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Part of the book series: Computational Microelectronics ((COMPUTATIONAL))

Abstract

Electrons in a perfect crystal1 can be described in terms of Bloch states, whose wave functions can be written as

$$ {\Psi_{{nk}}}(r) = {u_{{nk}}}(r){e^{{ik \cdot r}}} $$
((2.1.1))

where n is a band index, ħ k is the quasi momentum of the electron, and u nk (r) is a function of the space coordinate r with the periodicity of the crystal.

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References

  1. Ashcroft, N. W., Mermin, N. D.: Solid State Physics. Philadelphia: Saunders. 1976.

    Google Scholar 

  2. Kohn, W., Luttinger, J. M.: Phys. Rev. 108 590 (1957).

    MathSciNet  MATH  Google Scholar 

  3. Kadanoff L. P., Baym, G.: Quantum Statistical Mechanics. New York: Benjamin. 1962.

    MATH  Google Scholar 

  4. Barker J. R., Ferry, D. K.: Phys. Rev. Lett. 42 1779 (1979).

    Google Scholar 

  5. Barker, J. R.: Fundamental Aspects of Quantum Transport. In: Handbook on Semionductors (Moss, T. S., ed.), Vol. 1. North-Holland. 1982.

    Google Scholar 

  6. Reggiani, L.: Physica 134B 123 (1985) and references therein.

    MathSciNet  Google Scholar 

  7. Mahan, G. D.: Physics Reports (Review Section Letters) 145 251 (1987).

    Google Scholar 

  8. Jacoboni, G., Ferry, D. K. (eds.): Quantum Transport in Semiconductors. Plenum (to be published).

    Google Scholar 

  9. Kane, E. O.: J. Phys. Chem. Solids 1 82 (1956).

    Google Scholar 

  10. Ottaviani, G., Reggiani, L., Canali, G., Nava, F., Alberigi-Quaranta, A.: Phys. Rev. B12 3318 (1975).

    Google Scholar 

  11. Dresselhaus, G., Kipp, A. F., Kittel, G: Phys. Rev. 98 368 (1955).

    Google Scholar 

  12. Costato, M., Gagliani, G., Jacoboni, G., Reggiani, L.: J. Phys. Chem. Solids 35 1605 (1974).

    Google Scholar 

  13. Bosi, S., Jacoboni, G., Reggiani, L.: J. Phys. C12 1525 (1979).

    Google Scholar 

  14. Smith, R. A.: Semiconductors. Cambridge: Cambridge University Press 1964.

    Google Scholar 

  15. Conwell, E. M., Vassel, M. O.: Phys. Rev. 166 797 (1968).

    Google Scholar 

  16. Fawcett, W., Boardman, D. A., Swain, S.: J. Phys. Chem. Solids 31 1963 (1970).

    Google Scholar 

  17. Paige, E. G. S.: The Electrical Conductivity of Germanium (Gibson, A. F., Burgess, R. E., eds.). London: Heywood. 1964.

