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 isuseful; he studies it because he delights in it,and he delights in it because it is beautiful. Ifnature were not beautiful, it would not beworth knowing, and if nature were not worthknowing, life would not be worth living.

Henri PoincaréHenri Poincaré Henri PoincaréHenri Poincaré

Dedicated to…Dedicated to…Dedicated to…Dedicated to…

my loving Parents and Sisters, my loving Parents and Sisters, my loving Parents and Sisters, my loving Parents and Sisters,

Alka and ShaliniAlka and ShaliniAlka and ShaliniAlka 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. The Compact Muon Solenoid (CMS) Experiment 7

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

Chapter 2: 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

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 55

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

3.3. Validation – An Absolute Requirement 60

Chapter 4: Effect of Metal-Overhang on Silicon Strip Detectors 61

4.1. High-Voltage Si Detectors: Techniques to

Improve Breakdown Voltage 62

4.2. Modulation of Electric Field by Extended

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

5.4. 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. 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

5.6.1. Irradiation Facility 128

5.6.2. Measurement Set-ups 128

5.6.3. Measurement Results on Irradiated Sensors 130

5.7. Conclusions 133

Chapter 6: 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

7.3.1. Contributions to Direct Photons 155

7.3.2. Backgrounds to Direct Photons 157

7.3.3. Motivation 159

7.4. Theoretical Formalism 161

7.4.1. Scale Sensitivity 161

7.4.2. Pseudorapidity Dependence 162

7.4.3. Isolation Technique 163

7.4.4. KT Smearing 164

7.5. Monte Carlo Simulation 165

7.6.Direct Photon Production at Tevatron: Comparison of Data

With Theory at s =1.8 TeV & s =630 GeV 165

7.7. 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

7.8. Conclusions 175

Bibliography 177

i

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.

iii

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

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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.

1

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

2

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.

3

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.

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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.

5

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 cross-

section 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.

6

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-

7

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

8

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.

9

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

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

10

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 TTT ppp 1.0~/∆ (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.

11

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 di-

photon 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 ( 61.2653.1 ≤≤ η ) 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 ( ZW ′′, ) 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).

13

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 γγ→H , 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

),4(/ * channelplatedgoldlllllZZZZH ±−+−+→→ . 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 ν22 ±→→ lWWH , having highest branching ratio (six times larger than the ±l4 channel). Also, it has a distinct signature, two high pT leptons and high miss

TE .

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

14

channels jjlWWH ν±→→ , νν−+→→ llZZH , and jjllZZH −+→→ 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: 00 , Hh , 0A 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

15

having very good tracking, calorimetry and muon system, would be able to detect most

promising decay channels which have small branching ratios like, 00 / Sd KJB ψ→ , and

−+→ ππ0dB ; with −+→ µµψ/J and −+→ ππ0

SK . These channels would measure

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 00SS BB − oscillations, the mixing parameter Sχ can

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 ( ttgg → )

rather than from ( ttqq → ) and will be ttσ ~ 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.

16

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

61.2653.1 ≤≤ η 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 ( γγ→H ), 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

17

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 γγ→H , 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 γγ→H 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 γγ→H . 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

18

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.

19

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.

20

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 base-plate. 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.

21

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

22

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

23

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.

24

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

25

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 Next-

to-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).

26

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

27

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

28

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.

29

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

Ev ee µ= & Ev hh µ= (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.,

inpn == , (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

30

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

TkE

TkE

vciB

g

B

g

eTeNNnpn−−

∝== 32. (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 n-

type 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

nqpnq npn µµµρ 1

)(1 =+

= for n >> p (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

31

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)

)(Vbi png qVqVEq +−= , (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.

32

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:

si

xxE

dxVd

ερ )(

2

2

=∂∂=− [ ])()()()( xNxNxnxpq

ADsi

−+ −+−=ε

(2.6)

which for the abrupt junction under the depletion layer approximation becomes

(assuming that all impurity ions are ionized)

02

2

≤<−−≈− xxforNqdx

VdpA

Siε (2.7)

nDSi

xxforNq ≤<≈ 0ε

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

0)()( <≤−+−

= xxforxxqNxE ppSi

A

ε (2.8)

nnSi

D xxforxxqN≤<−= 0)(

ε

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

Si

pA

Si

nDm

xqNxqNxEEεε

==== )0( (2.9)

Potential distribution along with the built in potential can be obtained by integrating

equation (2.8) once again

−=

WxxExV m 2

)(2

(2.10)

WEWxVV mbi 21)( === , (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,

biDA

DAsi VNNNN

qW

+=ε2

(2.12)

33

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,

biB

Sin V

qNxW

ε2=≈ , (2.13)

)()( WxqNxESi

B −=ε

(2.14)

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

−=

qTkV

qNW B

biB

Si 22ε (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,

+−= V

qTkV

qNVW B

biB

Si 22)(

ε (2.16)

For reverse voltage larger in comparison with

−

qTkV B

bi2

(Vbi ~ 0.6 V and

kBT/q ~ 25 mV at room temperature), a simplified expression can be used for the

depletion of the SCR width on the applied voltage:

B

si

qNV

VWε2

)( = (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,

34

sinsi

BFD

ddqNVερµε

22

2== (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]

)(])

2[(

)(2 VWWqNd

WqNddVdQ

C Si

Si

B

Bcj

ε

ε

=== (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:

FDSi

FDBSi

j

VVford

VVforVNqC

>=

<=

ε

ε2 (2.20)

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.

