semiconductors - gbv
TRANSCRIPT
SEMICONDUCTORS
BY
R. A. S M I T H M.A., PH.D.
Head of the Physics Department Royal Radar Establishment
Malvern
C A M B R I D G E
AT THE UNIVERSITY PRESS J959
CONTENTS
Chapter 1. The Elementary Properties of Semiconductors
I . I Early work on semiconductors i
I . I . I 'Excess'and'defect'semiconductors 4
1.1.2 The alkali halides 5
1.1.3 Surface and bulk effects 5
1.2 Applications of semiconductors 6
1.3 Elementary theory of semiconductors 9
1.3.1 Conduction processes 17
1.4 Control of carrier density 19
Chapter 2. Energy Levels in Crystalline Solids
2.1 Wave mechanics of free electrons 22
2.2 Motion in a periodic potential 27
2.3 Form of the energy bands 30
2.4 Positive holes 37
2.5 Motion of electrons and holes in a crystal under the infiuence of an external field of force 38
2.6 Energy-level diagrams 41
2.7 Resistance to motion of electrons and holes in a crystal 44
Chapter 3. Impurities and Imperfections in Crystals
3.1 Types of imperfection 45
3. I . I Impurities 45
3.1.2 Interstitial atoms and vacancies 45
3.1.3 Dislocations 47
3.1.4 Polygonization and dislocation walls 49
X CONTENTS
3.2 Chemical binding in semiconductors 51
3.2.1 Ionic bonds 5 1
3.2.2 Homopolar bonds 53
3.2.3 Mixed bonds 56
3.3 Substitutional impurities in group IV semiconductors 58
3.3.1 Energy levels of group III or group V impurities in group IV semiconductors 61
3.3.2 Energy levels of other impurities in group IV
semiconductors 64
3.3.3 Impurities in polar semiconductors 64
3.3.4 Impurities in the groups I I I -V semiconductors 68
3.4 Excitons 68
Chapter 4. Carrier Concentrations in Thermal Equilibrium
4.1 Distribution of electrons between the various energy levels 74
4.2 Intrinsic semiconductors 76
4.3 Semiconductors with impurity levels 82
Chapter 5. Electron Transport Phenomena
5.1 Collisions with crystalline imperfections—relaxation time, T 93
5.2 Constant relaxation time T 97
5.2.1 Electrical conductivity 97
5.2.2 The Hall effect 100
5.2.3 Transverse magneto-resistance 107
5.3 Relaxation time a function of E or v 108
5.3.1 Boltzmann's equation 108
5.3.2 Electrical conduction 110
5.3.3 Variation of T with energy E 114
5.3.4 Hall effect for semiconductor with spherical con-stant-energy surfaces 117
5.3.5 Hall effect for semiconductor with multiple energy maxima or minima 120
CONTENTS XI
5.3.6 Magneto-resistance of semiconductor with spherical constant-energy surfaces 123
5.3.7 Magneto-resistance of semiconductor with constant-energy surfaces in the form of ellipsoids 127
5.4 S catter ing mechanisms 135
5.4.1 Scattering by lattice vibrations 136
5.4.2 Phonons 141
5.4.3 Relaxation time for lattice scattering 145
5.4.4 Impurity scattering 148
5.4.5 Scattering by dislocations 153
5.4.6 Other types of scattering 154
5.5 High-field effects 156
Chapter 6. Thermal Effects in Semiconductors
6.1 Thermal conductivity 165
6.2 Thermo-electric power 170
6.3 Thermomagnetic effects 176
6.3.1 The Ettingshausen effect 180
6.3.2 The Nernst effect 183
6.3.3 The Righi-Leduc effect 184
6.4 Condition of degeneracy 185
6.5 Strong magnetic fields 186
6.6 Relative magnitudes of the magnetic effects 187
Chapter 7. Optical and High-frequency Effects in Semiconductors
7.1 Optical constants of semiconductors 189
7.2 The fundamental absorption 193
7.2.1 Direct transitions, kmin = kmax 193
7.2.2 Direct transitions, ßm l n #= ßmax, 199
7.2.3 Indirect transitions, kmin 4= Ä m t t 201
Indirect transitions, km,„ = %„,.,. 210
XÜ C O N T E N T S
7.3 Exciton absorption 211
7.4 Photo-conductivity 214
7.5 The photo-magnetic effect 216
7.6 Free-carrier absorption 216
7.7 Plasma resonance 222
7.8 High-frequency effects in a magnetic field 222
