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Lindhard formula for the longitudinal dielectric function is given by Thomas-Fermi screening assumes that the total potential varies very slowly, the chemical potential of the system is constant and the temperature is very low.ġ Lindhard formula 2 Analysis of the Lindhard formula 2.1 Three Dimensions 2.1.1 Long Wave-length Limit 2.1.2 Static Limit 2.2 Two Dimensions 2.2.1 Long Wave-length Limit 2.2.2 Static Limit 2.3 One Dimension 2.3.1 Experiment 3 See also 4 References Thomas-Fermi screening is one of many approximation methods for describing the screening.
#Thomas fermi screening constant plus#
(14) The left hand side of this equation is the total energy (kinetic plus potential) for an electron at the top of the Fermi sea, which is the constant e 0. (q) and f is the carrier distribution function which is the Fermi-Dirackĭistribution function(see also FermiDirac statistics) for electrons in thermodynamic equilibrium. (13) gives the kinetic energy of an electron at the top of the Fermi sea, and Eq.
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However this Lindhard formula is valid also for nonequilibrium distribution functions.įor understanding the Lindhard formula, let's consider some limiting cases in 3 dimensions and 2 dimensions. The former condition corresponds, in a real experiment, to keeping the metal/fluid in electrical contact with a fixed potential difference with ground. Inserting these to Lindhard formula and taking limit, we obtain Three DimensionsLong Wave-length Limit First, consider the long wave-length limit (1 of 7 1 dimension case is also considered in other way. In the ThomasFermi approximation, named after Llewellyn Thomas and Enrico Fermi, the system is maintained at a constant electron chemical potential (Fermi level) and at low temperature. This result is same as the classical dielectric function. Static Limit Second, consider the static limit ( ). Is 3D screening wave number(3D inverse screening length) defined as Then, the 3D statically screened Coulomb potential is given by Inserting above equalities for denominator and numerator to this, we obtainĪssuming a thermal equilibrium Fermi-Dirac carrier distribution, we get And Fourier transformation of this result gives