Band-to-Band Transitions

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

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Optically induced band-to-band transitions are resonance transitions and related to the band structure by the momentum matrix-element and the joint density of states. For transitions near the band edge, the theory of optical transitions between the valence and conduction bands can be simplified with an effective-mass approximation, assuming parabolic band shapes and arriving at quantitative expressions for the absorption as a function of the photon energy. Depending on the conduction-band behavior, strong direct or weak indirect transitions occur at the band edge. In addition, a contribution of forbidden transitions modifies the absorption further away from the band edge. Deviations from the ideal, periodic crystal lattice provide tailing states extending beyond the band edge, usually as an Urbach tail which decreases exponentially with distance from the band edge. In quantum wells the two-dimensional joint density of states leads to a steplike increase of the absorption for increasing photon energy.


Absorption coefficient Band structure Band tailing Direct transitions Forbidden transitions Indirect transitions Joint density of states Momentum-matrix element Optical transitions Parabolic bands Urbach tail Van Hove singularities 


  1. Adagi S (2005) Properties of group-IV, III-V and II-VI semiconductors. Wiley, ChichesterCrossRefGoogle Scholar
  2. Albrecht S, Reining L, Del Sole R, Onida G (1998) Ab initio calculation of excitonic effects in the optical spectra of semiconductors. Phys Rev Lett 80:4510CrossRefADSGoogle Scholar
  3. Aulbur WG, Jonsson L, Wilkins JW (2000) Quasiparticle calculations in solids. Solid State Phys 54:1CrossRefGoogle Scholar
  4. Bardeen J, Blatt FJ, Hall LH (1956) Indirect transition from the valence to the conduction band. In: Breeckenridge R, Russel B, Halm T (eds) Proceedings of photoconductivity conference. Wiley, New York, p 146Google Scholar
  5. Bassani GF (1966) Methods of band calculations applicable to III–V compounds. In: Willardson RK, Beer AC (eds) Semiconductors and semimetals, vol 1. Academic Press, New York, p 21Google Scholar
  6. Bassani GF, Pastori Parravicini G (1975) Electronic states and optical transitions in solids. Pergamon Press, OxfordGoogle Scholar
  7. Bhattacharya R, Mondal R, Khatua P, Rudra A, Kapon E, Malzer S, Döhler G, Pal B, Bansal B (2015) Measurements of the electric field of zero-point optical phonons in GaAs quantum wells support the Urbach rule for zero-temperature lifetime broadening. Phys Rev Lett 114:047402CrossRefADSGoogle Scholar
  8. Brust D, Phillips JC, Bassani F (1962) Critical points and ultraviolet reflectivity of semiconductors. Phys Rev Lett 9:94CrossRefADSGoogle Scholar
  9. Bube RH (1974) Electronic properties of crystalline solids. Academic Press, New YorkGoogle Scholar
  10. Cody GD, Tiedje T, Abeles B, Brooks B, Goldstein Y (1981) Disorder and the optical absorption edge of hydrogenated amorphous silicon. Phys Rev Lett 47:1480CrossRefADSGoogle Scholar
  11. Cohen ML, Chelikowsky JR (1988) Electronic structure and optical properties of semiconductors. Springer, BerlinCrossRefGoogle Scholar
  12. Dash WC, Newman R (1955) Intrinsic optical absorption in single-crystal germanium and silicon at 77°K and 300°K. Phys Rev 99:1151CrossRefADSGoogle Scholar