35

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). Impact-

ionization 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]

nP

i

ppnnnpnU

ττ )()( 11

2

+++−

= , (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.,

36

−=

−=

TkEE

npTkEE

nnB

tii

B

iti exp;exp 11 , (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,

tthn

ntthP

p NvNv στ

στ 1&1 == , (2.23)

where Nt is the density of trapping centers, σn and σp are the respective capture cross-

sections for the electron and holes respectively, and thv 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,

IVIIIIII IIIII +++= (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]:

37

WAUqI I ||= (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

011

2

2ττττi

g

i

nP

i nnpn

nU ≡≡+

= , (2.26)

and

−−+

−=

+=

TkEE

TkEE

npn

B

itn

B

itp

i

npg expexp11 ττ

τττ (2.27)

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

reduces to 02ττ =g , 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

02τ

WAqnI i

I = (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],

ssII AqUI = (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],

ois snU21= (2.30)

where so is the surface recombination velocity and is defined as sttho Nvs σ= for centers

with energy levels Et = Ei., and Nst is the surface density of R-G centers. Thus,

2

0 siII

AsqnI = (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

38

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]

effnB

niIVIII LN

ADnqII,

2

=+ , (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.

22

0

0

Sii AsqnWAqnI +=

τ (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

39

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.

40

Extensive measurements of these coefficients for silicon have been conducted

[2.9] and are found to vary with electric field as: Ε−Ε− == // & pn b

ppb

nn eaea αα (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] 735108.1 Eipn

−×≅≅≅ ααα (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]

'''

0

' )()(1)( dxxMdxxMxMW

xn

x

p ∫∫ ++= αα (2.36)

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

A solution of this equation is:

−= ∫

'

0

)(exp)0()( dxMxM n

x

p αα (2.37)

41

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

( )∫ ∫

∫

−−

−

=W x

npn

x

np

dxdx

dxxM

0 0

'

0

'

exp1

)(exp)(

ααα

αα (2.38)

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

( ) 1exp'

0 0

' =

−∫ ∫

W x

npn dxdxααα (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)

∫ ='

0

1W

i dxα (2.40)

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)

∫ =

−× −

'

0

735 1)(108.1

W

Si

B dxWxNqε

(2.41)

Using this equation, the depletion layer width at breakdown for the parallel-plane

junction can be obtained [2.12]: 8/7101067.2 −×=′ BPP NW (2.42)

where subscript “PP” means plane-parallel junction and NB is expressed in cm-3. Critical

electric field at breakdown )(PPcE can be found ([2.12]) replacing xn by PPW ′ in the

maximum electric field expression (equation (2.9)) and using equation (2.42)

8/14010 BSi

PPBc NWqNE

PP=

′=

ε (2.43)

where the field is expressed in Vcm-1.

42

Similarly breakdown voltage (PPBDV ) for the one sided abrupt plane parallel

junction can be obtained ([2.12]) replacing Em by PPcE , and W by PPW ′ in equation

(2.11), and using equation (2.42)

( ) 4/3131034.521 −×=′= BPPcBDpp NWEV

PP (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:

2/)( 1 dEEV cBDPT+= (2.45)

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

43

2

2

′−

′≅

Wd

Wd

VV

PP

PT

BD

BD (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].

Fig2.5: (a) Planar diffusion process which forms junctiothe diffusion mask. rj is the radius of curvature, and (b) Tcylindrical and spherical regions by diffusion through a re

Edge effect - Cylindrical junction: Solving the P

coordinates, electric field distribution is given by

(a) )

(b

n curvature near the edges of he formation of approximately ctangular mask.

oisson equation in cylindrical

44

−Ν=Ε

rrrqr d

Si

B22

2)(

ε (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]:

7/1

,

,

43

′=

jPPc

CYLc

rW

EE

(2.48)

′−

′+

′+

′=

7/67/87/62

21ln221

Wr

rW

Wr

Wr

VV j

j

jj

BD

BD

PP

CYL (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]

−= 2

33

3)(

rrrqNrE d

Si

B

ε (2.50)

7/1

,

,

813

′=

jPPc

SPc

rW

EE

(2.51)

′+

′−

′+

′=

3/27/1337/62

314.2Wr

Wr

Wr

Wr

VV jjjj

BD

BD

PP

SP (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

45

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

46

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.

