10. Appendix

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574 <strong>Appendix</strong> A On the Prehistory of Angular Resolved Photoemission Neville V. Smith Lawrence Berkeley Laboratory, Berkeley, USA Band mapping using angle-resolved photoemission started in the early 1970s. Interest in the angular dependence of the photoelectric effect, however, goes back much further. Figure 1 shows an apparatus used in the 1920s by Herbert Ives and coworkers [1] at the Bell Telephone Laboratories. These workers were definitely not concerned with band structures. Wave mechanics was a newfangled concept, and solid-state physics had yet to be invented. They were concerned rather with optimizing the efficiency of photocathodes for use in television and eventually videotelephony. The sample (C) sits at the center of a spherical collector (B). Application of retarding potentials to the collector permits measurement of the photoelectron energy spectra. A finger (F) moving around a slot in the collector permits measurements as a function of angle of emission. We recognize here a resemblance to modern experimental methods. More striking is the resemblance to the apparatus used by Clinton Davisson and Lester Germer in establishing the wave nature of the electron [2]. This is not surprising. These scientists were all working at the same time in the same building in Manhattan. It is diverting to speculate on the interactions between Ives and Davisson. It seems likely, on the artistic evidence, that they were using the services of the same glass blower! But what did they talk about? Would they have been pleased to know that their separate lines of research would converge half a century later into the indispensable technique of band mapping? Evan Kane proposed in a prescient paper published in 1964 that bands could in principle be mapped using the angular dependence of photoemission spectra [3]. A decade elapsed, however, before bands were actually mapped [4]. Mort Traum and I approached this problem in the early 1970s but with some hesitance. There were persuasive proponents of the view that photoelectrons would be so thoroughly scattered before emerging from the sample that all memory of angular information would be lost. We were so intimidated by this that we built only a minimal apparatus, essentially the same as that of Ives but with a channel electron multiplier in place of the finger F. To circumvent the indeterminacy of k⊥, we looked at two-dimensional materials, the layer compounds TaS2 and TaSe2. Frank DiSalvo was manufacturing single crystals of these compounds in his laboratory a few doors down the corridor. Len Mattheiss was calculating their band structures just a few further doors down the corridor, and we found beautiful agreement with his predictions [5].
On the Prehistory of Angular Resolved Photoemission 575 Fig. 1. Apparatus used by Ives et al. [1] With these shortcuts and fine collaborators we were able to perform the first demonstration of band mapping [4]. In hindsight, it is embarrassing to contemplate our hesitance and timidity. It is all now so obvious and commonplace. References 1 H.E. Ives, A.R. Olpin, A.L. Johnsrud: Phys. Rev. 32, 57 (1928) 2 C.J. Davisson, L.H. Germer: Phys. Rev. 30, 705 (1927) 3 E.O. Kane: Phys. Rev. Lett. 12, 97 (1964) 4 N.V. Smith, M.M. Traum, F.J. DiSalvo: Solid State Commun. 15, 211 (1974) 5 L.F. Mattheiss: Phys. Rev. B 8, 3719 (1973)
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 and 12: Cyclotron Resonance and Structure o
Page 13 and 14: References Cyclotron Resonance and
Page 15 and 16: Optical Properties of Amorphous Sem
Page 17 and 18: Optical Spectroscopy of Shallow Imp
Page 19 and 20: Optical Spectroscopy of Shallow Imp
Page 21: Optical Spectroscopy of Shallow Imp
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
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Solution to Problem 5.5 627 To obta
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Ùm ∞ NLOq 0 2 apple dq 0 ∞
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plus Jz ·Fz Solution to Problem 5
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Solution to Problem 6.7 633 axes. F
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which can be found in standard text
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Solution to Problem 6.11 637 The co
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Solution to Problem 6.19(a) 639 if
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Solution to Problem 6.19(a) 641 k.
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Solution to Problem 6.19(a) 643 The
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Solution to Problem 6.21 645 by a s
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Solution to Problem 6.21 647 °25
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Equating the two expressions for Nn
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Solution to Problem 7.5 651 erties
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A Short Cut to the Calculation of t
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The diagram for the process labeled
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Solution to Problem 7.12 657 or sca
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Solution to Problem 8.1 Solution to
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Solution to Problem 8.9 661 of 19.5
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Solution to Problem 8.10 663 corres
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Solution to Problem 9.2 Solution to
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Solution to Problem 9.4 667 Table 9
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Solution to Problem 9.14 669 Again
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Solution to Problem 9.14 671 Note t
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674 Appendix C A4.1.2 Historical Ba
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676 Appendix C from the slopes of t
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678 Appendix C Fig. A4.3 The electr
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680 Appendix C Fig. A4.5 (a)-(d)The
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682 Appendix C tion of alloying (se
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684 Appendix C 17 -3 Hall Concentra
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Appendix D: Recent Developments and
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Chapter 1 689 ing up the glass to a
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Chapter 2 691 Popov, V. N., Lambin,
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Chapter 2 693 and zinc-blende group
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Chapter 3 695 Inelastic x-ray Scatt
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Chapter 4 697 results from a better
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Chapter 5 699 K. Alberi, K. M. Yu,
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Chapter 5 701 P. Ramvall, N. Carlss
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Chapter 6 Ab initio calculations of
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Chapter 6 705 Strain-induced birefr
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Chapter 7 707 S. Baroni, S. de Giro
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Chapter 7 709 W. Windl, K. Karch, P
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Chapter 8 711 Strain Shift Coeffici
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Chapter 9 713 Z. J. Zhao, F. Liu, L
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Chapter 9 715 S. F. Ren, W. Cheng,
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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
Page 221 and 222:
- - LA phonons 512 - - LO phonons 5
Page 223:
- structure 142 - symmetry operatio
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