Kirti Final Complete Phd Thesis

LARGE PT PARTICLE PRODUCTION IN p-p COLLISIONS AT LHC ENERGIES

THESIS SUBMITTED TO THE UNIVERSITY OF DELHI FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

KIRTI RANJAN SUPERVISOR: PROF. R. K. SHIVPURI

DEPARTMENT OF PHYSICS AND ASTROPHYSICS UNIVERSITY OF DELHI DELHI 110007 INDIA 2002

The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.

Henri Poincaré

Dedicated to… my loving Parents and Sisters, Alka and Shalini

Contents Acknowledgements

i

List of Publications

iv

Chapters Chapter 1:

Motivation and Framework: The CMS Experiment at LHC

1

1.1. Introduction

1

1.2. CERN

2

1.3.

The Large Hadron Collider (LHC) Machine

4

1.3.1. Some interesting Features

4

1.3.2. LHC Experiments

6

1.4.

7

The Compact Muon Solenoid (CMS) Experiment

1.4.1. CMS Detector Overview

7

1.4.1.1.

Magnet

8

1.4.1.2.

Central Tracking System

10

1.4.1.3.

Muon System

10

1.4.1.4.

Hadron Calorimeter

10

1.4.1.5.

Electromagnetic Calorimeter

11

1.4.2. The Physics Potential of CMS / LHC

12

1.5.

Preshower Detector: raison d’être

16

1.5.1. Need of Preshower: Physics Goal

16

1.5.2. Design Criterion Imposed by the Physics Goal

18

1.5.3. Expected Response to Single and Double Photons

20

1.6.

Motivation for the Present Work

21

1.7.

Thesis Organization

23

Physics of Silicon Detectors – A Résumé

26

2.1.

Silicon Detector: An Introduction

26

2.2.

Semiconductors: General properties

28

2.3.

Reverse Biased p - n Junction

30

Chapter 2:

2.3.1. Abrupt p - n junction

30

2.3.2. Expressions of Some Useful Physical Quantities for Abrupt p-n Junction

32

2.3.3. Reverse Leakage Current

34

2.3.4. Breakdown Voltage

38

2.4.

Principle of Silicon Detector Operation

45

2.5.

Silicon Microstrip Detector for CMS Preshower

46

2.5.1. Silicon Microstrip Detector

47

2.5.2. Wafer Parameters

47

2.5.3. Sensor Design / Geometry

47

2.5.4. Fabrication

48

2.5.5. Acceptance Criterion

50

Chapter 3:

Semiconductor Device Simulation

51

3.1.

Why Simulation ?

51

3.2.

TMA MEDICI - A Device Simulation Program

53

3.2.1 Physical Description

53

3.2.1.1.

Drift-Diffusion Model

53

3.2.1.2.

Physical Models

54

3.2.1.3.

Boundary Conditions

54

3.2.2 Numerical Methods

3.3.

Chapter 4: 4.1.

3.2.2.1.

Discretization

55

3.2.2.2.

Nonlinear System Solutions

56

3.2.2.3.

Simulation Grid

56

3.2.3 MEDICI Program Description

57

Validation – An Absolute Requirement

60

Effect of Metal-Overhang on Silicon Strip Detectors

61

High-Voltage Si Detectors: Techniques to Improve Breakdown Voltage

4.2.

55

Modulation of Electric Field by Extended

62

Electrode: Origin of Metal-Overhang Technique

63

4.3.

Device Structure Used in Simulation

66

4.4.

Influence of Various Parameters on Silicon Strip Detector Equipped with Metal-Overhang

68

4.4.1. Comparison between the Structures without and with metal-overhang

68

4.4.2. Effect of Field-Oxide Thickness

73

4.4.3. Effect of Junction Depth

78

4.4.4. Effect of the Width of Metal-Overhang

82

4.4.5. Effect of Substrate Parameters: Device-Depth and Substrate Doping Concentration

85

4.4.6. Effect of Surface Charges

86

4.5.

Comparison with Experimental Work

94

4.6.

Conclusions

95

Chapter 5:

Effect of Passivation on Breakdown Performance of Metal-Overhang Equipped Si Sensors

97

5.1.

Passivation in Si Detectors

98

5.2.

Radiation Damage in Si Sensors

100

5.3.

Device Structure & Simulation Technique

101

5.3.1. Modeling of Radiation Damage

102

Comparison between Semi-Insulator vs. Dielectric Passivation

104

5.4.1. Effect of Field-Oxide Thickness and Junction Depth

104

5.4.2. Effect of Metal-Overhang Width

112

5.4.3. Effect of Passivation Layer Thickness

114

5.4.4. Effect of Surface Charges

115

5.4.

5.4.5. Effect of Device Depth and Substrate Doping Concentration 117 5.4.6. Effect of Bulk Damage on Full Depletion and Breakdown Voltage

119

5.5.

Comparison with Experimental Work

125

5.6.

Static Measurements on Irradiated Si Sensors

128

5.7.

Chapter 6:

5.6.1. Irradiation Facility

128

5.6.2. Measurement Set-ups

128

5.6.3. Measurement Results on Irradiated Sensors

130

Conclusions

133

Comparison of Junction Termination Techniques for High-Voltage Si Sensors: Metal-Overhang vs. Field Limiting Ring

135

6.1.

FLR Structure

135

6.2.

Device Model

137

6.3.

Comparison of FLR and MO Structures

138

6.3.1. Effect of Guard Ring Spacing (for FLR structure) and Field-Oxide Thickness (for MO structure)

138

6.3.2. Effect of Junction Depth

140

6.3.3. Effect of Relative Permittivity of Passivant

143

6.3.4. Effect of Surface Charges

145

6.3.5. Effect of the Width of Guard Ring (GW; for FLR structures) and Metal-Extension (WMO; for MO structures)

147

6.4. Comparison with Experimental Work

149

6.5. Conclusions

150

Chapter 7:

Large Transverse Momentum (pT) Direct Photon Production at LHC

151

7.1.An Introduction to Standard Model and QCD

151

7.2.QCD Phenomenology of High pT Inclusive processes

153

7.3.Direct Photons in the QCD framework

155

7.4.

7.3.1. Contributions to Direct Photons

155

7.3.2. Backgrounds to Direct Photons

157

7.3.3. Motivation

159

Theoretical Formalism

161

7.4.1. Scale Sensitivity

161

7.4.2. Pseudorapidity Dependence

162

7.5.

7.4.3. Isolation Technique

163

7.4.4. KT Smearing

164

Monte Carlo Simulation

165

7.6.Direct Photon Production at Tevatron: Comparison of Data With Theory at 7.7.

7.8.

s =1.8 TeV &

s =630 GeV

165

Expectations for Direct Photons at LHC

168

7.7.1. Leading Order (LO) Cross section

168

7.7.2. Next-to-Leading Order Cross Section

169

7.7.3. K-factor

170

7.7.4. Scale Dependence of Inclusive Cross Sections

171

7.7.5. Sensitivity to Gluon Distributions

171

7.7.5.1.

The pT Spectrum

171

7.7.5.2.

The η Spectrum

172

7.7.6. Pseudorapidity Dependence

174

7.7.7. Cone Size Dependence

175

Conclusions

175

Bibliography

177

Acknowledgments Nobody lives in complete isolation, and we accomplish nothing without the input and encouragement of those around us. Although I have asserted that the work presented in this thesis is entirely my own, it is a delight to acknowledge here the important contributions that many people have made over the past few years which have allowed me to get where I am today. I would like to express my largest gratitude to my supervisor, Prof. R. K. Shivpuri for his constant support, continuous encouragement and guidance throughout this investigation, and the outstanding working conditions at the Laboratory. He is the best advisor and teacher I could have wished for, actively involved in the work of all his students, and clearly always has their best interest in mind. Time after time, his vast knowledge, deep insights, tremendous experience and easy grasp of physics at its most fundamental level helped me in the struggle for my own understanding. It was both a privilege and honour to work with him. I have learned various things, from him, such as the way of thinking, and the way of proceeding in research, and so on. I am indebted to him for connecting me with CMS experiment, thereby opening avenues for me to gain experience in doing physics analysis as well as hardware work. I am also obliged to the Head of the Department of Physics, Prof. K. C. Tripathi for providing the necessary facilities in the Department. In the Lab, I was surrounded by knowledgeable and friendly people who helped me daily. They helped to create an informal and congenial atmosphere that, in my opinion, makes thesis writing a much less onerous task than it otherwise might be. First and foremost, I gladly acknowledge my debt to my colleague Ashutosh Bhardwaj. Without his constant friendship, encouragement and advice, I would never have reached here. I can never forget the long teatime discussions with him and also the wonderful time he has provided me as a friend and colleague during our visits to various research institutes and in particular CERN, Geneva. Thanks a lot, Ashutosh! I would also like to thank Namrata for providing invaluable comments, ideas, and general assistance. Thanks are due to Sudeep Chatterji and Ajay K. Srivastava, with whom I had many productive scientific and general discussions. I would also express my gratitude to other members of

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my group, Manoj Kumar, Shailesh Kumar, Bani Mitra and Bipul Bhuyan. My junior colleague Ashish Kumar deserves a special mention as he helped me a lot with the PYTHIA software and direct photon physics. I would like to express my gratitude to Dr. Philippe Bloch and Dr. Anna Peisert for providing wonderful working conditions at CERN, and also for giving me freedom to work anytime at the Detector Lab, CERN. I owe a lot to them regarding the installation and working of I-V and C-V systems. I also thank Dr. Dave Barney who helped me with my online presentation at CERN and also spared his precious time to show me the wonderful CMS site and snow-covered Zura mountains. Special thanks are due to Apollo Go who introduced me to LabVIEW programming language and CRISTAL Database. I also wish to thank Dr. Gagan Mohanti, Dr. Swagato Banerjee and Dr. Pratibha Vikas for giving me a good company and providing homely environment at CERN. I also express my sincere thanks to our collaborators from B.A.R.C., Dr. S. K. Kataria, Mr. M. D. Ghodgaonkar, Mr. V. B. Chandratre, Dr. Anita Topkar, Mr. M. Y. Dixit and Mr. Vijay Mishra for their assistance, cooperation and valuable annotations at various India-CMS meetings. Thanks are also due to a dear friend, Vishal D. Srivastava, BARC for many useful discussions carried on long-distance via e-mail. I am very thankful to him as he alongwith Mr. V. B. Chandratre introduced me to the nitty-gritty of the Process and Device Simulation. I also extend my gratitude to our other collaborators from T.I.F.R., Prof. S. N. Ganguli, Prof. Atul Gurtu and Prof. Sunanda Banerjee and from Panjab University, Prof. J. M. Kohli, Prof. Suman Beri, Dr. Manjeet Kaur and Dr. J. B. Singh for their encouragement in accomplishing this work. I extend my appreciation to Dr. O. P. wadhwan and Dr. G. S. Virdi, CEERI, Pilani and Mr. Subhash Chandran, Mr. Prabhakar Rao and Mr. Shanker Narayan, BEL, Bangalore for providing me with detailed information about the detector fabrication I wish to thank Mr. P. C. Gupta for his support and general assistance. I also appreciate the continuous assistance I received from Mr. Rajendra Mishra and Mr. Mohammad Yunus. This work was financially supported by the Council for Scientific and Industrial Research, India through the Junior and the Senior Research Fellowships. I gratefully acknowledge their generosity.

ii

In addition to the people in University, I am lucky enough to have the support of many good friends. Life would not have been the same without them. There are too many people to mention individually, but some names stand out. I wish to thank my friends in high school (Hitesh Dighe, Rhitu Parn, Sandeep Tewatia and Brijesh Rawat), my friends as an undergraduate (Devendar Nahar and Sai Bhushan), and my friend as a graduate student (Abhinav Kranti), for helping me get through the difficult times, and for all the emotional support, camaraderie, entertainment, and caring they provided. It would, of course, be completely amiss for me to end my acknowledgements without recognizing the immense contribution that my family has made to my work. Their love and support has been a major stabilizing force over these past years. Their unquestioning faith in me and my abilities has helped to make all this possible and for that, and everything else, I dedicate this thesis to them.

KIRTI RANJAN

iii

List Of Publications 1. “Analysis and Optimal Design of Si Microstrip Detector with Overhanging Metal Electrode”, K. Ranjan et al., Semicond. Sci. Technol. 16, 635 (2001).

2. “Analysis and Comparison of the breakdown performance of Semi-insulator and dielectric passivated Si Strip detectors”, K. Ranjan et al., CMS-NOTE (CERN,Geneva),

2002/014, also accepted for publication in Nuclear

Instruments and Methods in Physical Research A.

3. “Performance characteristics of semi-insulator and dielectric passivated Si strip detectors”, K. Ranjan et al., Physica Status Solidi (a) 191(2), 658 (2002).

4. “High-voltage planar Si detector for high-energy physics experiment: comparison between metal-overhang and field-limiting ring techniques”, K. Ranjan et al., communicated to Journal of Applied Physics.

Paper presented

1.

“Influence of electrode geometry on electric field distribution within silicon microstrip detector”, K. Ranjan et al., Workshop on CMS at LHC held on 11-15 Dec., 2000 at TIFR, Mumbai, India.

2. “Comparison of the passivants on the Breakdown Performance of Si strip detectors”, K. Ranjan et al., National Seminar on Physics of Materials for Electronic and Optoelectronic Devices held on 25-27 Feb. 2002 at J. N. Vyas University, Jodhpur, Rajasthan, India.

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Chapter 1

---------------------------------------------------------------Motivation and Framework: The CMS Experiment at LHC ---------------------------------------------------------------1.1

Introduction From the time humans began to ask questions about themselves and their world,

they have wondered what the world is made of and how it behaves. Over and over, in different ages and by different methods, people have tried to answer the questions, “What is the smallest possible piece of matter? What are the fundamental forces of nature?”. Today, the fundamental science of high-energy, or particle physics continues to pursue answers to these most ancient, and most modern questions. To a great degree, the progress of particle physics has followed from progress in accelerator science and instrumentation. There is no substitute for experiment, and experimental techniques require inventions in both hardware and software and continuous innovation in analysis. Currently, the large experimental particle physics programs (CDF and D0) have undergone major upgrades and are taking data right now at the Tevatron, Fermi National Accelerator Lab, Chicago, USA. The confirmation with very high precision of the Standard Electroweak and Quantum Chromodynamics (QCD) models by these experiments has prompted new physics questions which can only be answered by the construction of new specialized accelerators, and associated detectors. One such accelerator, the Large Hadron Collider (LHC) is now being constructed at CERN, Geneva and will become operational from the year 2007. This proton-proton (pp) collider will have a peak luminosity of L = 1034 cm-2s-1 and a collision energy of

s =14 TeV,

about seven times larger than at the Tevatron collider at Fermilab. The primary goal of the LHC machine will be the search for the Higgs boson, which results from spontaneous

1

symmetry breaking mechanism in the Standard Model. The confirmation of the existence or non-existence of the Higgs boson will be the greatest achievement of the LHC. In addition, some other interesting topics, like search for various Minimum Supersymmetric Model Higgs bosons, gluino and squark, new massive vector bosons, CP- violation measurements in B sector, quark gluon plasma etc. will also be addressed. To exploit the physics capability of the LHC, four large detectors are being constructed. These detectors are significantly more complex than their present generation counterparts because of physics and operational requirements. The Compact Muon Solenoid (CMS) experiment is a general-purpose detector designed to exploit the physics of pp collisions over the full range of luminosities expected at the LHC. One of the CMS design objectives has been to construct a very high performance Electromagnetic Calorimeter (ECAL), which will play a significant role in the detection of Standard Model Higgs boson in low mass range (mH < 140 GeV/c2) through the two-photon decay mode. A Preshower silicon strip detector has been included in the endcaps of ECAL to reduce the background to this Higgs channel by facilitating γ−π0 separation. Since this exciting physics programme at CMS will be carried out in an extremely difficult experimental environment, hence it imposes very challenging requirements on the silicon detector specifications. This chapter provides an overview of the CERN LHC machine and CMS detector. Since most of the work reported in this thesis is on the detailed analysis of the breakdown performance of silicon strip sensors to be used in Preshower at CMS, hence a more detailed discussion on the Preshower detector is presented. Finally, the motivation behind the work and the thesis organization is described.

1.2

CERN CERN (Conseil Europeen pour la Recherche Nucleaire) is the European

Laboratory for Particle Physics situated in Geneva (at the border of Switzerland and France), and is the world’s largest particle research center. The creation of this laboratory was recommended at the UNESCO meeting in Florence in 1950 as the only way forward for front-line particle physics research in Europe. 2

Accelerators at CERN: CERN's accelerator complex is the most versatile in the world and represents a considerable investment. It includes particle accelerators and colliders, can handle beams of electrons, positrons, protons, antiprotons, and heavy ions. Each type of particle is produced in a different way, but then passes through a similar succession of acceleration stages, moving from one machine to another. The first steps are usually provided by linear accelerators, followed by larger circular machines. CERN has 10 accelerators altogether, so far the biggest being the Large Electron Positron collider (LEP). CERN's first operating accelerator, the Synchro-Cyclotron, was built in 1954, in parallel with the Proton Synchrotron (PS).

Fig.1.1: Accelerators at CERN. The PS is today the backbone of CERN's particle beam factory, feeding other accelerators with different types of particles. The 1970s saw the construction of the Super Proton Synchrotron (SPS), at which Nobel-prize winning work was done in the 1980s. The SPS continues to provide beams for experiments and is also the final link in the chain of accelerators providing beams for the 27 km LEP machine. CERN's next big machine, due to start operating in 2007, is the Large Hadron Collider (LHC). A more clear view of the accelerators can be seen in Fig.1.1.

3

1.3

The Large Hadron Collider (LHC) Machine The LHC machine being constructed at CERN in the LEP tunnel would be

operational in 2007. The LHC will collide counter-rotating beams of protons with total center of mass energy ( s ) of 14 TeV. In order to maintain an equally effective physics programme at a higher energy E, the luminosity of a collider (a quantity proportional to the number of collisions per second) should increase in proportion to E2, since the cross section of the particle production decreases like 1/E2. Whereas in past and present colliders the luminosity culminates around L = 1032 cm-2 s-1, in the LHC it will reach L = 1034 cm-2 s-1. It is expected that the LHC machine would reach one-tenth of the peak luminosity during the first year of operation, and one-third & two-third of the peak luminosity respectively in the following two years (referred to as low luminosity period) [1.1]. LHC will operate at its full limit from the fourth year onward. This will be achieved by filling each of the two rings with 2835 bunches of 1011 particles each. The separation between the two bunches would be 25 ns (~ 7.5 m) with ~ 23 pp interactions for each bunch crossing. The LHC energy and luminosity would be about an order of magnitude higher than the present collider machines, which would allow for the search of new massive particles produced with small cross-sections and probe the structure of matter at extremely small distances.

1.3.1 Some Interesting Features Several interesting features of the LHC machine, as shown in Fig.1.2, have enormous consequences for the detector design, which are described below. •

The bunch spacing of 25 ns means that interactions of one bunch crossing occur before all particles from interactions of a previous bunch crossing have traversed the detector. In order to prevent the pile-up of interactions over several bunch crossings, a fast detector signal response, small detector dead time, and extensive signal pipelining prior to initial trigger decisions is required.

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Fig.1.2: Schematic layout of the collisions at LHC. •

To achieve the design luminosity, the colliding proton bunches are short (~ 7.5 m) and intense (~ 1011 protons per bunch). The total inelastic, non-diffractive crosssection at the LHC energies is expected to be 80 mb, corresponding to an interaction rate of 109 Hz. Fig.1.3 shows the cross-section for several Standard Model processes as a function of

s [1.2]. Typically, in case of the Higgs particle

with mass = 500 GeV, about 17 K events are expected per operating year (107 s) at design LHC luminosity, compared to a total of 1.7 x 1016 events from inelastic interactions. The LHC experiments must identify rare processes at this level. •

At the design luminosity, ~ 23 interactions occur in each bunch crossing. This results in ~ 104 tracks in the detector each 100 ns, the typical duration of a pulse in the detectors. The individual detector element must therefore be highly granular in order to minimize the contribution of the pile-up in a given detector cell.

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Fig.1.3: Energy dependence of some characteristic cross-sections at pp colliders.

• The high flux of particles from pp interactions places the detectors and associated electronics in a high-radiation environment. Only radiation resistant detectors and read-out electronics have to be used.

1.3.2 LHC Experiments Among the four experiments (CMS [1.3], ATLAS [1.4], ALICE [1.5] and LHC-B [1.6]) being constructed for operations at LHC (Fig.1.4), the design philosophy has been determined by the physics goals of the experiments and the relevant available technology able to meet the experimental requirements. In the case of the LHC, the LHC-B and ALICE detectors are optimized to their specific roles – a respective study of the b-quark physics sector, and the study of heavy ion collisions. The CMS and ATLAS are general-

6

purpose detectors, and differences in their design reflect choices of the collaborations with technologies able to meet the design requirements.

Fig.1.4: Schematic layout of the LHC.

1.4

The Compact Muon Solenoid (CMS) Experiment The main design goals of CMS detector are a highly performant muon system, the

best possible electromagnetic calorimeter, a high quality central tracking system and a hermetic hadron calorimeter. The CMS detector is designed to measure the energy and momentum of photons, electrons, muons, and other charged particles with high precision, resulting in an excellent mass resolution for many new particles ranging from the Higgs boson up to a possible heavy Z ′ in the multi-TeV mass range. Fig.1.5 shows the CMS detector which has an overall length of 21.6 m, with a calorimeter coverage to a pseudorapidity of η = 5 (θ ~ 0.80), a radius of 7.5 m, and a total weight of 12500 tonnes [1.7].

1.4.1 CMS Detector Overview CMS consists of a powerful inner tracking system based on fine-grained silicon microstrip and pixel detectors, a scintillating crystal calorimeter followed by a sampling hadron calorimeter made of plastic scintillator tiles inserted between copper absorber 7

plates, and a high-magnetic-field (4T) superconducting solenoid coupled with a multilayer muon chamber (Fig.1.5). Figures 1.6(a) and 1.6(b) show the transverse and the longitudinal view of the CMS detector respectively. The key elements of the CMS detector (Fig.1.5) are described briefly in the subsequent sections.

1.4.1.1

Magnet The choice of magnet system was the starting point for the CMS detector design.

The requirement for a compact design led to the choice of solenoidal magnet system of length 13 m and inner diameter 5.9 m, which can generate a strong magnetic field of 4 T, which guarantees a good momentum resolution for high momentum (~ 1 TeV) muons up to rapidities of 2.5 without strong demands on the chamber space resolution. The magnetic flux is returned through a 1.8 m thick saturated iron yoke instrumented with four layers of muon chambers.

Fig.1.5: Three-dimensional layout of the CMS detector showing internal detectors.

8

Fig.1.6(a): Transverse view of the CMS detector.

Fig.1.6(b): Longitudinal view of the CMS detector.

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1.4.1.2

Central Tracking System The CMS tracking system is designed to reconstruct high-pT muons, isolated

electrons and hadrons with high momentum resolution and an efficiency better than 98% in the range |η| < 2.5. It is also designed to allow the identification of tracks coming from detached vertices. The momentum resolution required for isolated charged leptons in the central rapidity region is ∆pT / pT ~ 0.1 pT (pT in TeV).

In the new “full silicon” design [1.8], the tracker is constituted by an innermost region, instrumented with silicon pixel sensors and an external region, instrumented with silicon strip sensors, that extends up to the region once covered by gas chambers [1.9].

1.4.1.3

Muon System Muons are expected to provide clean signatures for a wide range of physics

processes. The task of the muon system is to identify muons and provide, in association with the tracker, a precise measurement of their momentum. In addition, the system provides fast information for triggering purposes - a challenging problem at the LHC. At the LHC, the efficient detection of muons from Higgs bosons, W, Z and tt decays requires coverage over large rapidity interval. The muon detectors, placed behind the calorimeters and the coil, consist of four muon stations interleaved with the iron return yoke plates. They are arranged in concentric cylinders around the beam line in the barrel region, and in disks perpendicular to the beam line in the endcaps. CMS will use three types of gaseous particle detectors for muon identification: Drift Tubes (DT) in the central barrel region, Cathode Strip Chambers (CSC) in the endcap region and Resistive Parallel Plate Chambers (RPC) in both the barrel and endcaps.

1.4.1.4

Hadron Calorimeter The Hadronic Calorimeter (HCAL) plays an essential role in the identification

and measurement of quarks, gluons, and neutrinos by measuring the energy and direction of jets and of missing transverse energy flow in events. Missing energy forms a crucial signature of new particles, like the supersymmetric partners of quarks and gluons. For good missing energy resolution, a hermetic calorimetry coverage to |η| = 5 is required.

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The HCAL will also aid in the identification of electrons, photons and muons in conjunction with the tracker, electromagnetic calorimeter, and muon systems. Barrel & Endcap: The hadron barrel (HB) and hadron endcap (HE) calorimeters are sampling calorimeters with 50 mm thick copper absorber plates which are interleaved with 4 mm thick plastic scintillator sheets. The HB is constructed of two half-barrels each of 4.3 m length. The HE consists of two large structures, situated at each end of the barrel detector and within the region of high magnetic field. Because the barrel HCAL inside the coil is not sufficiently thick to contain all the energy of high-energy showers, additional scintillation layers (HO) are placed just outside the magnet coil. Forward: There are two hadronic forward (HF) calorimeters, one located at each end of the CMS detector, which complete the HCAL coverage to |η| = 5. The HF is built of steel absorber plates since steel suffers less activation under irradiation than copper. Hadronic showers are sampled at various depths by radiation-resistant quartz fibers, of selected lengths, which are inserted into the absorber plates.

1.4.1.5

Electromagnetic Calorimeter The physics process that imposes the strictest performance requirements on the

Electromagnetic Calorimeter (ECAL) is the light mass Higgs decaying into two photons. Thus the benchmark against which the performance of the ECAL is measured is the diphoton mass resolution. CMS has chosen lead tungstate (PbWO4) crystals (over 80000) which have high density, a small Molière radius and a short radiation length allowing for a very compact calorimeter system. A high-resolution crystal calorimeter enhances the H → γγ discovery potential at the initially lower luminosities at the LHC. The crystal will project tower geometry each 230 mm in length and 22 mm x 22 mm in cross-section. The time-constant of scintillation light coming from crystals is only 10 ns. In CMS light will be detected by Si-avalanche photodiodes which can provide gain of 50 even in high magnetic field environment. In order to facilitate γ/π0 separation in the forward-backward region ( 1.653 ≤ η ≤ 2.61 ) a Preshower silicon strip detector is included in the baseline CMS design.

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1.4.2 The Physics Potential of CMS / LHC The CMS detector has been designed to provide answers to the most important open questions in High-Energy Physics (HEP). LHC will address one of the key questions in particle physics namely that of the origin of the Spontaneous Symmetry Breaking (SSB) mechanism in the electroweak sector of the Standard Model. Amongst others, some questions involve the following specific challenges [1.10]: •

Standard Model (SM) Higgs boson search at masses above the maximum reach of LEP and Tevatron, order of 100 GeV – 1 TeV.

•

Search for Minimal Supersymmetric Standard Model (MSSM) Higgs bosons up to masses of 2.5 TeV. In this framework, five Higgs bosons are expected.

•

Search for SUper SYmmetric (SUSY) partners of quarks and gluons – squark and gluino up to masses of 2.5 TeV.

•

Study of CP – violation in the B sector and time dependent mixing of b – mesons.

•

Search for new heavy gauge bosons ( W ′, Z ′ ) up to masses 4.5 TeV.

•

Detailed studies of production and decays of top quark.

•

Search for composite structures of quarks and leptons.

•

Search for quark – gluon plasma (QGP) in heavy ion collisions. In the subsequent sections a brief discussion on the aforementioned topics would

be given.

Search for Standard Model Higgs Boson: In the framework of the Standard Model particles acquire mass through their interaction with Higgs field. This implies the existence of a new particle: the Higgs boson (H). The theory does not predict the mass of the H, but it does predict its production rate and decay modes as a function of its mass. With beam energies of the 102 GeV for the CERN LEPII accelerator, the LEP experiments exclude mH < 108 GeV/c2 [1.11]. Depending on the Higgs mass, the detection of a SM Higgs involves several different signatures (Fig.1.7).

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Fig.1.7: Expected observability of SM Higgs boson and mass range in CMS.

The most promising channel for a SM Higgs with mass between the expected LEPII limit (~ 108 GeV) and 140 GeV is the decay H → γγ , which has the cleanest signal but suffers from the small branching ratio (1000 times smaller than most other channels). This signal has to be detected above a large background from continuum γγ events. The CMS detector has excellent electromagnetic calorimetry, which can measure γ energy and direction to 1% accuracy. In the mass range 130 < mH < 700 GeV the most promising decay channel is

H → ZZ / ZZ * → l + l − l + l − (4l ± , gold plated channel ) . The detection relies on the excellent performance of the muon chambers, the tracker and the electromagnetic calorimeter. The reconstruction of the l+l- makes it practically background free and has very significant branching ratio. However, for Higgs mass between 130 GeV – 200 GeV this channel suffers from very low branching ratio. Another important channel in this range is H → WW → 2l ± 2ν , having highest branching ratio (six times larger than the 4l ± channel). Also, it has a distinct signature, two high pT leptons and high ET

miss

.

For large Higgs mass, 500 GeV < mH < 1 TeV, the natural width is already quite large and the mass resolution becomes less important. Therefore, in this case the decay

13

channels H → WW → l ±ν jj , H → ZZ → l + l −νν , and H → ZZ → l + l − jj are expected to provide more favourable signals. In these channels the biggest background comes from single W (or Z) production along with QCD jets. The CMS simulation studies show that double forward jet tagging can control the background and extend the Higgs search up to 1 TeV [1.3]. Fig.1.8 shows the explorable mass range of Higgs at LHC.

Fig.1.8: Explorable mass range of Higgs at LHC.

SUSY Higgs and SUSY Particles Searches: Supersymmetry (SUSY) is believed to be the most promising and elegant extension of the Standard Model. The Minimal Super Symmetric Model (MSSM) requires the existence of two Higgs doublet, resulting in five physical Higgs bosons: h 0 , H 0 , A 0 and H ± decaying through a variety of decay modes to γ, e±, µ±, τ± and jets in final states. Higgs bosons masses and couplings can be expressed in terms of two parameters, mA and tanβ. Within this model the lightest neutral Higgs boson h0 has a mass smaller than 130 GeV. The masses of the other four Higgs bosons are under lesser constraints. At the LHC, the strongly interacting gluinos ( g ) and squark ( q ) dominate the SUSY particle production. With increasing luminosity, the LHC will allow the search for these particles in the TeV range.

Charge-Parity (CP) Violation: The LHC would be working as a B-factory, producing 1012 – 1013 bb per year, which would open the way for precise measurements of parameters characterizing the CP violation effects in the B-system. The CMS detector

14

having very good tracking, calorimetry and muon system, would be able to detect most promising decay channels which have small branching ratios like, Bd → J /ψ K S , and 0

0

Bd → π +π − ; with J /ψ → µ + µ − and K S → π + π − . These channels would measure 0

0

two β and α angles of the unitary triangle. The first reaction has a relatively high branching ratio and clear signature. It is easier to trigger on multi-muon with low pT or a single muon. With an integrated luminosity of 104 pb-1 in CMS, an accuracy in measurements of sin2α = 0.057 and sin2β = 0.05 can be achieved. Both LHC machine and CMS detector are very favourable to study this aspect of physics. Furthermore by observing the time development of BS − BS oscillations, the mixing parameter χ S can 0

0

be measured for values up to 20 [1.3].