47

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

48

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:

49

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).

50

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 Criterion

Width (W) W ≤ 63 mm Mechanical tolerances Thickness (t) 300 µm ≤ t ≤ 340 µm

I-V

I ≤ 5 µA at VFD

I ≤ 10µA at 300 V

VBD ≥ 300 V for category 1

VBD ≥ 500 V for category 2

Global measurements

C-V VFD ≤ 100 V

I

Max. 1 strip with I ≥ 1 µA at VFD

Max. 1 strip with I ≥ 5 µA at 300 V

Strip-by-strip measurements

C No strips connected to the neighbour or

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.

51

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, TMA-

MEDICI [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

52

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

53

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: SAD NNnpq ρψ −−+−−=∇∈ −+ )(2 (3.1)

Continuity equation for electrons: nn UJqt

n −∇=∂∂

.1 (3.2)

Continuity equation for holes: pp UJqt

p −∇−=∂∂

.1 (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.

54

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

55

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., ++=+ Ds-

As N p N n . 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.

snn σψεψε =∇−∇ 2211 .ˆ.ˆ

(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

56

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 non-

uniform 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

57

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.

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.

P+

N-

58

Table 3.1: The structure and related command statements of the MEDICI.

Command Group

Related Statements

Comments

Mesh

Initiates the mesh generation or to read a previouslygenerated 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 Specifies impurity profile for the structure. Regrid Allows refinement of coarse mesh.

Structure Specification

Stitch Append the generated structure to the simulation mesh.

Material Specifies material properties. Mobility Specifies parameters associated with mobility models. Impurity Specifies parameters associated with impurities. Contact Specifies parameters associated with electrodes; specifies

special boundary conditions.

Coefficients & Material Parameters

Interface Specifies interface parameters for the structure. Models Enables the use of physical models during solution. Symbolic Performs a symbolic factorization. Method Sets parameters associated with solution algorithms.

Solution Specification

Solve Generates solutions for specified biases. Extract Extracts selected data over device cross-section. Plot.1d Plots a quantity along a line through the structure; plots

terminal characteristics from data in a log file. Plot.2d Plots device boundaries, junctions, and depletion edges

in two dimensions. Plot.3d Initiates three-dimensional plots. Contour Plots two-dimensional contours of a quantity. Log Specifies files for storing terminal and user-defined data. Load Reads a solution stored in a file.

Input/Output Statements

Save Writes solution or mesh information to a file.

F

$ An example of a typical MEDICI program $ Create an initial Simulation Mesh and save the mesh file MESH OUT.F=<filename> X.MESH X.MAX= H1= H2= H3= Y.MESH N= location= ratio= Y.MESH Y.MAX= H1= H2= H3= $ $ Region Definition REGION NAME= <name> $ $ Electrode Definition ELECTR NAME=<name> x.min= x.max= y.min= y.max= $ $ Specify Impurity Profiles PROFILE N-TYPE N.PEAK= <value> 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=<name> EG300 =1.12 $ Define Models, example Shockley Read Hall recombination with concentration $ dependent lifetimes, concentration dependent mobility and impact ionization modelMODEL 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=<filename> $ $ Now start the solutions and save the solution file using continuation method SOLVE CONTINUE electrod=<name> c.vstep= c.vmax= c.imax= SAVE OUT.F=<filename> $ END

59

ig. 3.1: Example of a MEDICI program.

60

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.

61

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

62

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.

63

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 junction-

strip 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

64

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

65

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 field-

plate 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].

66

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 metal-

overhang. The structure is symmetric around the center of the device so only one half of

67

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 metal-overhang.

68

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 metal-

overhang 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

69

“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 metal-

overhang. 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 meta-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.

70

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 metal-overhang 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.

71

Fig.4.5(b): 3-D impact-ionization carrier generation rate for a structure 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.4.6: I-V characteristics for a structure without metal-overhang & with metal-overhang 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.

72

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 metal-

overhang.

(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.

73

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 metal-

overhang 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.

74

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000

4200

4400

-2 0 2 4 6 8 10 12 14 16

Oxide thickness (microns)

Bre

akdo

wn

volta

ge(v

olt)

XJ=1.0 micronNB=1x1012 /cm3

WMO = 30 micronsWN =300 micronsQF = 0

tOX > tOX(OPT)tOX < tOX(OPT)

tOX(OPT)

Fig.4.8: Breakdown voltage vs. field-oxide thickness.

0.0E+00

2.0E+04

4.0E+04

6.0E+04

8.0E+04

1.0E+05

1.2E+05

1.4E+05

-2 0 2 4 6 8 10 12 14

oxide thickness (microns)

Max

imum

elc

etric

fiel

d (v

olt/c

m)

XJ=1.0 micronNB=1x1012 /cm3

WMO = 30 micronsWN =300 micronsQF = 0

tOX > tOX(OPT)tOX < tOX(OPT)

tOX(OPT)

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

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

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

75

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.

