Skip to main content

Methods of Calculation of Energy Bands in Solids

  • Chapter
Electrons in Finite and Infinite Structures

Part of the book series: NATO Advanced Study Institutes Series ((NSSB,volume 24))

Abstract

These lectures present a review of the basic principles and methods of the calculation of energy bands. The procedures in current use are surveyed briefly. Recent developments are noted. The problems of the construction of a crystal potential are examined in regard to the representation of the exchange interaction.

Supported in part by the U.S. National Science Foundation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. C. Slater “Quantum Theory of Molecules and Solids, Vol. 2, Symmetry and Energy Bands in Crystals”, McGraw Hill, New York, 1965.

    MATH  Google Scholar 

  2. F. Bloch, Z. Phys. 52, 555 (1928).

    ADS  MATH  Google Scholar 

  3. J. Callaway “Quantum Theory of the Solid State”, Academic Press, New York, 1974, Ch. 4.

    Google Scholar 

  4. G. C. Fletcher, “The Electron Band Theory of Solids”, North Holland, Amsterdam, 1971.

    Google Scholar 

  5. P. M. Marcus, J. F. Janak, and A. R. Williams, eds. “Computational Methods in Band Theory”, Plenum Press, New York, 1971.

    MATH  Google Scholar 

  6. B. Alder, S. Fernbach, and M. Rotenberg, eds., “Energy Bands in Solids”, Vol. 8 of “Methods in Computational Physics”, Academic Press, New York, 1968.

    Google Scholar 

  7. J. M. Ziman, Solid State Physics 26, 1 (1971).

    Article  Google Scholar 

  8. J. Callaway “Energy Band Theory”, Academic Press, New York, 1964.

    MATH  Google Scholar 

  9. H. Jones “The Theory of Brillouin Zones and Electronic States in Crystals”, North-Holland, Amsterdam, 1960.

    MATH  Google Scholar 

  10. C. J. Bradley and A. P. Cracknell “The Mathematical Theory of Symmetry in Solids”, Oxford University Press, 1972.

    Google Scholar 

  11. E. Wigner and F. Seitz, Phys. Rev. 43, 804 (1933).

    Article  ADS  Google Scholar 

  12. C. Herring, Phys. Rev. 57., 1169 (1940).

    Google Scholar 

  13. T. O. Woodruff, Solid State Phys. 4, 367 (1967).

    Article  Google Scholar 

  14. F. Herman, Rev. Mod. Phys. 30, 102 (1958).

    Article  ADS  Google Scholar 

  15. F. Herman, R. L. Kortum, C. D. Kuglin, and R. A. Short in “Quantum Theory of Atoms, Molecules, and the Solid State”, edited by P. O. Löwdin, Academic Press, New York, 1966, p. 381.

    Google Scholar 

  16. D. R. J. J. J. Stuckel, R. N. Euwema, T. C. Collins, F. Herman, and L. Kortum, Phys. Rev. 179, 740 (1969); T. C. Collins, D. Stuckel, and R. N. Euwema, Phys. Rev. B 1, 724 (1970); D. Stuckel and R. N. Euwema, Phys. Rev. B 1, 1635 (1970).

    Google Scholar 

  17. J. Callaway, Phys. Rev. 97, 933 (1955).

    Article  ADS  MATH  Google Scholar 

  18. E. Brown and J. A. Krumhansl, Phys. Rev. 109, 30 (1958); F. A. Butler, F. K. Bloom, and E. Brown, Phys. Rev. 180, 744 (1969); D. M. Gray and R. M. Karpien in Marcus, Ref. 5, p. 144.