Quark-Gluon Plasma Search: At the LHC, collisions of high-energy Pb ions can be studied at center of mass energy of 6.3 TeV per nucleon pair and a luminosity of 1.8 x 1027 cm-2s-1 [1.1]. The heavy ion beams at LHC will provide collision energy densities well above the threshold for the formation of quark gluon plasma (QGP). In this new state of matter all heavy quark bound states, except for Υ , are suppressed by color screening [1.3]. The CMS detector has got one of the best muon system. So measurement of µµ pairs rate coming from Υ family can be made to examine the suppression of Υ ′ and Υ ′′ relative to Υ in different heavy ion collisions and relative to pp collisions [1.12]. The CMS detector will be used to detect low momentum muons produced in the heavy ion collisions and reconstruction of Υ , Υ ′ and Υ ′′ mesons. Another probe of QGP formation is the jet production, where jet quenching is expected [1.13]. The CMS calorimetry also allows this to be tested.

Top Quark Physics: The top quark has been identified at Tevatron and a few hundred events have been produced. The mass has been measured with an accuracy of ~ ± 5 GeV/c2, and the top pair production cross-section has been measured to be ~ 6 pb. At the LHC, the pair production cross-section will be largely from the process ( gg → tt ) rather than from ( qq → tt ) and will be σ tt ~ 800 pb. Assuming an integrated luminosity of only 1040 cm-2year-1, a total of ~ 8 x 109 pairs will be produced. This will allow a measurement of the top mass with a precision of ± 1 - 2 GeV/c2, limits on new physics such as resonant tt production, and limits or even the discovery of rare decays.

15

Heavy Flavour Production: Heavy flavour production is potentially a vast domain of physics that can be studied at low luminosity. The cross-sections are very large at the LHC, typically ~ 1mb for beauty and ~ 1 nb for top.

1.5

Preshower Detector: raison d’être The CMS ECAL consists of one crystal barrel (EB), two crystal endcaps (EE),

and two Preshower endcaps (SE). The EE and SE form a combined system for the ECAL endcaps. The Preshower consists of two self-contained disc-shaped structures situated between the tracker and the EE. These two structures are known as SE+ and SE-, one for each endcap of CMS. The Preshower detector coverage is the rapidity interval 1.653 ≤ η ≤ 2.61 as shown in Fig.1.9 [1.14].

Fig.1.9: Longitudinal view showing the Preshower coverage.

1.5.1 Need of Preshower: Physics Goal One of the principal objectives of CMS is the discovery of the postulated Higgs boson – the “missing link” in the Standard Model of particle physics. Current theoretical predictions, and measurements from LEP, point to a relatively low mass Higgs; around 130 GeV/c2. If this is the case, the most promising channel will be via its decay into two photons ( H → γγ ), even though this channel has a tiny probability of occurrence (< 1%). The two photons from the decay will have rather high transverse momenta (pT), due to

16

the mass of the Higgs and, in general, will be isolated from each other and from other particles. Fig.1.10 shows a Feynman diagram depicting the decay of Higgs boson into two photons. However, high pT photons can also originate from other sources, forming background to H → γγ , shown in Fig.1.11.

Fig.1.10: The two-photon decay of the standard model Higgs boson. It is important to note that on right hand side of the diagram there are two photons traveling in different directions.

Fig.1.11: Background to the H → γ γ channel at LHC. The relevant observation is that in each case there are two single-photon-like objects on the right hand side (the “squiggles”) which could be interpreted as originating from the decay of Higgs boson.

Two types of background are irreducible – real isolated pairs of photons are produced at the interaction point, due to either quark annihilation or gluon-gluon fusion. It is impossible, on the basis of the detection of two photons alone, to distinguish between this type of event and a H → γγ . The remaining two types of background are reducible. The first of these results in one photon close in space to other particles: requiring the photon to be greater than a given distance from any neighbouring particles can reduce this background. The second of the reducible backgrounds is due to neutral pions (π0s) in jets: the π0s decay at the interaction point to two closely spaced photons; these two photons may be so close together that a coarse-grain calorimeter may not be able to resolve them. A typical π0 faking a Higgs photon may have a pT of 60 GeV/c. In the barrel of CMS the typical separation of the two photons from the π0 decay will be around 1 cm, whereas in the endcaps it is just a few mm. In the barrel the crystal calorimeter is sufficiently granular to be able to distinguish energy deposits from single photons and 17

closely-spaced double photons. However, this is not the case for the endcaps, where the photon separation is smaller and the granularity of the crystal is lower, and hence the need of preshower detector. Thus, the principal purpose of the CMS Preshower detector is to reject neutral pions in the endcaps.

1.5.2 Design Criterion Imposed by the Physics Goal The main requirement of the Preshower detector is the incorporation of fine-grain sensors responsive to photons. CMS has chosen to construct the Preshower as a sampling calorimeter: lead absorbers initiate electromagnetic showers from incoming photons and silicon strip sensors placed immediately afterwards measure the energy deposited due to charged particles within the showers. The transverse shower shape seen by the silicon sensors differ for incident single photons and closely spaced double photons. In the Preshower, the absorber should be thick enough to initiate photon showers, however, a too thick absorber can degrade the energy resolution of EE. The optimum thickness of absorber was found to be around 3 radiation lengths (3X0). Thus, the initial design of the CMS Preshower comprised a single 3 X0 absorber followed by two orthogonal layers of silicon sensors [1.3]. However, the performance of this setup, in terms of π0 rejection, was found to be less than expected [1.15]. To improve the performance, silicon sensors are required to be placed as close as possible to the absorber [1.15]. A repercussion of this is that it is necessary to have two separate absorber layers, each of which is followed by a plane of silicon sensors. Indeed this is the approach which has been adopted for the CMS Preshower [1.14]. A transverse view of the Preshower is shown in Fig.1.12. It is formed with two orthogonal planes of silicon detectors, each plane is preceded by a thin absorber of 2 X0 and 1 X0 respectively.

18

Fig.1.12: The final schematic structure of the Preshower.

Each Preshower disk is segmented longitudinally (along the beam direction) into passive and active parts. Passive parts include aluminium honeycomb “windows” filled with paraffin wax, cooling planes and “absorber” planes (used to initiate and develop electromagnetic showers). The total thickness of the Preshower is 20 cm. The active part of the Preshower comprises of two orthogonal planes of silicon strip sensors, built from a large number of identical micromodules. Each micromodule comprises an aluminium tile that allows detector overlap in one direction (along the strips), onto which a thin ceramic support is glued. A 6.3 x 6.3 cm2, 320 ± 20 µm thick, silicon sensor, divided into 32 strips at 1.9 mm pitch, is then glued to the ceramic. The hybrid containing the analogue front-end electronics (PACE) is also glued to the ceramic and bonded to the sensor (Figures 1.13(a) and 1.13(b)). The micromodules are assembled on ladders containing two adjacent columns of detectors (Fig.1.13(c)), which are attached to the absorbers to form an X-Y grid of detectors. There are a total of 4288 micromodules in the complete Preshower.

19

Fig.1.13: (a) A silicon detector and a single micromodule used for preshower, (b) real micromodule used in beam tests, and (c) Number of micromodules assembled on a baseplate. These modules together with the motherboard (containing digital electronics etc.) constitute a “ladder”. 

1.5.3 Expected Response to Single and Double Photons Detailed Monte-Carlo simulations have been performed in order to examine the performance of the Preshower in terms of π0 rejection and energy resolution. These simulations have enabled to tune the Preshower design in both coarse and subtle ways. Figures 1.14(a) and 1.14(b) show two simulated events in the SE + EE due to a single photon and a double photon (from π0 decay) respectively.

Fig.1.14: (a) a single 30 GeV pT photon (dotted line) incident on the SE and EE, and (b) two closely spaced photons (in this case around 1cm – event chosen for clarity) from the decay of a 30 GeV pT π˚ incident on the SE and EE. Note that for electromagnetic shower only charged particles are shown.

20

The histograms associated with each figure (dark area) show the approximate pulse height seen in a group of silicon strips for the second plane in the SE due to the passage of particles produced in the electromagnetic showers.

1.6 Motivation for the Present Work Silicon microstrip sensors (along with the silicon pixel sensors) are the most precise electronic tracking detectors for charged particles in the present generation of high-energy physics experiments. However, the first and the most important issue, which has to be considered in the unprecedented radiation environment at LHC, is the long-term operation of the silicon detectors. The radiation damage, among other things, results in the change of the effective doping concentration (Neff). It is found that the n-type detectors become progressively less n-type with increasing fluence until they invert to become effectively p-type (type-inversion). Beyond inversion the device continues to become more p-type under further irradiation, apparently without limit. The depletion voltage required to operate a silicon detector is directly proportional to Neff, hence at higher fluences Neff can be such that the required operating voltage exceeds the breakdown voltage of the device and efficient operation is no longer possible. For Preshower, the integrated fluence of charged hadrons and neutrons above 100 keV in the center of the Preshower detector will reach ~ 2 x 1014 particles/cm2 after 10 years of operation with 85% of them being neutrons and the operational voltage of the silicon detectors is expected to be about 400 V for the highest fluence [1.16]. This important issue of bulk damage in silicon sensors can be addressed in two ways. The first one is trying to produce detectors on silicon substrates which are less sensitive to the radiation damage. For this purpose collaboration between groups working in this field, namely the CERN RD-48 (ROSE) collaboration is carrying out studies on the use of oxygenated silicon as starting material [1.17]. However, its benefit is found to be limited to charged hadron environment. The other solution is to increase the detector bias voltage progressively so that full depletion can be eventually attained anyway; thus potentially leading to the occurrence of the early micro-discharges and avalanche breakdown. Hence, one of the main aims in the silicon detector development is to solve this problem by fabricating high-voltage planar

21

junctions with careful design strategies. In particular, the adoption of Metal-Overhang (MO) technique [1.18] has been suggested as an effective method to reduce breakdown risks. The principal goal of this thesis is to analyze the influence of various physical and geometrical parameters on the breakdown performance of silicon strip detectors equipped with metal-overhang. Such a complete analysis would be of great importance for optimization purposes. This analysis is performed using two-dimensional device simulation program, TMA-MEDICI [1.19]. The adoption of device simulation programs allows for the prediction of the characteristics of silicon detectors which helps in evaluating the device sensitivity to various design parameters, thus aid in optimizing the final design. It would be worth mentioning here that the metal-overhang technique is actually borrowed from the power device technology (where it is commonly referred to as “field plate” technique), but due to the completely different process parameters and the radiation environment, the optimization performed in the present work is an attempt for the first time. In recent years, high-energy physicists have arrived at a picture of the microscopic physical universe, called "The Standard Model", which unifies the nuclear, electromagnetic, and weak forces and enumerates the fundamental building blocks of the universe. One particular ingredient of the Standard Model that requires further quantitative investigation is Quantum Chromodynamics (QCD), which has emerged as a viable theory of strong interactions over the last two decades. QCD has been a successful theory in describing the interactions between the fundamental building blocks inside hadrons–quarks and gluons. In addition, it is in good agreement with experimental data collected both at fixed target and colliding beam experiments. However, the features of QCD, although qualitatively verified, are far from being completely understood. It is then crucial to investigate the properties of QCD at hadron colliders to probe the inner structure of the hadrons from the standpoint of perturbative QCD (pQCD) techniques and the parton model of strongly interacting particles. Study of direct photon production in high-energy hadronic collisions provides a clean tool for testing the essential validity of perturbative QCD predictions as well as for constraining the gluon distribution of nucleons. The motivation to work on direct photons at LHC energies stems from the fact that global QCD analysis of direct-photon 22

production processes show good agreement between data and QCD at high transverse momentum and thus provides an essential validity of the QCD predictions. This encouraged us to test QCD predictions at LHC energies. An understanding of high mass di-photon production will also be essential in the search for the light mass Higgs Boson (mH < 140 GeV/c2) decay via two-photons. We have used recent parton distribution functions and the latest version of event simulation program PYTHIA (version 6.2) to predict the direct-photon cross-section at LHC energies.

1.7 Thesis Organization The thesis is organized in seven chapters, a brief description of each chapter is given below. The present chapter, i.e., Chapter 1 provided an overview of the CERN LHC machine and CMS detector. Since the main emphasis of this thesis is on the detailed analysis of the breakdown performance of silicon strip sensors to be used in Preshower at CMS, hence a more detailed discussion on the Preshower detector is presented. The fundamental structure of most of the silicon detectors is the p-n junction, thus, an intuitive, non-rigorous description of the properties of p-n junctions can provide some grasp on the main aspects of detector operation. In Chapter 2, general properties of semiconductors (with emphasis on silicon) and reverse biased p-n junction are reviewed. The chapter also describes the principle of operation of silicon sensors, and the specifications/acceptance-criterion of the silicon strip detectors to be used in CMS Preshower. Because of the geometrical complexity of the metal-overhang structures, numerical simulations that aid design optimization are expected to be unwieldy. In the present work, two-dimensional device simulation tool, TMA-MEDICI is sought to analyze the breakdown performance of silicon detectors. Chapter 3 describes the methodology and approach of the simulation program. Various important aspects of the program including mesh generation, boundary conditions, physical models description, and numerical solution of the equations are briefly discussed. The values of the breakdown voltage obtained using simulation depend critically on the correct choice of the physical models, boundary conditions and most importantly on ionization coefficients. 23

We next address in Chapter 4 the breakdown voltage analysis of planar silicon microstrip detectors equipped with metal-overhang. The chapter traces some significant developments in the evolution of the overhang technique. The results reported in literature clearly suggest that this technique is simple and versatile. However, little data is available on the analysis and design of this technique. In this chapter, a physical interpretation of the beneficial aspects of the overhang structure in terms of interaction of charges in the space charge region and in metal-overhang is provided. The influence of the salient design parameters, namely, field-oxide thickness, junction depth, overhang width, device depth, substrate doping concentration and surface charges on the breakdown voltage of metal-overhang structures is studied. Such an exhaustive analysis of the structure equipped with metal-overhang correlating the breakdown voltage to these parameters is of great importance for device optimization. One of the primary objectives of the detector research in the high-energy physics experiments is to stabilize the long-term behaviour of silicon strip detectors and it is of utmost importance to protect the sensitive detector surfaces against moisture and other adverse atmospheric environment. This is achieved by depositing the final passivation layer over oxide of the silicon detector. Chapter 5 presents the influence of the relative permittivity of the passivant on the breakdown performance of the Si detectors using computer simulations. The semi-insulator and the dielectric passivated metal-overhang structures are then compared under optimal conditions. By analyzing simulation results, influences of all the salient physical and geometrical parameters on these structures have been elaborated. Another important factor, which can significantly affect the long-term functionality of the Si sensors, is the radiation damage and hence a crucial issue for the detectors at LHC is their stability at high operating voltages. The effect of bulk damage caused by hadron environment in the passivated Si detectors is simulated by varying effective carrier concentration and minority carrier lifetime. Static measurement results on some of the irradiated Si sensors, performed at CERN, Geneva along with the irradiation facility and measurement set-ups is also described in this chapter. In Chapter 6, we compare the two most commonly used termination techniques employed in silicon detector technology namely, metal-overhang and floating field limiting ring (or guard ring), under identical conditions with the aim of defining layouts and technological solutions suitable for the use of silicon detectors in harsh radiation 24

environment. The results demonstrate the superiority of metal-overhang technique over field limiting ring technique for planar shallow-junction high-voltage silicon detectors used in high-energy physics experiments. Chapter 7 starts with a brief review of the Standard Model and QCD, followed

by the study of direct photon physics. The chapter describes the study of direct photons in the kinematical regions accessible at LHC energy. For standardization purposes, the Fermilab Tevatron data on direct photons using latest version of event simulation tool PYTHIA (version 6.2) with recent parton distribution function CTEQ5M1 is presented. In order to explain the discrepancy between data and theory in the low transverse momentum of photons (pT), the effect of parton transverse momentum (kT) prior to hard scattering on the direct photon cross section is also investigated. It is found that the Nextto-Leading Order (NLO) theory supplemented with kT correction accounts to a great extent the low pT differences between data and theory. Predictions for direct photon cross section at

s =14 TeV for LHC along with various theoretical uncertainties is described.

It is found that the direct photons can be used to probe gluons at very low values of momentum fraction (x) and at very high values of momentum transfer between two partons (Q2).

25

Chapter 2

---------------------------------------------------------------Physics of Silicon Detectors: A Résumé ----------------------------------------------------------------

2.1 Silicon Detector: An Introduction Silicon detectors are used in almost all the High-Energy Physics (HEP) experiments built in the last fifteen years, from fixed target to large Collider experiments, and also in many specialized applications like spectrometers for space sciences or detectors for medical diagnostics. Some of the characteristics, which are the basis of the success of the silicon detectors and make them excellent devices for measurements, include (a) excellent speed (~ 10 ns), (b) spatial resolution of 10 µm, (c) compactness, (d) linearity of the response vs. deposited energy, (e) good resolution in the deposited energy (3.6 eV is needed to create an electron-hole pair as against 30 eV in a gas detector), (f) excellent mechanical properties, and (g) tolerance to high radiation doses up to ~ 10 Mrad. The very first semi-conductor detectors were built in the early 1950s and consisted of rectifying p-n junctions on crystalline germanium [2.1]. Germanium required substantial cooling for good energy resolution because of its low intrinsic resistivity and was rapidly overtaken by surface barrier silicon devices [2.2], which could be operated satisfactorily at room temperature. These detectors are also used in low energy spectroscopy. Due to the large electron-hole yield and low leakage currents, an energy resolution below 1 keV is routinely achieved. However, they were not commonly employed for particle detection. From the late 1950s through to early 1970s, nuclear emulsion and bubble chamber dominated the fixed target experiments. The situation, however, changed somewhat in the mid 1970s, after the discovery of the J/Ψ meson, a bound quark-antiquark pair state with a new quantum number called charm. Since charm

26

events are produced rarely, strategies had to be developed which allow the suppression of non-charm events. Only silicon detectors provided the excellent spatial resolution necessary to distinguish between non-charm events containing only tracks that originated from the interaction point, and the tracks originating from the charm decays which occur at a certain distance from the interaction point due to the small but finite lifetime of the charm particles. From there onwards, silicon detectors have been used extensively in vertex determination both in fixed target and colliding beam experiments. The first vertex detectors based on silicon strip technology were used successfully in MARK II experiment at SLAC (for e+-e- experiments) and in CDF at FNAL (for hadron collider). In a recently concluded Large Electron Positron (LEP) collider experiment at CERN, all four detector systems had vertex detectors using silicon strip detector technology [2.3]. A shift in paradigm occurred with the development of tracking detectors for hadron colliders, from D0 (FNAL) to CMS (CERN). The new emphasis is not only on vertexing but also on full tracking including charge and momentum determination in the magnetic field. Silicon detectors are best suited to meet the challenges of high accuracy and efficient track measurements because of the high level of possible segmentation into strips and pixels. Their compactness and possibility to integrate the front-end electronics on the same chip has also proved to be extremely advantageous. With an achieved position resolution of a few microns, silicon detectors have already contributed significantly to the study of τ−leptons, heavy quarks like charm and beauty and last but not least to the discovery of the top quark at FNAL. Future challenges: At present, the Si detector technology is well established and optimized for purposes of present generation HEP experiments like those at Tevatron (FNAL). Nevertheless, using these devices in the experiments such as those foreseen at the LHC implies solving problems which are quite new to this scenario. Although other materials such as gallium arsenide or diamond may be more radiation hard than silicon, however, silicon is still an attractive choice because the fabrication process along with the necessary electronics is developed to a high standard and reliability. The fundamental structure of most of the silicon detectors is the p-n junction, thus, an intuitive, non-rigorous description of the properties of p-n junctions can provide some grasp on the main aspects of detector operation. In the following sections, general

27

properties of semiconductors (with emphasis on silicon) and reverse biased p-n junction are reviewed. The chapter also describes the principle of operation of silicon sensors and the specification/acceptance-criterion of the silicon strip detector to be used in CMS Preshower.

2.2 Semiconductors: General Properties A. Band structure in solids: The most important result of the application of quantum mechanics to the description of electrons in the periodic lattice of crystalline materials is the formation of allowed energy levels grouped into bands. The energy of any electron within the pure material must be confined to one of these energy bands. The lower allowed energy band, called the valence band, corresponds to those electrons that are bound to specific lattice sites within the crystal. The next higher-lying allowed band is called the conduction band and represents electrons that are free to migrate through the crystal. These allowed energy levels are separated by gaps or ranges of forbidden energies that the electrons in a solid cannot possess, called forbidden gap or band gap. The band gap energy (Eg) is the energy difference between the top of the valence band and the bottom of the conduction band. In perfect semiconductor there are no electron energy levels in this band gap. For insulators, Eg is usually 5 eV or more, whereas for semiconductors, it is considerably small ~ 1 eV (for silicon, Eg ~ 1.12 eV at room temperature). B. Charge carriers: The phenomenon of conduction is of principal interest in the study of semiconductor physics. In the absence of thermal excitation (at 00 K), the semiconductors have a configuration in which the valence band is completely filled and the conduction band is completely empty, and hence no free electrons are available for electrical conduction. However, at any non-zero temperature, some bonds are broken and it is possible for a valence electron to be excited out of the covalent bond and elevated into the conduction band. The excitation process not only creates an electron in the otherwise empty conduction band, but it also leaves a vacancy (called a hole) in the otherwise full valence band. Both of these charges, electron in the conduction band and hole in the valence band, can conduct electricity under the influence of an applied electric field and hence contributes to the observed conductivity of the material.

28

At low and moderate electric fields, the drift velocity of electrons (ve) and holes (vh) is proportional to the applied field (E) and is given by ve = µ e E

&

vh = µ h E

(2.1)

where the proportionality constant µe and µh are the respective mobilities of electrons and holes. The electron and hole mobilities in a crystal are not equal, but are of the same order of magnitude unlike the case of electrons and positive ions in gases where the two values differ greatly. At higher electric fields, the drift velocity increases more slowly with the field. Eventually, a saturation velocity is reached ~ 107 cm-s-1 which becomes independent of further increase in electric field. C. Effect of impurities:

Intrinsic semiconductors - In a completely pure

semiconductor, all the electrons in the conduction band and all the holes in the valence band would be caused by thermal excitation. Since under these conditions each electron must leave a hole behind, the number of electrons in the conduction band (n) exactly equals the number of holes in the valence band (p), i.e., n = p = ni ,

(2.2)

where ni is called the intrinsic carrier concentration and its value in silicon at room temperature is 1.45 x 1010 cm-3. This intrinsic carrier dictates the lower limit of the leakage current in a reverse-biased diode. Doped semiconductors – The electrical properties of a semiconductor changes drastically with the addition of small concentration of impurities. We first consider that the impurity is pentavalent (like phosphorous). Because there are five valence electrons, surrounding the impurity atom, there is one left over electron after all covalent bonds are formed. This fifth electron is very loosely bound, its binding energy being about 2% of the Eg. In all practical situations due to thermal agitations, a large fraction of the impurities are ionized and the concentration of electron in the conduction band (n) can be as high as impurity doping density (ND). The impurity atom, which donates this free electron, is called a donor impurity, and the semiconductor is called the n-type semiconductor. In a similar manner, a trivalent impurity atom (like boron) can accept with a very small expenditure of energy an electron from the valence band. This leaves behind a hole in the valence band, which can move freely through the crystal. This type of impurity is known as acceptor impurity and the semiconductor is referred to as p-type

29

semiconductor. In this case the number of holes (p) can be as high as the acceptor density (NA). In real crystals, however, both donor and acceptor impurity atoms are present and the two atoms compensate each other. Thus the quantity of interest is always the net ionized impurity concentration (ND - NA): ND > NA for n-type semiconductor and ND < NA for p-type semiconductor. The added concentration of electrons in the conduction band for the case of n-type crystal increases the rate of recombination, shifting the equilibrium between the electrons and holes in a manner given by mass-action law 2

n. p = ni = N c N v e

−

Eg

∝T e

k BT

3

−

Eg k BT

(2.3)

where Nv and Nc are the effective density of states in the valence band and conduction band respectively, kB is the Boltzmann constant and T is the absolute temperature. Therefore, the net effect of doping is to increase the concentration of one type of carrier and reduce correspondingly the concentration of opposite type. Thus, in ntype semiconductor the electrons are called the majority carriers, and holes the minority carriers. One measure of the impurity level in the semiconductors is the electrical conductivity, or its inverse, resistivity which is given by

ρ=

1 q( µ n n + µ p p)

=

1 for n >> p qµ n n

(2.4)

For intrinsic silicon at room temperature ρ is equal to 227 kΩ-cm (µn = 1350 cm2V-1s-1, µp = 480 cm2V-1s-1). The resistivity of doped materials is lower, because of a high carrier density.

2.3

Reverse Biased p - n Junction

2.3.1 Abrupt p - n Junction When the doping concentration changes abruptly from a surplus of acceptors NA on the p-side to a surplus of donor ND on the n-side one obtains an abrupt p-n junction. Fig.2.1 represents an abrupt p-n junction in thermal equilibrium. The strong gradient of carriers across the junction causes diffusion of electrons in the p-type region and holes in the n-type region. The unbalanced fixed charges left 30

behind by diffusing carriers constitute the space charge region (SCR): negative ions in the p-region and positive ions in the n-region. An electric field appears across the junction due to the potential drop in the SCR. This results in a flow of drift current in the direction opposite to the diffusion current. The equilibrium is reached when the potential drop prevents further charge diffusion across the junction. This potential is called diffusion or built in potential (Vbi), and it is about 0.6 V for silicon. Since SCR is

depleted of the mobile carriers, it is also known as depletion region. In thermal equilibrium, with no applied voltage, the net flow of both electron and hole currents is zero. The diffusion potential (Vbi) is equal to (from Fig.2.1) qVbi = E g − (qVn + qV p ) ,

(2.5)

where q is the electron charge and Vn & Vp are the electrical potentials as shown in Fig.2.1.

Fig.2.1: Abrupt p-n junction in thermal equilibrium. (a) Space-charge distribution. The dashed lines indicate the majority carrier distribution tails. (b) Electric field distribution. (c) Potential variation with distance where Vbi is the built-in potential. (d) Energy-band diagram.

31

2.3.2 Expressions of Some Useful Physical Quantities for Abrupt p-n Junction The potential and electric field distribution in the depletion region can be calculated by solving the one dimensional Poisson equation: − d 2V ∂E ρ ( x) = = ∂x ε si dx 2

=

[

q p ( x) − n( x) + N D+ ( x) − N A− ( x) ε si

]

(2.6)

which for the abrupt junction under the depletion layer approximation becomes (assuming that all impurity ions are ionized) − d 2V q ≈− NA 2 ε Si dx ≈

for − x p < x ≤ 0

q ND ε Si

(2.7)

for 0 < x ≤ x n

The electric field is obtained by integrating equation (2.7) to yield, E ( x) = =

− qN A (x + x p ) ε Si

for − x p ≤ x < 0

qN D ( x − xn ) ε Si

for

(2.8)

0 < x ≤ xn

The electric field reaches its maximum value Em at the junction, i.e., at x = 0, E m = E ( x = 0) =

qN D x n qN A x p = ε Si ε Si

(2.9)

Potential distribution along with the built in potential can be obtained by integrating equation (2.8) once again  x2 V ( x) = E m  x − 2W  Vbi = V ( x = W ) =

  

(2.10)

1 E mW , 2

(2.11)

where W = xn + xp is the total width of the depletion region. Eliminating Em from the equations (2.9) and (2.11) yields for abrupt p-n junction, W=

2ε si q

 NA + ND   NAND

  Vbi 

32

(2.12)

Asymmetric junctions are often used in detector technology, which is obtained if the doping density in one side is very large as compared to the density in the other side. In particular if NA >> ND, one obtains one-sided abrupt p+-n junction, for which the extension of the depletion region in the p+ side can be neglected, i.e., xp<<xn ~W. Therefore, for this case the depletion width and electric field are given by, 2ε Si Vbi , qN B

(2.13)

qN B (x − W ) ε Si

(2.14)

W ≈ xn = E ( x) =

where NB = ND, i.e., doping concentration of the less doped region. A more accurate result for the depletion layer width can be obtained from equation (2.6) by including the correction factor coming from the Debye tail of the majority carrier distribution at the edges of the depletion region (shown as dashed line in Fig.2.1(a)), each of which introduces a term kBT/q. The depletion width is essentially the same as given by equation (2.13), except that Vbi is replaced by (Vbi – 2kBT/q) [2.4]. The depletion-layer width at thermal equilibrium for a one-sided abrupt junction becomes W=

2ε Si qN B

 2k T   Vbi − B  q  

(2.15)

p – n junction under reverse bias: The width of the SCR can be changed if an external voltage is applied to the diode. For an applied reverse bias (V), it is given as, W (V ) =

2ε Si qN B

  2k T Vbi − B + V  q  

(2.16)

 2k T  For reverse voltage larger in comparison with  Vbi − B  (Vbi ~ 0.6 V and q  

kBT/q ~ 25 mV at room temperature), a simplified expression can be used for the depletion of the SCR width on the applied voltage: W (V ) =

2ε siV qN B

(2.17)

The minimum voltage needed for full depletion is called the full depletion voltage (VFD), and can be deduced from equation (2.17), replacing W(V) by the detector thickness d, 33

qN B d 2 d2 = = 2ε si ρµ n ε si

VFD

(2.18)

Equation (2.17) implies that the depletion thickness is inversely proportional to the square root of substrate doping concentration NB. A silicon detector is normally fabricated from a lightly doped n-type wafer so that a large active volume can be obtained at small voltages. The depletion region can be regarded as a parallel plate capacitor because of the build up of the space charge. The junction or depletion layer capacitance per unit area is defined as [2.4] Cj =

ε dQc d (qN BW ) = = Si qN dV W (V ) d [( B )W 2 ] 2ε Si

(2.19)

where dQc is the incremental increase in charge per unit area upon an incremental change of the applied voltage dV. By substituting W from equation (2.17), the above relation for the reverse biased diode can be written as: Cj =

qε Si N B 2V

ε = Si d

for V < V FD

(2.20)

for V > V FD

The junction capacitance therefore decreases with the applied voltage till the whole volume is completely depleted; after which it remains constant reaching a value consistent with the geometrical one. It is clear from equation (2.20) that by plotting 1/C2 vs. V a straight line should result for a one sided abrupt junction till full depletion is attained and then the curve saturates. The slope of the curve gives the impurity concentration of the substrate (NB).

2.3.3 Reverse Leakage Current Reverse leakage current together with the breakdown voltage constitute two most important characteristics of the silicon detectors. In order to reduce noise below the acceptable levels, small values of leakage currents are desirable in silicon detectors.