76

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).

77

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 metal-overhang 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.

78

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.

1600

2000

2400

2800

3200

3600

4000

0 2 4 6 8 10 12 14

Oxide thickness (microns)

Bre

akdo

wn

volta

ge (v

olt)

XJ=0.2 micron

XJ=0.5 micronXJ=1.0 micron

XJ=2.0 micron

XJ=3.5 micron

NB=1x1012/cm3

WMO = 30 micronsWN = 300 micronsQF = 0

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

79

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)).

80

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

81

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.

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 2 4 6 8 10 12 14 16Junction depth (microns)

Max

imum

bre

akdo

wn

volta

ge (v

olt)

without metal-overhang

tOX = tOX(OPT)

NB = 1x1012/cm3

WN = 300 micronsWMO = 30 micronsQF = 0

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.

82

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 total-

detector 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.

83

0

500

1000

1500

2000

2500

3000

3500

4000

0 2 4 6 8 10 12 14 16Oxide thickness(micron)

Bre

akdo

wn

Volta

ge(v

olt)

XJ=0.2 micronsNB = 1x1012 /cm3

WN=300 micronsQF = 0

Without metal-overhang

WMO = 10 micronsWMO = 20 microns

WMO = 30 microns

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.

84

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.

85

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.

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 2 4 6 8 10 12 14Oxide thickness (microns)

Bre

akdo

wn

Volta

ge(v

olt)

WN=100 microns

WN=200 microns

WN=300 microns

XJ=1.0 micronsNB=1x1012 /cm3

WMO=30 micronsQF = 0

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

86

Also it is known that for Punch Through (PT) diodes, substrate doping

concentration (NB) has a negligible influence on the breakdown voltage of the plane-

parallel 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].

87

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.

88

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

89

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.

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 2E+11 4E+11 6E+11 8E+11 1E+12 1.2E+12

Fixed oxide charge density (/cm2)

Bre

akdo

wn

volta

ge (v

olt)

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

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

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

NB = 1x1012/cm3

WN = 300 micronsWMO=30 microns

XJ = 1.0 micron

without metal-overhang

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

90

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.

91

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.

92

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.

93

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.

1.0E+03

5.1E+04

1.0E+05

1.5E+05

2.0E+05

2.5E+05

3.0E+05

3.5E+05

0.0E+00 2.0E+11 4.0E+11 6.0E+11 8.0E+11 1.0E+12 1.2E+12

Oxide charge density (/cm2)

Max

imum

ele

ctric

fiel

d (v

olt/c

m)

at the MO edge (EMO)

at the surface near the junction edge (ES)

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

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

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.

94

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.

2250

2450

2650

2850

3050

3250

3450

3650

0 2 4 6 8 10 12 14 16Junction depth (microns)

Max

imum

bre

akdo

wn

volta

ge (v

olt)

QF = 3x1011 /cm2

NB = 1x1012/cm3

WN = 300 micronsWMO = 20 microns

QF = 0

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.

95

Table 4.5: Comparison of the simulation results with the experimental work.

NB(1014/cm3) XJ

(micron)

tOX

(micron)

VBD(volt)

Present

work (P)

VBD(volt)

Experiment

(E)

(P-E)/P

(%)

0.30 127 137 -8

0.41 142 160 -13

0.56 183 190 -4

8.5

Ref.[4.31]

5.0 0.90 215 225 -5

2.15 553 570 -3 1.01

Ref.[4.11]

4.0

2.65 599 615 -3

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 metal-

overhang, 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

96

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.

97

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

98

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

99

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-

100

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 [5.14-

5.17].

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.

101

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

)2/exp()( 2 TkETTI Bg−∝ (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 neutron-

induced 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

102

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 metal-overhang.

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

103

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 pre-

irradiation 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.

))(,()())(,())(,(0, aeqYeqcaeqAaeqeffeffeff TtNNTtNTtNNN φφφφ ++=−=∆ (5.2)

effN∆ 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]

eqceqceqc gcNN φφφ +−−= ))exp(1()( 0 (5.3)

)exp(a

aeqAtgN

τφ −= (5.4)

)/1

11(y

eqyY tgN

τφ

+−= (5.5)

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:

eqkφττ

+=0

11 , (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.

104

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

105

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.

800

1100

1400

1700

2000

2300

2600

2900

3200

3500

3800

4100

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Oxide thickness (microns)

Bre

akdo

wn

volta

ge (V

)

XJ=0.2 microns

NB = 1x1012 /cm3

WN = 300 micronsWMO=20 micronsQF=3x1011/cm 2

semi-insulator

εεεεdie=1.0

εεεεdie=7.5

εεεεdie=3.9

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 semi-

insulator 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

106

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 semi-

insulator 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 semi-

insulator 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.

107

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.

108

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.

109

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.

