10. Appendix

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564 <strong>Appendix</strong> A irradiation of n- or p-type material. By modulating the optical excitation the detection of the absorption signal was made highly sensitive [3]. In addition, if there is any doubt about the sign of the carriers, circularly polarized microwaves can be (and were) used to distinguish the sense of rotation of the carriers in the magnetic field. The most surprising result of the original experiments was the observation of two effective masses (m ∗ ) for the Ge holes: m ∗ /m0 0.04 and 0.3, both approximately isotropic. Frank Herman and Joseph Callaway had calculated that the top of the valence band in Ge occurs at the center of thr Brillouin zone and is threefold degenerate (sixfold with spin), corresponding to p bonding orbitals on the Ge atoms. This would have given rise to three hole masses. We suggested [4,5] that the spin–orbit (s.o.) interaction splits the p orbitals into fourfold degenerate (related to p3/2 orbitals) and twofold degenerate (related to p1/2 orbitals) bands at the zone-center. We found that the most general form of the energy of the upper valence bands in the diamond structure to second order in wavevector k is (2.62) E(k) Ak 2 ± [B 2 k 4 C 2 (k 2 x k2 y k2 y k2 z k2 z k2 x )]1/2 . This was perhaps the first application of the spin–orbit interaction in semiconductors. The “s.o. split-off” or lower band in Ge is 0.30 eV below the top of the valence band edge. This s.o. splitting and the lower band itself are explored best by optical absorption. The analysis by Kahn [6] of the available experiments was an important confirmation of our model developed from cyclotron resonance. One of the early applications of the results of cyclotron resonance experiments in Si and Ge was to the theory of the ionization energies of the shallow donor and acceptor states in these materials. The approximate ionization energies are 0.04 eV for electrons and 0.05 eV for holes in Si, and 0.01 eV for both electrons and holes in Ge. The near equality of the ionization energies for both electrons and holes was astonishing, at the time, because their band edge structures were known to be completely different (thanks to cyclotron resonance). The problem was discussed in the summer of 1954 with visitors to Berkeley, notably Freeman Dyson and Joaquin Luttinger. The near equality turns out to be merely a matter of coincidence after the electron and hole ionization energies are calculated separately. The donor ionization energy was calculated first at Berkeley [7]. We used the hamiltonian for an ellipsoidal energy surface at any of the degenerate band edges for electrons and the dielectric constant of the bulk crystal. The calculated energies are in good agreement with experiment, at least for donors with atomic numbers close to that of the host crystal. For heavier donors, central cell corrections must be made. The acceptor problem is more difficult because of the fourfold degeneracy of the valence band edges at the zone center, and is reviewed by Walter Kohn [8], with satisfying results.
References Cyclotron Resonance and Structure of Conduction and Valence Band Edges 565 1 G. Dresselhaus, A.F. Kip, C. Kittel: Phys. Rev. 92, 827 (1953) 2 G. Dresselhaus, A.F. Kip, C. Kittel: Phys. Rev. 100, 618 (1955) 3 G. Dresselhaus, A.F. Kip, C. Kittel: Phys. Rev. 98, 368 (1955) 4 G. Dresselhaus, A.F. Kip, C. Kittel: Phys. Rev. 95, 568 (1954) 5 R.J. Elliot: Phys. Rev. 96, 266 (1954) 6 A.H. Kahn: Phys. Rev. 97, 1647 (1955) 7 C. Kittel, A.H. Mitchell: Phys. Rev. 96, 1488 (1954) 8 W. Kohn, in Advances in Solid State Physics, Vol. 5, ed. by F. Seitz, D. Turnbull (Academic, New York 1957), p. 257–320
Page 1 and 2: Appendix A: Pioneers of Semiconduct
Page 3 and 4: Ultra-Pure Germanium 555 Ultra-Pure
Page 5 and 6: References Ultra-Pure Germanium 557
Page 7 and 8: Two Pseudopotential Methods: Empiri
Page 9 and 10: The Early Stages of Band-Structures
Page 11: Cyclotron Resonance and Structure o
Page 15 and 16: Optical Properties of Amorphous Sem
Page 17 and 18: Optical Spectroscopy of Shallow Imp
Page 23 and 24: On the Prehistory of Angular Resolv
Page 25 and 26: The Discovery and Very Basics of th
Page 27 and 28: The Birth of the Semiconductor Supe
Page 29 and 30: Number of papers 500 200 100 50 20
Page 31 and 32: Appendix B: Solutions to Some of th
Page 33 and 34: Solution to Problem 2.6 585 transfo
Page 35 and 36: ⎧ ⎫ 2apple ⎪⎨ cos (y z)
Page 37 and 38: Partial solution to Problem 2.8 589
Page 43 and 44: Solution to Problem 2.16 Solution t
Page 45 and 46: Solution to Problem 2.20 597 to the
Page 47 and 48: Therefore the result of I ′ on
Page 49 and 50: Solution to Problem 3.2(c) Solution
Page 51 and 52: Solution to Problem 3.5 603 Similar
Page 53 and 54: Solution to Problem 3.7 (b and c) 6
Page 55 and 56: u3. The above equation can be reduc
Page 57 and 58: Solution to Problem 3.8 (a, c and d
Page 59 and 60: Solution to Problem 3.11(a,b and c)
Page 61 and 62: Solution to Problem 3.16 613 (1) Al
Page 63 and 64:
Solution to Problem 3.17 Solution t
Page 65 and 66:
Solution to Problem 3.17 617 forces
Page 67 and 68:
Solution to Problem 4.1 619 the abo
Page 69 and 70:
C dz ′ z ′ i° Solution to Pro
Page 71 and 72:
R -R A y E’-E y E’-E R x Soluti
Page 73 and 74:
Solution to Problem 5.3(a) 625 tion
Page 75 and 76:
Solution to Problem 5.5 627 To obta
Page 77 and 78:
Ùm ∞ NLOq 0 2 apple dq 0 ∞
Page 79 and 80:
plus Jz ·Fz Solution to Problem 5
Page 81 and 82:
Solution to Problem 6.7 633 axes. F
Page 83 and 84:
which can be found in standard text
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Solution to Problem 6.11 637 The co
Page 87 and 88:
Solution to Problem 6.19(a) 639 if
Page 89 and 90:
Solution to Problem 6.19(a) 641 k.