34

Recombination-generation (R-G): Recombination-generation is the basic

mechanism giving rise to all type of currents observed in p-n junctions. There are three basic R-G processes [2.4]: Radiative, Auger and Shockley-Read-Hall (SRH). The transition of an electron from the conduction band to valence band is made possible by emission of a photon (radiative or band-to-band process) or by transfer of energy to another free electron or hole (Auger process). The third process is the recombination via trapping centers (or R-G centers) present in the forbidden energy gap due to the presence of impurity atoms or crystal defects (SRH or multiphonon process). Each of these recombination processes has a generation counterpart. Direct optical transition (or photogeneration) is the counterpart of radiative process and impact-ionization is that of Auger process. The inverse of SRH recombination is the thermal electron-hole (e-h) pair generation. In reverse biased p-n junctions, there is a paucity of charge carriers in the depletion region and e-h pair once generated, get separated under the influence of electric field and hence their probability of recombination is diminished. Thus, generation mechanism is chiefly responsible for the current-flow in the reverse biased silicon detectors. Optical generation is important in direct band-gap materials (like gallium arsenide) but plays little role in indirect band-gap semiconductors (like silicon). Impactionization plays a significant role only at very high electric fields. Thus, under dark and low field condition, optical generation and impact ionization are almost negligible in silicon detectors. SRH generation takes place whenever there are impurities or defects. Since semiconductors always contain some impurities, this mechanism is always active and is particularly important for silicon diodes. For single level generation process in which only one trapping energy level (Et) is involved, the net generation rate (U) due to SRH process is given by [2.5] U =

ni2 − np , (n1 + n)τ P + ( p1 + p)τ n

(2.21)

where ni is the intrinsic concentration, n and p are the electron and hole concentrations and p1 and n1 are the equilibrium value of the hole and electron concentrations if the fermi level (EF) were at the trap level (Et), i.e.,

35

 E − Ei n1 = ni exp t  k BT

  ; 

 E − Et p1 = ni exp i  k BT

  , 

(2.22)

Ei is the intrinsic energy level, τp and τn in equation (2.21) are minority carrier lifetimes for hole and electron respectively and are defined as,

τp =

1 σ P vth N t

& τ

n

=

1 , σ n vth N t

(2.23)

where Nt is the density of trapping centers, σn and σp are the respective capture crosssections for the electron and holes respectively, and vth is the carrier thermal velocity. Leakage current in Silicon detectors: Currents in p+-n silicon detectors due to e-h pair

generation at some place in the device are shown in Fig.2.2 [2.6] (we will assume ideal junctions free of pinholes, defects etc.). Total current (I) can be written as the sum of the currents in each separate region, I = I I + I II + I III + I IV

(2.24)

where, II = Due to R-G centres in the space-charge region III = Due to interface traps at the SiO2/Si interface IIII = Due to R-G centres in the undepleted (quasi-neutral) bulk IIV = Due to the high-low (n-n+) junction at the back surface

Fig.2.2: Subdivision of the diode structure into four regions, according to which the leakage current is calculated. W is the width of the depleted region and t ′ is the width of the undepleted region.

Region I: In Region I, current-flow depends upon the generation rate of e-h pairs in the depletion region and is given as [2.5]: 36

I I = q | U | WA

(2.25)

where q is the electron charge, W is the depletion width, A is the cross-sectional area of the p-n junction and U is the net generation rate as given in equation (2.21). In this region, both the electron and hole concentration can be neglected (n, p = 0) and assuming U to be constant over the entire layer [2.7], equation (2.21) reduces to U =

and

τg =

n1τ p + p1τ n ni

ni2 n n ≡ i ≡ i , n1τ P + p1τ n τ g 2τ 0

 E − Ei = τ p exp t  k BT

  E − Ei  + τ n exp − t k BT  

(2.26)   

(2.27)

τg is the SRH generation lifetime and for particular case when Et = Ei and σn = σp, it reduces to τ

g

= 2τ 0 , where τ0 is defined as the effective lifetime within a reverse biased

depletion region. Substituting U in equation (2.25), the current in region I is given as qniWA 2τ 0

II =

(2.28)

The presence of W in this equation implies that this component of the leakage current increases with increase in reverse bias ( V dependence) and saturates at full depletion voltage [2.4, 2.5, 2.7]. Region II: The surface generation component in Region II is given as [2.5], I II = qU s As

(2.29)

where As is the junction area at the surface and Us is the surface generation rate per unit area at the oxide-silicon interface. For the completely depleted surface [2.5], Us =

1 ni s o 2

(2.30)

where so is the surface recombination velocity and is defined as s o = σv th N st for centers with energy levels Et = Ei., and Nst is the surface density of R-G centers. Thus, I II =

qni s 0 As 2

(2.31)

The complicated geometry and field distribution at the surface region of a silicon detector makes it difficult to predict the depleted interface area As. The amount of 37

interface states contributing to the surface recombination velocity s0 is a characteristic of the quality of the SiO2 processing during fabrication. Surface current is an unavoidable component of microstrip detector leakage current, however, the inclusion of guard rings, which are the diodes surrounding the detector, can help in minimizing this component. Regions III & IV: Regions III and IV are undepleted and thus the diffusion of minority carriers (holes in our case) determines the contribution of these regions to the leakage current. The combined contribution is given by [2.6] I III + I IV =

q ni2 Dn A , N B Ln ,eff

(2.32)

where the diffusion length Ln,eff is an effective diffusion length that couples the bulk diffusion length Ln (region III) with the surface generation velocity at the back surface sc (region IV). For simplicity the SCR width at the surface is assumed to be identical to that in the bulk as shown in Fig.2.2. A small contribution to the diffusion current also comes from the undepleted p+ region (electrons being the minority carrier). Although diffusion component is the dominant current source at room temperature for semiconductors with high ni like germanium (because of ni2 dependence of diffusion current), but for silicon it is less important. Moreover, for a fully depleted silicon detector, this component is almost negligible for operating temperatures below 100°C [2.5]. Thus, the total reverse current in silicon detector where the depletion region extends mainly in the n-side, can be expressed as the sum of the generation currents in region I and region II. I=

qniWA qni s 0 AS + 2τ 0 2

(2.33)

2.3.4 Breakdown Voltage In the reverse bias p-n junction, the breakdown is defined as the steep rise in current when the reverse bias goes above a certain limit (VBD). The high current flowing in the breakdown regime makes silicon detector unusable and could destroy the device if the bias is not rapidly decreased below VBD. Therefore, it is important to keep VBD of the silicon sensors as high as possible. Three basic breakdown mechanisms [2.4] in the

38

reverse biased p-n junctions are: thermal instability, tunneling or Zener breakdown and avalanche multiplication.

A. Thermal instability: At high reverse voltages, the heat dissipation caused by the reverse current increases the junction temperature, which in turn, further increases the reverse current and causes thermal runaway. However, this effect is particularly important for semiconductors with relatively small band gaps (for example, germanium) and not so important in silicon.

B. Tunneling or Zener breakdown: Due to the occurrence of very high fields within the depletion region at high reverse voltages, some of the covalent bonds between neighbouring atoms are “torn” apart, resulting in the generation of conduction electrons and holes. This corresponds to the tunneling of electrons from the valence band edge of p-type to the conduction band edge on the n-side. Zener breakdown occurs in p-n junctions that are heavily doped on both sides of the metallurgical junction and hence is relatively unimportant for silicon detectors, where the substrate is almost intrinsic.

C. Avalanche multiplication: The most common mode of breakdown mechanism in silicon detectors is the avalanche breakdown. When a semiconductor is subjected to an increasing electric field, a point is reached when mobile carriers in the depletion region attain saturation drift velocity. With further increase in electric field, the velocity of individual carriers exceeds their thermal velocity, i.e., they become “hot” carriers. At a critical electric field, these carriers gain sufficient kinetic energy so that their collisions with the lattice atoms can knock-on the valence electrons, leaving a hole behind. This process of generation of electron-hole (e-h) pairs is called impact ionization (Fig.2.3). Each newly generated carrier also gets involved in the ionization of further e-h pairs. Consequently, impact ionization is a multiplicative phenomena and the device is considered to undergo avalanche breakdown when the process attains an infinite rate. Ionization Coefficients: To characterize the avalanche process it is useful to

define ionization coefficients for holes (αp) & electrons (αn) [2.8]: αp : number of e-h pairs produced by a hole traversing 1cm through the depletion layer along the direction of electric field. αn : number of e-h pairs produced by an electron traversing 1cm through the depletion layer along the direction of electric field.

39

Extensive measurements of these coefficients for silicon have been conducted [2.9] and are found to vary with electric field as:

α n = a n e −b

n

/Ε

& α p = ape

−b p / Ε

(2.34)

where an = 7 x 105 cm-1, bn = 1.23 x 106 Vcm-1, ap = 1.6 x 105 cm-1, bp =2 x 106 Vcm-1 [2.10]. These expressions are found to be applicable for electric fields ranging from 1.75 x 105 to 6 x 105 Vcm-1 [2.10]. In many cases an approximation of the ionization coefficients is found to be useful to obtain a closed-form expression for breakdown voltage and is given by [2.11]

α n ≅ α p ≅ α i ≅ 1.8 × 10 −35 E 7

(2.35)

Breakdown condition: Assume that an e-h pair is generated within the

depletion region at a distance x from the junction. In p+-n junctions under reverse bias, the hole will be swept towards the junction side (p+) and the electron toward the depletion layer edge. When traversing a distance dx, the hole will create αpdx e-h pairs and the electron will produce αndx e-h pairs [2.8]. The average total number of e-h pairs created in the depletion layer due to single e-h pair initially generated at x (called Multiplication coefficient) is given as [2.9] x

M ( x) = 1 + ∫ α p M ( x )dx + '

0

'

W

∫α

n

M ( x ' )dx '

(2.36)

x

Fig.2.3: The process of impact ionization and avalanche multiplication, from [2.5].

A solution of this equation is: x  M ( x) = M (0) exp  ∫ (α p − α n ) dx '  0 

40

(2.37)

Eliminating M(0) from equations (2.37) using (2.36), we get:

M ( x) =

W

1− ∫ 0

x  exp  ∫ (α p − α n ) dx '  0  x   α n exp  ∫ (α p − α n ) dx '  dx 0 

(2.38)

Avalanche breakdown occurs when M(x) tends to infinity, i.e., when W'

∫ 0

x α n exp  ∫ (α p − α 0

) dx  dx = 1 '

n

(2.39)



where W ′ is the depletion layer width at breakdown. This is the general condition of avalanche breakdown in reverse biased p-n junctions. This equation can be simplified using equation (2.35) W'

∫α

i

dx = 1

(2.40)

0

One-sided plane-parallel abrupt junction (non-punch through case): A closed

form analytical expression for the VBD using electric field distribution given by equation (2.14) and ionization coefficient approximation (equation (2.35)) can be obtained using equation (2.40) 7

W'

∫ 1.8 × 10 0

− 35

 qNB   ( x − W )  dx = 1  ε Si 

(2.41)

Using this equation, the depletion layer width at breakdown for the parallel-plane junction can be obtained [2.12]: ′ = 2 . 67 × 10 10 N B− 7 / 8 W PP

(2.42)

where subscript “PP” means plane-parallel junction and NB is expressed in cm-3. Critical ′ in the electric field at breakdown ( E cPP ) can be found ([2.12]) replacing xn by WPP maximum electric field expression (equation (2.9)) and using equation (2.42) E cPP =

′ qN BWPP = 4010 N B1 / 8 ε Si

where the field is expressed in Vcm-1.

41

(2.43)

Similarly breakdown voltage ( V BDPP ) for the one sided abrupt plane parallel ′ in equation junction can be obtained ([2.12]) replacing Em by E cPP , and W by WPP (2.11), and using equation (2.42) V BDpp =

(

)

1 ′ = 5.34 ×1013 N B−3 / 4 E cPP WPP 2

(2.44)

i.e., the breakdown voltage is given by the area under E vs. x curve. One-sided plane-parallel abrupt junction (punch through case): It was assumed

hitherto that the lightly doped side of the junction extends beyond the edge of the depletion layer under avalanche breakdown. This is not always true, and in particular in case of radiation detector which has to be operated in full depletion mode, the device depth (d) is smaller than W ′ and such a diode is called punch-through (PT) diode. Assuming that breakdown of each device occurs for the same critical electric field Ec, let E1 be the electric field at x = d when the field at the junction reaches its critical value (Ec), (Fig.2.4).

Fig.2.4: A comparison of the non-punch through (NPT) and punch-through (PT) diode.

The breakdown voltage for PT diodes is given by: V BDPT = ( E c + E1 )d / 2

Using equation (2.44), it can be shown that [2.4]

42

(2.45)

V BDPT V BDPP

 d   d  ≅ 2  −  W ′  W ′ 

2

(2.46)

Thus, the breakdown voltage of the punched through diode is always less than that of its normal counterpart. The punch through usually occurs when doping concentration NB is sufficiently low. An interesting aspect of the plane-parallel PT diodes is that the NB has a negligible influence on its breakdown voltage [2.13]. Planar diffuse junction termination (edge effect): In the previous sections, we

assumed an infinite extension of the junctions without any edges. But in real situation, when the junction is fabricated by diffusing the dopants through the mask windows (as in planar technique), the impurities also diffuse laterally at the edges of the mask window (Fig.2.5(a)). For purposes of breakdown analysis, the lateral diffusion can be considered to be equal to the junction depth to a good approximation. This results in the formation of cylindrical junctions inside the diffusion windows and spherical junctions at the edges for the actual diodes (Fig.2.5(b)). For actual devices therefore, it becomes imperative to consider edge effects (cylindrical and spherical regions) since the curvature limits the breakdown voltage to values much below the ‘ideal’ limits set by the plane-parallel junction [2.4]. (b)

(a)

Fig2.5: (a) Planar diffusion process which forms junction curvature near the edges of the diffusion mask. rj is the radius of curvature, and (b) The formation of approximately cylindrical and spherical regions by diffusion through a rectangular mask. Edge effect - Cylindrical junction: Solving the Poisson equation in cylindrical

coordinates, electric field distribution is given by

43

Ε( r ) =

qΝ B 2ε Si

 rd 2 − r 2      r  

(2.47)

where rd is the radius of curvature of the depletion layer edge. Examination of equation (2.47) shows that for cylindrical junctions, the high field region is largely confined to small values of r near the boundary of the metallurgical junction. This allows an approximation for the electric field distribution E(r) = K/r (K being some constant independent of r) [2.9, 2.12] and substituting this in the ionization integral equation (2.40), the ratio of Ec and VBD for cylindrical and plane-parallel junction are given as [2.12]: Ec ,CYL E c , PP V BDCYL V BDPP

 3W ′   =  4r   j 

1/ 7

(2.48)

8/7 6/7 6/7   r  2  W ′    r j   r j     1  j     + 2   ln 1 + 2   =  −  r   W ′   ′  2  W ′  W        j     

(2.49)

Here, rj is the junction depth. Edge effect – spherical junction: Following the same approach as used in the

previous section, and with an approximation of electric field distribution E(r) = K/r2 [2.9, 2.12] for calculating the ionization integral for spherical junction, the expressions corresponding to equations (2.47), (2.48), and (2.49) are given by [2.12] qN B E (r ) = 3ε Si E c , SP E c , PP

VBDSP VBDPP

 rd 3 − r 3     r2   

 13W ′   =  8r  j  

(2.50)

1/ 7

(2.51)

6/7 13 / 7 2 / 3  r 2   r j  3  r r        j j j  + 2.14   −   + 3    =     W ′   W ′    W ′   W ′    

   

(2.52)

Fig.2.6 shows the plot of normalized breakdown voltage against the normalized radius of curvature both for cylindrical and spherical junction. It can be seen that the breakdown voltage for the spherical junction is less than that of the cylindrical junction, and that of cylindrical junction is less than the breakdown voltage of plane parallel

44

junction. However, it is also clear that the breakdown voltage of curved junctions (both cylindrical and spherical) increases with increase in the radius of curvature and begins to approach the parallel plane case for large values of junction depth.

Fig.2.6: Normalized breakdown voltage as a function of the normalized radius of curvature both for cylindrical and spherical junctions [2.4].

2.4 Principle of Silicon Detector Operation A silicon detector is essentially a reverse biased diode with the depleted zone acting as a solid-state ionization chamber. When charged particles pass through a silicon detector, many e-h pairs get produced along the path of the particle. Average energy required to create a single e-h pair is about 3.6 eV for silicon. The energy loss in silicon can be measured by “counting” the total number of created pairs. Under the application of reverse bias, electrons drift towards the n+ side and holes to the p+ side. This charge migration induces a current pulse on the read out electrodes and constitutes the basic electrical signal. Integration of this current equals the total charge and hence is proportional to the energy loss of the particle. The high mobility of electron and holes enables this signal charge to be collected very quickly. It should be pointed out here that only the charge released in the depletion region can be collected, whereas the charge created in the neutral, non-depleted zone recombines with the free carriers and is lost. For this reason silicon detectors usually operate with an applied voltage sufficient to fully

45

deplete all the crystal volume. Fig.2.7 shows the principle of operation of silicon microstrip detector. A minimum ionizing particle traversing a <111> oriented Si layer of depth 300 µm deposits the most probable energy of about 90 keV and produces about 25000 e-h pairs (~ 4f C).

Fig.2.7: Principle of operation of silicon strip detector.

2.5

Silicon Microstrip Detector for CMS Preshower India’s participation in Preshower detector of the Compact Muon Solenoid (CMS)

experiment was agreed upon in early 1997 and under this agreement, Delhi University (DU) and Bhabha Atomic Research Centre (BARC) are responsible for the development of silicon strip detectors. Three other groups, EHEP – Tata Institute of Fundamental Physics (TIFR) (Mumbai), HECR – TIFR (Mumbai) and Panjab University have contributed to the fabrication of the Outer Hadron Calorimeter (HO–B) of CMS. All five groups have agreed to work together and formed an India–CMS collaboration. The R&D of the detector technology has been jointly carried out by scientists at DU, BARC, Bharat Electronics Limited (BEL), Bangalore and Central Electronics Engineering Research Institute (CEERI), Pilani. Initially the technology was developed at CEERI on 2-inch wafer and later on the prototypes were fabricated using 4-inch wafers at BEL. Each silicon detector is a square of 63 x 63 mm2 divided into 32 strips. 46

2.5.1 Silicon Microstrip Detector The silicon microstrip detector is by far the most widely used semiconductor particle tracking device. At its simplest, the microstrip detector consists of a series of reverse biased diodes constructed on a single silicon wafer. Microstrip detectors, thus, provide the measurement of one coordinate of the particle’s crossing point with high precision. Using very low noise readout electronics, the measurement of the centroid of the signal over more than one strip further improves the precision. Usually strips are p+ implants to provide p+-n junction in the n-bulk, which may be DC or AC coupled to the read out electronics. On the ohmic side, n+ is implanted to provide the ohmic contact to bias the detector.

2.5.2 Wafer Parameters [2.14] The detectors have been fabricated on float zone n-type, <111> oriented, 2.5 - 4 KΩ-cm wafers supplied by TOPSIL or Wacker. The quality of wafers is a critical factor for detector fabrication, as even a single defect occurring over the detector area, which is quite large, would result in a bad strip giving non-acceptable performance. Hence wafers with zero defect density and high life time of the order of milliseconds have been used for detector fabrication. Since Preshower strip capacitance is dominated by back plane capacitance, there is no particular advantage to use <100> orientation, and a more classical <111> orientation has been chosen which has the largest number of available bonds per unit area. Single-sided polished wafer is considered because of cost effectiveness and availability. Also it is found that it is the thickness of the back plane implant and not the quality of the back surface which influences the detector performance. Resistivity of 2.5 - 4 kΩ-cm is chosen to achieve low leakage current, high breakdown voltage and satisfactory performance after bulk inversion due to radiation damage. A wafer thickness of 320 ± 20 µm is chosen to achieve a satisfactory S/N ratio and desired operating voltage.

2.5.3 Sensor Design / Geometry [2.14] Detector dimension of 63 x 63 mm2 is the maximum available area possible on a 4-inch wafer. Strip-pitch of 1.9 mm is governed by the photon separation (from π0s) and transverse shower spread. Strip-width of 1.78 mm is the optimum compromise between 47

reduction in interstrip capacitance and good charge collection for irradiated sensors. The metal-overhang of 10 µm on each side of the strip improves the breakdown performance. A good ohmic contact between metal and silicon at the backside is achieved by using n+ implant of suitable thickness [2.14] and very high doping. Table 2.1 provides the specifications for the wafer & geometry of the Preshower silicon sensor.

Table 2.1: Preliminary specifications (wafer/geometry) of the Preshower silicon sensor. Parameter

Value

Wafer size

4"

Thickness

320 ± 20 µm

Resistivity

2.5 KΩ cm − 4 KΩ cm

Polishing

Single-sided

n+ layer thickness

> 2.5 µm

Total area

63 x 63 mm2

Number of strips

32

Strip pitch

1.9 mm

p+ strip width

1.78 mm

Al strip width

1.8 mm

2.5.4 Fabrication Planar technology is the principal method of fabricating modern semiconductor devices [2.15] (Fig.2.8). In total, four masks are used including passivation. For cost effectiveness, the p+ strips are Directly Coupled (DC) to the Aluminium readout lines and the front-end electronics includes a leakage current compensation mechanism [2.16]. Figures 2.9(a), 2.9(b), and 2.9(c) show the layout, cross-section and the complete 63 x 63 mm2 CMS Preshower silicon strip detector. The basic planar process used at CEERI, Pilani and BEL, Bangalore to fabricate the silicon microstrip detectors involve the following steps:

48

1. Initial Oxidation 2. p+ lithography 3. Oxidation for screen oxide 4. Re-expose p+ mask 5. Implantation of Boron for p+ strips and guard rings 6. n+ implant at the backside 7. Implant anneal and redistribution 8. Contact lithography 9. Front Metallization 10. Metal lithography 11. Metal sintering at 450 ˚C 12. Passivation Fig.2.8: Main steps in the planar fabrication process of detectors [2.15].

Fig.2.9: (a) Layout of silicon preshower sensor, (b) Cross-section of a preshower silicon microstrip detector, and (c) complete 63 x 63 mm2 CMS Preshower Si detector (with front-end electronics).

49

2.5.5 Acceptance Criterion [2.17] The silicon sensors to be used in Preshower detector have to meet the specifications as listed in Table 2.2, specified by Preshower group at CERN. The VBD > 500 V is required for sensors to be placed in the central ring, close to the beam pipe where the expected radiation flux is maximum, whereas 300 V detectors will be placed in the periphery where the flux level will be less than by an order of magnitude. Table 2.2: Acceptance criterion for the Preshower silicon sensor [2.17]. Test

Width (W) Mechanical tolerances

Thickness (t)

Criterion

W ≤ 63 mm 300 µm ≤ t ≤ 340 µm I ≤ 5 µA at VFD

I-V Global measurements

I ≤ 10µA at 300 V VBD ≥ 300 V for category 1 VBD ≥ 500 V for category 2

C-V I Strip-by-strip measurements

VFD ≤ 100 V Max. 1 strip with I ≥ 1 µA at VFD Max. 1 strip with I ≥ 5 µA at 300 V No strips connected to the neighbour or

C

guard ring

In India, the silicon detectors are being fabricated at BEL, Bangalore to meet the desired specifications. Theoretically, breakdown voltage of 500 volt can be obtained for high resistivity substrates used in Preshower, however, due to the large area, junction curvature, and surface charges, it becomes very difficult to obtain high yield. As discussed earlier, metal-overhang of 10 µm is chosen in the PSD baseline design to improve the breakdown voltage. However, in order to effectively utilize the advantages of metal-overhang, effect of various geometrical and physical parameters on its design is a prerequisite. In Chapters 4 and 5, we have studied and analyzed the influence of these parameters on overhang structures using computer simulation.

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Chapter 3

---------------------------------------------------------------Semiconductor Device Simulation ---------------------------------------------------------------Since most of the work done in this thesis is based on the results obtained from device simulation, it is imperative to discuss the various aspects of a simulation program. This chapter describes the methodology and approach of the simulation program, TMAMEDICI [3.1], used in the present work.

3.1

Why Simulation ? The reduction in active device dimensions to micron and submicron geometries

has resulted in an intimate coupling of the process conditions and device behaviour to a degree unknown a few years ago. It becomes more and more difficult to develop new processes due to the inherent complexity of semiconductor device fabrication. The use of Computer-Aided Design (CAD) tools has emerged as a very elegant mechanism to aid process and device engineers in their task of finding an optimum process and hence proven to be invaluable in the development of new technologies. Traditionally, a new technology development has been guided by an experimental “trial-and-error” approach. Starting with an existing process, certain steps in the process are changed, together with the structural dimensions. The modified process is then used to fabricate several lots of a device. However, this approach requires many iterations to optimize a new process, and fabricating one lot in a modern process can cost considerable amount of money and consume weeks or even months of effort. The use of accurate simulation tools in the proper computing environment, on the other hand, allows for comparatively inexpensive and time-saving “computer experiments”. Reduction of both

51

optimization time and prototypization expenses is therefore expected from the adoption of device simulation. A Boon for Silicon Detector Development: Technology-CAD tools are routinely used in IC production and development environment; however, their diffusion within the HEP community is relatively recent. Some of the advantages of using device simulation for the development of silicon sensors are as follows: •

The development of silicon detectors for LHC demands large resources, both in terms of time and money. Device simulation programs may help in the prediction of the characteristics of silicon detectors, depending upon their geometry and fabrication parameters.

•

Numerical simulation gives an opportunity to look into the internal device mechanism of silicon detectors by examining quantities like electric field and carrier distribution, thus, allowing for the physical interpretation of several interesting experimental findings and phenomena.

•

Simulations make it possible to find a connection between non-measurable physical quantities (like electric field, impact ionization generation rate etc.) and measurable terminal parameters (like terminal voltage and current).

•

In order to optimize the breakdown performance of the detector design, it is of utmost importance to identify regions at which leakage current may preferentially develop, and to correlate the threshold of such phenomena to geometrical and physical device characteristics. The adoption of CAD tools allows for evaluating the actual field distribution within the device and makes it possible to identify critical regions.

•

Simulation helps in evaluating the device sensitivity to various design parameters and thus aid in optimizing the final design.

•

Because of the large number of silicon sensors and the difficulty to replace defective devices in the Preshower detector system, the operation time of these sensors has to be at least 10 years in the CMS experiment. In this period an equivalent irradiation dose of more than 1014 cm-2 hadrons is expected, which has never been obtained before in any HEP experiment. This requires a good prediction of the effect of radiation-induced changes in silicon detectors. Since it is not possible to actually

52

predict the changes in bulk characteristics in advance, a good estimate of the device behaviour after radiation damage can be obtained using device simulation.

3.2

TMA-MEDICI – A Device Simulation Program TMA-MEDICI is a powerful two-dimensional device simulation program that can

be used to simulate the behaviour of p-n junctions, MOS & bipolar transistors, and other semiconductor devices. The program can be used to predict the electrical characteristics of a device for arbitrary bias conditions. MEDICI can also perform AC small signal analysis in addition to DC steady state and transient analysis. The different aspects of the program used in this work, which includes the physical description and the numerical methods along with a sample program is briefly described in the following sections.

3.2.1 Physical Description 3.2.1.1 Drift-Diffusion Model The primary function of MEDICI is to solve three semiconductor partial differential equations (PDEs) self-consistently, Poisson’s equation for the electrostatic potential (Ψ) and two current continuity equations for the electron and hole concentrations, n and p respectively. These equations describe the electrical behaviour of semiconductor devices. +

−

Poisson equation:

∈ ∇ 2ψ = − q( p − n + N D − N A ) − ρ S

(3.1)

Continuity equation for electrons:

∂n 1   = ∇.J n − U n ∂t q

(3.2)

Continuity equation for holes:

∂p 1  = − ∇.J p − U p q ∂t

(3.3)

where ND+ and NA- are the ionized impurity concentrations, ρS is the surface charge density, Jn and Jp are the respective current densities, and Un & Up are the respective net recombination rate for electrons and holes. MEDICI incorporates both Boltzmann and Fermi-Dirac statistics, including the incomplete ionization of impurities.

53

3.2.1.2 Physical Models A number of models are incorporated into the program for accurate simulations. MEDICI supports Shockley-Read-Hall (SRH) (including tunneling in strong electric fields), Auger & direct recombination, and also an additional recombination component at insulator-semiconductor interfaces (described by surface recombination velocity). Both concentration and temperature dependent lifetimes are included. MEDICI provides several mobility model choices, which accounts for scattering mechanism in electrical transport. For low electric fields, several mobility choices are available which includes the effect of local impurity concentration, temperature and carrier-carrier scattering. Along insulator-semiconductor interfaces, the carrier mobilities can be substantially lower than in bulk due to surface scattering. An enhanced surface mobility model [3.2] has been included to consider the phonon scattering, surface roughness scattering and charged impurity scattering. For considering the effects due to high field in the direction of current flow, field-dependent mobility model based on the Caughey-Thomas [3.3] expressions is also available. In order to predict the breakdown voltage accurately, generated carriers due to impact-ionization can be included self-consistently in the solution of the device equations. This method is particularly advantageous in predicting the avalanche-induced breakdown of a reverse biased silicon detector. To simulate the effect of junction curvature (as in case of planar process), lateral doping extension can also be specified. Since ionization coefficients play a significant role in predicting the breakdown voltage accurately, a correct choice of these coefficients is very essential. In MEDICI, the dependence of ionization coefficients on the local electric field and temperature is based on the Selberherr Model [3.4]. The values of the coefficients are found to be best described by Overstraeten and DeMan data [3.5] for the breakdown voltage analysis in the present work.

3.2.1.3 Boundary Conditions MEDICI supports four types of basic boundary conditions: Ohmic contacts, Schottky contacts, contacts to insulators and Neumann (reflective) boundaries. Ohmic

contacts are implemented as simple Dirichlet boundary conditions, in which the surface potential and electron & hole concentrations (ψs, ns, ps) are fixed. The minority and 54

majority carrier quasi-Fermi potentials are equal and are set to the applied bias of that electrode (φn = φp = VBias). The surface potential is fixed to a value consistent with zero -

+

space charge, i.e., n s + N A = p s + N D . Schottky contacts to the semiconductor are defined by a work function of the electrode metal and optional surface recombination velocity. Contacts to insulators generally have a work function, dictating a value for surface potential similar to that used in ohmic contacts. The electron and hole concentrations within the insulator and at the contact are forced to be zero. Along the outer (noncontacted) edges of the devices, homogeneous Neumann boundary conditions are imposed to make sure that the current only flows out of the device through contacts. Additionally, in the absence of surface charges along such edges, the normal component of the electric field goes to zero and current is not permitted to flow from the semiconductor into an insulating region. In general, at the interface between the two different materials, the difference between the normalized components of the respective electric displacements must be equal to the surface charge density present along the interface.

  ε 1 nˆ.∇ψ 1 − ε 2 nˆ .∇ψ 2 = σ s

(3.4)

As discussed in the subsequent chapters, surface charge density (σS) is a very important physical parameter in determining the breakdown performance of silicon detectors. It arises due to fabrication process itself and also due to ionizing radiation damage and is unavoidable. MEDICI incorporates both fixed and trapped charges during simulation.

3.2.2 Numerical Methods In order to solve the semiconductor PDEs described by equations (3.1) - (3.3), these equations are discretized in a simulation grid. The resulting set of algebric equations is coupled and nonlinear, and is solved using non-linear iteration methods.

3.2.2.1 Discretization To solve the device equations on a computer, they must be discretized on a simulation grid. The continuous functions of the PDEs are represented by vectors of function values at the nodes, and the differential operators are replaced by suitable difference operators. Thus, instead of solving 3 unknown functions (ψ, n, p), MEDICI 55

solves for 3N real numbers, where N is the number of grid points. The key to discretizing the differential operators is the Box Method [3.6]. Each equation is integrated over a small volume enclosing each node, yielding 3N nonlinear algebric equations. The integration equates the incoming flux with the sources and sinks inside it. The integrals involved are performed on an element-to-element basis, leading to a simple and elegant way of handling general surfaces and boundary conditions.