    Google Scholar 

  18. Jacoboni, G., Reggiani, L.: Rev. Mod. Phys. 55 645 (1983).

    Google Scholar 

  19. Gagliani, G., Reggiani, L.: Nuovo Cimento B30 207 (1975).

    Google Scholar 

  20. Jacoboni, G., Nava, F., Canali, G., Ottaviani, G: Phys. Rev. B24 1014 (1981).

    Google Scholar 

  21. Herring, G, Vogt, E.: Phys. Rev. 101 944 (1956).

    MATH  Google Scholar 

  22. Jacoboni, G., Reggiani, L.: Advances in Physics 28 493 (1979).

    Google Scholar 

  23. Chelikowsky, J. R., Cohen, M. L.: Phys. Rev B14 556 (1976).

    Google Scholar 

  24. Ivey, J. L., Mieher, R. L.: Phys. Rev. Letters 29 176 (1972).

    Google Scholar 

  25. Jacoboni, G., Minder, R., Majni, G: J. Phys. Chem. Solids 36 1129 (1975).

    Google Scholar 

  26. Littlejohn, M. A., Houser, J. R., Glisson, T. H.: J. Appl. Phys. 48 4587 (1977).

    Google Scholar 

  27. Eastman, L. F.: Physics Today, October 1986, p. 77.

    Google Scholar 

  28. Milnes, A. G: Solid-State Electr. 29 99 (1986).

    Google Scholar 

  29. Hartstein, A., Ning, T. H., Fowler, A. B.: Surf. Sci. 58 178 (1976).

    Google Scholar 

  30. Hauser, J. R., Littlejohn, M. A., Glisson, T. H.: Appl. Phys. Lett. 28 458 (1976).

    Google Scholar 

  31. Bir, G. L., Pikus, G E.: Symmetry ad Strain-Induced Effects in Semiconductors. (Translated by Shelnitz, P., translation edited by Louvish, D.) New York: Wiley. 1974.

    Google Scholar 

  32. Froehlich, H.: Proc. R. Soc. (London) A188 521 and 532 (1947).

    Google Scholar 

  33. Stratton, R.: Proc. R. Soc. (London) A246 406 (1958).

    Google Scholar 

  34. Eaves, L., Hoult, R. A., Stradling, R. A., Tidey, R. J., Portal, J. G, Askenazy, S.: J. Phys. C8 1034 (1975).

    Google Scholar 

  35. Fawcett, W., Paige, E. G. S.: J. Phys. C4 1801 (1971).

    Google Scholar 

  36. Alberigi-Quaranta, A., Jacoboni, G., Ottaviani, G: Riv. Nuovo Cimento 1 445 (1971).

    Google Scholar 

  37. Norton, P., Levinstein, H.: Phys. Rev. B6 470 (1972).

    Google Scholar 

  38. Asche, M., Boichenko, B. L., Bondar, V. M., Sarbei, O. G: Phys. Stat. Sol. (b) 44 173 (1971).

    Google Scholar 

  39. Dienys, V., Kancleris, Z.: Phys. Stat. Sol. (b) 67 317 (1975).

    Google Scholar 

  40. Jacoboni, G: Proc, 13th Intern. Conf. Phys. Semic. (Fumi, G, ed.), p. 1195. Roma: Marves. 1976.

    Google Scholar 

  41. Nash, J. G., Holm-Kennedy, J. W.: Appl. Phys. Lett. 24 139 (1974).

    Google Scholar 

  42. Lugli, P., Ferry, D. K: Physica B129 532 (1985);

    MATH  Google Scholar 

  43. Lugli, P., Ferry, D. K: IEEE El. Dev. Lett. EDL6 25 (1985).

    Google Scholar 

  44. Ziman, J. M.: Principles of the Theory of Solids. Cambridge: Cambridge University Press. 1972.

    Google Scholar 

  45. Reggiani, L., Calandra, G: Phys. Lett. A43 339 (1973).

    Google Scholar 

  46. Wiley, J. D.: Phys. Rev. B4 2485 (1971).

    Google Scholar 

  47. Kittel, G: Quantum Theory of Solids. New York: Wiley. 1963.

    Google Scholar 

  48. Harrison, W. A.: Phys. Rev. 104 1281 (1956).

    MathSciNet  Google Scholar 

  49. Bir, G. L., Pikus, G. E.: Fiz. Tverd. Tela (Leningrad) 2, 2287 (1961) [Sov. Phys. Solid State 2 2039 (1961)].

    MathSciNet  Google Scholar 

  50. Ziman, J. M.: Electrons and Phonons. Oxford: Oxford University Press. 1960.

    MATH  Google Scholar 

  51. Lawaetz, P.: Phys. Rev. 183 730 (1969).

    Google Scholar 

  52. Vogl, P.: Phys. Rev. 13 694 (1976).

    Google Scholar 

  53. Poetz, W., Vogl, P.: Phys. Rev. B24 2025 (1981).

    Google Scholar 

  54. Poetz, W., Kocevar, P.: Phys. Rev. B28 7040 (1983).

    Google Scholar 

  55. Bordone, P., Jacoboni, G., Lugli, P., Reggiani, L., Kocevar, P.: J. Appl. Phys. 61 1460 (1987).

    Google Scholar 

  56. Lugli, P., Jacoboni, G., Reggiani, L., Kocevar, P.: Appl. Phys. Lett. 50 1251 (1987).

    Google Scholar 

  57. Costato, M., Reggiani, L.: Nuovo Cimento Lett. 4 1179 (1970).

    Google Scholar 

  58. Conwell, E. M.: High Field Transport in Semiconductors. (Solid State Phys., Suppl. 9.) New York: Academic Press. 1967.

