PRINCIPLES OF h^m Intorartmi) IN Mattw Itowlinii 4th Edition Claude Leroy Universite de Montreal, Canada Pier-Giorgio Rancoita Istituto Nazionale di Fisica Nucleare, Milan, Italy World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING SHANGHAI HONG KONG TAIPEI CHENNAI
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Principles of radiation interaction in matter and detection · xvi Principles of Radiation Interaction in Matter and Detection 2. Electromagnetic Interaction of ChargedParticles in
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PRINCIPLES OF
h^m Intorartmi)IN Mattw Itowlinii
4th Edition
Claude LeroyUniversite de Montreal, Canada
Pier-Giorgio RancoitaIstituto Nazionale di Fisica Nucleare, Milan, Italy
World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI
Contents
Preface to the Fourth Edition vii
Preface to the Third Edition ix
Preface to the Second Edition xi
Preface to the First Edition xiii
Particle Interactions and Displacement Damage 1
1. Introduction 3
1.1 Radiation and Particle Interactions 5
1.2 Particles and Types of Interaction 7
1.2.1 Quarks and Leptons 9
1.3 Relativistic Kinematics 9
1.3.1 The Two-Body Scattering 13
1.3.2 The Invariant Mass 16
1.3.2.1 Lorentz-Invariant Quantities and Phase Space 18
1.3.3 Relativistic Doppler Effect 21
1.3.3.1 Redshift Parameter and Astronomy 24
1.4 Atomic Mass, Weight, Standard Weight and Mass Unit 26
1.5 Cross Section and Differential Cross Section 27
1.6 Coulomb Single-Scattering Differential Cross Section in
Laboratory and CoM Systems 30
1.6.1 Rutherford's Formula and Average Energy Transferred 35
1.7 Detectors and Large Experimental Apparata 39
1.7.1 Trigger, Monitoring, Data Acquisition, Slow Control. .
41
1.7.2 General Features of Particle Detectors and Detection
Media 41
1.7.3 Radiation Environments and Silicon Devices 48
XV
xvi Principles of Radiation Interaction in Matter and Detection
2. Electromagnetic Interaction of Charged Particles in Matter 51
2.1 Passage of Ionizing Particles through Matter 52
2.1.1 The Collision Energy-Loss of Massive Charged Particles 52
2.1.1.1 The Barkas-Andersen Effect 62
2.1.1.2 The Shell Correction Term 64
2.1.1.3 Energy-Loss Minimum, Density Effect and
Relativistic Rise 66
2.1.1.4 Restricted Energy-Loss and Fermi Plateau. .
69
2.1.2 Energy-Loss Formula for Compound Materials 73
2.1.3 Energy-Loss Fluctuations 75
2.1.3.1 5-Rays, Straggling Function, and Transport
Equation 75
2.1.3.2 The Landau-Vavilov Solutions for the
Transport Equation 78
2.1.3.3 The Most Probable Collision Energy-Loss for
Massive Charged Particles 80
2.1.3.4 Improved Energy-Loss Distribution and
Distant Collisions 84
2.1.3.5 Distant Collision Contribution to Energy
Straggling in Thin Silicon Absorbers 88
2.1.3.6 Improved Energy-Loss Distribution for
Multi-Particles in Silicon 91
2.1.4 Ionization Yield in Gas Media 92
2.2 Energy Loss of Light and Heavy Ions 94
2.2.1 Nuclear Stopping Power at Non-Relativistic Energies .97
2.2.1.1 Non-Relativistic Screened Nuclear Cross
Section 105
2.2.2 Nuclear Stopping Power at Relativistic Energies and
Energetic Recoil 109
2.2.3 Range of Heavy Charged Particles and Bragg Curve. .
118
2.3 Passage of Electrons and Positrons through Matter 124
2.3.1 Collision Losses by Electrons and Positrons 125
2.3.1.1 Most Probable Energy-Loss of Electrons and
Positrons 128
2.3.2 Practical Range of Electrons 130
2.3.3 Radiation Energy-Loss by Electrons and Positrons...