3.2.2.2 Nonlinear System Solutions As already mentioned, discretization gives rise to a set of coupled nonlinear equations, which must be solved by nonlinear iteration method. Two approaches are commonly used: Decoupled solutions (Gummel’s method) and coupled solutions (Newton’s method). Newton’s approach, with Gaussian elimination method is by far the most stable solution method. Full Newton is the method of choice for two carrier simulations at high currents. For low current solutions, the Gummel method offers an attractive alternative, in which the PDEs are solved sequentially. MEDICI contains a powerful continuation method (used with two-carrier Newton method) for the automatic tracing of I-V characteristics. This method automatically selects the bias step and boundary conditions appropriately for the bias conditions and is particularly helpful in predicting breakdown voltages.

3.2.2.3 Simulation Grid Grid (or Mesh) plays a very important role in device simulation and its correct allocation is absolutely essential for obtaining accurate results. MEDICI uses a nonuniform triangular simulation grid and can model arbitrary device geometries with both

planar and non-planar surface topographies. The primary goal of the grid generation is to achieve accurate simulation results with the least amount of simulation time. A coarse mesh implies less simulation time but less accurate results whereas a fine grid increases accuracy at the expense of time. This requires a suitable trade-off between the two. Generally, the grid should have most node points where the gradients of the physical quantities (like doping, potential etc.) are the highest and a less dense mesh in a uniform region. User specification is thus, the most difficult aspect of general grid structure. To minimize this effort, MEDICI provides a regridding mechanism that automatically

56

refines an initial grid wherever a key variable varies by more than a specified tolerance. It is seen that distorting a rectangular mesh unavoidably introduces a large number of very obtuse triangles. MEDICI also provides mesh-smoothing procedures to deal with them. An example of a MEDICI mesh is shown in Fig.3.1.

P+

N-

Fig.3.1: A typical MEDICI mesh (regridding is performed around the junction region).

3.2.3 MEDICI Program Description In this work, TMA-MEDICI version 2000.4 is used to analyze the breakdown performance of silicon detectors equipped with metal-overhang. For that, firstly a suitable grid is generated in accordance with the device structure and then the models and the solution algorithms are specified to simulate the electrical characteristics. A command input file needed for the simulation generally has the specific structure/organization ordered in four groups: (a) Structure specification, (b) Coefficient and Material parameters, (c) Solution specification and (d) Input / Output statements. The MEDICI program structure with important command statements and comments is given in Table 3.1. An example of a typical MEDICI program is given in Fig.3.2.

57

Table 3.1: The structure and related command statements of the MEDICI. Command Group Structure Specification

Coefficients & Material Parameters

Solution Specification

Input/Output Statements

Related Statements Mesh

Comments

Initiates the mesh generation or to read a previously generated device structure from a data file.

Region

Specifies the location of material regions in the structure.

Electrode

Specifies the location of electrode in the structure.

Profile Regrid Stitch

Specifies impurity profile for the structure. Allows refinement of coarse mesh. Append the generated structure to the simulation mesh.

Material Mobility

Specifies material properties. Specifies parameters associated with mobility models.

Impurity Contact Interface Models

Specifies parameters associated with impurities. Specifies parameters associated with electrodes; specifies special boundary conditions. Specifies interface parameters for the structure. Enables the use of physical models during solution.

Symbolic Method Solve

Performs a symbolic factorization. Sets parameters associated with solution algorithms. Generates solutions for specified biases.

Extract Plot.1d

Plot.3d Contour Log Load

Extracts selected data over device cross-section. Plots a quantity along a line through the structure; plots terminal characteristics from data in a log file. Plots device boundaries, junctions, and depletion edges in two dimensions. Initiates three-dimensional plots. Plots two-dimensional contours of a quantity. Specifies files for storing terminal and user-defined data. Reads a solution stored in a file.

Save

Writes solution or mesh information to a file.

Plot.2d

58

$ An example of a typical MEDICI program $ Create an initial Simulation Mesh and save the mesh file MESH OUT.F= X.MESH X.MAX= H1= H2= H3= Y.MESH N= location= ratio= Y.MESH Y.MAX= H1= H2= H3= $ $ Region Definition REGION NAME= $ $ Electrode Definition ELECTR NAME= x.min= x.max= y.min= y.max= $ $ Specify Impurity Profiles PROFILE N-TYPE N.PEAK= x.min= x.max= y.min= y.max= $ $ Specify Surface Oxide Charge Density at the Si-SiO2 Interface (say 3x1011 cm-2) INTERFAC QF=3E11 $ $ Material Specifications, All parameters are set by default values, but I want to show $ how to specify user defined values. If I want to change the band-gap of Silicon from 1.08eV $ (default) to another value, say 1.12eV, we may write MATERIAL REGION= EG300 =1.12 $ Define Models, example Shockley Read Hall recombination with concentration $ dependent lifetimes, concentration dependent mobility and impact ionization model MODEL CONSRH CONMOB IMPACT.I $ $ Solution for zero bias using Gummel algorithm SYMB GUMMEL CARRIERS=0 METHOD ITLIMIT=20 SOLVE v<electrode>=0 $ $ Switch to Newton for high biases with two carriers SYMB NEWTON CARRIERS=2 METHOD ITLIMIT=20 $ Save log file for I-V plot LOG OUT.F= $ $ Now start the solutions and save the solution file using continuation method SOLVE CONTINUE electrod= c.vstep= c.vmax= c.imax= SAVE OUT.F= $ END

Fig. 3.1: Example of a MEDICI program.

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3.3

Validation: An Absolute Requirement A major drawback with computer models is the way they are used. It is not difficult

to get wrong results from simulation. Using the wrong input parameters, a mesh which is too coarse, or using a model outside its range of validity can each lead to incorrect answers. Thus, the models of the physical systems, which we choose to use, cannot be trusted without extensive validation and it is essential to subject the results of simulations to very rigorous scrutiny. The only way to test the validity of the simulation results is by comparison with experiments. In order to support the simulation analysis in this work, TMA-MEDICI has been calibrated against the experimental data reported in literature. Since a part of this thesis deals with the simulation of metal-overhang detectors (both passivated and unpassivated), experimental data available on such structures are reported and simulated in subsequent chapters. A very good agreement between the experiments and simulations is found, thus validating the present effort.

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Chapter 4

---------------------------------------------------------------Effect of Metal-Overhang on Silicon Strip Detectors ---------------------------------------------------------------The contribution of Si microstrip detectors to the past and present generation High-Energy Physics (HEP) experiments can hardly be overemphasized. Their exploitation in future, high luminosity colliders, like LHC where the unprecedented luminosity levels will be unleashed, however, requires some serious issues concerning radiation hardness to be carefully considered. For example, progressive radiation damage suffered by operating detectors influences their performance in many respects: most notably bulk defects are introduced, acting as deep-level traps, and this eventually results in the “type-inversion” phenomena [4.1]. This, inter-alia, lowers the Charge Collection Efficiency (CCE) of the working detectors [4.2]. In order to compensate for the performance degradation induced by the radiation, the detector bias voltage needs to be progressively increased so that full depletion can be eventually attained anyway [4.3], thus potentially leading to the occurrence of the early micro-discharges and avalanche breakdown. Hence, one of the main aim in the development of Si detectors is to solve this problem. Such phenomena, however, are inherently “localized” at some device critical regions, strip-edge or surface, so that careful design strategies may help in pushing the device operating limit farther away. In particular, with reference to Si microstrip detectors, the adoption of overhanging metal contacts has been suggested as an effective mean to reduce junction breakdown risks [4.4]. In this chapter, we will first briefly discuss about the techniques used in Si detectors to improve the breakdown performance and then a report on the investigations done so far on the Metal-Overhang (MO) analysis is presented. A computer based analysis of Si microstrip detectors will then be discussed with the aim of investigating the

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influence of various physical and geometrical parameters on the breakdown performance of detectors equipped with metal-overhang.

4.1

High-Voltage

Si

Detectors:

Techniques

to

Improve

Breakdown Voltage The introduction of low-noise planar technology to the Si detectors fabrication by Kemmer [4.5] has certainly helped in adapting Si sensors to the vastly different needs of HEP experiments, for example, in vertex determination, in electromagnetic calorimeter and in relativistic particle detection. However, in the planar technology, the plane-portion of the junction is terminated by the curved regions. Electric field crowding at these curved regions severely limits the breakdown voltage [4.6]. Several junction termination techniques have been developed, both for power devices and for detector development. In power devices and in IC technology, floating Field Limiting Ring (FLR) (or the guard ring) [4.7], Junction Termination Extension (JTE) [4.8], REduced SURface Field (RESURF) [4.9], Variation in Lateral Doping (VLD) [4.10] and Field Plate (FP) [4.11] (a more common name of “Metal-Overhang” (MO) in power devices) are found to be suitable. However, for detector-grade planar Si technology, only FLR and MO have been found to be attractive as these techniques are simple in fabrication and suitable for vertical current flow devices. The FLR technology has already been studied extensively by many investigators [4.12 - 4.15] and this has resulted in a considerable improvement in the design of detectors. Multiguard structures, however, suffer from instabilities caused by high electric fields and surface charges [4.16]. An alternative strategy to minimize the instabilities caused by the oxide charges and improve the breakdown performance of Si detectors is the implementation of the “Metal-Overhang” (MO) technique, proposed by Ohsugi et al. [4.4]. The adoption of “overhanging” metal contacts helps in distributing the electric field, reducing corner effects and thus minimizing breakdown risks. This technique is attractive for Si strip detectors also because of its small area and minimized dead wafer space.

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4.2

Modulation of Electric Field by Extended Electrode: Origin of Metal-Overhang Technique Ohsugi et al. [4.4, 4.17, 4.18] investigated the early micro-discharge phenomena

(and also the avalanche breakdown) due to the high fields that occur along the junctionstrip edge inside Si bulk, which is potentially a serious problem in operating the Si sensors in a high radiation environment. They found that there are three major sources of the high fields along the strips: 1.) Bias effect - reverse bias applied to the sensor to achieve full depletion, 2.) Metal-Oxide-Semiconductor (MOS) effect – due to the potential difference between the external readout electrode and the implant-strip, which is a specific problem to the AC coupled readout sensors, and 3.) Oxide charge effect – due to the charge trapped at an interface between SiO2/Si or at defects inside the SiO2. On the basis of this understanding of the causes of micro-discharge, they proposed some new ideas of improved geometry. The first one was a simple idea to weaken the field strength around the strip-edge by rounding off the implant-strip edge (by increasing the junction depth). The second idea was to “relax” the corner field of the implant-strip by adding an extended electrode, which was placed on the SiO2, and is called “Metal-Overhang” (MO), having the same potential as the implant-strip. A definite advantage of the overhang structure is also seen as reducing the effect of the oxide charge trapped in the Si/SiO2 interface. In fact, except for the MOS effect, all these arguments were also found to be applicable to the single-sided and/or direct-coupled sensors. The idea of the extended-electrode was also encouraged to be applied in conjunction with the FLR technique to suppress both the micro discharge and the junction breakdown. The work was well supported by the experimental results on the sensors irradiated with γ−rays. The physical explanation of this observation, in terms of potential and electric field distribution using 2-D device simulation, was provided by Passeri et al. [4.19] (simulated structure is shown in Fig.4.1). They studied the influence of MO width on the strip-pitch (P) and strip-width (W). A significant increase in the breakdown voltage was also obtained with overhanging electrodes for heavily irradiated structures, and this behaviour was confirmed by performing experimental measurements. The usefulness of MO equipped detector in improving the breakdown performance of heavily irradiated 63

structure was also experimentally verified by Demaria et al. [4.20]. In fact, for these reasons, the adoption of MO has recently been assumed as a baseline design requirement for detectors to be installed at the inner tracker [4.21] and also in the Preshower Detector of CERN CMS experiment [4.22].

Fig.4.1: Cross-sectional schematic of the MO equipped structure used by Passeri et al. [4.19]. Beck et al. [4.23] showed the robustness of this technique to the oxide charges, which for detectors is relatively important and becomes more so as a result of ionizing radiation damage. The importance of MO in improving the breakdown voltage of the Si detectors is also boosted by the fact that it can be used in conjunction with other field termination technique, for example with field limiting ring as reported by some authors [4.24, 4.25]. It is worth mentioning here that the use of MO (or “field plate”) has earlier been proposed in Ref. [4.26, 4.27] in HEP experiments. However, in the former [4.26], it is considered as a tool to study the effect of surface charges as MO offers the possibility of changing the surface charge density during operation of the detectors by simply changing its potential. In [4.27], it is used for a different Si detector technology, the surface barrier detectors (Schottky effect) in H1/HERA experiment. None of them, however, studied the effect of MO on junction termination. Many contributions on the study of MO can also be found in the technical literature together with analytical works for the conventional diodes [4.11, 4.28 – 4.31]. In fact, the use of “field plate effect” in power devices dates back to 1967, when Grove & Fitzgerald [4.28] showed that the breakdown voltage of either p+/n or n+/p junctions can be modulated over a wide range by the application of an

64

external surface field. F. Conti & M. Conti [4.11] made a detailed analysis of the breakdown voltage by means of an analytical mode and computer simulation for fieldplate junctions. Since then, many workers have investigated and analyzed the field-plate technique for application in power devices and IC technology [4.29 – 4.33]. However, the optimization procedure developed in these reports needs to be reconsidered when MO is applied to the Si sensors in HEP experiments for the following reasons: 1.) These studies were developed over ten years ago and they were mainly committed to the power device and IC technology. When MO is applied to the Si detectors, changes in process parameters like substrate resistivity, implant profile, passivation layer material and thickness etc. must be taken into account. Although some of the works on power devices are very detailed but they suffer from the fact that every result strongly depends on the technology used. Moreover for IC fabrication, both n-type and p-type silicon are used, doping concentration used are much higher and the life time of minority carriers are some orders of magnitude lower. For silicon detector fabrication, p+-n junctions are obtained on high resistivity substrates (NB ~ 1011 - 1012 /cm3), typically a few hundred microns thick on n-type silicon of <111> orientation are used. Minority carrier lifetimes are extremely high to have low leakage current. 2.) The irradiation induces modifications of the electrical behaviour of the Si sensors and hence the optimization must take care of the effects of the irradiation also. 3.) All the breakdown voltage analysis of the junction without MO & with MO were based on the integration of the ionization coefficients along a radial path, on the assumption that the field is cylindrically symmetric at the edge of the planar junction, and good agreement with the measurement has been demonstrated in the bulk doping range (NB) ~ 1014 - 1016 /cm3 & for junction depth (XJ) > 1.0 µm. However, it should be expected that in the practical planar structure of interest, the presence of the planar region results in a larger depletion radius and reduced field strength at the termination compared to the pure cylindrical junction. The radial field approximation should consequently become less accurate as either substrate doping concentration and/or junction depth is reduced [4.23].

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Experimental work reported in literature clearly suggests that the MO technique is simple and versatile and therefore, it is attractive for wide range of blocking voltages in Si strip detectors. However, almost all the work done on the Si detectors with MO [4.4, 4.17, 4.18, 4.19, 4.23] are more concerned about the overhang design dependence on the strip-width/strip-pitch and oxide charges. Thus, despite the significant developments in the performance of MO technique, none of the investigations done so far have reported the influence of the various geometrical and physical parameters taken altogether, like oxide thickness and junction depth on the breakdown performance of MO equipped detectors. In particular it is found that a simple, general and widely applicable design consideration is lacking even for structures having uniform field oxide under the MO. A complete analysis of the structure equipped with metal-overhang correlating the breakdown voltage to these parameters is of great importance for optimization purpose. In the present work, effect of the various parameters on the breakdown performance of the Si microstrip detector is analyzed to achieve design optimization. The parameters are: 1) tOX, thickness of oxide below metal-overhang, 2) XJ, radius of cylindrical junction, 3) WN, thickness of n-layer below the field oxide, 4) NB, substrate doping concentration, 5) WMO, width of metal-overhang and 6) QF, surface charge density. A judicious choice of these parameters is required to achieve the maximum realizable breakdown voltage. The optimization of the various parameters is performed using two-dimensional device simulation program, TMA-MEDICI, version 2000.4 [4.34].

4.3

Device Structure Used in Simulation The detailed knowledge of the applied detector technology is an essential input

for correct device simulations. As already mentioned, the fabrication of detectors used in the present study is currently in progress at Bharat Electronics Ltd. (BEL), India, to be used in the Preshower detector of CMS at LHC, CERN and hence the parameters used in the simulation are assumed on the basis of the technological process characteristics. A cross-section of the simulated device structure analyzed in the present work (Fig.4.2), consists of a two-strip subset of a single-side micro-strip array with metaloverhang. The structure is symmetric around the center of the device so only one half of

66

the cross-section of each of the strip had to be taken into account. Such a detector is built on an n-type, 4 KΩ-cm (NB ~1x1012 /cm3), 300 µm thick and <111> oriented Si wafer. The p+ strips doping profile is Gaussian with a peak surface concentration of 5x1019 /cm3. The p+-n junction is assumed to be cylindrical at its edge with the lateral curvature equal to 0.8 times the vertical junction depth. Depletion is achieved by positively biasing the back ohmic contact. Al electrode extending over the thicker oxide, which covers the interstrip gap, acts as a metal-overhang. For simulating the effect of surface charge, it is assumed that all the trapped charges are located at the Si-SiO2 interface. This typically results in an equivalent surface charge density (QF) of the order of 3x1011 /cm2 for the non-irradiated detector with moderately good oxides, whereas the amount of trapped charge is expected to saturate at 1.0x1012 /cm2, even under heavy irradiation condition, for the <111> Si orientation used in detector fabrication [4.35].

Fig.4.2: Cross-sectional schematic of two-strip subset of a Si strip detector with metaloverhang.

67

4.4

Influence of Various Parameters on Silicon Strip Detector Equipped with Metal-Overhang As mentioned earlier, the parameters which determine the breakdown voltage

(VBD) of the metal-overhang structure are: 1.) tOX : thickness of oxide below metal overhang, 2.) XJ : radius of cylindrical junction, 3.) WN : thickness of n-layer below the field oxide 4.) NB : substrate doping concentration 5.) WMO : width of metal-overhang and 6.) QF : density of surface charge These parameters can be classified into two categories: Substrate parameters and process parameters. The substrate parameters WN and NB depend on the silicon substrate chosen; a careful and judicious choice of this is necessary. The process parameters tOX, XJ, QF and WMO can be tailored during process to obtain desired results. Therefore, in order to achieve design optimization, the effects of these parameters are presented in subsequent sections.

4.4.1 Comparison between the structures without and with metaloverhang A first simulation result is shown in figures 4.3 - 4.6, which compare the 2-D equipotential distribution, surface electric field, 3-D avalanche generation and the I-V plot for a device featuring no overhang and a 30 µm wide overhang respectively. Due to the junction curvature the Space Charge Region (SCR) also extends laterally, however, at the surface the electron accumulation layer underneath the oxide in structures without MO prevents this extension. Thus, the applied voltage drops across a shorter distance (Fig.4.3(a)). This results in the potential crowding and hence a local increase in electric field (Fig.4.4) at the junction curvature. Hence the avalanche generation initiating breakdown occurs close to the Si-SiO2 interface. When the overhanging contact is present, it acts there as a p-channel MOS gate, which under the given bias conditions, suppresses the accumulation layer and tends to deplete the underlying region. This

68

“pushes” the potential gradient away from the implant corner (Fig.4.3(b)) and hence distributes the potential more uniformly as compared to a structure without metaloverhang. Thus, metal-overhang reduces the crowding of the electric field within the Si substrate by distributing it at two points: One situated near the curved portion of the junction (‘A’ in Fig.4.2) and the second near the metal-overhang edge (‘B’ in Fig.4.2). In this way it decreases the maximum electric field within the silicon substrate (Fig.4.4) and thus, at a given bias, impact-ionization carrier generation is less for a MO structure (Fig.4.5) and hence its breakdown voltage (VBD) is considerably large as compared to a structure without MO (Fig.4.6).

Fig.4.3: 2-D potential distribution within the device for a structure (a) without metaoverhang & (b) with metal-overhang of width 30 µm at VBIAS = 500 volt. Values of the parameters used for simulation are: XJ = 1.0 µm, tOX =1.6 µm, WN = 300 µm, NΒ=1x1012/cm3 & QF=0.

69

Fig.4.4: Surface electric field for a structure (a) without metal-overhang & (b) with metal-overhang of width 30 µm at VBIAS = 500 volt. Values of the parameters used for simulation are: XJ = 1.0 µm, tOX =1.6 µm, WN = 300 µm, NΒ=1x1012/cm3 & QF=0.

Fig.4.5(a): 3-D impact-ionization carrier generation rate for a structure without metaloverhang at VBIAS = 500 volt. Values of the parameters used for simulation are: XJ = 1.0 µm, tOX =1.6 µm, WN = 300 µm, NΒ=1x1012/cm3 & QF=0. 70

Fig.4.5(b): 3-D impact-ionization carrier generation rate for a structure with metaloverhang of width 30 µm at VBIAS = 500 volt. Values of the parameters used for simulation are: XJ = 1.0 µm, tOX =1.6 µm, WN = 300 µm, NΒ=1x1012/cm3 & QF=0.

Fig.4.6: I-V characteristics for a structure without metal-overhang & with metaloverhang of width 30 µm. Values of the parameters used for simulation are: XJ = 1.0 µm, tOX =1.6 µm, WN = 300 µm, NΒ=1x1012/cm3 & QF=0.

71

Qualitatively, the effect of metal-overhang can be very well explained in terms of the charge interaction that take place between (1) the positive space charge in the n-side depletion region, (2) the negative space charge in the p+ side depletion region and (3) the negative charge in the metal overhang, as shown in Fig.4.7.

Fig.4.7: Cross-sectional schematic of a metal-overhang structure showing the charge distribution in the space charge region and in the metal-overhang. For convenience, the positive space charge in the n-side depletion region is divided into 4 parts: (i) QPP: in the plane-parallel part of the n-side depletion region beneath the p+ junction. (ii) QCY: in the curved portion of the n-side depletion region around the junction curvature. (iii) QPP-MO: in the plane-parallel part of the n-side depletion region under the metaloverhang. (iv) QCY-MO: in the curved portion of the n-side depletion region around the MO edge. In the planar junction termination without MO, only the first two components (i) and (ii) are present, whereas in the structures equipped with MO, (iii) & (iv) are also present, which strongly modify the potential and electric field distribution. In a planar cylindrical junction without MO, the electric flux lines emanating from the positive QCY terminate on the negative space charge in the curved portion of the p+ side depletion region. Since the electric flux per unit area crossing the curved portion of the junction is more than that at the plane portion of the junction, there is a field crowding at the curved portion. This field crowding limits the VBD of such junctions to values much lower than that of an ideal plane-parallel junction. 72

In the planar junctions equipped with MO, the electric flux that emanates from positive QCY terminates not only on the negative charge on the cylindrical portion but also on the negative charge on the metal-overhang. As a consequence, the potential is now distributed between the junction curvature and the MO edge, which in turn reduces the field crowding and increases the breakdown voltage. However, in this case it should be noted that the capacitive coupling between the QCY-MO and negative charge on the metal-overhang also takes place, and hence the breakdown of this structure can take place either at the junction curvature or at the MO edge. In short, the space charge region on the lightly doped side (n) of the junction is primarily responsible for causing a severe field crowding at the curved portion of the junction when the overhang is absent. However, in the presence of overhang, this charge interacts very strongly with the charge on the metal overhang thereby leading to the dramatic reduction in the field crowding at the junction curvature.

4.4.2 Effect of Field-Oxide Thickness Due to the qualitative similarity between the field crowding at the MO edge and at the junction curvature, the thickness of the oxide (tOX) in the MO structure plays a role similar to the junction depth. Fig.4.8 shows the plot of VBD vs tOX for XJ =1.0 µm. It can be seen that VBD increases with increase in tOX, attains a maximum value corresponding to a certain optimum oxide thickness tOX(OPT) and then decreases for further increase in tOX. Thus, tOX(OPT) apparently divides the whole plot into two regions, i.e., tOX < tOX(OPT) and tOX > tOX(OPT). In order to understand this behaviour, maximum electric field within the device (both at the MO edge and at the junction curvature) vs. oxide thickness is plotted in Fig.4.9. In the region tOX > tOX(OPT), and for very thick oxides (For example, tOX = 12 µm) the space-charge in the substrate does not interact appreciably with the charges on metaloverhang and hence the potential crowding at the junction curvature remains same as it would be without metal-overhang. Thus, the dominant peak electric field (Fig.4.10(a)) and the avalanche breakdown occurs at the junction curvature only.

73

4400 tOX < tOX(OPT)

4200

tOX > tOX(OPT)

Breakdown voltage(volt)

4000

tOX(OPT)

3800 3600 3400 3200

XJ=1.0 micron 12

3

NB=1x10 /cm WMO = 30 microns WN =300 microns

3000 2800

QF = 0 2600 2400 2200 -2

0

2

4

6

8

10

12

14

16

Oxide thickness (microns)

Fig.4.8: Breakdown voltage vs. field-oxide thickness. 1.4E+05

at junction curvature ('A' in Fig.4.2)

Maximum elcetric field (volt/cm)

1.2E+05

tOX(OPT)

1.0E+05

8.0E+04

XJ=1.0 micron

6.0E+04

NB=1x1012 /cm3 WMO = 30 microns WN =300 microns QF = 0

tOX > tOX(OPT)

tOX < tOX(OPT)

4.0E+04

2.0E+04

at MO edge ('B' in Fig.4.2)

0.0E+00 -2

0

2

4

6

8

10

12

14

oxide thickness (microns)

Fig.4.9: Maximum electric field (at the junction curvature and at the metal-overhang edge) vs. field-oxide thickness at VBIAS = 500 volt.

74

However, as the field-oxide thickness is reduced (For example, tOX = 4 µm), the coupling between the positive QCY and the negative charge on the metal-overhang increases, thus “pushing” the potential crowding away from the junction curvature to the overhang edge. This reduces the peak surface electric field at the junction (Fig.4.9). However, at the same time, the capacitive coupling between the positive QCY-MO and the negative charge on the MO increases, and hence an increase in the peak surface field at the MO edge is also observed (Fig.4.9). Thus, as shown in Fig. 4.9, in the region tOX > tOX(OPT) as tOX is reduced, there is a systematic decrease in the peak electric field at the junction curvature with the simultaneous increase in the field at the overhang edge. Due to this distribution, the overall field distribution becomes milder and the maximum electric field within the Si bulk decreases, hence the breakdown voltage increases. At optimal oxide thickness, i.e., for tOX = tOX(OPT) the field distribution is such that the maximum electric field within the device is almost same at the overhang edge and the junction curvature (Fig.4.10(b)), and the impact-ionization simultaneously occurs at the two edges. Since the maximum electric field within the device (either at the junction curvature or at the MO edge) for this case (tOX = tOX(OPT)) is less than that for any other value of the oxide thickness (Fig.4.9), we get the maximum breakdown voltage. For further reduction in tOX, i.e. in the region tOX < tOX(OPT), the coupling between the QCY and the negative charge on the metal increases continuously, which “pushes” the potential crowding further away from the junction edge, so the peak surface electric field at the junction edge is reduced. However, at the same time the interaction between the QCY-MO and metal charge becomes so strong that a dominant electric field now appears at the MO edge (Fig.4.10(c)). Thus, in this region, as tOX is reduced the peak electric field at the MO edge (and hence in the device) increases (Fig.4.9) and hence VBD decreases.

75

Fig.4.10: Surface electric field plot for a structure with metal-overhang of width 30 µm at VBIAS = 500 volt for (a) tOX > tOX(OPT), (b) tOX = tOX(OPT), and (c) tOX < tOX(OPT).

76

This picture can also be understood by looking at the impact-ionization carrier generation rate at VBIAS = 500 volt as shown in Figures 4.11(a), 4.11(b) and 4.11(c). It can be seen that for the region tOX > tOX(OPT), VBD takes place at the junction curvature (Fig.4.11(a)) and for tOX < tOX(OPT) it occurs beneath the MO edge (Fig.4.11(c)). For tOX = tOX(OPT) (Fig.4.11(b)), it simultaneously takes place at the two edges (carrier generation is almost same along the two paths). The field distribution is such that the generation rate is minimum for tOX = tOX(OPT) and hence the maximum breakdown voltage is obtained for this case.

Fig.4.11: 3-D impact-ionization carrier generation rate plot for a structure with metaloverhang of width 30 µm at VBIAS = 500 volt for (a) tOX > tOX(OPT) & (b) tOX = tOX(OPT). Values of the parameters used for simulation are: XJ = 1.0 µm, tOX =1.6 µm, WN = 300 µm, NΒ=1x1012/cm3 & QF=0. 77

Fig.4.11(c): 3-D impact-ionization carrier generation rate plot for a structure with metal-overhang of width 30 µm at VBIAS = 500 volt for tOX < tOX(OPT). Values of the parameters used for simulation are: XJ = 1.0 µm, tOX =1.6 µm, WN = 300 µm, NΒ=1x1012/cm3 & QF=0.

4.4.3 Effect of Junction Depth Fig.4.12 shows the plot of VBD vs tOX with junction depth (XJ) as a running parameter. The qualitative behaviour of the VBD is same for all values of XJ. An interesting point to note from the figure is that for the region tOX < tOX(OPT), VBD is almost same for all values of XJ, i.e., VBD is independent of XJ whereas in the region tOX > tOX(OPT), VBD is heavily dependent on XJ.

Breakdown voltage (volt)

4000 3600 3200

XJ=3.5 micron

2800

XJ=2.0 micron NB=1x1012/cm3 WMO = 30 microns WN = 300 microns QF = 0

2400 2000

XJ=1.0 micron XJ=0.5 micron XJ=0.2 micron

1600 0

2

4

6

8

10

12

14

Oxide thickness (microns)

Fig.4.12: Breakdown voltage vs. field-oxide thickness with junction depth as a running parameter.

78

To understand this nature, we have plotted the surface electric field for three different values of XJ in figures 4.13(a) and 4.13(b). From Fig.4.13(a), it is clear that in the region tOX < tOX(OPT) the peak surface electric field value within the value (which occurs at the MO edge) is almost same for all values of XJ. The magnitude of the surface electric field and the MO edge breakdown in this region, hence, depends only on the tOX and is independent of XJ. For tOX > tOX(OPT), the avalanche takes place at the junction curvature and hence in this situation XJ plays an important role in determining VBD. It is known that when the value of XJ is increased, the electric flux per unit area at the curved portion decreases and therefore the field crowding reduces. This is also featured in the Fig.4.13(b), where it can be seen that as XJ increases, the peak surface electric field at the junction decreases substantially. Thus, in this region VBD increases with increase in XJ.

