Advertisement

The Origin of Band Structure

  • Karl W. Böer
  • Udo W. PohlEmail author
Living reference work entry

Later version available View entry history

  • 123 Downloads

Abstract

Characteristic for much of the electronic behavior in solids is the existence of energy bands, separated by bandgaps. The bands are permitted for occupation with carriers, and their origin can be described by two complementary models. The proximity approach considers the effect of the neighborhood in a solid on the energy levels of an isolated atom; this model is particularly suited for organic semiconductors, amorphous semiconductors, and clusters of atoms. The periodicity approach emphasizes the long-range periodicity of the potential in a crystal. Electrons near the lower edge of a band in a crystal behave akin to electrons in vacuum; the influence of the crystal potential is expressed by an effective electron mass which increases with increasing distance from the band edge. This chapter describes the basic elements of the electronic band structure in solids.

Keywords

Band structure Bandgap Bloch function Effective mass HOMO Kronig-Penney model LUMO Organic crystals Periodicity approach Proximity approach Reduced k vector 

References

  1. Adler D (1985) Chemistry and physics of covalent amorphous semiconductors. In: Adler D, Schwartz BB, Steele MC (eds) Physical properties of amorphous materials. Plenum Press, New York, p 5–103Google Scholar
  2. Agarwal SC (1995) Electronic structure of amorphous semiconductors. Bull Mater Sci 18:669CrossRefGoogle Scholar
  3. Anderson PW (1963) Concepts in solids. W. A. Benjamin, New YorkGoogle Scholar
  4. Ashcroft NW, Mermin ND (1976) Solid state physics. Holt Reinhart and Winston, New YorkzbMATHGoogle Scholar
  5. Beeby JL, Hayes TM (1989) A calculation of the density of electronic states for amorphous semiconductors. J Non-Cryst Solids 114:253ADSCrossRefGoogle Scholar
  6. Bloch F (1928) Über die Quantenmechanik der Elektronen in Kristallgittern. Z Phys 52:555 (On the quantum mechanics of electrons in crystal lattices, in German)ADSCrossRefGoogle Scholar
  7. Bube RH (1992) Electrons in solids, an introductory survey, 3rd edn. Academic Press, New YorkGoogle Scholar
  8. Callaway J (1976) Quantum theory of solid state. Academic Press, New YorkGoogle Scholar
  9. Eberhart ME, Johnson KH, Adler D (1982) Theoretical models for the electronic structures of hydrogenated amorphous silicon. II. Three-center bonds. Phys Rev B 26:3138ADSCrossRefGoogle Scholar
  10. Fletcher GC (1971) Electron bond theory of solids. North Holland, AmsterdamGoogle Scholar
  11. Harrison WA (1980a) Solid state theory. Dover, New YorkGoogle Scholar
  12. Harrison WA (1980b) Electronic structure and the properties of solids: the physics of chemical bonds. Freeman, San FranciscoGoogle Scholar
  13. Haug A (1972) Theoretical solid state physics. Pergamon Press, OxfordGoogle Scholar
  14. Heine V (1980) Electronic structure from the point of view of the local atomic environment. Solid State Phys 35:1CrossRefGoogle Scholar
  15. Johnson KH, Kolari HJ, de Neufville JP, Morel DL (1980) Theoretical models for the electronic structures of hydrogenated amorphous silicon. Phys Rev B 21:643ADSCrossRefGoogle Scholar
  16. Kaplan TA, Mahanti SD (1995) Electronic properties of solids using cluster methods. Kluwer/Plenum, New YorkGoogle Scholar
  17. Karl N (1974) Organic semiconductors. Festkörperprobleme/Adv Sol State Phys 14:261Google Scholar
  18. Kittel C (2007) Introduction to solid state physics, 7th edn. Wiley, New YorkzbMATHGoogle Scholar
  19. Krieger JB, Iafrate GJ (1986) Time evolution of Bloch electrons in a homogeneous electric field. Phys Rev B 33:5494; and (1987), Quantum transport for Bloch electrons in a spatially homogeneous electric field. Phys Rev B 35:9644Google Scholar
  20. Kronig R de RL, Penney WG (1931) Quantum mechanics of electrons in crystal lattices. Proc R Soc Lond Ser A130:499Google Scholar
  21. Marder MP (2010) Condensed matter physics, 2nd edn. Wiley, HobokenCrossRefGoogle Scholar
  22. Mills RGJ, Montroll EW (1970) Quantum theory on a network. II. A solvable model which may have several bound states per node point. J Math Phys 11:2525Google Scholar
  23. Ovshinsky SR, Adler D (1978) Local structure, bonding, and electric properties of covalent amorphous semiconductors. Contemp Phys 19:109ADSCrossRefGoogle Scholar
  24. Reitz JR (1955) Methods of the one-electron theory of solids. Solid State Phys 1:1CrossRefGoogle Scholar
  25. Shinozuka Y (1999) Hybridization in electronic states and optical properties of covalent amorphous semiconductors. Mater Res Soc Symp Proc 588:309CrossRefGoogle Scholar
  26. Singh J, Shimakawa K (2003) Advances in amorphous semiconductors. CRC Press, Boca RatonCrossRefGoogle Scholar
  27. Slater JC, Johnson KH (1972) Self-consistent-field cluster method for polyatomic molecules and solids. Phys Rev B 5:844ADSCrossRefGoogle Scholar
  28. Street RA (2005) Hydrogenated amorphous silicon. Cambridge University Press, New YorkGoogle Scholar
  29. Ziman JM (1972) Principles of the theory of solids. Cambridge University Press, CambridgeCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.NaplesUSA
  2. 2.Institut für Festkörperphysik, EW5-1Technische Universität BerlinBerlinGermany

Personalised recommendations