800

1100

1400

1700

2000

2300

2600

2900

3200

3500

3800

4100

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Oxide thickness (microns)

Bre

akdo

wn

volta

ge (v

olt)

NB = 1x1012 /cm3

WN = 300 micronsWMO=20 micronsQF=3x1011/cm2

(a) XJ=1.0 micronssemi-insulator

εεεεdie=1.0

εεεεdie=3.9

εεεεdie=7.5

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

110

800

1100

1400

1700

2000

2300

2600

2900

3200

3500

3800

4100

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Oxide thickness (microns)

Bre

akdo

wn

volta

ge (v

olt)

NB = 1x1012/cm3

WN=300 micronsWMO=20 microns QF=3x1011 /cm2

(b) XJ=3.5 microns

εεεεdie=1.0

εεεεdie=7.5

εεεεdie=3.9

semi-insulator

2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Oxide thickness (microns)

Bre

akdo

wn

volta

ge (v

olt)

NB = 1x1012 /cm3

WN=300 micronsWMO=20 micronsQF=3x1011 /cm2

(c) XJ=15.0 micronssemi-insulator

εεεεdie=7.5

εεεεdie=3.9

εεεεdie=1.0

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

111

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.

0

0.4

0.8

1.2

1.6

2

2.4

0 2 4 6 8 10 12 14 16Junction depth (microns)

Opt

imal

oxi

de th

ickn

ess

(mic

rons

)

NB = 1x1012 /cm3

WN=300 micronsWMO=20 micronsQF=3x1011 /cm2

semi-insulator

εεεεdie=1.0

εεεεdie=3.9

εεεεdie=7.5

(a)

Fig.5.6(a): Optimal oxide thickness vs. junction depth vs. junction depth for the semi-insulator and dielectric passivated structure.

112

2400

2600

2800

3000

3200

3400

3600

3800

4000

0 2 4 6 8 10 12 14 16

Junction depth (microns)

Max

. VB

D (f

or t

OX=

t OX(

OPT

)) (vo

lt)

NB = 1x1012 /cm 3

WN=300 micronsWMO=20 micronsQF=3x1011 /cm2

semi-insulator

εεεεdie=1.0εεεεdie=3.9

εεεεdie=7.5

(b)

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.

500

1000

1500

2000

2500

3000

3500

4000

0 1 2 3 4 5 6 7 8 9 10 11 12 13Oxide thickness (microns)

Bre

akdo

wn

volta

ge (v

olt)

NB = 1x1012/ cm3

WN = 300 micronsXJ=0.2 micronsQF=3x1011/cm2

WMO=20 microns ( εεεεdie=3.9)

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

WMO=40 microns ( εεεεdie=3.9)

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.

113

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.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

5 10 15 20 25 30 35 40 45

Width of metal-overhang (microns)

t OX(

OPT

) (m

icro

ns)

semi-insulator

εεεεdie=1.0

εεεεdie=3.9

εεεεdie=7.5

NB = 1x1012 /cm3

WN=300 micronsXJ=0.2 microns QF=3x1011 /cm2

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

114

1500

1800

2100

2400

2700

3000

3300

3600

3900

5 10 15 20 25 30 35 40 45Width of metal-overhang (microns)

Max

. VB

D (f

or t O

X=t

OX(

OPT

)) (V

)

NB = 1x1012 /cm3

WN=300 micronsXJ=0.2 micronsQF=3x1011 /cm2

semi-insulator

εεεεdie=1.0εεεεdie=3.9

εεεεdie=7.5

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.

1350

1850

2350

2850

3350

3850

0 1 2 3 4 5 6 7 8 9 10

passivation layer thickness (microns)

V BD

(vol

t)

Unpassivated

εεεεdie=7.5

εεεεdie=3.9

semi-insulatorNB = 1x1012 /cm3

XJ=1.0 microntOX=0.4micronsWMO=20 micronsWN = 300 micronsQF=3x1011/cm2

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

115

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.

1000

1500

2000

2500

3000

3500

4000

0.0E+00 2.0E+11 4.0E+11 6.0E+11 8.0E+11 1.0E+12 1.2E+12Surface charge density (/cm2)

Bre

akdo

wn

volta

ge (v

olt)

XJ=0.2 microns

WN =300 microns

WMO=30 microns

semi-insulator

εεεεdie=1.0

εεεεdie=3.9

εεεεdie=7.5

(a) tOX < tOX(OPT)

NB = 1x1012 /cm3

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

116

(b) tOX = tOX(OPT)

800

1300

1800

2300

2800

3300

3800

0.00E+00 2.00E+11 4.00E+11 6.00E+11 8.00E+11 1.00E+12 1.20E+12Surface charge density (/cm 2)

Bre

akdo

wn

volta

ge(v

olt)

XJ=0.2 microns WN =300 microns

WMO=30 microns

εεεεdie=1.0εεεεdie=3.9

εεεεdie=7.5

semi-insulator

NB = 1x1012 /cm 3

(c) tOX > tOX(OPT)

0

250

500

750

1000

1250

1500

1750

2000

0.00E+00 2.00E+11 4.00E+11 6.00E+11 8.00E+11 1.00E+12 1.20E+12Surface charge density (/cm2)

Bre

akdo

wn

volta

ge(v

olt)

XJ=0.2 microns

WN =300 microns

WMO=30 microns

semi-insulator

dielectrics

NB = 1x1012

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-

117

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).