Fig.4.13: Surface electric field plot for a structure with metal-overhang of width 30 µm at VBIAS = 500 volt for different values of junction depth (a) tOX < tOX(OPT) and (b) tOX > tOX(OPT)). 79

Another important feature, which is conspicuous from Fig.4.12, is that in the region tOX > tOX(OPT), a given variation in the field oxide thickness effects a larger change in the VBD for a shallow junction than for a deep junction. For instance, when the oxide thickness is reduced from 12 µm to 1.6 µm, VBD increases from 2090 volt to 3660 volt (~ 75%) for XJ = 0.2 µm, whereas it increases from 3160 volt to 3900 volt (~ 23%) for XJ = 3.5 µm. This is because the capacitive coupling between the positive space charge and the negative charge on the MO is stronger for a shallow junction than for a deep junction as the distance separating these two charges is smaller in a shallow junction. Also for a given value of metal-overhang, tOX(OPT) required for achieving VBD depends upon the value of XJ (Table 4.1). Table 4.1: Breakdown voltages for different junction depths corresponding to optimized oxide thickness for WMO=30 microns. XJ (micron)

tOX(opt) (micron)

VBD(volt)

0.2

1.2

3800

0.5

1.2

3900

1.0

1.6

4015

2.0

1.6

3950

3.5

2.0

3900

Fig.4.14 shows the variation in the maximum breakdown voltage vs. junction depth for a structure with metal overhang under the optimal conditions. For comparison, the breakdown voltage of the structure without MO is also shown. In the absence of metal-overhang, breakdown voltage increases when the junction depth increases. For MO equipped structures, it can be seen that the VBD achieved for tOX(OPT) goes through a maximum for certain optimum junction depth XJ(OPT). For XJ < XJ(OPT), the maximum VBD increases with increase in XJ due to junction curvature effect and for XJ > XJ(OPT), VBD decreases due to reduction in n-layer thickness below the junction. However, the maximum VBD obtained under the optimal condition does not appreciably vary with XJ. From Fig.4.14, it can again be seen that the beneficial effects of the MO structure are more pronounced for the shallow junctions (as the difference in VBD between the two

80

curves is more for a shallow junction than for a deep junction). This is of great help for HEP experiments where shallow junctions are desired in order to have small dead layer. 4500 tOX = tOX(OPT)

Maximum breakdown voltage (volt)

4000 3500 3000

without metal-overhang

2500 2000 1500 NB = 1x1012/cm3 WN = 300 microns WMO = 30 microns QF = 0

1000 500 0 0

2

4

6 8 10 Junction depth (microns)

12

14

16

Fig.4.14: Breakdown voltage vs. junction depth without metal-overhang and with metal overhang of 30 µm (for optimum oxide thickness). However, it must be pointed out that if the metal-overhang does not extend for sufficiently large distance beyond the edge of the junction, VBD no longer remains sensitive to tOX and the effect of metal-overhang for such structures is practically negligible. This is evident from Table 4.2, which shows the values of VBD for different values of tOX for a structure with XJ = 15 µm. It is clear that for XJ = 15 µm and WMO = 30 µm, VBD shows only marginal increase (~ 7%), as the values of tOX increase by over an order of magnitude. This is because such a small width of metal-overhang is not sufficient to provide the flattening of equipotential lines for the large values of junction depth and consequently has no effect on VBD.

81

Table 4.2: Variation of breakdown voltage vs. oxide thickness for XJ=15 microns and WMO=30 microns. tOX(microns)

VBD (V)

0.4

3600

0.8

3650

1.2

3750

1.6

3750

2.0

3800

4.0

3850

12.0

3850

4.4.4 Effect of the Width of Metal-Overhang Fig.4.15 shows the variation of VBD with oxide thickness for different values of MO width (WMO). Again the VBD of the structure without metal-overhang is also shown for comparison. It can be seen that VBD increases with the increase in WMO, which is due to the flattening of the equipotential lines near the junction edge. The limiting value of VBD is approached as soon as the equipotential lines spread out to the maximum possible extent and then VBD becomes almost constant for further increase in WMO. However, for microstrip detectors, strip-pitch becomes a limiting factor for deciding WMO. Interstrip capacitance (Cint) also increases with the increase in WMO, which in turn results in increasing noise. Hence it is necessary to optimize WMO depending upon the specification needed for a particular detector operation. In Si Preshower detector at CMS with large strip-pitch and device depth, back-plane capacitance plays a dominant role in the totaldetector capacitance. Hence, the increase in VBD due to increase in WMO can be taken as a guiding factor in deciding the width of metal-overhang.

82

4000 3500

XJ=0.2 microns NB = 1x1012 /cm 3 WN=300 microns QF = 0

Breakdown Voltage(volt)

3000 2500

WMO = 30 microns

2000

WMO = 20 microns WMO = 10 microns

1500 1000

Without metal-overhang

500 0 0

2

4

6

8

10

12

14

16

Oxide thickness(micron)

Fig.4.15: Breakdown voltage vs. field-oxide thickness with width of metal-overhang as a running parameter. The influence of the increasing the width of the metal-overhang can be perhaps more easily understood by looking at the electric field distribution within the device near the junction curvature and the metal-overhang edge (Fig.4.16): the action of the increase in the width of metal overhang, which “pushes” the potential gradient and hence the field crowding away from the implant corner can be straightforwardly appreciated there. For a simple case of no-overhanging structures, a field peak is located at the p+ edge (Fig. 4.16(a)). A systematic decrease of electric field amplitude within the silicon substrate is observed as WMO is increased, clearly showing the benefits of increasing the extension of overhang. It should be noted that the effect of increasing the extension of the metal contact significantly enhances the electric field amplitude within the SiO2. Nevertheless, due to the much higher breakdown critical fields, discharge phenomena within the oxide are not of practical concern, at least within the usual operating voltage range of silicon detectors.

83

Fig.4.16: 2-D electric field distribution plot at VBIAS = 500 volt for tOX = 0.4 µm & XJ = 0.2 µm for structure with (a) no-overhang, (b) WMO = 10 µm, (c) WMO = 20 µm, (d) WMO = 30 µm, and (e) WMO = 40 µm.

84

Also, for a given XJ, tOX(OPT) takes different values for different values of WMO as listed in Table 4.3.

Table 4.3: Breakdown voltages for different metal-overhang widths corresponding to optimized oxide thickness for XJ=0.2 microns. Wmo(micron)

tOX(opt) (micron)

VBD(volt)

10

0.8

2660

20

1.2

3370

30

1.2

3800

4.4.5 Effect of Substrate Parameters: Device-Depth and Substrate Doping Concentration It is well known that for the punch through diodes, device depth (WN) primarily determines the breakdown voltage of p+-n- -n+ junction. Fig.4.17 shows that the VBD increases with the increase in WN for all values of tOX. The maximum VBD occurs at the same value of tOX(OPT) for all WN.

4500 XJ=1.0 microns

4000

12

3500 Breakdown Voltage(volt)

3

NB=1x10 /cm WMO=30 microns QF = 0

3000

WN=300 microns

2500 WN=200 microns

2000 1500

WN=100 microns

1000 500 0 0

2

4

6

8

10

12

14

Oxide thickness (microns)

Fig.4.17: Breakdown voltage vs. field-oxide thickness with device-depth as a running parameter.

85

Also it is known that for Punch Through (PT) diodes, substrate doping concentration (NB) has a negligible influence on the breakdown voltage of the planeparallel junction [4.36]. However, in the planar devices with cylindrical termination, NB affects the optimal conditions and the breakdown voltage. To study the effect of NB on the planar MO terminated junctions, we have varied the doping concentration from 5x1011 /cm3 to 5x1012 /cm3. These concentrations approximately correspond to the resistivity of about 1 – 10 KΩ-cm, which are close to the resistivity of the silicon wafers used for Si detector fabrication. Table 4.4 lists the variation in the optimal oxide thickness and maximum breakdown voltage as a function of NB. It can be seen that the maximum VBD decreases only marginally and the optimal oxide thickness increases with an increase in NB. Table 4.4: Breakdown voltages for different values of substrate doping concentration corresponding to optimized oxide thickness for XJ=1.0 microns (WMO = 30 µm). NB(/cm3)

tOX(opt) (micron)

Maximum VBD(volt)

5x1011

1.1

4080

7.5x1011

1.3

4050

1x1012

1.6

4015

2.5x1012

1.7

3950

5x1012

1.9

3900

4.4.6 Effect of Surface Charges Till now we have been considering the ideal condition for Si/SiO2 interface in simulation, where the interface was assumed to be charge free. However, in practical Si detectors, interface traps and oxide charges exist, that, in one way or another, affects the ideal interface characteristics. The basic classification of these traps and charges are shown in Fig.4.18 [4.37], and described below. (1.) Interface trapped charges, located at the Si/SiO2 interface with energy states in the Si forbidden bandgap, can exchange charges with Si in short time. However, most of the interface charge can be neutralized by low-temperature hydrogen annealing [4.37].

86

Fig.4.18: Charges associated with the thermally oxidized silicon [4.37]. Value of x in SiOx lies between 1 & 2.

(2.) Oxide charges include the oxide fixed charge (QF), the oxide trapped charge (Qot), and the mobile ionic charge (Qm). The fixed oxide charge cannot be charged or discharged over a wide variation of surface potential and hence is “fixed”. It is generally located within the order of 10 Å of the Si/SiO2 interface. It is generally positive and its density depends on the oxidation and annealing conditions, and on the Si orientation. The passage of ionizing radiation in the oxide causes the built up of trapped charge in the oxide layers of the detector by breaking Si-O bonds. The electron-hole pairs created in the oxide either recombine or move in the oxide electric field: the electrons toward the SiO2/Si interface, the holes toward the metallic contact. The electrons are considerably more mobile than the holes and are injected into the Si bulk whereas the less mobile holes drift much more slowly and trapped in the oxide. The trapped holes at the SiO2-Si interface constitute the radiation induced positive oxide trapped charge (Qot). These trapped holes may also be responsible for the increased interface trap density.

87

In simulation, surface damage can be taken into account by properly characterizing the oxide-trapped charge and the surface recombination centers. To a first order approximation, the damage caused by ionizing radiation can also be taken into account by increasing the oxide charge density [4.19, 4.24]. For a p+/n Si detector, these charges are responsible for the dense surface accumulation layer, which in turn results in narrower depletion region along the surface compared to the situation in the planar bulk area or if oxide charges were not present (as shown in Fig.4.19). With a constant bias applied across the depletion region, the contraction of the depletion region at the surface leads to an increase in the electric field in the silicon close to the Si/SiO2 interface and hence results in the premature breakdown of the device.

Fig.4.19: Cross section of a p+-n junction showing that positive oxide charges can increase the lateral field in the depletion layer of a p+-n junction: (a) no oxide charges (b) oxide charges pinching the depletion layer near the Si-SiO2 interface. Surface avalanche breakdown is considered the most common breakdown mechanism for standard silicon detectors. In summary, the breakdown performance of the Si detectors is greatly affected by the presence of surface charges. This prompts us to investigate the effect of oxide charges on the optimal conditions of the MO terminated junctions. Fig.4.20 shows the plot of breakdown voltage as a function of surface charge density (QF) with tOX as running parameter. It can be seen that, as expected, VBD decreases as Qf increases for all values of tOX. However, for tOX > tOX(OPT), the

88

deterioration in VBD is comparatively sharp even for very small values of Qf. In order to understand this behaviour, we have plotted the 2-D potential contours in Fig. 4.21(a, b & c) and Fig. 4.22 (a, b & c) for tOX < tOX(OPT) and tOX > tOX(OPT) respectively. 4500 XJ = 1.0 micron

4000 3500 Breakdown voltage (volt)

NB = 1x1012/cm3 WN = 300 microns WMO=30 microns

tOX = 1.6 micron (tOX = tOX(OPT))

3000 2500

tOX = 0.4 microns (tOX < tOX(OPT))

2000 1500 1000

tOX = 12.0 microns (tOX > tOX(OPT))

500

without metal-overhang

0 0

2E+11

4E+11

6E+11

8E+11

1E+12

1.2E+12

2

Fixed oxide charge density (/cm )

Fig.4.20: Breakdown voltage vs. fixed oxide charge density with tOX as a running parameter. In the region tOX < tOX(OPT), and in the absence of oxide charge the avalanche is located under the MO edge as shown by the potential crowding in Fig.4.21(a). However, this situation is strongly modified by the presence of the oxide charge. As QF is increased, potential crowding increases both at the junction and under the MO edge (figures 4.21(b), 4.21(c) and 4.21(d)). At QF ~ 5x1011/cm2, simulation results indicate that the crowding of equipotential lines at the junction curvature becomes so strong (Fig.4.21(c)) that electric field at the junction edge exceeds its value at the MO edge, and hence the breakdown takes place at the junction curvature. Although, a large fraction of the reverse bias is still sustained beyond the MO edge, as is evident from Fig.4.21(c), a

89

further increase in QF causes a rapid fall towards the unguarded junction value. In conclusion, the MO is screened from the Si bulk as the oxide charge density increases. For tOX > tOX(OPT), breakdown takes place at the junction curvature even for QF =0 (Fig.4.22(a)). Hence the effect of increasing oxide charges results in further dense crowding of the equipotential lines at the junction edge (figures 4.22(b), 4.22(c) & 4.22(d)). In this case the Si bulk is already partially screened from the MO by the thick oxide, and due to the presence of oxide charges, the advantage of using MO is completely lost. In fact the value of VBD for tOX =12.0 µm approaches that of an unguarded junction for large values of QF as indicated in Fig.4.20. The importance of optimization can perhaps be best appreciated from Fig.4.20. It can be seen that for structures without MO, and for MO equipped structures with very thick oxides, the value of VBD reduces to meager ~ 140 volt for QF = 1 x 1012 /cm2 and the silicon sensor would no longer be able to sustain full depletion voltage (VFD). However, optimization of field-oxide thickness presents an attractive alternative, as the VBD for the optimized structure remains 1600 volt, well above the VFD. In fact it can be seen from Fig.4.20 that the VBD obtained for the optimized MO structure is always maximum.

90

Fig.4.21: 2-D equipotential distribution plot at VBIAS = 50 volt in the region tOX < tOX(OPT) with XJ = 1.0 µm and WMO = 30 µm for (a) QF=0, (b) QF=2.5x1011 /cm2, (c) QF=5x1011/cm2, and (d) QF = 1x1012/cm2.

91

Fig.4.22: 2-D equipotential distribution plot at VBIAS = 50 volt in the region tOX > tOX(OPT) with XJ = 1.0 µm and WMO = 30 µm for (a) QF=0, (b) QF=2.5x1011 /cm2, (c) QF=5x1011 /cm2, and (d) QF = 1x1012 /cm2.

92

The effect of oxide charge can also be understood from Fig.4.23 in which the plot of maximum electric field within the device (both at the surface near the junction curvature and at the MO edge) vs. QF is shown for two different values of tOX, i.e., for tOX < tOX(OPT) and tOX > tOX(OPT). It can be seen that as QF increases, maximum electric field at the surface near the junction edge (ES) and at the overhang edge (EMO) increases for both the cases. Due to the formation of accumulation layer, however, increase in ES is more as compared to EMO. Also, it is found that increase in ES is more rapid for tOX = 12 µm than for tOX = 0.4 µm. For instance, as QF is increased from 0 to 2.5x1011 /cm2, ES increases from 1.6 x 104 volt/cm to 16.6 x 104 volt/cm for tOX = 12 microns, whereas it increases from 0.9 x 104 volt/cm to 6.7 x 104 volt/cm for tOX = 0.4 microns. This indicates that for thick oxides, MO is almost completely screened by the oxide charges even for QF = 2.5x1011 /cm2. However, the difference between the values of ES for different tOX goes on decreasing with increased charge level, thus implying that oxide charges play an important role in determining the breakdown voltage in the MO equipped junctions for large values of QF. It must be pointed out that even for QF=1x1012 /cm2, the value of ES for tOX = 0.4 µm is less than that for tOX = 12 µm, indicating that MO still helps in improving the breakdown voltage. 3.5E+05

Maximum electric field (volt/cm)

3.0E+05

tOX = 12 microns (tOX > tOX(OPT)) tOX = 0.4 microns (tOX < tOX(OPT))

2.5E+05 2.0E+05 1.5E+05 1.0E+05

at the surface near the junction edge (ES)

5.1E+04

at the MO edge (EMO) 1.0E+03 0.0E+00

2.0E+11

4.0E+11

6.0E+11

8.0E+11

1.0E+12

1.2E+12

2

Oxide charge density (/cm )

Fig.4.23: Maximum electric field value in the Si substrate vs. field-oxide thickness for two different values of tOX at VBIAS = 50 volt. 93

Another important effect of the QF on VBD is conspicuous from Fig.4.24, where the plot of maximum VBD vs. XJ is shown for two different values of QF. It can be seen that the maximum breakdown voltage of the shallow junctions are more affected by QF as compared to the deep junctions. 3650

Maximum breakdown voltage (volt)

3450

QF = 0

3250

QF = 3x1011 /cm2

3050

2850

2650 NB = 1x1012/cm3 WN = 300 microns WMO = 20 microns

2450

2250 0

2

4

6 8 10 Junction depth (microns)

12

14

16

Fig.4.24: Maximum breakdown voltage vs. junction depth for two different values of QF .

4.5

Comparison with Experimental Work In order to verify the simulated results and to validate the numerical accuracy of

the computer program used in this work, experimental data available in the literature [4.11] and [4.31] on the field-plate diodes were simulated. These results are given in Table 4.5 along with information on the salient parameters of the device structure whose experimentally measured breakdown voltage data are compared with the values estimated in the present work. It can be seen that there is in general a good agreement between the present simulation and experiments, thus validating the present effort.

94

Table 4.5: Comparison of the simulation results with the experimental work. NB(1014/cm3)

XJ

tOX

VBD(volt)

VBD(volt)

(P-E)/P

(micron)

(micron)

Present

Experiment

(%)

work (P)

(E)

0.30

127

137

-8

0.41

142

160

-13

0.56

183

190

-4

0.90

215

225

-5

2.15

553

570

-3

2.65

599

615

-3

8.5 Ref.[4.31]

1.01

5.0

4.0

Ref.[4.11]

4.6

Conclusions Due to high luminosities of the future HEP colliders, Si detectors are required to

sustain very high voltage operation well exceeding the bias voltage needed to fully deplete them. Because of its definite advantages over other termination schemes, the “overhanging” metal contact is an attractive technique for improving the breakdown performance of these detectors. In this chapter, punch through planar Si-microstrip detector with metal-overhang is analyzed taking all the salient physical and geometrical parameters into account, using a 2-D computer simulation programs. It can be concluded that this technique provides highly effective means of increasing breakdown voltage, but necessarily require the optimization of the various parameters. The design of a Si microstrip detector equipped with metal-overhang involves a proper choice of the parameters: the junction depth, oxide thickness, width of metaloverhang, device depth, substrate doping concentration and surface charges so as to obtain the VBD close to the maximum achievable value. It is shown that for structures equipped with metal-overhang, maximum VBD occurs for a given set of substrate parameters and XJ when the oxide thickness is optimized to tOX(OPT). Breakdown voltages of most planar junction termination techniques like field limiting ring are very sensitive

95

to the variation in junction depth. A definite advantage of the metal-overhang is observed here, as maximum breakdown voltage of the detectors equipped with metal-overhang remains almost constant for a wide variation in junction depth in the absence of surface charge. This feature can help in fabricating the Si sensors with shallow junctions and very high breakdown voltages and thus minimizing the dead wafer space. However, for very small junction depths, VBD is very sensitive to the variation in tOX, thus demanding a critical process control. Although, the surface-state oxide charge should be controlled in the fabrication processes, the increase in the level of oxide-trapped charge is clearly of concern for detectors in a radiation environment. Breakdown voltage of the silicon sensors decreases sharply with increase in surface charge density, however, the maximum breakdown voltage can still be obtained for the structure with the optimal oxide thickness. It is also found that the breakdown voltage increases with increase in metal-overhang width due to the flattening of the equipotential lines near the junction edge. Comparison of the present computed results with several sets of experimental data has shown a good agreement validating the present analysis and verifying accuracy of the computer program.

96

Chapter 5

---------------------------------------------------------------Effect of Passivation on Breakdown Performance of Metal-Overhang Equipped Si Sensors ---------------------------------------------------------------One of the main aims of the detector research in the High-Energy Physics (HEP) experiments is to stabilize the long-term behaviour of Si strip detectors. However, normal operating conditions for Si detectors in HEP experiments are in most cases not as favourable as for experiments in nuclear physics. In HEP experiments the detector may be exposed to moisture and other adverse atmospheric environment. It is therefore of utmost importance to protect the sensitive surfaces against such poisonous effects. These instabilities can be nearly eliminated and the performance of Si detectors can be remarkably improved by implementing suitably passivated detectors. Dielectric is commonly used as a surface passivant for this purpose both in power devices and in Si detector technology. Since its introduction, however, semi-insulators have gained a lot of interest in view of their application as a surface passivation material for high-voltage metal-overhang (MO) equipped structures in power devices. Although well appreciated in the power devices field, the use of semi-insulating film in the Si sensors for HEP experiments has not been investigated. In the previous chapter, we have analyzed the breakdown performance of Si detector equipped with MO in detail. It is very interesting to compare the effects of the two type of passivation films (dielectric vs. semi-insulator) on the breakdown performance and the long term stability of the MO terminated Si detectors in HEP experiments. This chapter presents the results on the effect of relative permittivity of the passivant on the breakdown performance of the Si detectors using computer simulations. The semi-insulator and the dielectric passivated MO structures are then compared under

97

optimal conditions. Influence of the salient design parameters such as field oxide thickness, junction depth, metal-overhang width, device depth, substrate doping concentration and the surface charge on the breakdown performance of these structures are systematically analyzed, thus providing a comprehensive picture of the behaviour of MO structures and helping in the detector optimization task. Another important factor, which can significantly affect the long-term functionality of the Si sensors, is the radiation damage and hence a crucial issue for the detectors at LHC is their stability at high operating voltages. Recently an interesting experimental result was reported by Bloch et al. [5.1] in which the breakdown voltage of the Si detectors was found to be increased after neutron and proton irradiation. A similar result was also found earlier by Albergo et al. [5.2]. The results of the I-V and C-V measurements taken on some Si sensors for Preshower detector, presented in this chapter, also verifies this result. This inspired us to investigate the effect of radiation damage on the passivated Si sensors. Although interaction of the radiation with Si is a complex phenomena and its detailed analysis is not yet possible, however, the simulation results obtained in references [5.3] and [5.4] showed us a simple but effective way to realize it. These results were also supported by experimental observations. Using the same methodology the effect of bulk damage caused by hadron environment in the passivated Si detectors is also simulated in this chapter by varying effective carrier concentration (calculated using Hamburg Model [5.5]) and minority carrier lifetime (using Kraner [5.6]). Static measurement results on some of the irradiated Si sensors, performed at CERN, Geneva along with the irradiation facility and measurement set-ups is also described in this chapter.

5.1

Passivation in Si Detectors The electrical behaviour of a Si microstrip detector can be influenced during

operation by surface contamination, high humidity and surface moisture [5.7]. Working with Si detectors for long periods of time has shown that the reverse current and breakdown voltage change drastically, sometimes hours after biasing a seemingly good detector. A severe contamination of the surface (say by touching it with fingers) may lead

98

to increase of surface leakage current by orders of magnitude [5.8]. These instabilities are believed to be caused mainly by charge density variations on the oxide surface. The surface resistivity of the oxide changes dramatically with humidity or in dry conditions, and this can cause potential spreading on the oxide surface [5.9]. For example, for unprotected p+-n junction devices, under dry or vacuum condition, positive surface charges at the Si-SiO2 interface are fully effective and as already mentioned in the previous chapter, an accumulation layer under the oxide is created. This may lead to very high electric field densities at the edge of the p+ implantation (junction edge) and to a breakdown at voltages much lower than needed for full depletion of the detector. In the other extreme case, when the negative charges collect on the oxide surface due to the exposure of uncovered oxide surface to high humidity, an inversion layer under the oxide is developed. This leads to an extension of the depletion zone towards the edge of the detector; the reverse current can increase by an order of magnitude due to electron-hole pair generation [5.10]. It is thus, crucial to control surface contamination for long term stabilization of fully depleted p+/ n- /n+ Si detector. This is achieved by depositing the final passivation layer over oxide of the Si detector. The need for the final passivation in planar structures was also well emphasized by Kemmer [5.8] while introducing the planar technology for low noise detector fabrication and suggested the use of Si3N4 as passivation layer. Since then in the detector grade technology, dielectrics are generally chosen as passivant. Instabilities due to the drift of sodium ions in SiO2 film can be suppressed by depositing dielectrics (like Si3N4) [5.11] or Phospho-Silicate-Glass (PSG) [5.12] over the oxide film. A similar situation was also faced in high voltage power devices and IC technology where stability in terms of breakdown voltage is essential. There also, dielectrics were commonly used as a surface passivant for this purpose [5.13]. However, it has been found by Matsushita et al. [5.14] that there are still some problems in the planar process with dielectrics as passivation. They introduced a novel passivation scheme, the Semi-Insulating Polycrystalline Silicon (SIPOS) as a surface passivant which solved many of the problems as the film was semi-insulating and almost electrically neutral. This technique proved to be particularly beneficial for field plate (or MO) terminated high voltage planar junctions. Jaume et al. [5.15] showed that since semi-

99

insulator linearizes the potential at the MO edge, thus it reduces the peak surface electric field over there and hence the edge breakdown can be largely suppressed with the use of SIPOS. Since then semi-insulator films are being largely used in the fabrication of high voltage planar junctions terminated with MO in power devices and IC technology [5.145.17].

5.2

Radiation Damage in Si Detectors Irradiation damage in Si detectors can be broadly categorized into surface damage

and bulk damage. Surface damage: The passage of an ionizing radiation in Si detectors causes accumulation of positive trapped charge and produces traps at the Si-SiO2 interface called interface states. This results in the formation of electron accumulation layer beneath the surface resulting in the contraction of the depletion region over there and hence causing a premature breakdown of the device. This effect is already discussed in detail in the previous chapter. Another major consequence of surface damage is the increase in interstrip capacitance (Cint) and decrease in interstrip isolation. However, it has been found that with careful design, the change in Cint can be limited to 10-20% at operational frequencies of LHC electronics [5.18-5.20]. Bulk damage: There is a general consensus that in the hadron environment, the viability of long-term operation and performance of Si detectors is affected mainly due to bulk damage [5.5 & 5.21]. Bulk damage in Si detectors by hadrons is caused mainly by Non-Ionizing Energy Loss (NIEL) interaction of primary particle with a lattice Si atom displacing a Primary Knock-on Atom (PKA) out of its lattice site resulting in a Si interstitial (I) and a left over vacancy (V) (Frenkel pair). These vacancies and interstitials migrate through the Si lattice and undergo numerous reactions with each other and the impurity atoms existing in the Si to form stable complexes. The major macroscopic effects expected from bulk damage are [5.5, 5.22]: (a) increase in the leakage current since the defects act as centers to increase the generation bulk current; (b) deterioration of charge-collection efficiency (CCE) as the defects also act as the trapping centers; (c) change in the effective carrier concentration (Neff) due to the removal of donor levels and creation of acceptor like states, leading to the type-inversion.

100

Reverse leakage current is strongly temperature dependent, given by [5.23]:

I (T ) ∝ T 2 exp(− E g / 2k B T )

(5.1)

where T is the operating temperature in Kelvin, Eg the band-gap energy and kB the Boltzmann constant. Thus, reverse current can be largely reduced by operating the Si sensors at low temperature (-5 °C for CMS), and hence is not a fundamental problem to the long-term operation. The main obstacle to the operation of Si detectors is the change in the effective dopant concentration, which results in an increased full depletion voltage at high hadron fluences. In order to ensure a good charge collection efficiency even after irradiation, one of the recently developed approach is the use of oxygenated Si as starting material, which helps in reducing full depletion voltage at high fluence. The ROSE collaboration (Research & Development On Silicon for future Experiments) has done extensive research in this direction [5.5, 5.21, 5.22, 5.24-5.27]. However, such an improvement is only observed for charged hadron irradiation whereas for neutroninduced damage the diffusion oxygenated float zone (DOFZ) silicon leads only to benefits in connection with low resistivity Si [5.5, 5.21, 5.22, 5.24-5.27]. An alternative, and more conventional approach of improving CCE is to increase the detector bias voltage progressively so that the full depletion can be eventually attained anyway [5.28]. However, operating the detectors at high biases is constrained by the breakdown phenomena. Thus, high breakdown voltage is imperative for the operation of detectors at high neutron fluences.

5.3

Device Structure & Simulation Technique The device structure and the parameters used in the present simulation are same

as used in the previous chapter. However, an additional passivation layer is also incorporated in the structure, which can be either a dielectric or a semi-insulator as shown in Fig.5.1. The semi-insulator effect as a passivant is simulated with a linear potential distribution along the field oxide-passivation layer interface. Therefore, the solution to the Laplace equation in the passivation layer becomes redundant. In contrast, for the metal-overhang structure passivated with dielectric, the Laplace equation is solved within the passivation layer also. In order to simulate a more realistic situation, the value of

101

surface charge density (QF) is kept fixed at 3x1011/cm2 (unless otherwise specified), which corresponds to QF for the non-irradiated <111> oriented Si detector with moderately good oxides.

Fig.5.1: Cross-sectional schematic of two-strip subset of a Si strip detector with metaloverhang.

5.3.1 Modeling of Bulk Damage The generation of electrically active defects and the donor removal effect result in a fairly complicated picture of the radiation damage defects: the implementation of the defect levels within the present device simulator is presently infeasible. Considering that the dominant macroscopic parameter is the effective doping concentration, in Ref. [5.3] Li et al. pursued a simplified approach; the effect of radiation damage was simulated by simply varying Neff and the results were supported by the experimental observation. In another work by Richter et al [5.4], this simulation approach has been successfully used; in which, in addition to Neff, the minority carrier lifetime (τ) was also varied to take into account the changes in reverse leakage current. The simulated results were again verified experimentally indicating that this approach is indeed helpful in predicting the electric 102

field and the junction breakdown of the irradiated silicon detectors. In the present work we have followed similar approach to analyze the electric field distribution and breakdown phenomena after irradiation. Considering a detector being under continuous neutron irradiation as will be the case for PSD at CMS, we have simulated a preirradiation condition characterized by bulk doping concentration Neff = 1 x 1012 cm-2 and τ = 1 x 10-3 s, and further damage is taken into account by varying Neff and τ. In this work Neff is parameterized using Hamburg model [5.5, 5.25], which includes the self-annealing effect during long periods of operation as projected in the actual experiment. ∆N eff = N eff , 0 − N eff (φ eq , t (Ta )) = N A (φ eq , t (Ta )) + N c (φ eq ) + N Y (φ eq , t (Ta ))

(5.2)

∆N eff consists of three components, a short term beneficial annealing NA, a stable damage

part Nc, and the reverse annealing component NY, which are given as [5.5, 5.25] N c (φ eq ) = N c 0 (1 − exp(−cφ eq )) + g cφ eq

t ) τa

(5.4)

1 ) 1+ t /τ y

(5.5)

N A = φ eq g a exp(−

N Y = g yφ eq (1 −

(5.3)

The values of different parameters used in the simulation for calculation of Neff are given in Table 5.1 [5.5, 5.29]. This model is chosen for simulation because it best describes actual operating scenario of LHC environment. To incorporate the effect of increase in leakage current with fluence, we have changed the minority carrier lifetime (τ) in our simulation package using the definition of Kraner [5.6] as: 1 1 = + k φ eq , τ τ0

(5.6)

where τ0 is the minority carrier lifetime of the initial wafer, Φeq is the integrated fluence, and k is the damage constant. The initial minority carrier lifetime used is 0.1 ms and value of k used is 4 x 10-8 cm2 s-1 as given by Kraner [5.6] for a minimum ionizing particle.

103

Table 5.1: Damage parameters used for calculation [5.5, 5.29]: Parameters

Values

Neff0

1x1012 cm-3 (for 4.2 kΩ cm), 1.6x1012 cm-3 (for 2.5 kΩ cm)

Nc0

0.7 x Neff0

c

2.5x10-14 cm-2

gc

1.5x10-2 cm-1

ga

1.8x10-2 cm-1

ta

55 hrs. at 200C, 3587 hrs. at –50C

gy

5.2x10-2 cm-1

ty

480 days at 200C, 64760 days at –50C

5.4

Comparison

between

Semi-Insulator

vs.