    Google Scholar 

  59. Tiersten, M.: IBM J. Res. Dev. 5 122 (1961).

    MATH  Google Scholar 

  60. Tiersten, M.: J. Phys. Chem. Solids 25 1151 (1964).

    Google Scholar 

  61. Reggiani, L., Canali, G., Nava, F., Ottaviani, G.: Phys. Rev. B16 2781 (1977).

    Google Scholar 

  62. Lawaetz, P.: Doctoral Dissertation, University of Lyngby, 1967.

    Google Scholar 

  63. Costato, M., Reggiani, L.: Phys. Status Solidi B58 47 and 471 (1973).

    Google Scholar 

  64. Streitwolf, H. W.: Phys. Status Solidi B37 K47 (1970).

    Google Scholar 

  65. Lax, M., Birman, J. L.: Phys. Status Solidi B49 K153 (1972).

    Google Scholar 

  66. Asche, A., Sarbei, O. G.: Phys. Status Solidi B103 11 (1981).

    Google Scholar 

  67. Paige, E. G. S.: The Electrical Conductivity of Germanium (Gibson, A. F., Burgess, R. E., eds.). London: Hey wood. 1964.

    Google Scholar 

  68. Birman, J., Lax, M., Loudom, R.: Phys. Rev. 145 620 (1966).

    Google Scholar 

  69. Eaves, L., Hoult, R. A., Stradling, R. A., Tidey, R. J., Portal, J. G., Askenazy, S.: J. Phys. C8 1034 (1975).

    Google Scholar 

  70. Ferry, D. K.: Phys. Rev. B14 1605 (1976).

    Google Scholar 

  71. Ridley, B. K.: Quantum Processes in Semiconductors. Oxford: Clarendon. 1982.

    Google Scholar 

  72. Froehlich, H.: Proc. R. Soc. (London) A188 521 (1947).

    Google Scholar 

  73. Conwell, E. M., Weisskopf, V. F.: Phys. Rev. 77 388 (1950).

    MATH  Google Scholar 

  74. Brooks, H., Herring, G: Phys. Rev. 83 879 (1951).

    Google Scholar 

  75. Chattopadhyay, D., Queisser, H. J.: Rev. Mod. Phys. 53 745 (1981).

    Google Scholar 

  76. Reggiani, L.: Phys. Rev. B17 2800 (1978).

    Google Scholar 

  77. Bohm, D., Pines, D.: Phys. Rev. 92 609 (1953).

    MathSciNet  MATH  Google Scholar 

  78. Madelung, O.: Introduction to Solid State Physics. Berlin-Heidelberg-New York: Springer. 1978.

    Google Scholar 

  79. Lugli, P.: Ph. D. Dissertation, Colorado State University, 1985.

    Google Scholar 

  80. Kumenov, S. E., Perel, V. I.: Sov. Phys. Semicon. 16 1982 (1982).

    Google Scholar 

  81. Davidov, B. L: In: Plasma Physics and the Problem of Controlled Thermonuclear Reactions, Vol. 1. AN SSR. 1958.

    Google Scholar 

  82. Ehrenreich, H.: J. Phys. Chem. Solids 8 1996 (1965).

    Google Scholar 

  83. Varga, B. B.: Phys. Rev. 137 1896 (1965).

    Google Scholar 

  84. Mooradian, A., Wright, G. B.: Phys. Rev. Lett. 16 999 (1966).

    Google Scholar 

  85. Kim, M. E., Das, A., Centuria, S. D.: Phys. Rev. B18 6890 (1978).

    Google Scholar 

  86. Wolf, P. A.: In: Proc, Int. Conf. Light Scatt. Spectra Solids. Berlin-Heidelberg-New York: Springer. 1969.

    Google Scholar 

