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Thomas–Fermi screening is a theoretical approach to calculate the effects of electric field screening by electrons in a solid. 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 is much smaller than the fermi wavevector, i.e. the long-distance limit. It is named after Llewellyn Thomas and Enrico Fermi.
The Thomas–Fermi wavevector is
Under many circumstances, including semiconductors that are not too heavily doped, n ∝ e, where kB is Boltzmann constant and T is temperature. In this case,
i.e. 1/k0 is given by the familiar formula for Debye length. In the opposite extreme, in the low-temperature limit T = 0,electrons behave as quantum particles. Such an approximation is valid for metals at room temperature, and the Thomas–Fermi screening wavevector kTF given in atomic units is