    Google Scholar 

  19. A. B. Kunz, Phys. Rev. 180, 934 (1969).

    Article  ADS  Google Scholar 

  20. R. A. Deegan and W. D. Twose, Phys. Rev. 164, 993 (1967).

    Article  ADS  Google Scholar 

  21. R. N. Euwema, Phys. Rev. B 4, 4332 (1971).

    Article  ADS  Google Scholar 

  22. L. Kleinman and E. Carruthers, Phys. Rev. B 10, 3213 (1974).

    Article  ADS  Google Scholar 

  23. W. W. A. Harrison “Pseudopotentials in the Theory of Metals”, A. Benjamin, New York, 1966.

    Google Scholar 

  24. V. Heine, Solid State Physics 24, 1 (1970).

    Article  Google Scholar 

  25. M. L. Cohen and V. Heine, Solid State Physics 24, 37 (1970).

    Article  Google Scholar 

  26. V. Heine and D. Weaire, Solid State Phys. 24, 249 (1970).

    Article  Google Scholar 

  27. J. C. Phillips and L. Kleinman, Phys. Rev. 116, 287 (1959).

    Article  ADS  MATH  Google Scholar 

  28. B. J. Austin, V. Heine, and L. J. Sham, Phys. Rev. 127, 276 (1962).

    Article  ADS  MATH  Google Scholar 

  29. E. Lafon and C. C. Lin, Phys. Rev. 152, 579 (1966).

    Article  ADS  Google Scholar 

  30. R. C. Chaney, T. K. Tung, C. C. Lin, and E. E. Lafon, J. Chem. Phys.. 52, 361 (1970).

    Article  ADS  Google Scholar 

  31. D. E. Ellis and G. S. Painter, Phys. Rev. B 2, 2887 (1970).

    Article  ADS  Google Scholar 

  32. J. Callaway and J. L. Fry in Marcus, Ref. 5, p. 512.

    Google Scholar 

  33. J. C. Slater and G. F. Koster, Phys. Rev. 94, 1498 (1954).

    Article  ADS  MATH  Google Scholar 

  34. G. Dresselhaus and M. S. Dresselhaus, Phys. Rev. 160, 649 (1967).

    Article  ADS  Google Scholar 

  35. L. Hodges, H. Ehrenreich, and W. D. Lang, Phys. Rev. 152, 505 (1966).

    Article  ADS  Google Scholar 

  36. F. M. Mueller, Phys. Rev. 153, 659 (1967).

    Article  ADS  Google Scholar 

  37. V. Heine, Phys. Rev. 153, 673 (1967).

    Article  ADS  Google Scholar 

  38. H. Ehrenreich and L. Hodges, Methods. Comp. Phys. 8, 149 (1968).

    Google Scholar 

  39. E. I. Zornberg, Phys. Rev. B 1, 244 (1970).

    Article  ADS  Google Scholar 

  40. J. C. Slater, Phys. Rev. 51, 846 (1937).

    Article  ADS  Google Scholar 

  41. M. M. Saffren and J. C. Slater, Phys. Rev. 92, 1126 (1953).

    Article  ADS  MATH  Google Scholar 

  42. H. Schlosser and P. M. Marcus, Phys. Rev. 131, 2529 (1963).

    Article  ADS  MATH  Google Scholar 

  43. T. L. Loucks “Augmented Plane Wave Method: A Guide to Per-forming Electronic Structure Calculations”, W. A. Benjamin, New York, 1967.

    Google Scholar 

  44. L. F. Mattheiss, J. H. Wood, and A. C. Switendick, Methods Computat. Phys. 8, 64 (1968).

    Google Scholar 

  45. J. O. Dimmock, Solid State Physics 26, 103 (1971).

    Article  Google Scholar 

  46. J. Korringa, Physica 1, 3, 392 (1947).

    MathSciNet  Google Scholar 

  47. W. Kohn and N. Rostoker, Phys. Rev. 94, 1111 (1954).

    Article  ADS  MATH  Google Scholar 

  48. F. S. Ham and B. Segall, Phys. Rev. 124, 1786 (1961).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  49. A. R. Williams, J. F. Janak, and V. L. Moruzzi, Phys. Rev. B 6, 4509 (1972).

