10. Appendix

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670 <strong>Appendix</strong> B to the waves A1 and B1 via a product of transfer matrices M1, M2, ..., Mn1: A1 An1 M1M2...Mn B1 Bn1 Each transfer matrix Mi isa2× 2 matrix of the form: Mi Mi(1, 1) Mi(1, 2) Mi(2, 1) Mi(2, 2) whose elements are given in Eqs. (9.59a) to (9.59d): M1(1, 1) M1(1, 2) M1(2, 1) M1(2, 2) 1 m1k2 exp i(k2 k1) d2 2 2m2k1 d1 2 1 m1k2 exp i(k2 k1) d2 2 2m2k1 d1 2 1 m1k2 exp i(k2 k1) d2 2 2m2k1 d1 2 1 m1k2 exp i(k2 k1) d2 2 2m2k1 d1 2 (9.14c) (9.14d) (9.14e) (9.14f) (9.14g) (9.14h) The transfer matrices M2, M3, and M4 can be obtained similarly. The product (Mij) of the four matrices M1, ..., M4 can be calculated with a computer program, such as Mathematica, Mathcad etc. T(0) can obtained by assuming that there will be no reflected wave in region 5 so B5 0 and A1 M11A5: T(0) |A5/A1| 2 |1/M11| 2 . The following plot of T(0) vs E has been obtained by using the program Mathcad. The program codes are shown in a separate file labeled as Problem9.14 Codes.mcd which can be downloaded from the website: http://pauline.berkeley.edu/book/SolutionsNew.html.
Solution to Problem 9.14 671 Note that in obtaining this plot we have assumed that the electron effective masses in the well (m1) and in the barrier (m2) are equal, respectively, to 0.037 and 0.0023 times the free electron mass. Electron Energy (eV) Transmission curve obtained for m1=0.037mo and m2=0.0023mo. To calculate the transmission coefficient under applied bias one has to tilt the barrier and the well and approximate the tilted potential with piece-wise constant potentials. With slight variation in the computer program this computation can be done easily and is left as an exercise for the students. The students are also urged to vary the effective masses and other parameters to see their effects on the transmission curve.
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Appendix A: Pioneers of Semiconduct
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Ultra-Pure Germanium 555 Ultra-Pure
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References Ultra-Pure Germanium 557
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Two Pseudopotential Methods: Empiri
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The Early Stages of Band-Structures
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Cyclotron Resonance and Structure o
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References Cyclotron Resonance and
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Optical Properties of Amorphous Sem
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Optical Spectroscopy of Shallow Imp
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Page 21 and 22:
Page 23 and 24:
On the Prehistory of Angular Resolv
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The Discovery and Very Basics of th
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The Birth of the Semiconductor Supe
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Number of papers 500 200 100 50 20
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Appendix B: Solutions to Some of th
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Solution to Problem 2.6 585 transfo
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⎧ ⎫ 2apple ⎪⎨ cos (y z)
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Partial solution to Problem 2.8 589
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Page 41 and 42:
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Solution to Problem 2.16 Solution t
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Solution to Problem 2.20 597 to the
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Therefore the result of I ′ on
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Solution to Problem 3.2(c) Solution
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Solution to Problem 3.5 603 Similar
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Solution to Problem 3.7 (b and c) 6
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u3. The above equation can be reduc
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Solution to Problem 3.8 (a, c and d
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Solution to Problem 3.11(a,b and c)
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Solution to Problem 3.16 613 (1) Al
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Solution to Problem 3.17 Solution t
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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
Page 85 and 86: 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: Solution to Problem 9.14 669 Again
Page 122 and 123: 674 Appendix C A4.1.2 Historical Ba
Page 124 and 125: 676 Appendix C from the slopes of t
Page 126 and 127: 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
Page 163 and 164: 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
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722 References 2.30 R. M. Wentzcovi
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724 References 3.23 R. M. Martin: E
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726 References Nye J. F.: Physical
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728 References Schubert E. F.: Dopi
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730 References Ferry D. K.: Semicon
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732 References 6.28 S. Logothetidis
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734 References 6.73 H. D. Fuchs, C.
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736 References 6.116 D. E. Aspnes:
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738 References Chapter 7 7.1 W. Hei
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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:
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Subject Index A ·-Sn (gray tin) 95
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C c(2 × 8)(111) surface of Ge - di
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Dielectric function 117, 246, 253,
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Emission rate vs frequency in Ge 34
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Galena (PbS) 1 Gamma-ray detectors
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Insulators 1 Integral quantum Hall
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- - vs T 222 - temperature dependen
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- frequency 253, 306, 335 - - of va
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Resonant Raman profile 403 Resonant
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- - LA phonons 512 - - LO phonons 5
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- structure 142 - symmetry operatio
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