500

1000

1500

2000

2500

3000

3500

4000

50 100 150 200 250 300 350

WN (microns)

Max

imum

bre

akdo

wn

volta

ge (v

olt)

εεεεdie = 1.0

εεεεdie = 7.5

semi-insulator

εεεεdie = 3.9

NB = 1x1012 /cm3

XJ=1.0 microntOX=0.4 micronsWMO=20 micronsQF=3x1011/cm2

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

118

It can be seen from Fig.5.11 that maximum breakdown voltage obtained for semi-

insulator 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.

0.7

0.9

1.1

1.3

1.5

1.7

0.0E+00 2.0E+12 4.0E+12 6.0E+12 8.0E+12 1.0E+13 1.2E+13

Substrate doping concentration ( /cm3)

opt

imal

oxi

de th

ickn

ess

(mic

rons

)

semi-insulator

εεεεdie=7.5

XJ=1.0 micronWN = 300 micronsWMO=20 micronsQF=3x1011/cm2

(a)

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

119

2300

2550

2800

3050

3300

3550

3800

4050

0.00E+00 2.00E+12 4.00E+12 6.00E+12 8.00E+12 1.00E+13 1.20E+13

Substrate doping concentration (/cm3)

Max

imum

VB

D (v

olt)

semi-insulator

εεεεdie=7.5

XJ=1.0 micronWN = 300 micronsWMO=20 micronsQF=3x1011/cm2

(b)

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:

iS

NeffFD

WqNV

ε2|| 2

= (5.7)

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 type-

inversion starts), whereas for 2.5 KΩ−cm resistivity wafer the type inversion is slightly

120

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.

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

Integrated fluence x 1013 (n/cm2)

Neff x 1011 (/cm3)

Minority carrier lifetime (ms)

1 0.2 0.2 9.16 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

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.

121

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.

122

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.

2300

2550

2800

3050

3300

3550

3800

4050

-4.0E+12 -3.0E+12 -2.0E+12 -1.0E+12 0.0E+00 1.0E+12 2.0E+12

Effective doping concentration (/cm3)

Bre

akdo

wn

volta

ge (v

olt)

semi-insulator

εεεεdie=7.5

n-type (before type-inversion)p-type (after type-inversion)

XJ = 1.0 micronWMO=20 micronsWN = 300 micronsQF=3x1011/cm2

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.

123

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.

124

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.

125

1.0E+04

6.0E+04

1.1E+05

1.6E+05

-4.0E+12 -3.0E+12 -2.0E+12 -1.0E+12 0.0E+00 1.0E+12 2.0E+12

Effective doping concentration (/cm3)

Max

imum

ele

ctric

fiel

d (v

olt/c

m)

n-type (before type-inversion)p-type (after type-inversion)

at front junction

at back junction

XJ = 1.0 micronWMO = 20 micronsWN = 300 micronsQF=3x1011/cm2

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

126

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.

127

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

Resistiv

ity

(ρ)

(Ω-cm)

Collector-base

junction

tOX

(µm)

Field plate-

stop channel

distance (∆L)

(µm)

Present

simulation

result (P)

(V)

Exp.data (E)

(V)

(P-E)/P

60 830 880 -6%

110 1005 1045 -4%

60

[5.16]

14 µm

(QF=3x1011

/cm2)

1.25

210 1080 1065 1%

80 1170 1150 2%

110 1200 1245 -4%

75

[5.16]

14 µm

(QF=3x1011

/cm2)

1.25

210 1540 1500 3%

Semi-insulator

(SIPOS) passivated

Nitride

passivated

ρ

(Ω-

cm)

XJ

(µm)

QF

(x1011)

(/cm2)

VBD

(P)

(V)

VBD

(E)

(V)

(P-E)/P

QF

(x1011)

(/cm2)

VBD

(P)

(V)

VBD

(E)

(V)

(P-E)/P

0.5 1260 1200 5% 0.75 1115 1190 -6%

1.0 1305 1390 -6% 2 1440 1420 1%

50

[5.31]

70

(tOX=1

µm) 4.5 1530 1500 2% 3.4 1560 1630 -4%

128

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 1-

MeV-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 High-

Voltage (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.

129

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.

130

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 (µµµµm) 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

131

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 3-

4. 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 bulk-

inversion. 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.

132

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.

133

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

134

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 high-

energy 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.

135

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].

136

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.

137

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.

138

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

139

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.

140

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

141

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.