133
2.3.3.1 The Landau-Pomeranchuk-Migdal Effect and
Bremsstrahhmg Suppression 146
2.3.3.2 Collision and Radiation Stopping Powers. . 160
2.3.3.3 Radiation Yield and Bremsstrahlung AngularDistribution 160
Contents xvii
2.3.3.4 Radiation Length and Complete ScreeningApproximation 162
2.3.3.5 Critical Energy 166
2.4 Scattering of Electrons on Nuclei 167
2.4.1 The Unscreened Mott Cross Section of Electrons and
Positrons on Nuclei 169
2.4.1.1 Approximate Solutions for the Mott Cross
Section 171
2.4.1.2 Improved Numerical Approach and 7£Mott
Interpolated Expression 174
2.4.2 Complete Treatment of Electron Scattering on Nucleus 179
2.4.2.1 Finite Nuclear Size 181
2.4.2.2 Finite Rest Mass of Target Nucleus 183
2.4.3 Nuclear Stopping Power of Electrons 185
2.5 Multiple and Extended Volume Coulomb Interactions 187
2.5.1 The Multiple Coulomb Scattering 187
2.5.2 Emission of Cerenkov Radiation 194
2.5.3 Emission of Transition Radiation 200
3. Photon Interaction and Electromagnetic Cascades in Matter 207
3.1 Photon Interaction and Absorption in Matter 207
3.1.1 The Photoelectric Effect 209
3.1.1.1 The Auger Effect 216
3.1.2 The Compton Scattering 217
3.1.2.1 The Klein-Nishina Equation for Unpolarized
Photons 220
3.1.2.2 Electron Binding Corrections to Compton and
Rayleigh Scatterings 228
3.1.2.3 The Thomson Cross Section 231
3.1.2.4 Radiative Corrections and Double Compton
Effect 234
3.1.2.5 Inverse Compton Scattering 235
3.1.2.6 Power Loss of Electrons due to Inverse Compton
Scattering 241
3.1.3 Pair Production 246
3.1.3.1 Pair Production in the Field of a Nucleus. .
246
3.1.3.2 Pair Production in the Electron Field 258
3.1.3.3 Angular Distribution of Electron and Positron
Pairs 260
3.1.4 Photonuclear Scattering, Absorption and Production . . 260
3.2 Attenuation Coefficients, Dosimetric and RadiobiologicalQuantities 264
xviii Principles of Radiation Interaction in Matter and Detection
3.3 Electromagnetic Cascades in Matter 279
3.3.1 Phenomenology and Natural Units of ElectromagneticCascades 280
3.3.2 Propagation and Diffusion of Electromagnetic Cascades
in Matter 281
3.3.2.1 Rossi's Approximation B and Cascade
Multiplication of Electromagnetic Shower . . 282
3.3.2.2 Longitudinal Development of the Electromag¬netic Shower 284
3.3.2.3 Lateral Development of ElectromagneticShowers 288
3.3.2.4 Energy Deposition in Electromagnetic Cascades 296
3.3.3 Shower Propagation and Diffusion in Complex Absorbers 297
4. Nuclear Interactions in Matter 299
4.1 General Properties of the Nucleus 299
4.1.1 Radius of Nuclei and the Liquid Droplet Model 302
4.1.1.1 Droplet Model and Semi-Empirical Mass
Formula 303
4.1.2 Form Factor and Charge Density of Nuclei 305
4.1.3 Angular and Magnetic Moment, Shape of Nuclei.... 308
4.1.4 Stable and Unstable Nuclei 309
4.1.4.1 The /3-Decay and the Nuclear Capture ....311
4.1.4.2 The a-Decay 313
4.1.5 Fermi Gas Model and Nuclear Shell Model 315
4.1.5.1 7 Emission by Nuclei 320
4.2 Phenomenology of Interactions on Nuclei at High Energy ....321
4.2.1 Energy and A-Dependence of Cross Sections 322
4.2.1.1 Collision and Inelastic Length 323
4.2.2 Coherent and Incoherent Interactions on Nuclei 327
4.2.2.1 Kinematics for Coherent Condition 327
4.2.2.2 Coherent and Incoherent Scattering 330
4.2.3 Multiplicity of Charged Particles and Angular Distribu¬
tion of Secondaries 335
4.2.3.1 Rapidity and Pseudorapidity Distributions.
.
