/N due to thebetter noise performance of the readout chip. In addition, shaping times of the order of thecharge collection time of about 20 ns for 320µm silicon can possibly lead to a ballistic deficitwhich is more pronounced for the faster shaping (see section 5.6). However the charge loss inthe inter-strip region is present for both shaping times.

The fact that theS/N ratio in region D is higher than in region E is consistent with the betternoise performance due to the smaller strip capacitance of this region. Conclusions concerningthew/p dependence of theS/N ratio for regions A,B and C should not be drawn since theinvolved correction procedure for region A and B artificially increases the noise and reduces thesignal.

Hit finding efficiencies are shown in figure 6.49. For the slow shaping time, theS/N apparentlyis large enough to reach maximum hit finding efficiency also in between the strips, while forthe fast shaping a significant efficiency loss is observed here. This is illustrated in figure 6.50,where the hit efficiency is shown as function of theS/N value. AS/N threshold of about 10 to11 above which the efficiency reaches its maximum is clearly visible independent of the shapingtime. Slow shaping time generally results in largerS/N values. The efficiencies determinedfor region A of the short ladder do not follow the same curve as observed for the other regions,but are shifted towards smaller values. This behaviour is observed for all bias voltages andshaping times. Its origin is not understood, but such a large deterioration is not regarded likelyto be caused by the small difference inw/p compared to the regions B and C. In order toavoid misleading conclusions in terms of thew/p dependence, this region is disregarded in thefollowing.

The measured efficiency values are affected by fake tracks due to noise hits in the telescope, ortracks that are badly reconstructed but still pass our selection cuts. The rate of fake tracks was


interstrip position0 0.2 0.4 0.6 0.8 1

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Figure 6.48:S/N of clusters as function of the relative inter-strip position of the track impactpoint on the sensor.S/N ratios are shown as an example for 90V bias voltage, long ladder andfor fast (filled circles) and slow (open circles) shaping.


track position0 0.2 0.4 0.6 0.8 1

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region E

Figure 6.49: Efficiency as function of the relative inter-strip position of the track impact point onthe sensor. Efficiencies are shown for 90V bias voltage, long ladder and for fast (filled circles)and slow (open circles) shaping.


fast shaping

S/N

effic

ienc

y

region A (short ladder)region B (short ladder)region Cregion Dregion E

0.94

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6 8 10 12 14 16 18 20 22 24

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effic

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0.94

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1

6 8 10 12 14 16 18 20 22 24

Figure 6.50: Cluster reconstruction efficiency as function ofS/N for fast and slow shaping.The different values ofS/N are obtained from different inter-strip positions of various regionsin the detector for the long (regions C,D and E) and short ladder (all regions).


studied by looking into correlations between the two test ladders. With a high cluster findingefficiency of> 98 %, for tracks from real particles, the probability of missing the reconstructionof a corresponding cluster in both ladders at the same time is almost negligible. With the appliedtrack quality cuts as described in chapter 6.3.4 it is found in this study, that in 70-75 % of thecases, where the algorithm apparently fails to reconstruct a cluster, this is not due to inefficiencyin our test ladders, but rather due to a fake track. In order to eliminate these fake tracks from theefficiency calculation for the long (short) ladder, a hit in the short (long) ladder is demanded.

6.3.6 Results

S/N ratios and efficiencies were studied as function of the bias voltage for slow and fast shapingtimes. Data were taken at 10 different voltage settings between 60 V and 200 V, in order toinvestigate the high voltage dependence of the loss ofS/N and efficiency in the inter-stripregion. Results from the voltage scans are shown for the different regions of the short and longladders.

The aim of this study was the determination of the optimal strip geometry of the sensor in termsof pitch andw/p. To avoid misleading conclusions for thew/p ratio dependence of theS/Nor efficiency, all regions identified previously with problems are omitted that are not assumedto be related to thew/p ratio. Therefore regions A and B from the long ladder are excluded aswell as regions A and E on the short ladder. This allows to make two comparisons of regionswith the same pitch and differentw/p, namely regions D with E and B with C for the long andthe short ladder, respectively.

TheS/N values on top of a readout strip are shown as function of the bias voltage in figure 6.51.As expected,S/N values are generally higher for the slow shaping. Results indicate a slightincrease of theS/N ratio with bias voltage up to 100 V in agreement with results from theprevious test beams.S/N values for region B are larger than those for region C of the shortladder for all bias voltages in accordance with the smallerw/p. This holds true for both theslow and the fast shaping time. For the long ladder regions D and E also show the expectedw/pdependence, however the effect is very small for the fast shaping.