Dielectric

Passivation 5.4.1

Effect of Field-Oxide Thickness and Junction Depth In the two-dimensional computer simulation studies on high voltage Si strip

detectors involving metal-overhang structure reported in literature [5.30] and also in the previous chapter, the dielectric medium was invariably taken to be air. However, in practice, a high-voltage device equipped with metal-overhang is protected by a suitable passivant. To study the influence of different passivants on VBD, Fig.5.2 shows the plot of breakdown voltage as a function of field-oxide thickness (tOX) for different passivants: two dielectrics (εdie=3.9 and εdie=7.5), a semi-insulator and also when the device is unpassivated (εdie=1). The qualitative nature of the curve is same in all the cases; VBD increases with increasing tOX, attains a maximum value corresponding to certain tOX(OPT) and then decreases for further increase in tOX. For the region tOX < tOX(OPT), breakdown occurs at the metal-overhang edge, whereas for tOX > tOX(OPT), it takes place at the

104

junction curvature. For tOX = tOX(OPT), electric field distribution is such that the breakdown simultaneously occurs at the two edges, and we get the maximum breakdown voltage. 4100 sem i-insulator

3800

XJ=0.2 microns

Breakdown voltage (V)

3500 3200

NB = 1x1012 /cm 3 WN = 300 m icrons WMO=20 m icrons QF=3x1011/cm 2

εdie=7.5

2900 2600 2300 2000 1700

εdie=3.9

1400 εdie=1.0

1100 800 0

1

2

3

4

5

6

7

8

9

10

11

12

13

Oxide thickness (m icrons)

Fig.5.2: VBD vs. tOX with different passivants for XJ = 0.2 µm.

It can be seen from Fig.5.2 that VBD in the region tOX < tOX(OPT) is very sensitive to the variation in εdie, implying that metal-overhang edge breakdown is strongly affected by the presence of dielectric passivation layer. However, in the region tOX > tOX(OPT), VBD is almost insensitive to changes in εdie indicating that junction breakdown is practically independent of the dielectric passivation layer. In the region tOX < tOX(OPT), VBD corresponding to εdie=3.9 is considerably higher than that for εdie=1.0, and VBD for εdie=7.5 is greater than VBD for εdie=3.9, thus demonstrating that the breakdown voltage increases with increasing εdie. It is also clear from Fig.5.2 that the breakdown voltage obtained for the semiinsulator passivated structure is significantly greater than that achieved using the dielectric passivation for all values of tOX. In order to understand this behaviour, the equipotential contours for the different cases are plotted in Fig.5.3(a)-(d). A careful observation of the potential distribution reveals that the equipotential contours spread out more in the dielectric medium when the εdie is larger, thus, relaxing the potential

105

crowding near the metal-overhang. Consequently, for a given voltage the electric field in Si bulk decreases resulting in higher VBD for large εdie. Comparing the potential contours of the dielectric and semi-insulator passivated structures, it can be seen that the semiinsulator layer linearizes the potential inside the field oxide, alleviating the potential crowding at the metal-overhang edge. Thus, the peak electric field at the metal-overhang edge is tremendously reduced and the voltage handling capability of the device is significantly improved. This can be better appreciated by looking at the electric field distribution plot within the Si substrate (Fig.5.4 (a)-(d)). It is clear that at a given bias, the peak electric field amplitude at the metal-overhang edge decreases as the εdie of the dielectric passivant layer increases. In fact, for the semi-insulator passivated structure, field crowding at the metal-overhang is completely eliminated due to the efficient potential contours spreading and hence the breakdown voltage obtained for semiinsulator passivated structure is maximum. In summary, junction curvature electric field effects are reduced by the presence of MO, however, this results in the field crowding at the MO edge. Semi-insulator layer spreads out the equipotential lines at this edge and hence the complementary functions of these two (MO and the semi-insulator layer) can be exploited to improve the breakdown performance of Si sensors.

Fig.5.3(a): Potential distribution near the surface at breakdown for XJ=0.2µm in the region tOX < tOX(OPT) for εdie=1.0.

106

Fig.5.3: Potential distribution near the surface at breakdown for XJ=0.2 µm in the region tOX < tOX(OPT) for (b) εdie=3.9, (c) εdie=7.5, and (d) semi-insulator passivated structure.

107

Fig.5.4: Electric field distribution near the surface at Vbias=500 volt for XJ=0.2 µm in the region tOX < tOX(OPT) for (a) εdie=1.0, (b) εdie=3.9, (c) εdie=7.5, and (d) semi-insulator passivated structure.

108

Further, it is clear from Fig.5.2 that the tOX(OPT), required to accomplish maximum breakdown voltage, is lower if εdie of the passivant layer is larger. Thus, higher values of εdie allows for reduction in tOX required for attaining a given breakdown voltage. It is seen from Fig.5.2 that tOX(OPT) is still lower for the semi-insulator passivated structure than for the dielectric passivated one. Thus, it is clear that a given VBD can be achieved at a lesser tOX if larger εdie is used, and at a still lower tOX if a semi-insulator is used. To study the effect of junction depth (XJ) on the breakdown voltage for different passivants, we show in Fig.5.2 and figures 5.5(a), 5.5(b) and 5.5(c) the variation of VBD vs. tOX for different values of XJ. It is known that when XJ increases, the electric field crowding at the junction curvature decreases due to decrease in flux per unit area leading to increase in VBD. A qualitatively similar behaviour is observed when the junction depth is increased, as shown in the plots (Fig.5.5 (a)-(c)). Increasing the junction depth results, however, in an increase in the breakdown voltage for all the passivants.

4100 3800

(a) XJ=1.0 microns

semi-insulator

Breakdown voltage (volt)

3500 εdie=7.5

12

3

2900

NB = 1x10 /cm WN = 300 microns WMO=20 microns

2600

QF=3x10 /cm

3200

11

2300

2

εdie=3.9

2000 1700

εdie=1.0

1400 1100 800 0

1

2

3

4

5

6

7

8

9

10

11

12

13

Oxide thickness (microns)

Fig.5.5(a): Breakdown voltage vs. field oxide thickness with different passivants for XJ=1.0µm.

109

4100

(b) XJ=3.5 microns

semi-insulator 3800 εdie=7.5

3500

Breakdown voltage (volt)

3200 2900 2600 εdie=3.9

2300

NB = 1x1012/cm3 WN=300 microns

2000

WMO=20 microns 1700

QF=3x1011 /cm2 εdie=1.0

1400 1100 800 0

1

2

3

4

5

6

7

8

9

10

11

12

13

Oxide thickness (microns)

4000 semi-insulator

(c) XJ=15.0 microns

3800

Breakdown voltage (volt)

3600 3400 εdie=7.5 3200 3000 εdie=3.9

NB = 1x1012 /cm3 WN=300 microns WMO=20 microns

2800 2600

QF=3x1011 /cm2

2400 2200

εdie=1.0

2000 0

1

2

3

4

5

6

7

8

9

10

11

12

Oxide thickness (microns)

Fig.5.5: Breakdown voltage vs. field oxide thickness with different passivants for (b) XJ=3.5 µm, and (c) XJ=15.0 µm.

110

13

An important characteristic of the semi-insulator passivated structure, which is conspicuous from Fig.5.2 and figures 5.5(a), (b) & (c) is that in the region tOX < tOX(OPT), the oxide thickness is not a very critical parameter, as VBD varies only marginally for all junction depths. This is contrary to the MO with dielectric passivated devices where the edge breakdown voltage changes rapidly with change in oxide thickness in the same region. Figures 5.6(a) & 5.6(b) depict another important feature of the semi-insulator passivated structure. As can be seen that the optimal oxide thickness (Fig.5.6(a)) and the maximum breakdown voltage (Fig.5.6(b)) increases with increase in junction depth for dielectric passivated structure, whereas the maximum breakdown voltage obtained under the optimal conditions for the semi-insulator passivated structure is nearly constant over a wide range of junction depth (Fig.5.6(b)). Specifically, VBD changes by a marginal 4% for a semi-insulator passivated structure, whereas it changes by as much as 27% for a dielectric passivated structure (εdie = 7.5), when the junction depth is increased from 1.0 µm to 15 µm. This aspect of the semi-insulator makes it an extremely important passivant for developing high-voltage Si detector with relatively shallow junctions. Also, it is clear from Fig.5.6(a) that for all junction depths, the optimal oxide thickness for the semi-insulator passivated structure is less than that of the dielectric passivated structure.

Optimal oxide thickness (microns)

2.4 εdie=1.0

2

εdie=3.9 εdie=7.5

1.6

(a)

1.2 semi-insulator

0.8 NB = 1x1012 /cm3 WN=300 microns WMO=20 microns

0.4

QF=3x1011 /cm2 0 0

2

4

6

8

10

12

14

16

Junction depth (microns)

Fig.5.6(a): Optimal oxide thickness vs. junction depth vs. junction depth for the semiinsulator and dielectric passivated structure. 111

4000 Max. V BD (for t OX=tOX(OPT)) (volt)

sem i-insulator 3800 εdie=7.5

3600

εdie=3.9 εdie=1.0

3400

(b)

3200 NB = 1x1012 /cm 3 WN=300 m icrons WMO=20 m icrons QF=3x1011 /cm 2

3000 2800 2600 2400 0

2

4

6

8

10

12

14

16

Junction depth (m icrons)

Fig.5.6(b): Maximum breakdown voltage (for tOX = tOX(OPT)) vs. junction depth for the semi-insulator and dielectric passivated structure.

5.4.2

Effect of Metal-Overhang Width The influence of the metal-overhang extension (WMO) on the VBD of the semi-

insulator and dielectric passivated metal-overhang structure is compared in Fig.5.7. 4000

WMO=40 microns ( semi-insulator) WMO=20 microns ( semi-insulator)

Breakdown voltage (volt)

3500 3000

12

3

NB = 1x10 / cm WN = 300 microns XJ=0.2 microns

2500

11

2

QF=3x10 /cm

2000

WMO=40 microns ( εdie=3.9) 1500 1000

WMO=20 microns ( εdie=3.9)

500 0

1

2

3

4

5

6

7

8

9

10

11

12

Oxide thickness (microns)

Fig.5.7: Breakdown voltage vs. field oxide thickness with different metal-overhang widths for the semi-insulator and dielectric (εdie=3.9) passivated structure.

112

13

At a first glance, the effect of increasing the extension of the metal contact enhances the VBD for both the cases due to the flattening of the equipotential lines near the junction edge. However, the increase in VBD with WMO for dielectric passivated structure is large as compared to semi-insulator passivated structure for all values of tOX. The figure also shows that for any given value of the metal-overhang width, the VBD for the semi-insulator passivated structure is greater than that for the dielectric passivated structure. It can be seen from Fig.5.8(a) that for the dielectric passivated Si strip detector, the optimum oxide thickness increases with increase in metal-overhang extension, attains a maximum value and then decreases with further increase in WMO. The maximum VBD (Fig.5.8(b)) obtained under the optimal condition increases continuously with increase in WMO. Ideally, an infinite metal-overhang extension is required to maximize its advantage for high-voltage devices. However, in Si strip detectors, strip-pitch becomes a limiting factor for extending the overhang beyond a certain value and in fact, noise associated to the strip capacitance also increases with an increase in overhang width. Here, the semi-insulator passivated structure offers a decisive advantage over its dielectric counterpart because for such structures the maximum breakdown voltage obtained and also the optimal oxide thickness required for accomplishing it remain practically constant over a wide variation in metal-overhang. 1.4 NB = 1x1012 /cm 3 W N=300 microns X J=0.2 microns

1.2

tOX(OPT) (microns)

1

QF=3x1011 /cm 2

0.8

εdie=1.0 εdie=3.9

0.6

εdie=7.5 0.4 semi-insulator 0.2 0 5

10

15

20

25

30

35

40

45

Width of metal-overhang (microns)

Fig. 5.8(a): Optimal oxide thickness vs. metal-overhang width for the semi-insulator and dielectric passivated structure.

113

3900 semi-insulator Max. VBD (for tOX=tOX(OPT) ) (V)

3600 3300 3000 2700

12

3

NB = 1x10 /cm WN=300 microns XJ=0.2 microns

2400

11

2100

εdie=7.5

1800

εdie=3.9

QF=3x10

/cm

2

εdie=1.0

1500 5

10

15

20 25 30 Width of metal-overhang (microns)

35

40

45

Fig.5.8(b): Maximum breakdown voltage (for tOX = tOX(OPT)) vs. metal-overhang width for the semi-insulator and dielectric passivated structure.

5.4.3 Effect of Passivation Layer Thickness Fig.5.9 shows the variation of VBD with passivation layer thickness (tpass) for different passivants. 3850

3350

VBD (volt)

semi-insulator

NB = 1x1012 /cm3 XJ=1.0 micron tOX=0.4microns WMO=20 microns WN = 300 microns

2850

QF=3x1011/cm2 εdie=7.5

2350 εdie=3.9 1850

Unpassivated

1350 0

1

2

3

4

5

6

7

8

passivation layer thickness (microns)

Fig.5.9: Breakdown voltage vs. passivation layer thickness for different passivants.

114

9

10

It can be seen that for dielectric passivated structure, VBD increases with increase in tpass, however, this increase is gradual for higher values of tpass. The effect of increasing tpass significantly increases the spreading of equipotential lines along the surface of the device, reduces the electric field crowding and hence increases the VBD. However, the semi-insulator effect is based on the linearization of the potential at the oxide/passivation layer interface and hence VBD remains independent of tpass for semi-insulator passivated structures.

5.4.4 Effect of Surface Charges As already mentioned in the previous chapter, the SiO2-embedded positive charge layer causes a thin electron accumulation layer to build up at the Si-SiO2 surface. This results in a reduction of the depletion width, increasing the electric field in the Si close to the Si-SiO2 interface, eventually causing an avalanche breakdown in that region at much smaller voltages. Results for the breakdown voltage as a function of surface charge density are plotted in Fig.5.10(a)-(c) for three cases, i.e., tOX < tOX(OPT), tOX = tOX(OPT) and tOX > tOX(OPT) respectively. (a) tOX < tOX(OPT) 4000

semi-insulator

Breakdown voltage (volt)

3500

3000

2500

2000

ε die=7.5

NB = 1x10 /cm

ε die=3.9

WN =300 microns

ε die=1.0

XJ=0.2 microns

12

3

WMO=30 microns 1500

1000 0.0E+00

2.0E+11

4.0E+11 6.0E+11 8.0E+11 2 Surface charge density (/cm )

1.0E+12

Fig.5.10(a): Breakdown voltage as a function of surface charge density with different passivants for tOX < tOX(OPT).

115

1.2E+12

(b) tOX = tOX(OPT) 3800 Breakdown voltage(volt)

sem i-insulator 3300 2800

NB = 1x1012 /cm 3

2300

WN =300 m icrons XJ=0.2 m icrons WMO=30 m icrons

1800

εdie=7.5 εdie=3.9

1300

εdie=1.0 800 0.00E+00

2.00E+11

4.00E+11 6.00E+11 8.00E+11 Surface charge density (/cm 2)

1.00E+12

1.20E+12

(c) tOX > tOX(OPT) 2000 semi-insulator Breakdown voltage(volt)

1750 1500

NB = 1x1012 WN =300 microns

1250 dielectrics

XJ=0.2 microns

1000

WMO=30 microns

750 500 250 0 0.00E+00

2.00E+11

4.00E+11 6.00E+11 8.00E+11 Surface charge density (/cm2)

1.00E+12

1.20E+12

Fig.5.10: Breakdown voltage as a function of surface charge density with different passivants for (b) tOX = tOX(OPT), and (c) tOX > tOX(OPT).

In the region tOX < tOX(OPT), VBD of dielectric passivated structure decreases with increase in QF. However, in the same region, Fig.5.10(a) shows that the semi-insulator passivated structure remains almost insensitive to the surface charge for the same variation of QF, thus showing its superiority over the dielectric passivated structure. A similar behaviour is also observed for the case when tOX = tOX(OPT) (Fig.5.10(b)). Here also, only a marginal decrease in the value of the computed VBD is found with increasing oxide charge, thus indicating that the semi-insulator structure offers nearly total-

116

immunity against the surface charge for tOX ≤ tOX(OPT), which is again an outstanding attribute of semi-insulator passivated structures in adverse radiation conditions. However, the situation is different for tOX > tOX(OPT) (Fig.5.10(c)), when the breakdown occurs at the junction edge, the simulation results indicate that the breakdown voltage assumes almost the same value after QF = 4.0x1011 /cm2 for all the dielectric passivated structures. In fact, the VBD for the semi-insulator passivated structure also overlaps with that of the dielectric passivated structure after QF = 6.5x1011 /cm2. Thus, in the region tOX > tOX(OPT) and for large values of QF, VBD of the device is mainly governed by QF irrespective of the type of passivant used. From the above discussion, it is clear that in order to make full use of the passivant properties of the semi-insulator, the field oxide thickness used in the fabrication of the Si strip detectors, should be kept less than or equal to its optimal value.

5.4.5 Effect of Device Depth and Substrate Doping Concentration We have also investigated the dependence of VBD on the depletion layer width (which is almost equal to device depth (WN) for punch-through (PT) structures) and substrate doping concentration (NB).

Maximum breakdown voltage (volt)

4000 semi-insulator

NB = 1x1012 /cm3 XJ=1.0 micron tOX=0.4 microns WMO=20 microns

3500 3000

εdie = 7.5

QF=3x1011/cm2

2500

εdie = 3.9 εdie = 1.0

2000 1500 1000 500 50

100

150

200

250

300

WN (microns)

Fig. 5.11: Maximum breakdown voltage vs. device depth for different passivants.

117

350

It can be seen from Fig.5.11 that maximum breakdown voltage obtained for semiinsulator structure is greater than that achieved for dielectric passivated structures for all values of WN. To study the effect of NB on the optimal conditions, we have varied the doping concentration from 1 x 1012 to 1 x 1013 /cm3. Fig.5.12(a) and Fig.5.12(b) show the variation in the optimal oxide thickness and breakdown voltage as a function of NB respectively for the dielectric and semi-insulator passivated structures. It can be seen that the variation of both the optimal oxide thickness and the breakdown voltage is smaller for semi-insulator passivated structure. This shows that the semi-insulator passivated structures can be employed in a wide range of Si detectors (different resistivities and device depth) used in the HEP experiments.

optimal oxide thickness (microns)

1.7

XJ=1.0 micron WN = 300 microns WMO=20 microns 11

1.5

QF=3x10 /cm

εdie=7.5

2

(a)

1.3

semi-insulator 1.1

0.9

0.7 0.0E+00

2.0E+12

4.0E+12

6.0E+12

8.0E+12

1.0E+13

1.2E+13

3

Substrate doping concentration ( /cm )

Fig.5.12(a): Optimal oxide thickness voltage vs. substrate doping concentration for two passivants (a dielectric and a semi-insulator).

118

4050 semi-insulator

Maximum VBD (volt)

3800

(b)

3550 XJ=1.0 micron WN = 300 microns WMO=20 microns

3300 3050

11

2

QF=3x10 /cm

2800

εdie=7.5

2550 2300 0.00E+00

2.00E+12

4.00E+12

6.00E+12

8.00E+12

1.00E+13

1.20E+13

3

Substrate doping concentration (/cm )

Fig.5.12(b): Maximum breakdown voltage vs. substrate doping concentration for two different passivants (a dielectric and a semi-insulator).

5.4.6

Effect of Bulk Damage on Full Depletion and Breakdown Voltage

The depletion voltage required to operate a Si detector is directly proportional to Neff, and is given as: VFD =

| N eff | q WN

2

(5.7)

2ε S i

For Preshower, the fluence profile per year integrated with time [5.29] along with the minority carrier lifetime (using Kraner’s definition [5.6]) is given in Table 5.2. In Fig.5.13, we have plotted variation of Neff and VFD as a function of time and fluence during the 10 years of LHC operation for two initial resistivities of 4.0 KΩ cm (Neff =1.0 x 1012 cm-3) and 2.5 KΩ cm (Neff =1.68 x 1012 cm-3) using equations (5.2) and (5.7). The values of Neff considered here correspond to the various levels of the fluence expected over the full LHC operation. It is considered that the Si detectors will operate at –5oC for 10 years of operation with the exception of 2 days/year at room temperature needed for detector maintenance [5.29]. From Fig.5.13 it can be seen that the Si detector with initial resistivity of 4.0 KΩ−cm becomes intrinsic after about 3 and a 1/2 year (after which typeinversion starts), whereas for 2.5 KΩ−cm resistivity wafer the type inversion is slightly

119

delayed (intrinsic after about 4 years). Also, it is clear that VFD approaches 244 volt for 4.0 KΩ−cm wafer, and is marginally lower for 2.5 KΩ−cm wafer after 10 years. Table 5.2: Fluence profile (along with Neff and τ) of neutrons expected for PSD detectors.

1

Fluence (each ear) x 1013 (n/cm2) 0.2

Integrated fluence x 1013 (n/cm2) 0.2

Neff x 1011 (/cm3) 9.16

Minority carrier lifetime (ms) 0.01111

2

0.6

0.8

7.19

0.00303

3

1.2

2.0

3.68

0.00123

4

2.5

4.5

-2.62

0.00055

5

2.5

7.0

- 8.18

0.00036

6

2.5

9.5

- 13.5

0.00026

7

2.5

12.0

- 18.8

0.00021

8

2.5

14.5

- 24.3

0.00017

9

2.5

17.0

- 29.9

0.00014

10

2.5

19.5

- 35.6

0.00013

Year

Fig.5.13: Variation of effective carrier concentration (Neff) and full depletion voltage as a function of time and fluence during the 10 years of LHC operation.

120

Fig.5.14(a) and Fig.5.14(b) show the plot of 2-D electric field distribution for the dielectric passivated structure. It is clear that before type-inversion the depletion region spreads from the front side however, after type-inversion it grows from the rear side indicating that the main junction has shifted from the front side to the backside. Also, after type-inversion, another dominant electric field also develops around the curvature of the front p+/p junction (Fig.5.14(b)). Thus, two dominant peak electric fields are obtained after type-inversion, one at the back junction (p-/n+) and other at the front junction (p+/p-).

Fig.5.14: Simulated electric field distribution within the detectors at an applied bias of 35V for two values of Neff : (a) before type inversion (n-type), Neff =1 x 1012 cm-3, and (b) after type inversion (p-type) Neff = -8.18 x 1011 cm-3. 121

Fig.5.15 shows the plot of breakdown voltage as a function of Neff for a dielectric (εdie =7.5) and semi-insulator passivated structures. It can be seen that breakdown voltage continuously increases with increasing fluence. In order to understand this behavior, figures 5.16(a)-(d) show the three-dimensional electric field distribution within the device for progressive radiation.

p-type (after type-inversion)

n-type (before type-inversion)

4050

semi-insulator

Breakdown voltage (volt)

3800

3550

3300

εdie=7.5 3050 XJ = 1.0 micron WMO=20 microns WN = 300 microns 11

2800

2

QF=3x10 /cm

2550

2300 -4.0E+12

-3.0E+12

-2.0E+12

-1.0E+12

0.0E+00

1.0E+12

2.0E+12

3

Effective doping concentration (/cm )

Fig.5.15: Breakdown voltage vs. Neff for different passivants.

In the p+/n/n+ detector, the electric field before type-inversion is strongest at the front p+ strip junction and breakdown occurs over there (either at the junction curvature or at the metal-overhang edge). It can be seen that as Neff is decreased from 1 x 1012 cm-3 (Fig.5.16(a)) to 1.5 x 1010 cm-3 (Fig.5.16(b)), the peak electric field at the front junction decreases due to the effective spreading of the potential at the junction curvature. Thus VBD increases, as device becomes less n-type before type-inversion.

122

Fig.5.16: 3-D electric field distribution within the detectors at an applied bias of 500V for different values of Neff: (a) before type inversion (n-type), Neff =1 x 1012 cm-3, (b) intrinsic, Neff =1.5 x 1010 cm-3 & (c) after type inversion (p-type), Neff = -8.18 x 1011 cm-3.

123

Fig.5.16(d): 3-D electric field distribution within the detectors at an applied bias of 500V for Neff = -3.56 x 1012 cm-3 after type inversion (p-type).

As the device is inverted to p-type (Fig.5.16(c)), the depletion layer spreads from the rear side. As a consequence of homogeneous irradiation, the field is higher near the back junction and since the back junction is plane-parallel the field is very uniform also. This, in turn, results in the smooth down of local field peak at curvature of front junction. An important feature of Fig.5.16(c) is that after type-inversion, although the main junction is at the rear side, the maximum electric field and hence the avalanche breakdown still occurs at the front side. This is because of the difference in the nature of two junctions: front junction has a curvature whereas back junction is plane parallel and for a given bias, electric field at the curved junction is greater than the electric field at the plane parallel junction. Thus, bulk inversion results in the reduction in the potential crowding at the front junction (and hence within the silicon bulk), which in effect leads to an improvement in the breakdown performance. This is also clear from the maximum electric field vs. Neff plot as shown in Fig.5.17, wherein it can be seen that as the detector is inverted and becomes progressively p-type, the peak electric field at the front junction (and hence in the Si substrate) decreases at a given bias, thus improving the breakdown performance of Si detectors with radiation.

124

n-type (before type-inversion)

p-type (after type-inversion)

Maximum electric field (volt/cm)

1.6E+05

1.1E+05

at front junction

6.0E+04

XJ = 1.0 micron WMO = 20 microns WN = 300 microns 11

2

QF=3x10 /cm

at back junction

-4.0E+12

-3.0E+12

-2.0E+12

-1.0E+12

1.0E+04 0.0E+00

1.0E+12

2.0E+12

3

Effective doping concentration (/cm )

Fig.5.17: Variation of maximum electric field at the front and back junction with Neff at an applied bias of 500 V.

It can also be seen from Fig.5.15 that VBD of semi-insulator passivated structure is less sensitive to Neff as compared to dielectric passivated detectors. This can be attributed to the fact that in semi-insulator structures, the potential distribution is more uniform before type-inversion also and the field crowding at the front junction edge beneath the metal-overhang is already alleviated. Another important result is that for all values of Neff, maximum VBD for semi-insulator structure is greater than that of the dielectric passivated ones.

5.5

Comparison with Experimental Work In order to support the simulation analysis performed for the passivated structures,

the simulator has been calibrated against the experimental data [5.16 & 5.31]. For clarity, cross-sections of the structures given in these references are shown in Fig.5.18(a) [5.16] and Fig.5.18(b) [5.31]. The results are given in Table 5.3 along with the information on

125

salient device parameters. A very good agreement between the experiments and simulations is found, thus validating our present effort.

Fig.5.18: Cross-sections of the structures simulated for experimental verification. (a) corresponds to structure given in Ref. [5.16] and (b) is for Ref. [5.31]. Figures are not to scale.

126

Table 5.3: Comparison of the simulation results with the experimental work

Resistiv Collector-base

tOX

Field plate-

Present

Exp.data (E)

(µm)

stop channel

simulation

(V)

(ρ)

distance (∆L)

result (P)

(Ω-cm)

(µm)

(V)

60

830

880

-6%

110

1005

1045

-4%

ity

junction

14 µm

(P-E)/P

60

(QF=3x1011

[5.16]

/cm2)

210

1080

1065

1%

14 µm

80

1170

1150

2%

110

1200

1245

-4%

210

1540

1500

3%

75

(QF=3x1011

[5.16]

/cm2)

1.25

1.25

ρ

XJ

Semi-insulator

Nitride

(Ω-

(µm)

(SIPOS) passivated

passivated

cm) QF

VBD

VBD

QF

VBD

VBD

(x1011)

(P)

(E)

(x1011)

(P)

(E)

(/cm2)

(V)

(V)

(/cm2)

(V)

(V)

70

0.5

1260

1200

5%

0.75

1115

1190

-6%

50

(tOX=1

1.0

1305

1390

-6%

2

1440

1420

1%

[5.31]

µm)

4.5

1530

1500

2%

3.4

1560

1630

-4%

(P-E)/P

127

(P-E)/P

5.6

Static Measurements on Irradiated Si Sensors The static measurements (Current-Voltage (I-V) and Capacitance-Voltage (C-V))

were performed at CERN, Geneva, on five irradiated Si microstrip detectors of different designs and coming from four manufacturers. Measurements on these detectors were carried out earlier, both before and after irradiation, by Dr. Anna Peisert, CERN. We have compared our measurements with the earlier set of measurements to analyze the improvement in I-V characteristics and study the variation in full depletion and breakdown voltage.

5.6.1 Irradiation Facility The Irradiation of all the detectors were carried out at the CERN Proton Synchrotron (PS). The damage factor for this beam is 0.5 to 0.6, i.e., the equivalent 1MeV-neutron fluence is about half the 24 GeV-proton fluence. The period needed to achieve the fluences between 2.8x1014 p/cm2 and 3.2 x 1014 p/cm2 (error ~ 6% [5.32]) was about 6-10 days. During irradiation, the detectors were kept under realistic operating conditions, cooled to a temperature of about –7°C, with an applied bias of 150 volt. Sensors were stored at temperatures below –3°C after the exposure and taken out into ambient conditions only for measurements.

5.6.2 Measurement Set-ups Set-up used for measuring the static characteristics (I-V and C-V) of the sensors is shown in Fig.5.19. Total current and capacitance measurements were performed with HighVoltage (HV) source (Keithley 237), which also acts as the current meter and LCR meter (HP4284A) (along with an isolation box) connected to a PC running LabVIEW program.

128

Fig.5.19: I-V & C-V setup at CERN

Total detector current (I) was measured by connecting all the 32 strips together as shown in Fig.5.20(a). Keithley 237, which can supply up to 1100 volt, biases the detector and also measures the current. Non-irradiated sensors were measured at room temperature and the irradiated ones at temperature below 00C. For irradiated detectors current is calibrated at -5°C using the relation I = a ebT, where values of

a and b were already calculated using current vs temperature

measurement for different fluences.  For total capacitance, the measurements were carried out using HP4284 LCR Meter using Keithley 237 HV source to bias the detector (Fig.5.20(b)). An HV isolation box was used to decouple the HV from the LCR meter. For the measurement, AC frequency of 100 kHz was used for non-irradiated detectors and 5kHz for the irradiated ones with 30 mV AC amplitude.

129

Fig.5.20: Test set-up for measurement of (a) total current and (b) total capacitance.

5.6.3 Measurement Results on Irradiated Sensors The detectors used in the study along with device depth and irradiation fluence are listed in Table 5.4. Table 5.4: Tested detectors, their depths and the irradiation flux to which they were exposed. Detector

Depth (µm)

Fluence (p/cm2)

India 2000-1

300

3 x 1014

Elma RTS 12-24-21

282

3 x 1014

Taiwan 1-3

310

2.8 x 1014

Greece N4

384

2.8 x 1014

Taiwan H-8044-4

325

3.16 x 1014

Figures 5.21(a) & 5.21(b) show an example of the I-V & C-V characteristics of one of the sensors fabricated at Bharat Electronics Limited (BEL). It can be seen that before irradiation, detector has a very low leakage current at small voltages and the breakdown occurs at about 60-70 volt. Here, we define the breakdown voltage as a voltage at which the leakage current shows a sharp increase, accompanied by a rapid

130

increase in the capacitance (or a decrease of 1/C2 Fig.5.21(b)). When the measurement was performed after irradiation, the leakage current increases manifold, by an order of 34. However, an interesting fact to notice is that the current behaviour is now stable up to 400 volt without any signs of breakdown. In the subsequent measurements, when the detectors were kept at cold temperature, the improvement both in terms of leakage current and breakdown voltage is observed. The value of full depletion voltage is deduced from the 1/C2 vs. VBias plot. It can be seen that immediately after irradiation, VFD increases from 50 volt (before irradiation) to 210 volt indicating the occurrence of bulkinversion. The decrease in the value of VFD in the next measurements after irradiation signifies that beneficial annealing has taken place. In fact, its value has come down to 145 volt in the measurement taken on 2nd May 2001.