Page 91 and 92:
Solution to Problem 6.19(a) 643 The
Page 93 and 94:
Solution to Problem 6.21 645 by a s
Page 95 and 96:
Solution to Problem 6.21 647 °25
Page 97 and 98:
Equating the two expressions for Nn
Page 99 and 100:
Solution to Problem 7.5 651 erties
Page 101 and 102:
A Short Cut to the Calculation of t
Page 103 and 104:
The diagram for the process labeled
Page 105 and 106:
Solution to Problem 7.12 657 or sca
Page 107 and 108:
Solution to Problem 8.1 Solution to
Page 109 and 110:
Solution to Problem 8.9 661 of 19.5
Page 111 and 112:
Solution to Problem 8.10 663 corres
Page 113 and 114:
Solution to Problem 9.2 Solution to
Page 115 and 116:
Solution to Problem 9.4 667 Table 9
Page 117 and 118:
Solution to Problem 9.14 669 Again
Page 119:
Solution to Problem 9.14 671 Note t
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674 Appendix C A4.1.2 Historical Ba
Page 124 and 125:
676 Appendix C from the slopes of t
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678 Appendix C Fig. A4.3 The electr
Page 128 and 129:
680 Appendix C Fig. A4.5 (a)-(d)The
Page 130 and 131:
682 Appendix C tion of alloying (se
Page 132 and 133:
684 Appendix C 17 -3 Hall Concentra
Page 135 and 136:
Appendix D: Recent Developments and
Page 137 and 138:
Chapter 1 689 ing up the glass to a
Page 139 and 140:
Chapter 2 691 Popov, V. N., Lambin,
Page 141 and 142:
Chapter 2 693 and zinc-blende group
Page 143 and 144:
Chapter 3 695 Inelastic x-ray Scatt
Page 145 and 146:
Chapter 4 697 results from a better
Page 147 and 148:
Chapter 5 699 K. Alberi, K. M. Yu,
Page 149 and 150:
Chapter 5 701 P. Ramvall, N. Carlss
Page 151 and 152:
Chapter 6 Ab initio calculations of
Page 153 and 154:
Chapter 6 705 Strain-induced birefr
Page 155 and 156:
Chapter 7 707 S. Baroni, S. de Giro
Page 157 and 158:
Chapter 7 709 W. Windl, K. Karch, P
Page 159 and 160:
Chapter 8 711 Strain Shift Coeffici
Page 161 and 162:
Chapter 9 713 Z. J. Zhao, F. Liu, L
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Chapter 9 715 S. F. Ren, W. Cheng,
Page 165:
Chapter 9 717 V. P. Gusynin, S. G.
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720 References tions II. Misfitting
Page 170 and 171:
722 References 2.30 R. M. Wentzcovi
Page 172 and 173:
724 References 3.23 R. M. Martin: E
Page 174 and 175:
726 References Nye J. F.: Physical
Page 176 and 177:
728 References Schubert E. F.: Dopi
Page 178 and 179:
730 References Ferry D. K.: Semicon
Page 180 and 181:
732 References 6.28 S. Logothetidis
Page 182 and 183:
734 References 6.73 H. D. Fuchs, C.
Page 184 and 185:
736 References 6.116 D. E. Aspnes:
Page 186 and 187:
738 References Chapter 7 7.1 W. Hei
Page 188 and 189:
740 References 7.43 G. Finkelstein,
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742 References 7.82 J. R. Sandercoc
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744 References 7.122 D. C. Reynolds
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746 References 8.27 A. Goldmann, J.
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748 References Electronic and Surfa
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750 References 9.31 A. Pinczuk, G.
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752 References 9.68 J. P. Palmier:
Page 203 and 204:
Subject Index A ·-Sn (gray tin) 95
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C c(2 × 8)(111) surface of Ge - di
Page 207 and 208:
Dielectric function 117, 246, 253,
Page 209 and 210:
Emission rate vs frequency in Ge 34
Page 211 and 212:
Galena (PbS) 1 Gamma-ray detectors
Page 213 and 214:
Insulators 1 Integral quantum Hall
Page 215 and 216:
- - vs T 222 - temperature dependen
Page 217 and 218:
- frequency 253, 306, 335 - - of va
Page 219 and 220:
Resonant Raman profile 403 Resonant
Page 221 and 222:
- - LA phonons 512 - - LO phonons 5
Page 223:
- structure 142 - symmetry operatio
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