7.8.1 Cyclotron resonance 223
7.9 Magnetic quantization 226
7.9.1 The magnetic band shift 227
7.9.2 The oscillatory magneto-absorption effect 228
7.10 Impurity absorption 229
7.10.1 Spin resonance due to impurities 231
7.11 Lattice absorption 232
7.12 Infra-red emission from semiconductors 233
Chapter 8. Diffusion of Electrons and Positive Holes
8.1 Inhomogeneous semiconductors 234
8.2 Einstein's relationship 235
8.3 Departures from thermal equilibrium 237
8.4 Electron-hole recombination 239
8.5 Diffusion and conduction in extrinsic material (n ^> p or
p^> n) 240
8.5.1 The equation of continuity 240
8.5.2 Small electric field 241
8.5.3 Carrier injection (ßsmall) 244
8.5.4 Carrier extraction {£small) 245
8.5.5 Large electric field (^ > o) 245
8.5.6 General Solution (p <4 n) 247
8.6 Drift of a pulse of minority carriers in an electric field 250
CONTENTS XÜi
8.7 Near-intrinsic material 251
8.7.1 Small field condition 257
8.7.2 Carrier exclusion 258
8.7.3 Carrier accumulation 259
8.8 Comparison of contact phenomena 260
8.9 The p-n junction 261
8.9.1 Barrier-layer capacity 268
8.9.2 Current-voltage characteristic f 269
8.9.3 High-frequency behaviour oiap-n junction 274
8.10 The n+-n and p+-p junctions 276
8.11 Surface properties of semiconductors 278
8.11.1 The field effect 281
8.12 Metal-semiconductor contacts 283
8.13 Recombination mechanisms 287
8.13.1 Radiative recombination 288
8.13.2 Recombination through traps 291
8.13.3 Recombination at dislocations 295
8.13.4 Recombination with donors or acceptors at low temperatures 296
8.13.5 Surface recombination 297
8.14 Mean lifetime in filaments and thin strips 299
8.15 Photo-conductivity 303
8.15.1 Uniform absorption rate 304
8.15.2 Effect of trapping 307
8.15.3 Effect of surface recombination 309
8.15.4 Non-uniform absorption rate 310
8.16 The transverse photo-voltage 313
8.17 The photo-magnetic effect 314
Chapter 9. Methods of Determining the Characteristic Properties of Semiconductors
9.1 Band structure 318
9.2 The minimum energy gap, AE 320
XIV C O N T E N T S
9.3 Mobility of electrons and holes 325
9.4 Carrier concentration 331
9.5 Effective mass 332
9.6 Energy levels in the ' forbidden' band due to impurities 333
9.6.1 Thermal method 334
9.6.2 Impurity band conduction 334
9.6.3 Impurities with more than one level 335
9.6.4 Optical methods 337
9.7 Minority carrier lifetime 338
9.8 Injection ratio 342
Chapter 10. The Element Semiconductors
10.1 Germanium and Silicon 345
10.1.1 General physical properties 345
10.1.2 Crystal structure 346
10.1.3 Energy-band structure 347
10.1.4 Electron and hole mobility 353
10.1.5 Value of ni and cri 358
IO.I.Ö Hall coemcient 360
10.1.7 Magneto-resistance 361
10.1.8 Impurity energy levels 365
10.1.9 Optical properties 367
10.1.10 Pressure effects 368
I O . I . I I Thermo-electric power 369
10.1.12 Molten Ge 372
10.1.13 Other properties of Si and Ge 372
10.1.14 Crystal growth and purification 372
10.1.15 Ge-Si alloys 377
10.2 Diamond and gray tin 378
10.2.1 Type II b diamond 379
CONTENTS XV
10.2.2 Electron and hole mobility in high-resistivity
10.2.3
diamond
Properties of gray tin
Selenium
Tellurium
10.4.1
10.4.2
10.4.3
10.4.4
10.4.5
10.4.6
10.4.7
10.4.8
10.4.9
Boron
Other 1
Hall effect in Te
Electrical conductivity of Te
Forbidden energy gap, A.E
Optical properties of Te
Electron and hole mobility, and value of ni
Thermal effects in Te
Minority carrier lifetime in Te
Liquid Te
Te-Se alloys
Dossible dement semiconductors
380
380
38i
383
384
385
38S
38S 386
387
387 388
388
388
390
Chapter 11. Compound Semiconductors
I I . I Groups
11.2 I n S b
11.2.1
11.2.2
11.2.3
11.2.4
11.2.5
11.2.6
11.2.7
11.2.8
11.2.9
11.2.10
, IH-V intermetallic Compounds
.
