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Thomas–Fermi screening : ウィキペディア英語版
Thomas–Fermi screening
Thomas–Fermi screening is a theoretical approach to calculating the effects of electric field screening by electrons in a solid.〔N. W. Ashcroft and N. D. Mermin, ''Solid State Physics'' (Thomson Learning, Toronto, 1976)〕 It is a special case of the more general Lindhard theory; in particular, Thomas–Fermi screening is the limit of the Lindhard formula when the wavevector (the reciprocal of the length-scale of interest) is much smaller than the fermi wavevector, i.e. the long-distance limit.〔
The Thomas-Fermi wavevector (in Gaussian-cgs units) is〔
:k_0^2 = 4\pi e^2 \frac
where μ is the chemical potential (fermi level), ''n'' is the electron concentration and ''e'' is the elementary charge.
Under many circumstances, including semiconductors that are not too heavily doped, ''n''∝''e''''μ''/''k''B''T'', where ''k''B is Boltzmann constant and ''T'' is temperature. In this case,
:k_0^2 = 4\pi e^2 n/(k_BT)
i.e. 1/k0 is given by the familiar formula for Debye length.
For more details and discussion, including the one-dimensional and two-dimensional cases, see the article: Lindhard theory.
==Derivation==


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