0

200

400

600

800

1000

1200

1400

1600

0 10 20 30 40 50 60 70 80 90 100Guard ring spacing (microns)

Bre

akdo

wn

volta

ge (v

olt)

WN = 300 micronsNB = 1x1012/cm3

GW = 30 micronsQF = 2x1011/cm2

For FLR structure

XJ = 0.2 microns

XJ = 15 microns

XJ = 3.5 micronsXJ = 1.0 microns

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

0

200

400

600

800

1000

1200

1400

1600

0 2 4 6 8 10 12

Oxide thickness (microns)

Bre

akdo

wn

volta

ge (v

olt)

WN = 300 micronsNB = 1x1012/cm3

WMO = 30 micronsQF = 2x1011/cm2

For MO structure

XJ = 15 microns

XJ = 3.5 microns

XJ = 1.0 microns

XJ = 0.2 microns

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

142

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.

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16

Junction depth (microns)

Opt

imal

gua

rd ri

ng s

paci

ng (m

icro

ns)

0

1

2

3

4

5

6

7

Opt

imal

oxi

de th

ickn

ess

(mic

rons

)

Optimal oxide thickness ( for MO structure; WMO=30

microns )

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

WN = 300 micronsNB = 1x1012/cm3

QF = 2x1011/cm2

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

0

200

400

600

800

1000

1200

1400

1600

0 2 4 6 8 10 12 14 16

Junction depth (microns)

Max

imum

bre

akdo

wn

volta

ge (v

olt)

For MO structure

For FLR structureWN = 300 micronsNB = 1x1012/cm3

QF = 2x1011 /cm2

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

143

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.

144

600

800

1000

1200

1400

1600

0 1 2 3 4 5 6 7 8

Relative permittivity of passivant

Max

imum

bre

akdo

wn

volta

ge (V

)

For MO structure (WMO=30 microns)

For FLR structure (GW=30 microns)

WN = 300 micronsNB = 1x1012/cm3

XJ = 3.5 micronsQF = 2x1011/cm2

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

0

5

10

15

20

25

30

35

0 1 2 3 4 5 6 7 8Relative permittivity of passivant

Opt

imal

gua

rd ri

ng s

paci

ng (m

icro

ns)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Opt

imal

oxi

de th

ickn

ess

(mic

rons

)

For FLR structure (GW=30 microns)

For MO structure (WMO=30 microns)

WN = 300 micronsNB = 1x1012/cm3

XJ = 3.5 micronsQF = 2x1011/cm2

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

145

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).

0

5

10

15

20

25

30

35

1.0E+11 3.0E+11 5.0E+11 7.0E+11 9.0E+11 1.1E+12

Fixed oxide charge density (/cm2)

Opt

imal

gua

rd ri

ng s

paci

ng (m

icro

ns)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Opt

imal

oxi

de th

ickn

ess

(mic

rons

)For MO structure (WMO=30 microns)

For FLR structure (GW=30 microns)

WN = 300 micronsNB = 1x1012/cm3

XJ = 3.5 microns

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

146

0

200

400

600

800

1000

1200

1400

1.0E+11 3.0E+11 5.0E+11 7.0E+11 9.0E+11 1.1E+12

fixed oxide charge density (/cm2)

Max

imum

bre

akdo

wn

volta

ge (V

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

FLR structure( Optimal guard ring spacing for all QF)

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

WN = 300 micronsNB = 1x1012/cm3

XJ = 3.5 microns

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

147

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.

0

50

100

150

200

250

300

350

400

450

500

0 10 20 30 40 50 60Guard ring spacing (microns)

Bre

akdo

wn

volta

ge (v

olt)

WN=300 micronsNB=1x1012/cm3

XJ = 1.0 micronsQF = 2x1011/cm2

For FLR structure

GW=30 microns

GW=70 microns

GW=50 microns

(a)

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

148

0

200

400

600

800

1000

1200

1400

1600

0 1 2 3 4 5 6 7Oxide thickness (microns)

Bre

akdo

wn

volta

ge (v

olt)

WN=300 micronsNB=1x1012/cm3

XJ = 1.0 micronsQF = 2x1011/cm2

For MO structureWMO=70 microns

WMO=50 microns

WMO=30 microns

(b)

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.

149

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.

150

Table 6.1: Comparison of simulations with experimental results.

NB

(/cm3)

XJ

(micron)

tOX

(micron)

QF

(/cm2)

GS

(micron)

VBD(volt)

Present

work (P)

VBD(volt)

Experime

nt (E)

(P-E)/P

(%)

10 212 ~220 -4

20 295 ~310 -5

5 x 1011

[6.9]

1.2

0.85

7.5 x 1011

40 223 ~230 -3

6.5 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 metal-

extension (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.

151

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

7.1 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.

152

Table 7.1: The fundamental particles in the Standard Model.