The difference in theS/N between clusters close to a strip and those reconstructed in the inter-strip region is shown in figure 6.52 as function of the bias voltage. The size of the dip seemsto be basically independent of shaping time and bias voltage. The dip is more pronounced forthe short rather than for the long ladder. However, the size of the dip relative to the maximumS/N value on the strip is the same for all cases as seen in figure 6.53, indicating that the amountof charge lost is the same for the long and the short ladder. For the regions with smaller pitchthe size of the dip in the inter-strip region is considerably smaller than for the larger pitch.Similarly, the size of theS/N loss decreases with increasingw/p, indicating that wider implantwidths result in more efficient charge collection. Electrostatic simulations are ongoing to furtherunderstand this behaviour [81].

Hit efficiencies as function of the bias voltage are summarised in figure 6.54. The efficiencyfor tracks close to a strip exceeds 99.4 % for all bias voltages and strip geometry regions. Theefficiency does not show any bias voltage dependence in the considered range above 60 V. For


short ladder (fast shaping)

region B

region C

region D

bias voltage [V]

S/N

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rips

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Figure 6.51: TheS/N measured for clusters centred on the strips as function of the high voltage.The upper and lower plots refer to the fast and slow shaping, respectively.

the long ladder and fast shaping, in the inter-strip region the S/N is close to the minimum valueneeded for full efficiency (see figure 6.50). This results in a sizeable efficiency loss, as shownin figure 6.55. The efficiency loss decreases with increasing bias voltage for voltages of up to100 V but stays constant for higher bias voltages. For region C the size of the efficiency lossis considerably lower compared to the region D and E. The relative efficiency loss between thestrips in region C is about 1 % whereas it increases to about 3 % for the large pitch regions.



region B

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Figure 6.52: The difference inS/N between clusters centred on the strips and those in themiddle between two strips as function of the high voltage. The upper and lower plots refer tothe fast and slow shaping, respectively.



region B

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tive

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tive

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Figure 6.53: The relative difference inS/N between clusters centred on the strips and those inthe middle between two strips as a function of the high voltage. The upper and lower plots referto the fast and slow shaping, respectively.



region B

region C

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ienc

y on

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0.98

0.985

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0.985

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40 60 80 100 120 140 160 180 200

Figure 6.54: The cluster finding efficiency for tracks centred on the strips as function of thehigh voltage. The upper and lower plots refer to the fast and slow shaping, respectively.



region B

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region C

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-0.01

0

0.01

0.02

0.03

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40 60 80 100 120 140 160 180 200

Figure 6.55: The relative difference in the cluster finding efficiency for tracks that are centredon the strips and those that pass in the middle between two strips as a function of the highvoltage. The upper and lower plots refer to the fast and slow shaping, respectively.

Summary

The Inner Tracker for the LHCb experiment will be realised in a single-sided silicon strip tech-nology. A main focus of the R&D program for the LHCb Inner Tracker was the careful optimi-sation of the sensor geometry and the front-end of the readout amplifier as these are key factorsfor efficient and reliable operation of detector.

In this work the silicon sensor R&D for the LHCb Inner Tracker is described and results oflaboratory and test beam measurements are presented. In addition, studies on different front-end chips and results of signal simulations are discussed.

Two generations of multi-geometry prototype sensors with large readout pitch have been de-signed and produced for the LHCb Inner Tracker. Different strip pitches between 198µm and240µm and implant widths corresponding to values of the ratio strip width over pitchw/p of0.2-0.35 were implemented on these prototype sensors.

In order to characterise these prototype sensors a test stand for measurements of the leakage cur-rents and the capacitances of silicon sensors was built. The first prototype sensors exhibit lowbreakdown voltages and therefore fail the LHCb Inner Tracker requirements, whereas the elec-trical characteristics of the second generation of full-sized prototype sensors are very promising.

Laboratory measurements on the first prototype sensors were performed using a106Ru-sourceand an infrared laser system. The signal-to-noise performance was investigated on sensorsbefore and after irradiation. Results obtained with the laser setup indicate a sizeable loss of thecollected charge in the region in between two readout strips.

