Local field effects on the static dielectric constant of crystalline semiconductors or insulators

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Abstract
Local field effects are calculated in the R.P.A. approximation from two extreme points of view. The first consists of an analytical inversion of the dielectric matrix in reciprocal space. If confirms the results of recent numerical calculations, that local field effects tend to reduce the dielectric constant. The second treats these effects in real space in a tight-binding limit, thus leading to a Lorentz-Lorenz formula. In this limit it is shown, contrary to the usual belief, that local-field effects also tend to reduce ε. A detailed numerical analysis is performed in the case of purely covalent semiconductors, showing that the local field correction increases in the sequence C, Si, Ge, Sn