FERMIONS (matter constituents)

Leptons (spin = ½) Quarks (spin = ½)

Flavour Mass

(GeV/c2)

Electric

Charge

Flavour Appr. Mass

(GeV/c2)

Electric

Charge

νe < 7x10-9 0 u 0.005 2/3 1st gener.

e 0.000511 -1 d 0.01 -1/3

νµ < 0.0003 0 c 1.5 2/3 2nd gener.

µ 0.106 -1 s 0.2 -1/3

ντ <0.03 0 t 175 2/3 3rd gener.

τ 1.7771 -1 b 4.7 -1/3

Table 7.2: The fundamental interactions along with the force carriers.

FOUR INTERACTIONS Gauge Bosons as Force Carriers

Interaction Gauge Bosons

Mass (GeV/c2)

Electric Charge

Spin-parity Coupling Constant

Strong g (gluon) 0 0 1- αs ~ 1 γ (photon) 0 0 1- αem = 1/137

W+ 80.33 +1 1- 1.02 x 10-5 W- 80.33 -1 1- 1.02 x 10-5

Unified Electroweak

Z0 91.187 0 1+ 1.02 x 10-5 Gravity graviton 0 0 2+ 0.53 x 10-38

HIGGS BOSONS

Breaking EW symmetry H (higgs) > 105 0 0 ?

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,

153

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]:

)ln()233(12)( 22

2

Λ−=

QnQ

fs

πα (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

154

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],

++→×

=+→ ∑∫

)ˆˆˆ()()(ˆ

ˆ),(),()(

/

222

3

utszDcdabtd

d

zsQxGQxGdzdxdxXCAB

pddE

ccC

abcd cbBbaAacba

CC

δσπ

σ

(7.2)

where EC and pC are the energy and momentum of the final state hadron C. uandts ˆˆ,ˆ

are the Mandelstam variables for the massless parton subprocess, defined as 222 )(ˆ;)(ˆ;)(ˆ dacaba ppupptpps −=−=+= (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) ),( 2QxG aAa . )( ccC zD 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 cross-

sections 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

155

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.

156

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 γγ→gg ) in Fig.7.4(b).

157

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 γγ→H 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

158

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

Compton

Single bremsstrahlung

QCD-induced gγ coupling

αemαs

αemαs

αemαs

αemαs2

qq → γg

qg → γq

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

gg → γg

QED annihilation

Single bremsstrahlung

Double bremsstrahlung

Quark box

αem2

αem

2αs

αem2αs

2

αem2αs

2

qq → γγ

qg → γ (q → γ)

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

gg → γγ

159

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

160

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 .

161

7.4 Theoretical Formalism

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

the inclusive single prompt photon production, Xhh γ→21 , in transverse momentum

Tp and rapidity η can be written in a factorized form as

η

ση

ση

σddp

dddp

dddp

dT

brem

T

dir

T

+=

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

+= =

),,(2

)(ˆ2

)(),(),(

,,22/11/21 F

dirij

s

T

ij

gqji

shjhi

T

dir

MMKddp

dMxGMxGdxdx

ddpd µ

πµα

ησ

πµα

ησ

+×

= =

),,(2

)(ˆ

)2

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

,

,,,

2/22/11/221

Fbrem

kijs

T

kij

gqkji

sFkhjhi

T

brem

MMKddp

d

MzDMxGMxGzdzdxdx

ddpd

µπµα

ησ

πµα

ησ

γ

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 ( Tk ) prior to hard scattering.

The higher order correction terms to the direct and bremsstrahlung cross sections are

represented by Kijdir and Kij,k

brem 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

162

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,k

brem. 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 Tp .

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 s

px TT

2= , which is

related to the momentum fraction of the partons ( x ), as sxxs 21ˆ = . If the initial partons

are of nearly equal momenta, the photon-jet system will retain its center-of-mass back-to-

back nature in the laboratory frame. Then in the central region (η = 0), xxT = . 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

163

the proton than do quarks i.e. qg xx << , 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 ( 22R φη ∆+∆= : 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, γqqqq → or γqgqg → 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 Tx which is

reduced to 15-20% after the isolation cut is invoked [7.17].

164

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-to-

leading-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-to-

back 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

165

these high mass pairs illustrate the evidence for significant kT which increase almost

logarithmically with increasing centre of mass energies, from <kT> ~ 1GeV/c at fixed-

target 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: γγγ gggandqqqqqg →→→ , . 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 s =1.8

TeV and 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

166

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 photon candidate cluster must satisfy an isolation requirement

GeVEE RT

RT 0.22.04.0 <− ≤≤ , where 22R φη ∆+∆= 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

167

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,

168

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.

169

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.

170

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 higher-

order 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.

171

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 = Tp /2 and 2 Tp ) normalized to that for conventional choice of µ = Tp .

7.7.5 Sensitivity to Gluon Distributions

7.7.5.1 The Tp 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

172

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

173

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 < Tp < 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 < Tp < 400GeV.

174

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.

175

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 = Tp . 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

176

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.

177

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