10. Appendix

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556 <strong>Appendix</strong> A shallow hydrogenic donors or acceptors in a very cold crystal would lead to photoconductivity peaks which were very sharp and unique for each dopant species. Paul Richards, of the Physics Department at the University of California at Berkeley, had a home-built Fourier-transform far-infrared spectrometer and the necessary liquid helium temperature dewar. By the end of the first day of experimenting we had a spectrum of a p-type high-purity Ge crystal with only 10 10 cm 3 net amount of acceptors and we knew also that phosphorus and aluminum were the major residual impurities. In parallel with a number of novel and interesting physics studies we fabricated gamma-ray detectors at LBL. We broke records in the resolution of the gamma-ray photopeaks with our ultra-pure crystals [2]. Soon the commercial detector manufacturers became interested and started their own ultra-pure Ge crystal-pulling programs. In a few years several companies in the US and in Europe succeeded in developing large-diameter ( 8 cm) single crystals with incredibly good yield, excellent purity ( 2 × 10 10 cm 3 ) and very small concentrations (10 8 cm 3 ) of deep-level defects which would detrimentally affect the charge collection in large-size coaxial p-i-n diodes. In order to achieve the best spectral resolution, electrons and holes had to have mean-free-paths of up to several meters. Most semiconductor physicists simply shook their heads and could not comprehend these numbers. How pure is ultra-pure Ge? The person who cares only about electrically active impurities would say that crystals with a few 10 10 cm 3 of impurities are routinely grown. But are there other inactive impurities? Yes, of course there are. Hydrogen, oxygen, silicon and carbon are usually present at concentrations of up to 10 14 cm 3 , depending on the crystal growth conditions. These impurities do not interfere with Ge’s operation as radiation detectors provided certain rules are followed: no heating to temperatures above 350C and no rapid temperature changes. Can we reduce the concentration of these four electrically inactive impurities? Yes, we can, but we pay a price. Eliminating hydrogen by growing in vacuum leads to the introduction of impurities which can no longer be “flushed” out of the crystal puller. Furthermore, hydrogen will passivate the very small concentrations of deep-level defects and impurities which are always present. Free oxygen and silicon are generated by the reduction of the ultra-pure silica crucible by the liquid Ge. We do not know of any substance which can replace silica with, perhaps, the exception of graphite. Numerous attempts to grow ultra-pure Ge in graphite crucibles have failed so far because the resultant crystals contain too many Al acceptors. Most recently, the interest in Ge has sharply increased because isotopically pure Ge can be obtained from Russia. Isotopically pure Ge bulk crystals [9– 12] and isotope superlattices [13] have been grown. New phonon physics and electronic transport studies are currently being pursued by several groups with these isotopically controlled crystals and multilayers. Have we arrived at the ultimately ideal material: isotopically and chemically pure and crystallographically perfect Ge single crystals? Perhaps the answer is no, but I certainly do not know of another parameter that can be controlled.
References Ultra-Pure Germanium 557 1 R.N. Hall: in Proc. of the 12th Int. Conf. on Physics of Semiconductors, ed. by M.H. Pilkuhn (Teubner, Stuttgart 1974), p. 363 2 E.E. Haller, F.S. Goulding: Handbook on Semiconductors, Vol. 4, ed. by C. Hilsum (Elsevier, New York 1993), Chap. 11, p. 937–963 3 W.L. Hansen, E.E. Haller: Mater. Res. Soc. Proc. 16, 1 (1983) 4 R.N. Hall, T.J. Soltys: IEEE Trans. Nucl. Sci. NS-18, 160 (1971) 5 E.E. Haller, W.L. Hansen, F.S. Goulding: IEEE Trans. Nucl. Sci. NS-20, 481 (1973) 6 E.E. Haller, W.L. Hansen, G.S. Hubbard, F.S. Goulding: IEEE Trans. Nucl. Sci. NS- 23, 81 (1976) 7 E.E. Haller, W.L. Hansen, F.S. Goulding: Adv. Phys. 30, 93 (1981) 8 E.E. Haller: Physics 146B, 201 (1987) 9 E.E. Haller: Semicond. Sci. Technol. 5, 319 (1990) 10 E.E. Haller: Solid State Phenom. 32–33, 11 (1993) 11 G. Davies, J. Hartung, V. Ozhogin, K. Itoh, W.L. Hansen, E.E. Haller: Semicond. Sci. Technol. 8, 127 (1993) 12 H.D. Fuchs, P. Etchegoin, M. Cardona, K. Itoh, E.E. Haller: Phys. Rev. Lett. 70, 1715 (1993) 13 J. Spitzer, T. Ruf, M. Cardona, W. Dondl, R. Schorer, G. Abstreiter, E.E. Haller: Phys. Rev. Lett. 72, 1565 (1994)
Page 1 and 2: Appendix A: Pioneers of Semiconduct
Page 3: Ultra-Pure Germanium 555 Ultra-Pure
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 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
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Solution to Problem 3.8 (a, c and d
Page 59 and 60:
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
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Solution to Problem 4.1 619 the abo
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C dz ′ z ′ i° Solution to Pro
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R -R A y E’-E y E’-E R x Soluti
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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
Page 109 and 110:
Solution to Problem 8.9 661 of 19.5
Page 111 and 112:
Solution to Problem 8.10 663 corres
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Solution to Problem 9.2 Solution to
Page 115 and 116:
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:
Page 203 and 204:
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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10. Appendix

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