Fig.5.21(a): Leakage current of an Indian detector as a function of applied bias.

131

Fig.5.21(b): Inverse square capacitance of an Indian detector as a function of applied bias. The measured full depletion voltage is also indicated.

Similar I-V behaviour is also observed for the detectors (figures 5.22(a)-(c)) from other foundries. These results, thus, further validate the improvement in the breakdown performance of Si sensors after irradiation.

Fig. 5.22(a): Leakage current of a Taiwan detector as a function of applied bias. 132

Fig. 5.22(b): Leakage current of the 2nd Taiwan detector as a function of applied bias.

Fig. 5.22(c): Leakage current of another Indian detector as a function of applied bias.

5.7 Conclusions In this chapter, the application of the 2-D device simulation to the analysis and comparison of the dielectric and semi-insulator passivated metal-overhang structure has been described. By analyzing simulation results, influences of all the salient physical and geometrical parameters on these structures have been elaborated. It is demonstrated that higher values of relative permittivity (εdie) of the passivant dielectric play an important role in determining VBD, and results in an increase in breakdown voltage as compared to the unpassivated detector. Also, VBD increases with an 133

increase in εdie in the region tOX < tOX(OPT) for dielectric passivated structures. However, semi-insulator passivated structure results in still higher values of VBD for all values of tOX due to the better distribution of equipotential lines under the same conditions. It is found that the optimal oxide thickness decreases with increase in εdie for dielectric passivated structure and for the semi-insulator passivated structure, the decrease is still greater. For semi-insulator passivated structure, the maximum breakdown voltage achieved for the optimal field oxide thickness remains fairly constant over a wide variation in the junction depth. Thus, the present study shows that the semi-insulator passivated structures allow for a design of Si strip detectors with shallow junctions and thinner oxides, reducing dead layer and making the detectors more suitable for highenergy physics experiments. Also, for semi-insulator passivated structures, the maximum VBD obtained under the optimal conditions is found to be independent of the overhang width. The small values of metal-overhang would help in the design of high voltage and low noise Si strip detector, since increasing the metal extension results in higher interstrip capacitance and hence the noise associated with it. VBD of semi-insulator passivated structure is also found to be independent of tpass, whereas that of dielectric passivated structure increases with increase in tpass. Effect of the bulk damage in Si sensors shows that the increase in fluence results in the smooth down of the local field peak at the front side of the single sided p+/n/n+ detector (where the detector breakdown occurs) and hence an improvement in the breakdown performance is observed. Another very important feature of the semi-insulator passivated structure is the nearly constant breakdown voltage for a wide variation in QF for tOX ≤ tOX(OPT), this establishes its supremacy and offers an extremely important design flexibility when realizing high-voltage junctions for Si strip detector. Thus, the present study shows that semi-insulator passivated structures are attractive for achieving high breakdown voltages of Si strip detectors. The measurements performed on irradiated detectors show an improvement in terms of breakdown performance after irradiation. After irradiation, the depletion voltage and total leakage current of irradiated detectors are decreasing with time over the period.

134

Chapter 6

---------------------------------------------------------------Comparison of Junction Termination Techniques for High- Voltage Si Sensors: Metal-Overhang vs. Field Limiting Ring ---------------------------------------------------------------In Chapters 4 and 5, we have analyzed the influence of salient design parameters on the breakdown performance of silicon strip detectors equipped with metal-overhang (MO). Another attractive junction termination technique (Chapter 4), which is widely employed in Si detectors, is the floating Field Limiting Ring (FLR) (or guard ring) technique. Since high-voltage planar Si junctions are of great importance in High-Energy Physics (HEP) experiments, it is very interesting to compare these two techniques for achieving the maximum breakdown voltage under optimal conditions. Although both the structures have been investigated separately, yet none of the earlier works have reported the comparative analysis of these structures under similar physical and geometrical conditions. The purpose of this chapter is to compare these two termination techniques under identical conditions with the aim of defining layouts and technological solutions suitable for the use of Si detectors in harsh radiation environment. The results demonstrate the superiority of metal-overhang technique over field limiting ring technique for planar shallow-junction high-voltage Si detectors used in high-energy physics experiments. Before discussing the results, however, a brief description of the FLR technique is provided.

6.1

FLR structure The effect of crowding of the field lines in the proximity of the junction

termination can be reduced by means of a floating field limiting ring (FLR) [6.1- 6.6].

135

The FLR (or guard ring) structure produces a shaping of the lateral spread of space charge region, reduces the potential gradient along the silicon surface and thus limits the field intensity. It consists of diffused region (called guard ring) that is isolated from the main junction but sufficiently close to it. The guard ring is left floating and is free to adopt any potential during device operation. In Fig.6.1 the effect of a floating guard ring on the electric field crowding is exhibited. When a reverse bias is applied, the depletion layer is initially associated with the main junction and as the bias is increased it extends outward around the guard ring. The spacing between the main junction and the guard ring is such that the punch through occurs before the avalanche breakdown of the cylindrical junction associated with the main junction. Thus, the maximum electric field is limited; any further increase in the reverse voltage is taken up by the ring.

Fig.6.1: Comparison of the electric field crowding for a planar junction (a) without and (b) with a floating field limiting ring. The effect of FLR, however, becomes insignificant when the spacing between the main junction and the guard ring is too large or too small [6.7], hence, the FLR spacing must be optimized to get maximum breakdown voltage. A simple, but effective criterion to optimize the design of complex multiple floating guard ring structure is proposed in Ref. [6.7]. The criterion is very robust in the sense that it is applicable to a wide variation of various physical and geometrical parameters. However, it has been observed that the accumulated surface charge due to radiation damage affect the long-term stable behaviour of the FLR structure [6.8]. Also, as mentioned in chapter 5, the surface of the oxide layer is generally exposed to changing environmental conditions, resulting in the gradual build-up of charges and thus, changing the potential distribution in the guard structure with time.

136

6.2

Device Model The simulations are performed on devices of smaller dimensions leading to reduced

simulation time, still allowing for the study of desired effects. The FLR and MO structures investigated in the present work are shown in figures 6.2(a) and 6.2(b) respectively. In the FLR structure (Fig.6.2(a)), GS is the spacing between the main junction and the guard ring, and GW is the width of the field ring window. In the MO structure (Fig.6.2(b)), tOX is the field oxide thickness and WMO is the width of the metal extension.

Fig.6.2: Cross-sectional schematic of a Si detector (a) equipped with FLR, and (b) equipped with MO. Points marked as ‘A’ and ‘B’ in the figures corresponds to the peak electric field within the Si substrate for the two structures. Figures are not to the scale.

137

In the present simulation, the values of GW (for FLR structure) and WMO (for MO structure) are kept fixed at 30µm (unless otherwise specified). Such a detector is built on an n-type, 300µm thick and <111> oriented Si wafer. In both the structures, p+ region doping profiles are taken to be Gaussian with a peak concentration of 5x1019/cm3 at the surface and the substrate doping NB is taken to be uniform. It is assumed that lateral diffusion depth at the curvature of the p-region is equal to 0.8 times the vertical junction depth (XJ). These profiles are assumed to be identical for both the structures. In all the simulations, we consider the ideal condition where the detector is free from localized defects, pin-holes etc. and the breakdown occurs either at the junction curvature or at the metal-overhang edge.

6.3

Comparison of FLR and MO Structures To optimize the design of Si strip detectors, various physical and geometrical

parameters have to be taken into consideration, viz., substrate doping concentration (NB), junction depth (XJ), and oxide charge density (QF). The optimal design of a FLR structure in addition depends on ring-to-ring spacing, ring doping profiles & width of each ring and the optimal design of MO structure in addition depends on the width of the metal extension and oxide thickness. All of these parameters strongly affect the electric field, leading to a complex design through many trial geometries. For the sake of present comparative work, the FLR is optimized with respect to guard ring spacing (GS) as given in [6.7], and field oxide thickness is optimized for MO structure as in Chapter 4. For both the structures under optimal condition, effect of the various physical and geometrical parameters on the breakdown voltage is also analyzed.

6.3.1 Effect of Guard Ring Spacing (for FLR structure) and Field-Oxide Thickness (for MO structure) To optimize the guard ring spacing (GS) in the FLR structure, the spacing is varied between 10 µm and 80 µm in steps of about 10 µm. Fig.6.3 shows the plot of breakdown voltage (VBD) as a function of guard ring spacing (GS) for FLR structure. It can be seen that VBD increases with the increase in GS, attains a maximum value corresponding to certain GS(OPT) and then decreases for further increase in GS. For

138

GS < GS(OPT), avalanche occurs at the curvature of the guard ring (‘B’ in Fig.6.2(a)) and for GS > GS(OPT), it takes place at the curvature of the main junction (‘A’ in Fig.6.2(a)). At optimal condition, i.e., GS = GS(OPT), impact ionization simultaneously occurs at the curvature of the two junctions (at the main junction and the guard ring).

Fig.6.3: Breakdown voltage vs. guard ring spacing (for FLR structure) and field oxide thickness (for MO structure). Fig.6.3 also shows the variation of VBD with field oxide thickness (tOX) for MO structure. The qualitative nature of the behaviour of VBD is similar as in case of FLR. Here the optimized value of tOX, i.e., tOX(OPT) corresponds to the simultaneous occurrence of breakdown at the junction curvature (‘A’ in Fig.6.2(b)) and the metal-overhang edge (‘B’ in Fig6.2(b)). It can be seen from Fig.6.3 that in the region tOX < tOX(OPT), the VBD changes more sharply with change in tOX as compared to the variation of VBD with GS for GS < GS(OPT), thus demanding critical process control in MO structures. However, it is clear from the comparison that the maximum breakdown voltage obtained under the optimal condition is greater for MO structure than the FLR one. This can be better appreciated by looking at the two-dimensional electric field distribution plot shown in figures 6.4(a) and 6.4(b) for the FLR and MO structures respectively. These distributions are obtained under optimal condition at VBIAS = 500 volt. It can be seen that at a given bias, the peak electric field amplitude (Emax) within the device for the optimized FLR structure is greater than the Emax for the optimized MO structure, and hence the observed behaviour of breakdown voltage for the two structures.

139

Fig.6.4: Two-dimensional electric field distribution plot within the device at VBIAS = 500 volt for (a) optimized FLR structure, and (b) optimized MO structure.

6.3.2 Effect of Junction depth Fig.6.5(a) shows the plot of VBD vs. GS for FLR case and Fig.6.5(b) shows the plot of VBD vs. tOX for MO structure for different values of junction depth (XJ). For FLR structure, VBD increases with increase in XJ for all values of GS. This is because the electric flux per unit area at the junction curvature decreases with increase in XJ thus, increasing the VBD. However for MO technique, the metal-overhang edge breakdown

140

which takes place for tOX < tOX(OPT) is almost insensitive to the variation in XJ, whereas the breakdown voltage for tOX > tOX(OPT) depends on the changes in XJ. For each value of junction depth, values of GS and tOX are optimized. 1600 For FLR structure

Breakdown voltage (volt)

1400 1200 XJ = 15 microns 1000 WN = 300 microns 800

NB = 1x1012/cm3 GW = 30 microns

600

QF = 2x1011/cm2

400 XJ = 3.5 microns

200

XJ = 1.0 microns XJ = 0.2 microns

0 0

10

20

30

40

50

60

70

80

90

100

Guard ring spacing (microns)

Fig.6.5(a): Breakdown voltage vs. guard ring spacing (for FLR structure) with junction depth as a running parameter. 1600 For MO structure

Breakdown voltage (volt)

1400 XJ = 15 microns

1200 1000

XJ = 3.5 microns

800

XJ = 1.0 microns

600

XJ = 0.2 microns

WN = 300 microns 400

NB = 1x1012/cm3 WMO = 30 microns

200

QF = 2x1011/cm2

0 0

2

4

6

8

10

12

Oxide thickness (microns)

Fig.6.5(b): Breakdown voltage vs. oxide thickness (for MO structure) with junction depth as a running parameter.

141

Figures 6.6(a) and 6.6(b) show an important feature of the metal-overhang structure in which we have plotted GS(OPT) & tOX(OPT) vs. XJ and maximum VBD vs. XJ respectively.

7

60

6

WN = 300 microns NB = 1x1012/cm3

50

5

QF = 2x1011/cm2

40

4

Optimal oxide thickness ( for MO structure; WMO=30 microns )

30

3

20

2

10

1

Optimal guard ring spacing ( for FLR structure; GW=30 microns)

0

Optimal oxide thickness (microns)

Optimal guard ring spacing (microns)

70

0 0

2

4

6

8

10

12

14

16

Junction depth (microns)

Fig.6.6(a): Optimal oxide thickness and optimum guard ring spacing vs. junction depth for the MO and FLR structure respectively. 1600

Maximum breakdown voltage (volt)

1400

For MO structure

1200 1000 800

WN = 300 microns

For FLR structure

NB = 1x1012/cm3

600

QF = 2x1011 /cm2

400 200 0 0

2

4

6

8

10

12

14

16

Junction depth (microns)

Fig.6.6(b): Maximum breakdown voltage obtained under optimal conditions vs. junction depth for the FLR and MO structure.

142

It can be seen from Fig.6.6(a) that the variation of tOX(OPT) with XJ is smaller than that of GS(OPT) with XJ. In fact GS(OPT) increases continuously with the increase in XJ. Also, it is clear from Fig.6.6(b) that the maximum VBD of the MO technique is only weakly dependent on the junction depth as compared to the FLR structure under the optimal conditions. Specifically, maximum VBD increases from 950 V to 1360 V (30%) for the MO structure whereas it increases from 200 V to 1350 V (85%) for FLR technique as XJ is varied from 0.2 µm to 15 µm. Also, for shallow junctions, the MO technique offers a higher breakdown voltage than the FLR. This aspect of MO makes it an extremely useful technique for developing high-voltage Si detectors as this would permit the realization of high breakdown voltage with relatively shallow junctions, thus offering the much desired process compatibility. This inherent merit of MO design can be further appreciated by noting that the FLR and most other junction termination techniques vitally depend on increasing the junction depth for improving the breakdown voltage. However, for large values of XJ such as XJ=15 µm, the VBD of the two structures assume almost the same value.

6.3.3 Effect of Relative Permittivity of Passivant To see the influence of relative permittivity (εdie) of passivant dielectric on VBD of the FLR and MO structures, maximum VBD and optimal values of GS and tOX are plotted against εdie in figures 6.7(a) & 6.7(b) respectively. The structure is simulated for two passivants: SiO2 (εdie=3.9), Si3N4 (εdie=7.5), and also when the device is unpassivated (εdie=1). The qualitative nature of the variation of VBD with GS and tOX is same in all the cases. It can be seen from Fig.6.7(a) that for both FLR and MO structures, the VBD corresponding to εdie=3.9 is higher than that for εdie=1.0, and the VBD for εdie=7.5 is greater than VBD for εdie=3.9, thus demonstrating that εdie plays an important role in determining VBD of cylindrical junction. However, the increase in the maximum VBD for MO structure is greater than that of FLR design.

143

Maximum breakdown voltage (V)

1600 For MO structure (WMO=30 microns) 1400

1200

WN = 300 microns NB = 1x1012/cm3 XJ = 3.5 microns QF = 2x1011/cm2

1000 For FLR structure (GW=30 microns)

800

600 0

1

2

3

4

5

6

7

8

Relative permittivity of passivant

Fig.6.7(a): Maximum breakdown voltage obtained under optimal conditions vs. relative permittivity of the passivant for the FLR and MO structure.

35

4.5 For FLR structure (GW=30 microns)

Optimal guard ring spacing (microns)

3.5 25 3 20

2.5 For MO structure (WMO=30 microns)

WN = 300 microns

15

12

3

NB = 1x10 /cm XJ = 3.5 microns

2 1.5

QF = 2x1011/cm2

10

1 5

0.5

0

0 0

1

2

3

4

5

6

7

Relative permittivity of passivant

Fig.6.7(b): Optimal oxide thickness and optimum guard ring spacing vs. relative permittivity of the passivant for the FLR and MO structure. 144

8

Optimal oxide thickness (microns)

4

30

Another very important property of MO design is also clear from Fig.6.7(b) that the tOX(OPT), required to accomplish maximum breakdown voltage, is lower if εdie of the passivant layer is larger. Higher values of εdie allows for reduction in tOX required for attaining a given breakdown voltage in MO structures, thus reducing the dead area from the detector. Whereas for FLR structure, the value of GS(OPT) is independent of the εdie of the passivant dielectric.

6.3.4 Effect of Surface Charges In practice, a positive oxide fixed charge adversely affects the breakdown voltage of p+-n junctions, which are usually preferred over n+-p junctions for blocking high voltage. A termination technique that renders the VBD insensitive to this charge is attractive for high-voltage devices. Therefore, the influence of oxide fixed charge on the optimal conditions & maximum breakdown voltage of both FLR and MO structures are shown in figures 6.8(a) and 6.8(b). 35

4.5

Optimal guard ring spacing (microns)

For MO structure (WMO=30 microns)

25

3.5 3

20

2.5

For FLR structure (GW=30 microns)

15

10

2 WN = 300 microns NB = 1x1012/cm3 XJ = 3.5 microns

1.5 1

5

0.5

0 1.0E+11

Optimal oxide thickness (microns)

4

30

0 3.0E+11

5.0E+11

7.0E+11

9.0E+11

1.1E+12

Fixed oxide charge density (/cm2)

Fig.6.8(a): Optimal oxide thickness and optimum guard ring spacing vs. fixed oxide charge density for the FLR and MO structure.

145

1400

Maximum breakdown voltage (V)

1200 WN = 300 microns

1000

MO structure ( Optimal oxide thickness, same for all QF)

NB = 1x1012/cm3 XJ = 3.5 microns

800

FLR structure ( Optimal guard ring spacing for all QF)

600

400 FLR structure

200

0 1.0E+11

( Optimal guard ring spacing for QF=2x1011/cm2)

3.0E+11

5.0E+11

7.0E+11

9.0E+11 2

fixed oxide charge density (/cm )

Fig.6.8(b): Maximum breakdown voltage obtained under optimal conditions vs. fixed oxide charge density for the FLR and MO structure. It is clear from Fig.6.8(a) that the optimum oxide thickness (tOX(OPT)) for MO design is independent of oxide fixed charge; in contrast, the optimum field ring spacing for FLR structure is extremely sensitive to QF. In other words, the optimal MO design is applicable over a wide range of QF, whereas the optimal FLR design is confined to the specific value of QF, thus further revealing the performance leverages of the MO technique over the FLR technique. Also, it is evident from Fig.6.8(b) that the maximum VBD of the FLR structure is more sensitive to oxide fixed charge than the MO structure, thus clearly illustrating the superiority of the MO structure. Further, the problem of extending the optimal FLR design, valid for a particular value of QF to other values is also demonstrated. Here the optimum ring spacing obtained at QF = 2x1011/cm2 has been used. It is clear that VBD decreases more sharply if GS is optimized only for a single value of QF. Since QF is a physical parameter, which increases with increase in ionizing radiation, it is not possible to optimize GS for all values of QF once envisaged in the device structure. The above

146

1.1E+12

danger never exists in the design of the MO structure, where tOX(OPT) is almost insensitive to the variation in QF. Further, a multiple FLR structure occupies larger area than that required for a single FLR structure. In contrast, a multi-step MO structure occupies an area comparable to that of a single-step MO structure. Hence, a multi-step MO structure appears to be more compact than a multiple FLR structure.

6.3.5 Effect of the Width of Guard Ring (GW; for FLR structures) and Metal-Extension (WMO; for MO structures) Fig.6.9(a) shows the plot of VBD as a function of GS with GW as a running parameter and Fig.6.9(b) shows the plot of VBD vs. tOX with WMO as a running parameter. It can be seen from Fig.6.9(a) that for FLR structures, the maximum breakdown voltage increases around 70 volt as the GW is increased from 30 µm to 70 µm. For MO structures the corresponding increase in VBD is ~ 175 volt as WMO is increased from 30 µm to 70 µm. The reason for this increase in VBD is that as the width (GW for FLR structures and WMO for MO structures) increases, the depletion region is pushed further outwards, distributing the potential over a larger distance and making the overall picture more like a planar junction. However, it should be pointed out that after reaching a certain width, maximum VBD saturates due to the sufficient flattening of equipotential lines, and further increase in GW and WMO would no longer increase the VBD. 500

For FLR structure

Breakdown voltage (volt)

450 400 350

GW=70 microns

300 250

GW=50 microns

200

WN=300 microns

150 100

NB=1x1012/cm3 XJ = 1.0 microns

50

QF = 2x1011/cm2

GW=30 microns

(a)

0 0

10

20

30

40

50

60

Guard ring spacing (microns)

Fig.6.9(a): Breakdown voltage vs. guard ring spacing with GW as running parameter.

147

1600 For MO structure

Breakdown voltage (volt)

1400

WMO=70 microns

1200 WMO=50 microns 1000 800

WMO=30 microns

600

WN=300 microns

400

NB=1x1012/cm3 XJ = 1.0 microns

200

QF = 2x1011/cm2

(b)

0 0

1

2

3

4

5

6

7

Oxide thickness (microns)

Fig.6.9(b): Breakdown voltage vs. field oxide thickness with WMO as running parameter. It is also to be noted that optimized guard ring spacing (for FLR) and optimized field-oxide thickness (for MO) increases with increase in guard ring width (GW). In order to explain this behavior, we have plotted in figures 6.10(a) & 6.10(b), the plot of 2-D potential distribution around the main junction and the floating ring for GW = 30 µm and GW = 70 µm at fixed GS = 30 µm. It can be seen that the potential, to which a wide guard floats (Fig.6.10(b)) with respect to the inner biased region, is smaller than that for a narrower guard (Fig.6.10(a)). To illustrate, the 100 volt curve touching the outer edge of the floating guard for GW = 70 µm (Fig.6.10(b)) lies very much within the main diode and the guard ring for GW = 30 µm (Fig.6.10(a)). Thus, for GS = 30 µm, a wider guard has to support a large potential drop resulting in crowding of equipotential lines near the outer junction of the guard ring. Similar behaviour is also observed for metal-overhang structure.

148

Fig.6.10: 2-dimensional equipotential contours in step of 20 V at GS=30 µm for (a) GW = 30 µm and (b) GW = 70 µm for FLR structure.

6.4

Comparison with Experimental Work In our previous chapters, the simulation results have been verified for the metal-

overhang structures. In order to validate the simulated results for the guard ring structure, data available in the literature [6.9] was simulated. The results are given in Table 6.1. A good agreement between the simulation and experimental results is observed.

149

Table 6.1: Comparison of simulations with experimental results. NB 3

(/cm )

5 x 1011

XJ (micron)

1.2

tOX (micron)

0.85

QF 2

(/cm )

7.5 x 1011

[6.9]

6.5

GS

VBD(volt)

VBD(volt)

(P-E)/P

(micron)

Present

Experime

(%)

work (P)

nt (E)

10

212

~220

-4

20

295

~310

-5

40

223

~230

-3

Conclusions Numerical comparisons of the breakdown voltage of metal-overhang and field-

limiting ring techniques, presented in this chapter, have demonstrated the superiority of the MO design. For shallow junctions, the MO technique has higher breakdown voltage than the FLR structure. The MO structure can be used to improve the VBD of planar junctions without greatly increasing the junction depth, thus the MO technique is very important for achieving high breakdown voltages in Si strip detectors used in HEP experiments. In addition, the design layout of a MO structure is more flexible than the FLR structure. It is demonstrated that higher values of relative permittivity (εdie) of the passivant dielectric play an important role in determining breakdown voltage, and results in an increase in breakdown voltage as compared to the unpassivated detector. The optimal guard ring spacing is insensitive to the variation in εdie, whereas optimal oxide thickness decreases with increase in εdie for dielectric passivated structure. These results indicate that the MO structure is attractive for planar shallow-junction high-voltage devices. Effect of increasing the width of guard ring (for GR structure) and metalextension (for MO structure) shows that the breakdown voltage and the optimized spacing increase with increase in GW and WMO. Further, the breakdown voltage of a MO structure is practically immune to fixed oxide charge density (QF), and its optimal design is independent of QF. Thus, the present study shows that the MO structures allow for a design of Si strip detectors with shallow junctions and thinner oxides, reducing dead layer and making the detectors more suitable for HEP experiments.

150

Chapter 7

---------------------------------------------------------------Large Transverse Momentum (pT) Direct Photon Production at LHC ---------------------------------------------------------------Study of direct photon production in high-energy hadronic collisions provides a clean tool for testing the validity of perturbative Quantum Chromodynamics (QCD) predictions as well as for constraining the gluon distribution of nucleons. This chapter starts with a brief review of the Standard Model and QCD, followed by our simulation work on direct photon physics. The present analysis describes the study of direct photons in the kinematical regions accessible at LHC energy. After presenting the theoretical description of the Tevatron direct photon data, predictions for direct photon cross section at

7.1

s =14 TeV along with various theoretical uncertainties is described.

An Introduction to Standard Model and QCD In recent years, high-energy physicists have arrived at a picture of the

microscopic physical universe, called "The Standard Model", which unifies the nuclear, electromagnetic, and weak forces and enumerates the fundamental building blocks of the universe (as shown in Table 7.1). The Standard Model encompasses two families of subatomic particles that build up matter and that have spins of one-half unit (fermions). These particles are the quarks and the leptons, and there are six varieties, or "flavours," of each, related in pairs in three "generations" (Table 7.1). In the Standard Model, the forces are communicated between particles by the exchange of quanta which behave like particles of spin 1 (bosons) (Table 7.2). The Standard Model has proved a highly successful framework for predicting the interactions of quarks and leptons with great accuracy.

151

Table 7.1: The fundamental particles in the Standard Model. FERMIONS (matter constituents) Leptons (spin = ½) Mass

Electric

Appr. Mass

Electric

(GeV/c2)

Charge

(GeV/c2)

Charge

νe

< 7x10-9

0

u

0.005

2/3

e

0.000511

-1

d

0.01

-1/3

νµ

< 0.0003

0

c

1.5

2/3

µ

0.106

-1

s

0.2

-1/3

ντ

<0.03

0

t

175

2/3

τ

1.7771

-1

b

4.7

-1/3

Flavour 1st gener.

2nd gener.

3rd gener.

Quarks (spin = ½) Flavour

Table 7.2: The fundamental interactions along with the force carriers. FOUR INTERACTIONS Gauge Bosons as Force Carriers Electric Spin-parity Interaction Gauge Mass 2 Charge Bosons (GeV/c ) Strong g (gluon) 0 0 1Unified 0 0 1γ (photon) Electroweak W+ 80.33 +1 1W 80.33 -1 1Z0 91.187 0 1+ Gravity graviton 0 0 2+

H (higgs)

HIGGS BOSONS Breaking EW symmetry > 105 0

0

Coupling Constant αs ~ 1 αem = 1/137 1.02 x 10-5 1.02 x 10-5 1.02 x 10-5 0.53 x 10-38

?

Quantum Chromodynamics (QCD): One particular ingredient of the Standard Model that requires further quantitative investigation is the Quantum Chromodynamics (QCD), which has emerged as a viable theory of strong interactions over the last two decades. In this theory, the force acts between color charges carried by quarks and gluons. The magnitude of the force between two color charges is proportional to the product of the charges. The intrinsic strength of the interaction is defined by a dimensionless running coupling constant (αs). There are eight massless gluons in QCD,

152

which not only transmit the strong force but also change the color of the quarks. Quarks and gluons are collectively referred to as partons. The asymptotic freedom [7.1] in QCD allows one to apply the perturbative technique for calculating cross-section at high energies for processes that are dominated by short distance interactions. The QCD coupling constant, which is a function of momentum transfer between two partons (Q2), is given to the leading log in Q2 as [7.2]:

α s (Q 2 ) =

12 π (33 − 2n f ) ln(Q 2 Λ2 )

(7.1)

where Λ is the characteristic scale parameter, required by the theory and sets the scale for Q2 dependence and is of the order of several hundred MeV, and nf is the number of quark flavors kinematically available at the collision energy. The above equation shows that as Q2 increases, αs(Q2) decreases and as Q2 → ∞ (distance → 0), αs(Q2) →0. This means that at high momentum transfer, quark confinement [7.3] can be neglected, that the constituents are essentially free in the hadrons and the hadron-hadron interaction may be simply considered as a parton-parton interaction.

7.2

QCD Phenomenology of High pT Inclusive processes Parton – parton interaction can be well understood by large transverse momentum

(pT) inclusive particle production. Particles produced at large pT are well described by QCD. In parton – parton collisions, high pT mesons are produced by the fragmentation of partons into hadrons. These mesons come out as a jet in the parent parton direction. To study the characteristics of these hadrons one will have to rely on parton – parton scattering, as well as on parton fragmentation function. An alternative way to study the elementary process is to investigate the production of direct photons at large pT. Consider a basic diagram for hadronic interactions A + B → C + X as shown in Fig.7.1. A and B are interacting hadrons, C is the hadron with large pT, and X represents all other particles in the final state. The incoming particles A and B contain partons ‘a’ and ‘b’ respectively, which scatter, producing partons labeled ‘c’ and ‘d’ which have a large transverse momentum component qt. Subsequently hadron C is produced from parton ‘c’ via the fragmentation process. Since qt is the conjugate variable to the impact variable of the parton scattering process, large qt implies that partons have scattered at a 153

small distance where αs is small and Q2 is large. Hence perturbation theory can be applied.

Fig.7.1: Schematic diagram of a two-body reaction, A+B
C+X, which has been factorized according to the prescriptions of perturbative QCD. One can express the invariant cross section for A+B→C+X as the weighted sum of the differential cross-section, of all possible parton scatterings that can contribute [7.2], EC

 dσ sˆ 2 2 ( AB C X ) → + = dx a dxb dz c Ga A ( x a , Q )Gb B ( xb , Q ) 2 ∑ 3 ∫ d pC zc π abcd   dσ  × (ab → cd ) DC / c ( z c )δ ( sˆ + tˆ + uˆ )  dtˆ 

(7.2)

where EC and pC are the energy and momentum of the final state hadron C. sˆ, tˆ and uˆ are the Mandelstam variables for the massless parton subprocess, defined as sˆ = ( p a + p b ) 2 ; tˆ = ( p a − p c ) 2 ; uˆ = ( p a − p d ) 2

(7.3)

xa and xb are the fractions of the longitudinal momentum carried by partons ‘a’ and ‘b’ of hadrons A and B, zc is the fraction of the ‘c’ parton’s longitudinal momentum carried by hadron C. The probability of finding a parton in the interval between xa and xa+dxa is denoted by the parton distribution function (PDF) Ga A ( x a , Q 2 ) . DC c ( z c ) is the

probability that hadron C carries a momentum fraction between zc and zc+dzc of the parent parton’s (c) momentum and is referred to as the fragmentation function. Structure and fragmentation functions cannot be calculated using perturbation theory and must be obtained using data from various hard scattering processes. One can predict the crosssections if the structure functions, fragmentation functions and the cross sections for all the parton subprocesses are known. In equation (7.2), the partons have been assumed to

154

be massless and the initial and the final state partons are collinear with the corresponding hadrons, i.e., the partons have no intrinsic transverse momentum (kT).