  13. Dingle R (1975) Confined carrier quantum states in ultrathin semiconductor hetero-structures. In: Queisser HJ (ed) Festkörperprobleme, vol 15, Advances in solid state physics. Pergamon/Vieweg, Braunschweig, p 21CrossRefGoogle Scholar
  14. Dingle R, Wiegmann W, Henry CH (1974) Quantum states of confined carriers in very thin AlxGa1−xAs-GaAs-AlxGa1−xAs heterostructures. Phys Rev Lett 33:827CrossRefADSGoogle Scholar
  15. Dutton D (1958) Fundamental absorption edge in cadmium sulfide. Phys Rev 112:785CrossRefADSGoogle Scholar
  16. Gubarev SI, Ruf T, Cardona M, Ploog K (1993) Resonant magneto-luminescence of high quality GaAs. Solid State Commun 85:853CrossRefADSGoogle Scholar
  17. Hanke W, Sham LJ (1974) Dielectric response in the Wannier representation: application to the optical spectrum of diamond. Phys Rev Lett 33:582CrossRefADSGoogle Scholar
  18. Hybertsen MS, Louie SG (1985) First-principles theory of quasiparticles: calculation of band gaps in semiconductors and insulators. Phys Rev Lett 55:1418CrossRefADSGoogle Scholar
  19. Ihara T, Hayamizu Y, Yoshita M, Akiyama H, Pfeiffer LN, West KW (2007) One-dimensional band-edge absorption in a doped quantum wire. Phys Rev Lett 99:126803CrossRefADSGoogle Scholar
  20. Johnson EA (1967) Absorption near the fundamental edge. In: Willardson RK, Beer AC (eds) Semiconductors and semimetals, vol 3. Academic Press, London, pp 153–258Google Scholar
  21. Kane EO (1957) Band structure of indium antimonide. J Phys Chem Solids 1:249CrossRefADSGoogle Scholar
  22. Lautenschlager P, Garriga M, Vina L, Cardona M (1987a) Temperature dependence of the dielectric function and interband critical points in silicon. Phys Rev B 36:4821CrossRefADSGoogle Scholar
  23. Lautenschlager P, Garriga M, Logothetidis S, Cardona M (1987b) Interband critical points of GaAs and their temperature dependence. Phys Rev B 35:9174CrossRefADSGoogle Scholar
  24. Lax M, Hopfield JJ (1961) Selection rules connecting different points in the Brillouin zone. Phys Rev 124:115CrossRefADSzbMATHGoogle Scholar
  25. Legesse M, Nolan M, Fagas G (2014) A first principles analysis of the effect of hydrogen concentration in hydrogenated amorphous silicon on the formation of strained Si-Si bonds and the optical and mobility gaps. J Appl Phys 115:203711CrossRefADSGoogle Scholar
  26. Lines ME (1986) Ultralow-loss glasses. Annu Rev Mater Sci 16:113CrossRefADSGoogle Scholar
  27. Lyon SA (1986) Spectroscopy of hot carriers in semiconductors. J Lumin 35:121CrossRefGoogle Scholar
  28. Macfarlane GG, Roberts V (1955) Infrared absorption of silicon near the lattice edge. Phys Rev 98:1865CrossRefADSGoogle Scholar
  29. Mackenzie KD, Burnett JH, Eggert JR, Li YM, Paul W (1988) Comparison of the structural, electrical, and optical properties of amorphous silicon-germanium alloys produced from hydrides and fluorides. Phys Rev B 38:6120CrossRefADSGoogle Scholar
  30. Madelung O (1981) Introduction to solid state theory. Springer, Berlin/New YorkGoogle Scholar
  31. Martinez G, Schlüter M, Cohen ML (1975) Electronic structure of PbSe and PbTe II – optical properties. Phys Rev B 11:660CrossRefADSGoogle Scholar
  32. Mavroides JG (1972) Magneto-optical properties. In: Abeles F (ed) Optical properties of solids. North Holland, AmsterdamGoogle Scholar
  33. Miller RC, Kleinman DA, Nordland WA Jr, Gossard AC (1980) Luminescence studies of optically pumped quantum wells in GaAs-AlxGa1-xAs multilayer structures. Phys Rev B 22:863CrossRefADSGoogle Scholar