The noise performance and the pulse shape of the Beetle readout chip were investigated forseveral prototype chips. Based upon the results of the measurements on these test chips, afront-end was selected and has been implemented in the Beetle 1.2 chip. Calculations of thesignal form generated by minimum ionising particles were performed and used as an input fora Beetle simulation. Indication of a ballistic charge deficit are found for fastest shaping and abias voltage only slightly above the full depletion voltage of the sensor.

Several test beams were performed in order to study the signal-to-noise ratio, resolution, effi-ciency and noise rate of the prototype sensors. Particular importance was given to the determi-nation of the efficiency in the inter-strip region of the prototype sensors. All test beam resultsconfirm a charge and efficiency loss in the inter-strip region of silicon sensors with large pitch.The size of the effect strongly depends on the strip geometry and shaping time. In additiona bias voltage dependence below 100 V is suggested from the measurements. The maximumS/N measured for tracks close to readout strips is larger for smallw/p values. However better

115


efficiency performance in between readout strips is obtained for increasedw/p, without deteri-orating the efficiency for tracks close to the readout strips. These results clearly favour the useof silicon sensors with a readout pitch not exceeding 200µm and not too smallw/p.

For both prototype sensors and all strip geometries the spatial resolution outperforms the res-olution required for the LHCb Inner Tracker. Nonetheless, the analysis of the last test beamshowed that there is still a possibility for improvement, by using a clustering algorithm betteradapted to the particular shape of the clusters observed in these sensors.

With the setup of the last test beam all LHCb requirements are matched. Further improvementof S/N and efficiency are expected from a better noise performance of the Beetle 1.2 readoutchip and the foreseen operation temperature of 5C. Additional robustness can be obtained bychoosing a slower shaping time of the preamplifier. A more thorough study of the impact of thepulse width on the tracking performance is foreseen.

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Acknowledgments

This thesis would not have been possible without the contribution and support of many peo-ple. Firstly, I wish to thank my supervisor Prof. Ulrich Straumann. He has given support andguidance whenever I needed it.

Special thanks must go to Marcus Ziegler and Achim Vollhardt who it was a pleasure to workwith.

I also wish to thank Olaf Steinkamp and Frank Lehner for all the fruitful discussions and forproof-reading this thesis.

I also wish to express my gratitude to the staff of the MPI Heidelberg group. Michael Schmellingprovided a good deal of the analysis programs and has been a willing font of information. Chris-tian Bauer deserves a special mention for his support in the preparation and accomplishment ofthe test beams. His experimental intuition and skills have been indispensable and are rightlyfamous. I would also like to mention Michaela Agari and Valery Pugatch.

Thanks must go to Helge Voss who has been the driving force in the analysis of the last testbeam.

My sojourns at CERN were made highly enjoyable thanks to the hospitality of Rainer Wallny,Thorsten Wengler and Joannah Caborn.

Finally, I would like to thank my parents and Veronika and Rainer for their continuous encour-agement and support.

This work has been supported by the Swiss National Science Foundation.

Curriculum VitaePersonalien:

Name: Phillip SieversStaatsangehorigkeit: deutschGeboren: 23.April 1973 in Mannheim, Deutschland

Bildungsgang:

1979 - 1983 Grundschule in Mannheim Feudenheim1983 - 1992 Lessing-Gymnasium Mannheim1992 Abitur1992 - 1993 Zivildienst Theresienkrankenhaus Mannheim1993 - 1999 Studium der Physik an der Universitat Heidelberg1996 Vordiplom1998 - 1999 Diplomarbeit in Experimentalphysik unter der Leitung

von Prof. Dr. U. StraumannTitel: Untersuchungen zur Verbesserung derEnergiemessung im Ruckwartsbereich des H1-Experiments

1999 Diplom in Experimentalphysik1999 Wissenschaftliche Mitarbeit beim H1 Experiment am

Physikalischen Institut der Universitat Heidelberg1999 - 2003 Wissenschaftliche Mitarbeit am

Physik-Institut der Universitat ZurichDissertation bei Prof. Dr. U. StraumannTitel: A Silicon Inner Tracker for the LHCb Experiment

Documents

A Silicon Inner Tracker for the LHCb Experimentversitat Z¨ urich auf Antrag von Prof.Dr. Ulrich Straumann und Prof.Dr. Peter Tru¨ ol als Disser-¨ tation angenommen. Wenn man ein