340
4.2.4 Emission of Heavy Prongs 344
4.2.5 The Nuclear Spallation Process 347
4.2.6 Nuclear Temperature and Evaporation 350
4.3 Hadronic Shower Development and Propagation in Matter ..
. 354
4.3.1 Phenomenology of the Hadronic Cascade in Matter . . 355
4.3.2 Natural Units in the Hadronic Cascade 358
4.3.3 Longitudinal and Lateral Hadronic Development .... 360
Contents xix
5. Physics and Properties of Silicon Semiconductor 367
5.1 Structure and Growth of Silicon Crystals 368
5.1.1 Imperfections and Defects in Crystals 371
5.2 Energy Band Structure and Energy Gap 372
5.2.1 Energy Gap Dependence on Temperature and Pressure in
Silicon 375
5.2.2 Effective Mass 376
5.2.2.1 Conductivity and Density-of-States Effective
Masses in Silicon 378
5.3 Carrier Concentration and Fermi Level 384
5.3.1 Effective Density-of-States 385
5.3.1.1 Degenerate and Non-Degenerate
Semiconductors 391
5.3.1.2 Intrinsic Fermi-Level and Concentration of
Carriers 393
5.3.2 Donors and Acceptors 397
5.3.2.1 Extrinsic Semiconductors and Fermi Level. .
398
5.3.2.2 Compensated Semiconductors 405
5.3.2.3 Maximun Temperature of Operation of Extrin¬
sic Semiconductors 408
5.3.2.4 Quasi-Fermi Levels 409
5.3.3 Largely Doped and Degenerate Semiconductors 411
5.3.3.1 Bandgap Narrowing in Heavily Doped
Semiconductors 411
5.3.3.2 Reduction of the Impurity Ionization-Energy in
Heavily Doped Semiconductors 415
6. Transport Phenomena in Semiconductors 417
6.1 Thermal and Drift Motion in Semiconductors 418
6.1.1 Drift and Mobility 418
6.1.1.1 Mobility in Silicon at High Electric Fields or Up
to Large Doping Concentrations 422
6.1.2 Resistivity 428
6.2 Diffusion Mechanism 431
6.2.1 Einstein's Relationship 433
6.3 Thermal Equilibrium and Excess Carriers in Semiconductors . . 435
6.3.1 Generation and Recombination Processes, Carrier
Lifetimes 437
6.3.1.1 Bulk Processes in Direct Semiconductors. . .
437
6.3.1.2 Bulk Processes in Indirect Semiconductors. .
440
6.3.1.3 Surface Recombination 445
6.3.1.4 Lifetime of Minority Carriers in Silicon....
445
xx Principles of Radiation Interaction in Matter and Detection
6.4 The Continuity Equations 446
6.4.1 The Dielectric Relaxation Time and Debye Length . . . 450
6.4.2 Ambipolar Transport 451
6.4.3 Charge Migration and Field-Free Regions 454
6.4.3.1 Carrier Diffusion in Silicon Radiation Detectors 457
6.4.3.2 Measurement of Charge Migration in Silicon
Radiation Detectors 463
6.5 Hall Effect in Silicon Semiconductors 469
7. Radiation Effects and Displacement Damage in Semiconductors 477
7.1 Energy Loss by Atomic Displacements 479
7.1.1 Damage Function, NIEL and Displacement StoppingPower 480
7.1.1.1 Knock-On Atoms and Displacement Cascade 486