    Article  ADS  Google Scholar 

  50. G. S. Painter, Phys. Rev. B 7, 3521 (1973).

    Google Scholar 

  51. L. Kleinman and R. Shurtleff, Phys. Rev. 188, 1111 (1969).

    Article  ADS  Google Scholar 

  52. D. D. Koelling, A. J. Freeman, and F. M. Mueller, Phys. Rev. B 1, 1318 (1970).

    Article  ADS  Google Scholar 

  53. E. O. Kane, Phys. Rev. B 4, 1917 (1971).

    MathSciNet  ADS  Google Scholar 

  54. S. C. Keeton and T. L. Loucks, Phys. Rev. 168, 672 (1968).

    Article  ADS  Google Scholar 

  55. D. D. Koelling and A. J. Freeman, Phys. Rev. B 7, 4454 (1973).

    Article  ADS  Google Scholar 

  56. O. K. Andersen, Phys. Rev. B 12, 3060 (1975).

    Article  ADS  Google Scholar 

  57. O. K. Andersen in Marcus, Ref. 5, p. 178; O. K. Andersen and R. V. Kasowski, Phys. Rev. B 4, 1064 (1971).

    Google Scholar 

  58. Y. Onodera and M. Okazaki, J. Phys. Soc. Japan 21, 1273 (1966).

    Article  ADS  Google Scholar 

  59. S. Takada, Prog. Theor. Phys. Suppl. 36, 224 (1966).

    Article  Google Scholar 

  60. J. M. Ziman, Proc. Phys. Soc. (London) 86, 337 (1965).

    Article  MathSciNet  ADS  Google Scholar 

  61. J. C. Slater, Phys. Rev. 145, 599 (1966).

    Article  ADS  Google Scholar 

  62. J. Hubbard, Proc. Phys. Soc. (London) 92921 (1967).

    Google Scholar 

  63. D. G. Pettifor, J. Phys. C 5, 97 (1972).

    Article  ADS  Google Scholar 

  64. M. J. G. Lee, Phys. Rev. 178, 953 (1969).

    Article  ADS  Google Scholar 

  65. J. C. Shaw, J. B. Ketterson, and L. R. Windmiller, Phys. Rev. B5, 3894 (1972).

    ADS  Google Scholar 

  66. R. N. Euwema, D. L. Wilhite, and G. T. Surratt, Phys. Rev. B 7, 818 (1972); R. N. Euwema, G. G. Wepfer, G. T. Surratt and D. L. Wilhite, Phys. Rev. B 9, 5249 (1974).

    Google Scholar 

  67. A. B. Kunz, D. J. Mickish, and T. C. Collins, Phys. Rev. Letts. 31, 756 (1973).

    Article  ADS  Google Scholar 

  68. A. B. Kunz, Phys. Rev. B 1690 (1973), D. J. Mickish, A. B. Kunz, and S. K. Pantelides, Phys. Rev. B 10, 1369 (1974).

    Google Scholar 

  69. L. Kumar, H. J. Monkhorst, and F. E. Harris, Phys. Rev. B 4084 (1974).

    Google Scholar 

  70. F. E. Harris, L. Kumar and H. J. Monkhorst, Phys. Rev. B 7, 2850 (1973).

    Article  ADS  Google Scholar 

  71. F. Seitz “The Modern Theory of Solids”, McGraw Hill, New York, 1940, p. 421. J. Bardeen, Phys. Rev. 50, 1098 (1936).

    Google Scholar 

  72. S. Doniach in Marcus, Ref. 5, p. 500.

    Google Scholar 

  73. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).

    Article  MathSciNet  ADS  Google Scholar 

  74. W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).

    Article  MathSciNet  ADS  Google Scholar 

  75. R. Gaspar, Acta Phys. Acad. Sci. Hung. 3, 263 (1954).

    MathSciNet  MATH  Google Scholar 

  76. A. K. Rajagopal arid J. Callaway, Phys. Rev. B 7, 1912 (1973).

    Article  ADS  Google Scholar 

  77. F. Herman, J. P. van Dyke, and I. B. Ortenburger, Phys. Rev. Letts. 22, 807 (1969).

    Article  ADS  Google Scholar 

  78. J. C. Slater, J. B. Mann, T. M. Wilson, and J. H. Wood, Phys. Rev. 184, 672 (1969).

    Article  ADS  Google Scholar 

  79. J. F.Janak, A. R. Williams, and V. L. Moruzzi, Phys. Rev. B 11, 1522 (1975).

    Article  ADS  Google Scholar 

  80. C. S. Wang and J. Callaway, Phys. Rev. B 9, 4897 (1974).

    Article  ADS  Google Scholar 

  81. U. von Barth and L. Hedin, J. Phys. C 5, 1629 (1972).

    Article  ADS  Google Scholar 

  82. O. Gunnarson and B. Lundqvist, Phys. Rev. B 13, 4274 (1976).

    Article  ADS  Google Scholar 

  83. W. P. Menzel, C. C. Lin, D. F. Fouquet, E. E. Lafon, and R. C. Chaney, Phys. Rev. Letts. 30, 813 (1973).

    Article  ADS  Google Scholar 

  84. K. J. Duff and A. W. Overhauser, Phys. Rev. B 5, 2799 (1972).

    Article  ADS  Google Scholar 

  85. W. Y. Ching and J. Callaway, Phys. Rev. B 9, 5115 (1974).

    Article  ADS  Google Scholar 

  86. L. Dagens and F. Perot, Phys. Rev. B 8, 1281 (1973).

    Article  ADS  Google Scholar 

  87. W. Y. Ching and J. Callaway, Phys. Rev. Letts. 30, 441 (1973), Phys. Rev. B 11, 1324 (1975).

    Article  ADS  Google Scholar 

  88. S. P. Singhal, Phys. Rev. B 12, 564 (1975).

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1977 Plenum Press, New York

About this chapter

Cite this chapter

Callaway, J. (1977). Methods of Calculation of Energy Bands in Solids. In: Phariseau, P., Scheire, L. (eds) Electrons in Finite and Infinite Structures. NATO Advanced Study Institutes Series, vol 24. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-2811-7_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-2811-7_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-2813-1

  • Online ISBN: 978-1-4684-2811-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics