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Equilibrium Statistics of Carriers

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

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Abstract

Electrons and holes are the carriers of currents in semiconductors. The density of these carriers in equilibrium is obtained from the Fermi–Dirac statistics. The Fermi energy EF as a key parameter can be obtained from quasineutrality; it lies near the middle of the bandgap for intrinsic and near the donor or acceptor level for doped semiconductors. The difference between the respective band edge and the Fermi level represents the activation energy of a Boltzmann factor, whose product with the joint density of energy states yields the carrier density. The density of minority carriers may be frozen-in in semiconductors with a large bandgap and represented by a quasi-Fermi energy.

At high quasi-particle densities and low temperature, phase transitions take place with substantial changes in the optical and electronic behavior. An insulator-metal transition occurs above a critical Mott density of dopants. A similar process is initiated by sufficient optical generation of electrons and holes, leading to an electron–hole plasma and – at suitable conditions – to a condensation into an electron–hole liquid.

Keywords

Boltzmann distribution Bose–Einstein distribution Carrier density Degenerate semiconductor Density of states Density-of-state mass Effective density of states Electron–hole liquid Electron–hole plasma Extrinsic semiconductor Fermi–Dirac distribution Fermi energy Intrinsic carrier density Intrinsic semiconductor Mott density Mott transition 

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Copyright information

© Springer International Publishing AG 2020

Authors and Affiliations

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

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