Hall coefficient and conductivity of InSb
Electron and hole mobility
Value of w for InSb
Optical properties
Effective masses
Forbidden energy gap, AE
Minority carrier lifetime
Impurity levels
Crystal growth and purification
Other properties of InSb
392
393
393
394
395
396
398
4 0 0
4 0 1
4 0 2
4°3
403
XVi C O N T E N T S
11.3 Other groups I I I -V Compound semiconductors 405
11.3.1 InAs, InP 405
11.3.2 GaSb, GaAs, GaP 407
11.3.3 A 1 S b 4 ° 8
11.3.4 Alloys of groups I I I -V semiconductors 409
11.3.5 Summary of properties of groups II I -V semiconductors 409
11.4 Other intermetallic Compound semiconductors 410
11.4.1 Groups I-V Compound semiconductors 410
11.4.2 Groups I I - IV Compound semiconductors 411
11.4.3 Groups I I -V Compound semiconductors 413
11.5 Polar Compound semiconductors 413
11.6 PbS, PbSe, PbTe 414
11.6.1 Methods of crystal growth 416
11.6.2 Hall coefficient and conductivity 417
11.6.3 Electron and hole mobilities 420
11.6.4 Optical properties 421
11.6.5 Band structure 425
11.6.6 Minority carrier lifetime 426
11.6.7 Value of « 427
11.6.8 Impurities and deviations from stoichiometric composition 427
11.6.9 Other properties of PbS, PbSe, PbTe 432
11.7 CdS, CdSe, CdTe 432
11.8 Other semiconducting Compounds of S, Se, Te 434 11.8.1 Bi2Te3 435 11.8.2 Ternary and quaternary Compounds 437
11.9 Oxide semiconductors 438
11.9.1 Cu 20 438
11.9.2 ZnO, T i 0 2 439
11.9.3 Fe304 ) NiO 440
11.10 Silicon carbide 441
C O N T E N T S XVÜ
Chapter 12. Some Applications of Semiconductors
12.1 Use of semiconductors in electrical technology 443
12.2 Rectifiers 443
12.2.1 High-frequency and switching diodes 445
12.2.2 Zener or avalanche-breakdown diodes 446
12.2.3 Avalanche-injection diodes 447
12.2.4 Methods of making junction diodes 447
12.3 Transistors 449
12.3.1 The point-contact transistor 450
12.3.2 The filamentary transistor 452
12.3.3 The junction transistor 454
12.3.4 Equivalent circuits of the junction transistor 456
12.3.5 Energy-level diagram for the junction transistor
structure 461
12.3.6 Methods of manufacturing junction transistors 463
12.3.7 High-frequency and switching transistors 464
12.3.8 Other types of transistor 465
12.4 The photo-diode 466
12.5 The photo-electric power generator 469
12.6 Photo-cells 471
12.7 Infra-red detectors 471
12.7.1 PbS detectors ' 472
12.7.2 PbTe detectors 474
12.7.3 PbSe detectors 474
12.7.4 InSb detectors 475
12.7.5 Doped Ge detectors 477
12.8 Infra-red and microwave modulators 477
12.9 Applications of the Hall effect in semiconductors 478
12.10 Thermopiles and thermo-electric refrigerators 478
12.11 Thermistors, varistors and other non-linear resistors 479
Appendix. Some recent review articles on semiconductors 482
Index 483 •