  87. Asche, M., Sarbei, O. G: Phys. Status Solidi B126 607 (1984).

    Google Scholar 

  88. Osman, M. A.: Ph. D. Dissertation, Arizona State University, 1986.

    Google Scholar 

  89. Reif, F.: Fundamentals of Statistical and Thermal Physics. New York: McGraw-Hill. 1965.

    Google Scholar 

  90. Budd, H.: In: Proc, Int. Conf. Semiconductors, Kyoto. J. Phys. Soc. Japan Suppl. 21 420 (1966).

    Google Scholar 

  91. Price, P. J.: In: Proc, 9th Int. Conf. Phys. Semiconductors (Ryvkin, S. M., ed.), p. 753. Leningrad: Nauka. 1968.

    Google Scholar 

  92. Rees, H. D.: J. Phys. Chem. Solids 30 643 (1969).

    Google Scholar 

  93. Kurosawa, T.: In: Proc, Int. Conf. Phys. Semiconductors, Kyoto. J. Phys. Soc. Jpn. Suppl. 21 424 (1966).

    Google Scholar 

  94. Price, P. J.: Semiconductors and Semimetals, p. 249. New York: Academic Press. 1979.

    Google Scholar 

  95. Ehrenreich, H.: J. Phys. Chem. Solids 2, 131 (1957)

    Google Scholar 

  96. Ehrenreich, H.: J. Phys. Chem. Solids 12 97 (1959);

    Google Scholar 

  97. Ehrenreich, H.: Phys. Rev. 120 1951 (1960).

    Google Scholar 

  98. Long, D., Meyers, J.: Phys. Rev. 115 1107 (1959).

    Google Scholar 

  99. Canali, C., Jacoboni, C., Nava, F., Ottaviani, G., Alberigi-Quaranta, A.: Phys. Rev. B12 2265 (1975).

    Google Scholar 

  100. Fletcher, K., Butcher, P. N.: J. Phys. C5 212 (1972).

    Google Scholar 

  101. Costato, M., Reggiani, L.: Nuovo Cimento 68B 64 (1970).

    Google Scholar 

  102. Costato, M.L., Jacoboni, C., Reggiani, L.: Phys. Stat. Sol. (b) 52 461 (1972).

    Google Scholar 

  103. Jacoboni, C., Gagliani, G., Reggiani, L., Turci, O.: Solid State Electron. 27, 315 (1978).

    Google Scholar 

  104. Kittel, C: Elementary Statistical Physics. New York: Wiley. 1958.

    Google Scholar 

  105. Gunn, J. B.: Int. J. Sci. Technol. 46 43 (1965).

    Google Scholar 

  106. Ruch, J. G., Kino, G. S.: Phys. Rev. 174 921 (1968).

    Google Scholar 

  107. Houston, P. A., Evans, A. G. R.: Solid State Electron. 20 197 (1977).

    Google Scholar 

  108. Pozhela, J., Reklaitis, A.: Solid State Commun. 27 1073 (1978).

    Google Scholar 

  109. Brunetti, R., Jacoboni, C., Nava, F., Reggiani, L., Bosman, G., Zijlstra, R. J. J.: J. Appl. Phys. 52 6713 (1981).

    Google Scholar 

  110. Fawcett, W., Rees, H. D.: Phys. Lett. 11 731 (1969).

    Google Scholar 

  111. Ohmi, T., Hasuo, S.: Proc, 10th Int. Conf. Phys. Semiconductors, Cambridge, Massachusetts, p. 60, 1970.

    Google Scholar 

  112. Reggiani, L., Vaissière, J. C., Nougier, J. P., Gasquet, D.: In: Proa, 3rd Int. Conf. Hot Carriers in Semiconductors. J. Phys. (Paris) Colloq. 42 C7-357 (1981c).