7.3

Direct Photons in the QCD Framework QCD has been a successful theory in describing the interactions between the

fundamental building blocks inside hadrons – quarks and gluons. In addition, it is in good agreement with experimental data collected both at fixed target and colliding beam experiments. The analysis of enormous amounts of data led us to a deeper understanding of the properties of the fundamental interactions, and also revealed the inner structure of the hadrons. However, the features of QCD, although qualitatively verified, are far from being completely understood. It is then crucial to investigate the properties of QCD at hadron colliders to probe the inner structure of the hadrons from the standpoint of perturbative QCD (pQCD) techniques and the parton model of strongly interacting particles. The production of high transverse momentum direct (or prompt) photons [7.2, 7.4] from the parton–parton interactions [7.5] at the Fermilab Tevatron pp collider experiments and future LHC pp collider offers a good general testing ground for the validity of perturbative QCD and for an understanding of the contribution to the hard scatterings from the gluons, in particular. Here, direct means that the photons are generated in the hard scattering process, and not from secondary decays or as radiation product of initial or final state partons.

7.3.1 Contributions to Direct Photons Leading-Order (LO) Contributions: The major contributing physics processes for direct photon production to leading order of the strong coupling constant αs at large pT, where a perturbative expansion in QCD is expected to be valid, are the two Compton processes and the two annihilation processes that are shown in Fig.7.2 [7.2, 7.4]. Their respective contribution to the direct photon yield is clearly a function of the nature of the constituent distributions within any hadron.

155

Fig.7.2: The leading order diagrams for direct photon production.

Next–to–Leading-Order (NLO) Contributions: In recent years, NLO pQCD calculations have been performed for the direct photon production process, with a few diagrams shown in Fig.7.3. These are processes with extra gluons radiated from the initial or final state partons, or processes with gluon loops as correction to the original LO process.

Fig.7.3: A few higher order direct photon processes.

Direct Photon Pair Production: Occasionally two direct photons are produced in the hard scatter. At lowest order these photons are produced in quark-antiquark annihilation (Fig. 7.4(a)) with a production rate of ~1% of that for single direct photon. One higher order diagram that can contribute a significant portion of the cross section [7.6] is the quark box diagram

(gluon-fusion sub process gg → γγ ) in Fig.7.4(b).

156

Although this process is of the order αs2, the cross section is comparable to Born contribution and becomes even larger at high center of mass energies due to large gluon density at small value of photon momentum fraction x.

Fig.7.4: The leading contributions to the production of two prompt photons.

7.3.2 Background to Direct Photons The experimental candidate photon samples are always contaminated by substantial backgrounds, which greatly complicate the analysis of the direct photon signal. The dominant background to the prompt photon events comes from jets. While most jets consist of many particles, and are thus easily distinguishable from a single photon, a small fraction (one in 103-104) fragments in such a way that a single particle gains most of the energy of the parent parton. If that particle is a neutral meson, like π0 or η that can decay to two photons, the decay product may be indistinguishable from a single photon since at high energies the two photon showers coalesce into a single cluster in the calorimeter. The isolation criteria rejects bulk of these jets leaving about 0.1% of them which fragment this way and mimic a true photon signal [7.7]. While only one in 103-104 jets fragments this way, the dijet cross section is 103-104 times larger than that of photon cross section. Therefore, the rate at which single particle jets are produced is similar to the rate at which prompt photons are produced, thus contributing a severe background to the direct photon sample. It is therefore very important to understand the background evaluation and extraction as precisely as possible. Its precise knowledge is also crucial to pin down the existence of new particles such as H → γγ or any breaking down of symmetry in the Standard Model. The decay of π0 mesons into two photons forms the largest contribution [7.8] to background, since π0’s are most commonly produced.

Anomalous Contributions: As shown in Fig.7.5, there is another source of single photons: bremsstrahlung from an outgoing quark in a dijet event [7.9]. In this case the photon is not produced directly from the interaction vertex and is therefore not really 157

a direct photon. However, the existence of this production mechanism affects the way in which direct photons are measured and modeled theoretically. A careful choice of few selection cuts can usually minimize these contributions. Table 7.3 summarizes the processes that give rise to direct photons.

Fig.7.5: Examples of anomalous processes. Table 7.3: Various processes (order in αs and αem) contributing to the production of

single and double direct photons (along with the bremsstrahlung contributions). Description

Order

Subprocess

Annihilation

αemαs

qq → γg

Compton

αemαs

qg → γq

Single bremsstrahlung

αemαs

QCD-induced gγ coupling

αemαs2

gg → γg

QED annihilation

αem2

qq → γγ

Single bremsstrahlung

αem2αs

qg → γ (q → γ)

Double bremsstrahlung

αem2αs2

qq → (q → γ)(q → γ) gq → (g → γ)(q → γ) gg → (g → γ)(g → γ)

Quark box

αem2αs2

gg → γγ

158

qq → gq → qg → gg →

q(q g(q q(g g(g

→ → → →

γ) γ) γ) γ)

7.3.3 Motivation Direct photon production as a subject has been studied extensively on both the theoretical and experimental level. The reasons for the continuing interest in the study of direct photon physics are: 1.)

Simplicity: The importance of direct photon production arises from the well-

understood electromagnetic coupling of a photon to a quark and the consequent anchor that this process can provide in helping unfold the underlying quark-gluon dynamics and hadron structure. The great advantage of using direct photons is that they emerge from the collisions as free particles, carrying the full momentum of the partonic collisions and consequently provide pristine information about the hard scattering. In contrast, gluons or quarks must fragment into hadrons (of reduced pT), and the hadrons must first be associated with their respective partons before the extraction of the physics of constituent interaction can take place. 2.)

Fewer Number of Subprocesses: As photons do not carry electric charge they

cannot interact directly with each other. This greatly reduces the number of subprocesses which contribute to the direct photon production process. As shown in Fig.7.2, Compton and annihilation diagrams are the only two subprocesses which contribute to the first order direct photon production. There are only 18 diagrams for three quark subprocesses, compared to 127 separate two body scattering diagrams for three quarks flavour for single hadron production [7.2]. Also, because the photons do not carry charge, unlike gluons, they do not hadronize removing the inherent ambiguities present in the case of jets which can be either due to quarks or gluons. Experimentally, the photons can be clearly identified and their energy and direction can be measured precisely, unlike jets, which are messy due to fragmentation and can only be defined given a certain reconstruction algorithm. 3.)

Gluon Physics: As shown in Fig.7.2, gluons are involved in both the Compton

and annihilation diagrams. In the Compton diagram, the gluon is involved in the initial state whereas in the annihilation diagram, the gluon appears in the final state. By separating the contributions from the Compton diagram to the direct

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photon production process one can measure the gluon structure function of the colliding hadrons. The gluon fragmentation function can be measured by isolating the contributions from the annihilation diagram. The direct photon cross section is very sensitive to the gluon content of proton because of the dominant contribution from the quark-gluon hard scatterings at the LO in pp and pp collisions. This is in contrast with deep inelastic scattering (DIS) experiments where the quarks are the major participants and gluons enter only as second order effects. Thus prompt photon cross section constitutes a classical tool for constraining the gluon density [7.5] in conjunction with DIS processes especially at large longitudinal momentum fraction x (beyond x ~0.15), where there is large uncertainty. 4.)

QCD Tests: The next to leading log (NLL) [7.10] predictions for direct photon

production are available. The theory can be more reliably compared with the data over a wide kinematic range. 5.)

Window to a New World: Other than being a good testing ground of recent NLO

QCD calculations, the direct photons observed at the collider experiments can help us in searching for exotic phenomena like the excited quark states, q + g → q* → q + γ On the other hand, in the search for the Standard Model Higgs particle, photons play an important role since the di-photon signal is a unique signature of the neutral Higgs decay process in the light mass range H → γγ. The two major problems with using direct photons as probes are the following [7.4]: 1.)

The yield is greatly reduced relative to jet production (for analogous graphs, this is a factor of ~ 30 at the pT values of interest; however, as indicated previously, far more graphs contribute to hadron jets than to the yield of direct photons and consequently the overall γ/jet production ratio is ≤ 0.001);

2.)

There is substantial background from the decays of π0s and η0s mesons that make the extraction of direct photon signals challenging. Fortunately, because the photon carries away the entire pT in the elementary collision, whereas π0s or η0s are fragments of the constituents (typically, with small momentum fractions) it is expected that for fixed angle in the center of mass the γ/hadron production ratio will increase with pT, and the γ yield will eventually surpass that of π0s .

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7.4

Theoretical Formalism In the framework of QCD perturbation theory, the differential cross section for

the inclusive single prompt photon production, h1 h2 → γ X , in transverse momentum

p T and rapidity η can be written in a factorized form as dσ dpT dη

=

dσ dir dpT dη

+

dσ brem dpT dη

where we have distinguished the “direct” component σdir from the “bremsstrahlung” component σbrem. Each of these terms is known in the next-to-leading logarithm approximation [7.10] in QCD, i.e., we have ½ α ( µ ) ­ dσˆ ij α ( µ ) dir dσ dir K ij ( µ , M , M F )¾ = ¦ ³ dx1 dx 2 Gi / h1 ( x1 , M ) G j / h 2 ( x 2 , M ) s + s ® dpT dη i , j =q , g 2π 2π ¯ dpT dη ¿

α (µ ) 2 dσ brem dz ) = ¦ ³ dx1 dx 2 2 Gi / h1 ( x1 , M )G j / h 2 ( x 2 , M ) Dγ / k ( z , M F ) ( s dpT dη i , j ,k = q , g 2π z ­° dσˆ ij k ½° α (µ ) brem K ij ,k ( µ , M , M F )¾ ×® + s 2π °¯ dpT dη °¿ where the parton densities in the initial hadrons Gi/h1 and Gj/h2 and the parton to photon fragmentation function Dγ/k have been convoluted with the partonic cross sections of the hard scattering subprocesses, x being the parton’s momentum fraction and z being the longitudinal momentum fraction of parent parton carried by the bremsstrahlung photon. Here we have neglected the transverse motion of partons ( kT ) prior to hard scattering. The higher order correction terms to the direct and bremsstrahlung cross sections are represented by Kijdir and Kij,kbrem respectively. The parton distribution functions [7.11] and fragmentation functions [7.12] are extracted via global analysis of experimental data particularly from deep inelastic lepton-proton scattering.

7.4.1 Scale Sensitivity The intrinsic uncertainties of the NLO QCD predictions are related to the choice of three arbitrary scales: the renormalization scale µ which appears in the evolution of

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strong coupling constant αs, the factorization scale M associated with the initial state collinear singularities and the fragmentation scale MF related to the collinear fragmentation of a parton into a photon. Roughly speaking, these are the parameters which control how much of the higher effects are resummed in αs(µ), Gi/h and Dγ/k respectively and how much is treated perturbatively in Kijdir and Kij,kbrem. As these scales are unphysical, the theory can be considered reliable only in the region of the phase space where the predictions are stable with respect to the scale variations [7.13]. At the leading logarithm level, the photon cross section depends sensitively on the specific choice used for scales. When the next-to-leading logarithm terms are included, it makes the theory more complete and less sensitive to the choice of scales. Current NLO QCD calculations for direct photon cross section have been performed both analytically [7.10, 7.14] and in Monte Carlo framework [7.15] which conventionally choose all the three scales to be equal to the photon transverse momentum p T .

7.4.2 Pseudorapidity Dependence Previous theoretical analysis [7.16] has shown that the direct photon cross section has a pseudorapidity (η) dependence which is sensitive to the parameterization of the gluon distribution functions. This sensitivity is even more dramatic in the lower transverse momentum or in the forward regions of the detector. Since earlier direct photon experiments with the exception of DØ & CDF have concentrated on the central region, the forward direct photon detection capability of the CMS detector at LHC allows us a new kinematical region for investigating the pseudorapidity dependence where the gluon distribution within hadrons can be constrained. This motivation is based on the fact that the transverse momentum fraction probed by the photons is xT =

2 pT s

, which is

related to the momentum fraction of the partons ( x ), as sˆ = x1 x 2 s . If the initial partons

are of nearly equal momenta, the photon-jet system will retain its center-of-mass back-toback nature in the laboratory frame. Then in the central region (η = 0), xT = x . Now, if one parton is of much greater momentum than the other, then the system is boosted as the more energetic parton overwhelms the softer ones, and the final state objects tend to be on the same side of the event. Since gluons typically carry much less of the momentum of

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the proton than do quarks i.e. x g << x q , one expects that in direct photon production large momentum imbalances will dominate, and the final state will tend to be boosted in the direction of incoming quark. In other words, both the photon and the jet will tend to be produced at small angles, either both forward (η > 0) or both backward.

7.4.3 Isolation Technique Because the bremsstrahlung photons tend to be collinear with the quark, and therefore the jet, from which it is radiated, an isolation criterion is used routinely in the collider regime to suppress such events. This method is based on the expectation that direct photons are fairly isolated in the detector while photons from anomalous contributions usually have quite a few hadrons in their vicinity coming from fragmentation products of the outgoing parton. The isolation requirement is typically implemented by measuring the amount of energy in the calorimeter inside a cone of radius R ( R = ∆η 2 + ∆φ 2 : typically R = 0.4 - 1.0) centred on the photon candidate and requiring that the hadronic energy be smaller than a certain amount. This strongly discriminates against production of photons from bremsstrahlung process, but the backgrounds that mimic this process are too large to allow a direct measurement. This requirement, unfortunately, can do nothing to remove bremsstrahlung photons that are radiated at large angles with respect to jets. Such an isolation cut suppresses but does not totally remove this component. Theoretical calculations involve the non-perturbative fragmentation functions to account for bremsstrahlung contribution, which is partially removed by the isolation cut matching that of the experiment. At first guess, one might expect that bremsstrahlung (for example, qq → qqγ or qg → qgγ etc.) could be of the order O(αemαs2) and perhaps negligible in most regions of phase space. This however, is not the case entirely because the fragmentation function of a constituent into a photon scales as αem/αs and the cross section for bremsstrahlung component is of the same order O(αemαs) [7.16] as the two leading order fundamental QCD subprocesses. The bremsstrahlung photons contribute a large fraction (> 50%) of the total non-isolated photons at 1.8 TeV at low xT which is reduced to 15-20% after the isolation cut is invoked [7.17].

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7.4.4 kT Smearing The global QCD analysis [7.18] of the direct-photon production process from both fixed target and collider experiments spanning over a wide range of parton x-values (0.01 to 0.6) has been puzzling. The transverse momentum (pT) distribution of the measured inclusive direct-photon cross-section agrees qualitatively well with the next-toleading-order (NLO) QCD predictions for conventional choices of scales in the high pT region. But most data sets show deviations from the NLO QCD calculations and have a steeper pT distribution in the low pT region. Neither global fits with new parton distribution functions nor improved photon fragmentation functions can resolve this discrepancy since the deviation occurs at different x-values for experiments at different energies. The obvious source of uncertainty due to choice of scale can also not be responsible for the discrepancy since it provides a small normalization shift with no change in slope. The suspected origin of the disagreements is from effects of initial-state soft-gluon radiation which generates transverse components of initial-state parton momenta, referred to as kT effects. Current NLO QCD predictions assume that the interacting partons are collinear with the beam and the partons emerging after the hard scattering are produced back-toback with equal pT. However, in the hadron-hadron centre of mass frame, the colliding partons may no longer be collinear; i.e., they can have some transverse momentum kT with respect to each other, which gives a boost in the direction of one of the outgoing particles. It has been suggested that the smearing of transverse momentum of initial-state partons can probably explain the low pT discrepancy since any uniform smearing on a steeply falling pT distribution enhances significantly only the low pT end of the spectrum [7.19]. Such kT can arise from several sources. There is a primordial kT due to confinement of partons within hadron (~ 0.5 fermi in size) which is approximately 0.3 – 0.4 GeV/c. The majority of such transverse momentum can, however, be attributed to the emission of multiple soft gluon by the partons prior to the hard scatter. Evidence of significant kT has long been observed in measurements of dimuon, diphoton, and dijet production [7.19]. Studies of high mass pairs of particles such as direct photons and π0’s can be used to extract information about the parton kT. The kinematic distributions of

164

these high mass pairs illustrate the evidence for significant kT which increase almost logarithmically with increasing centre of mass energies, from ~ 1GeV/c at fixedtarget energies increasing to 3-4 GeV/c at the Tevatron collider. Fully resummed pQCD calculations for single direct photon production are anticipated shortly. Since current NLO QCD calculations do not account for the effects of multiple soft-gluon emissions, we employed a phenomenological model to incorporate kT effects in the NLO calculations of direct photons. We use LO pQCD (PYTHIA which incorporates kT effects using a Gaussian smearing technique) to create kT-enhancement factors as a function of pT for inclusive cross sections and then apply these factors to the NLO calculations. We recognize that this procedure involves a risk of double-counting since some of the kT-enhancement may already be contained in the NLO calculation. However, we expect the effect of such double-counting to be small [7.19].

7.5 Monte Carlo Simulation A Monte Carlo (MC) simulation based on PYTHIA 6.2 code [7.20] is used to calculate the direct photon cross section by generating N = 105 pp events at the center-of mass energy of 14 TeV. The parton level subprocesses employed to simulate γ-jet events were: qg → qγ , qq → qγ

and

gg → gγ . PYTHIA describes the hard scattering

between hadrons via leading order perturbative QCD matrix elements. The parton distribution functions used in the analysis were those given within PYTHIA.

7.6 Direct Photon Production at Tevatron: Comparison of Data with Theory at

s =1.8

TeV &

s =630

GeV

In Fig.7.6, we compare the measurement of the cross section for production of isolated prompt photons in proton-antiproton collisions at Tevatron [7.21] at TeV and

s =1.8

s = 630 GeV by CDF & DØ Collaboration with the corresponding theoretical

calculations. The data used here was collected during Run 1B [7.22]. The NLO QCD calculations [7.14] are derived using the latest PDF, CTEQ5M1 [7.23] with the renormalization, factorization and fragmentation scales set at pT. For CDF data, this

165

calculation imposes an isolation criterion, which rejects events with a jet of ET > 1 GeV in a cone of radius 0.4 around the photon. For DØ data, the total transverse energy near any ET

R ≤ 0.4

photon − ET

R ≤ 0.2

candidate

cluster

must

satisfy

an

isolation

requirement

< 2.0 GeV , where R = ∆η 2 + ∆φ 2 is the distance from the cluster

center.

Fig.7.6: The inclusive photon cross sections at center-of-mass energies 1.8 TeV and 630 GeV measured by the CDF & D0 collaborations compared to the NLO QCD predictions [7.24].

Fig.7.7: A comparison of the Run 1b data at 1.8 TeV and 630 GeV data to NLO QCD calculations [7.24] as a function of photon pT.

We see from Fig.7.6 that the NLO QCD predictions agree qualitatively with the measurements over a wide range of pT. The visual comparison between data and theory is aided by plotting (data-theory)/theory on a linear scale (Fig.7.7) which shows an

166

excess of photon cross section over theory in the low pT region. We notice that the CDF and DØ data sets at 630 GeV and 1.8 TeV are consistent with each other. Fig.7.8 shows the effect of different parameters on the 1.8 TeV data. The change of renormalization scale from µ = pT to µ = pT/2 or µ = 2pT changes the predicted cross sections by < 10% thus producing a small normalization shift throughout with almost no change in slope. Simultaneous variations of all the theoretical scales (renormalization scale µ, factorization scale M and fragmentation scale MF) [7.25] independently also produces a small change in the shape of the predictions, but does not reproduce the shape (Fig.7.7) of measured cross sections. However, one should not worry too much about the large pT regime keeping in mind that data have a 14 % normalization uncertainty, and that changing scales in the theory also produces roughly the same normalization shift.

Fig.7.8: A comparison of the CDF & DØ Run 1B data at 1.8 TeV to theories with NLO QCD using different choices of the renormalization, factorization and fragmentation scales [7.24].

The low pT excess of data over theory is consistent with previous observations [7.18, 7.19] at collider and fixed-target energies. This excess may originate in additional multiple soft-gluon radiations (which could give a recoil effect to the photon+jet system) [7.19] beyond that included in the QCD calculations, or reflect inadequacies in the parton distribution functions [7.26] and fragmentation contributions. It has been suggested [7.18,

167

7.19] that the smearing of transverse momentum of initial state partons (kT kick) can probably explain this low pT discrepancy since any uniform smearing on a steeply falling pT distribution enhances significantly only the low pT end of the spectrum. Higher order QCD calculations including soft-gluon effects through resummation technique are becoming available [7.27] but are not currently ready for detailed comparisons. To explore qualitatively the effect of kT on the comparisons, we have added a simplified Gaussian smearing in the NLO QCD calculations to see if the measurements could be sensitive to these effects. Fig.7.9 shows a comparison of the CDF and DØ data at 630 GeV to NLO QCD calculation using CTEQ5M1 with the addition of a 3 GeV kT correction (a value obtained from the diphoton measurement in CDF). We see that the NLO theory supplemented with kT correction accounts to a great extent the low pT discrepancy between data and theory.

Fig 7.9: The comparison of the CDF & D0 data at 630 GeV to NLO QCD calculations with 3 GeV kT correction [7.24].

7.7

Expectations for Direct Photons at LHC

7.7.1 Leading Order (LO) Cross Section Fig.7.10 shows the transverse momentum (pT) distribution of direct photons for various LO subprocesses normalized to the total rate at LHC energy in the kinematical range 20 GeV < pT < 400 GeV and pseudorapidity interval –3.0 < η < 3.0. The results were generated by simulating direct photon events using PYTHIA with the CTEQ5M1 parton distribution function and with the renormalization scale µ = pT.

168

Fig.7.10: Contributions of various subprocesses for direct photon production at the leading-order normalized to the total rate at LHC energy.

The results shown in Fig.7.10 reveal that the Compton scattering provides the dominant mode of direct photon production in the entire kinematical region which is indicative of the fact that the direct photon data from LHC would be handy in providing constraints on the gluon distribution in global fits of parton distributions in the high pT range. The annihilation scattering provides relatively small contribution in the low and intermediate pT regions, but its contribution increases with increase in pT. Also, the gluon-gluon initiated processes are not expected to play a significant role over the pT range shown.

7.7.2 Next-to-Leading Order (NLO) Cross Section Fig.7.11 shows the pT spectrum of NLO QCD predictions [7.14] for direct photon cross section at LHC along with the LO (PYTHIA) estimates, evaluated with the CTEQ5M1 parton distribution function and renormalization scale µ = pT in the same pseudorapidity interval –3.0< η <3.0. The NLO calculations use the same isolation cut as that of CDF. In comparison to the cross-section at Tevatron energy (Fig.7.6), this distribution extends to greater than three times than at the Tevatron. We see that the NLO QCD contribution is higher than the LO in the whole pT range under analysis.

169

Fig.7.11: LO & NLO QCD predictions for direct photon cross-section at LHC.

7.7.3 K - factor All PYTHIA cross-section estimates are based primarily on leading-order (LO) calculations. Often these LO cross-sections differ significantly from the theoretical NLO QCD calculations. The ratio of σ(NLO)/ σ(LO) defines the so-called K-factor. Fig.7.12 shows how the NLO results of direct photon cross-section at the LHC differ from the LO cross-section as a function of pT. Numerical PYTHIA “K-factors” [7.28] are derived for three PDF’s. K-factors of up to 2 have been plotted for CTEQ5M1 in Fig.7.12. We see that NLO contribution to the cross section decreases with rise in pT and considerably depends on the choice of PDFs. This is mainly due to considerable decrease in the higherorder soft-gluon corrections as pT increases. The theoretical predictions have greatly improved with precise PDF's.

Fig.7.12: Variation of relative contributions of LO & NLO contributions to direct photon cross-section at LHC as a function of pT.

170

7.7.4 Scale Dependence of Inclusive Cross Sections To see the renormalization scale (µ) dependence of the theoretical predictions for direct photon inclusive cross section we compare the LO and NLO QCD results with CTEQ5M1 parton distribution function. We choose the central rapidity region, η = 0, for scales µ = pT/2 and µ = 2pT normalized to the conventional scale µ = pT and the predictions are shown in Fig.7.13. We see that the LO calculations shows strong scale dependence at low pT. At pT = 20 GeV, the variation of scale between pT /2 and 2pT leads to a normalization uncertainty of ~25%. Again, the scale dependence gains more and more significance in the high pT region and at pT = 400 GeV, the variation of scale between the above limits changes the cross section by ~25%. This variation of LO QCD calculations with scale implies the need for incorporating higher order correction factors. As expected, we notice from Fig.7.13 that the NLO QCD calculations [7.24] are less sensitive to the choice of scale. The variation of scale between pT /2 and 2 pT leads to a normalization uncertainty of at most 14% over the whole pT range under consideration, thus showing the reliability of perturbative QCD predictions.

Fig.7.13: Ratio of LO & NLO QCD cross sections for direct photons at LHC for different choices of µ (µ = p T /2 and 2 p T ) normalized to that for conventional choice of µ = p T .

7.7.5 Sensitivity to Gluon Distributions 7.7.5.1

The p T spectrum As an illustration of sensitivity of direct photon production to the different

parameterizations of gluon distribution, we compare the pT spectrum of NLO QCD predictions for direct photon cross section averaged in the pseudorapidity region │η│< 3

171

due to different choices of parton distribution functions (PDFs): CTEQ3M, CTEQ4M, CTEQ5M, CTEQ5Hj, MRS99 [7.29] and GRV94M [7.30] normalized to that of CTEQ5M1 PDF (Fig.7.14). In general, theoretical uncertainties are greatly reduced for the ratio of cross sections. As can be seen from the Fig.7.14, the ratio of cross sections is almost insensitive to the choice of PDF at pT > 300 GeV, corresponding to xT > 0.05, but exhibits more and more sensitivity as we move to the low pT region.

Fig.7.14: Transverse momentum distribution of direct photon cross section at LHC for different parton distribution functions.

The ratio of the recent PDFs (CTEQ5M, CTEQ5Hj) and CTEQ5M1 is consistent with unity within at most 4% excess over the pT range under consideration. The MRS99 PDF coincides with the CTEQ5M1 at high pT and shows a deficit at low pT of at most 5%. GRV94M and CTEQ3M are significantly lower at low pT by at most ~10% and 20% respectively. Thus we notice that the pT spectrum of prompt photons is sensitive to the small-pT behaviour of gluon distribution.

7.7.5.2 The η spectrum Low pT Region: Fig.7.15 shows the pseudorapidity distribution of NLO QCD

cross section for direct photons with their transverse momenta, 20 GeV < pT < 50 GeV, for different parton distribution functions. We note that production of photons is fairly high in the central rapidity region. We also see that η spectrum is quite sensitive to the parton distribution function, particularly in the central region. This is more explicitly exhibited from the η spectrum of the ratio of cross section for different PDFs normalized

172

to that of CTEQ5M1. Thus η spectrum of direct photons is more helpful in obtaining information about the gluon distribution for small-x gluons.

Fig.7.15: Pseudorapidity spectrum of direct photon cross section at LHC for different PDF’s for transverse momentum of photons, 20 GeV < p T < 50 GeV. Large pT Region : Fig.7.16 shows the pseudorapidity distribution of NLO QCD

predictions for direct photon cross section with different PDFs for high transverse momentum of photons, 300 GeV < pT < 400 GeV. We see that from the η spectrum of direct photons it is very difficult to distinguish between the different parameterizations of the gluon distribution. Thus, the η distribution of direct photon cross section is almost insensitive to the large-x behaviour of gluons.

Fig.7.16: The Pseudorapidity spectrum of direct photon cross section at LHC for different PDFs for transverse momentum of photons, 300 GeV < p T < 400GeV.

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7.7.6 Pseudorapidity Dependence Fig.7.17 shows the pT distributions of LO & NLO QCD predictions for integrated direct photon cross section in different pseudorapidity windows. As expected, cross section is more for larger η interval.

Fig.7.17: LO and NLO QCD predictions for direct photon cross section at LHC integrated in different pseudorapidity intervals.

Fig.7.18 compares the averaged differential cross sections for direct photons in different pseudorapidity bins normalized to the cross section for η ~ 0. We see that direct photons are produced fairly copiously in the central region. The production rate decreases in the high η domain, particularly at high pT.

Fig.7.18: Ratio of direct photon cross section in different pseudorapidity bins normalized to the cross section in the central rapidity region.

174

7.7.7 Cone Size Dependence Fig.7.19 illustrates the cone size dependence of the NLO QCD predictions for direct photon cross section as a function of pT in the pseudorapidity bin (-3 < η < 3) using CTEQ5M1 parton distribution function and the renormalization scale µ = pT, wherein the pT spectrum of the ratio of cross sections with different cone sizes to that of cone size = 0.7 is shown. As can be seen from the figure, the cross section decreases as cone size increases. At pT = 50 GeV, changing the cone size from 0.1 to 0.4 and 0.7 reduces the cross section by 13% and 38% respectively. This behaviour is expected because the isolation criterion excludes events with a certain hadronic energy E0 inside a cone of size R. Now, keeping E0 fixed and increasing R means that we are not even allowing such events in a large cone, so it is a stricter criterion (keeping in mind that the jet cross section increases considerably with cone size [7.31]), and hence the cross section must decrease. We see from Fig.7.19 that cross section decreases almost uniformly over the whole pT region except at low pT for cone size = 0.1 where it shows some shape variation.

Fig.7.19: Ratio of cross sections for different cone sizes to that of the cross section for 0.7 cone size, from NLO QCD, with CTEQ5M1 and evaluated at µ = p T .

7.8

Conclusions Direct photon production continues to be an interesting arena to test modern

perturbative QCD calculations. In this chapter, we have compared the isolated prompt photon data measured by CDF at

s =1.8 TeV with the NLO predictions using the latest

175

parton distribution function. The data show a clear excess over theory for pT < 25 GeV. It suggests that a more complete theoretical understanding of processes that contribute to low pT behaviour of the photon cross section is needed which have been addressed by resuming higher order contributions. It is found that the NLO theory supplemented with kT correction accounts to a great extent the low pT discrepancy between data and theory. The LHC run with greatly extended kinematical range and high statistical precision of data will offer tremendous opportunities to refine our understanding of the production of photons in hard scattering processes. It is found that the rate of prompt photon production is expected to be very high at LHC compared to that at Tevatron. PYTHIA results indicate that the Compton scattering will dominate the production mechanism in the entire kinematical range considered in the analysis. The pT spectrum of the relative contributions of LO and NLO cross section shows that the higher order contribution dominates in the low pT region but decreases in importance considerably at high pT. The NLO QCD predictions depend only marginally on the choice of scale. The pT distribution of direct photon cross section is almost insensitive to the different parameterizations of gluon distributions in the high pT region (pT > 300 GeV), but shows quite a bit of sensitivity at small pT values. We also see that at low values of pT, the shape of the rapidity dependence of the photon cross section is very sensitive to the small-x behaviour of gluon distribution. It means that the η spectrum can be used to constrain the gluon distributions. It is found that direct photons are produced fairly copiously in the central rapidity region. Its production cross section depends strongly on the cone size (used in the isolation cut) and is found to decrease with increasing cone size.

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