  34. Millot M, Broto J-M, George S, González J, Segura A (2010) Electronic structure of indium selenide probed by magnetoabsorption spectroscopy under high pressure. Phys Rev B 81:205211CrossRefADSGoogle Scholar
  35. Millot M, Ubrig N, Poumirol J-P, Gherasoiu I, Walukiewicz W, George S, Portugall O, Léotin J, Goiran M, Broto J-M (2011) Determination of effective mass in InN by high-field oscillatory magnetoabsorption spectroscopy. Phys Rev B 83:125204CrossRefADSGoogle Scholar
  36. Moss TS, Burrell GJ, Ellis B (1973) Semiconductor optoelectronics. Wiley, New YorkGoogle Scholar
  37. Mott NF, Davis EA (1979) Electronic processes in non-crystalline materials. Claredon Press, Oxford, UKGoogle Scholar
  38. Phillips JC (1956) Critical points and lattice vibration spectra. Phys Rev 104:1263CrossRefADSMathSciNetGoogle Scholar
  39. Phillips JC (1966) The fundamental optical spectra of solids. Solid State Phys 18:55CrossRefGoogle Scholar
  40. Pinczuk A, Worlock JM (1982) Light scattering by two-dimensional electron systems in semiconductors. Surf Sci 113:69CrossRefADSGoogle Scholar
  41. Rochon P, Fortin E (1975) Photovoltaic effect and interband magneto-optical transitions in InP. Phys Rev B 12:5803CrossRefADSGoogle Scholar
  42. Roth LM, Lax B, Zwerdling S (1959) Theory of optical magneto-absorption effects in semiconductors. Phys Rev 114:90CrossRefADSGoogle Scholar
  43. Sari SO (1972) Excitonic effects in Landau transitions at the E1 edges of InSb and GaSb. Phys Rev B 6:2304CrossRefADSGoogle Scholar
  44. Sa-yakanit V, Glyde HR (1987) Urbach tails and disorder. Comments Condens Matter Phys 13:35Google Scholar
  45. Schulman JN, McGill TC (1981) Complex band structure and superlattice electronic states. Phys Rev B 23:4149CrossRefADSGoogle Scholar
  46. Shkrebtii AI, Ibrahim ZA, Teatro T, Richter W, Lee MJG, Henderson L (2010) Theory of the temperature dependent dielectric function of semiconductors: from bulk to surfaces. Application to GaAs and Si. Phys Status Solidi B 247:1881CrossRefADSGoogle Scholar
  47. Torabi A, Brennan KF, Summers CJ (1987) Photoluminescence studies of coupled quantum well structures in the AlGaAs/GaAs system. Proc SPIE 0792:152CrossRefADSGoogle Scholar
  48. van Hove L (1953) The occurrence of singularities in the elastic frequency distribution of a crystal. Phys Rev 89:1189CrossRefADSMathSciNetzbMATHGoogle Scholar
  49. Vrehen QHF (1968) Interband magneto-optical absorption in gallium arsenide. J Phys Chem Solids 29:129CrossRefADSGoogle Scholar
  50. Watanabe K, Uchida K, Miura N (2003) Magneto-optical effects observed for GaSe in megagauss magnetic fields. Phys Rev B 68:155312CrossRefADSGoogle Scholar
  51. Yafet Y (1963) g factors and spin-lattice relaxation of conduction electrons. In: Seitz F, Turnbull D (eds) Solid state physics, vol 14. Academic Press, New York, p 1Google Scholar
  52. Zawadzki W, Lax B (1966) Two-band model for Bloch electrons in crossed electric and magnetic fields. Phys Rev Lett 16:1001CrossRefADSGoogle Scholar
  53. Zunger A (1983) One-electron broken-symmetry approach to the core-hole spectra of semiconductors. Phys Rev Lett 50:1215CrossRefADSGoogle Scholar
  54. Zwerdling S, Lax B, Roth LM (1957) Oscillatory magneto-absorption in semiconductors. Phys Rev 108:1402CrossRefADSGoogle Scholar

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Authors and Affiliations

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

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