    Google Scholar 

  113. Sze, S. M.: Physics of Semiconductor Devices, 2nd edn. New York: Wiley. 1981.

    Google Scholar 

  114. Chang, L. L.: Solid State Electron. 8, 721 (1965)

    Google Scholar 

  115. Anderson, R. L.: Solid State Electron. 5, 341 (1962).

    Google Scholar 

  116. Milnes, A. G., Feucht, D. L.: Heterojunctions and Metal-Semiconductor Junctions. New York: Academic Press. 1972.

    Google Scholar 

  117. Gossard, A. C: IEEE J. Quantum Electron. QE22 1649 (1986).

    Google Scholar 

  118. Störnier, H. L.: Surf. Sci. 132 519 (1983).

    Google Scholar 

  119. Solomon, P. M., Morkoc, H.: IEEE Trans. El. Dev. ED31 1015 (1984).

    Google Scholar 

  120. Dingle, R., Stornier, H. L., Gossard, A. C., Wiegmann, W.: Appl. Phys. Lett. 33 655 (1978).

    Google Scholar 

  121. Dingle, R.: IEEE Trans. EL Dev. ED31 1662 (1984).

    Google Scholar 

  122. Hess, K.: Solid State Electron. 31 319 (1988); and references therein.

    Google Scholar 

  123. Muller, P. S., Kamins, T. L: Device Electronics for Integrated Circuits, 2nd edn. New York: Wiley. 1986.

    Google Scholar 

  124. Ando, T., Fowler, A. B., Stern, F.: Rev. Mod. Phys. 54 437 (1982).

    Google Scholar 

  125. Stern, F., Howard, W. E.: Phys. Rev. 163 816 (1967).

    Google Scholar 

  126. Ferry, D. K., Hess, K., Vogl, P.: In: VLSI Electronics: Microstructure Science, Vol. 2, p. 67. New York: Academic Press. 1981.

    Google Scholar 

  127. Hess, K., Vogl, P.: Solid State Comm. 30 807 (1979).

    Google Scholar 

  128. Harstein A., Ning, T. H., Fowler, A. B.: Surf. Sci. 58 178 (1976).

    Google Scholar 

  129. Stern, F., Das Sarma, S.: Phys. Rev. B30 840 (1984).

    Google Scholar 

  130. Ando, T.: J. Phys. Soc. Jap. 51 3893 (1982).

    Google Scholar 

  131. Yokoyama, K., Hess, K.: Phys. Rev. B33 5595 (1986).

    Google Scholar 

  132. Riddoch, F. A., Ridley, B. K.: Physica 134B 342 (1985).

    Google Scholar 

  133. Sawaki, N.: J. Phys. C19 4965 (1986).

    Google Scholar 

  134. Lugli, P., Goodnick, S. M.: Phys. Rev. Lett. 59 716 (1987).

    Google Scholar 

  135. Cai, W., Marchetti, G. M., Lax, M.: Phys. Rev. B35 1369 (1987).

    Google Scholar 

  136. Price, P. J.: Ann. Phys. 133 217 (1981).

    Google Scholar 

  137. Goodnick, S. M., Lugli, P.: Phys. Rev. 37 2578 (1988).

    Google Scholar 

  138. Ferry, D. K.: Phys. Rev. B14 5364 (1976).

    Google Scholar 

  139. Hao, C., Zimmermann, J., Charef, M., Fauquembergue, F., Constant, E.: Solid State Electr. 28 733 (1985).

    Google Scholar 

  140. Terashima, K., Hamaguchi, C., Taniguchi, K.: Superl. and Microstr. 1 15 (1985).

    Google Scholar 

  141. Ning, T. H., Sah, C. T.: Phys. Rev. B6 4605 (1972).

    Google Scholar 

  142. Ferry, D. K.: Thin Sol. Films 56 243 (1979).

    Google Scholar 

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Jacoboni, C., Lugli, P. (1989). Charge Transport in Semiconductors. In: The Monte Carlo Method for Semiconductor Device Simulation. Computational Microelectronics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6963-6_2

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