Efficient direct calculation method for dielectric response in semiconductors

An efficient direct method for calculating the diagonal part of the inverse dielectric matrix (IDM) ${\epsilon }_{\mathrm{GG}\mathcal{’}}^{\mathrm{-}1}$(q) is presented. The method is based on a self-consistent calculation of the response to an external perturbation in the form of a potential step by means of a superlattice band-structure calculation. By restricting the degrees of freedom to the potential shifts per layer, the model is discretized and the diagonal part of the IDM for q in the direction of the superlattice is obtained by a fast Fourier transformation. The method is applied to the semiconductors Si, Ge, GaAs, and ZnSe. The calculated macroscopic dielectric constants, either ${\lim }_{\mathrm{q}\to 0}$[1/${\mathrm{\epsilon }}_{00}^{\mathrm{-}1}$(q)] or the value obtained from a real-space determination, are found to be larger than the measured values by ∼10–30 %. The overestimate is attributed to the local-density approximation (LDA) to the exchange-correlation potential which is also well known to underestimate the energy gaps between valence and conduction bands. Adjusting the potentials so as to fit the band gaps at points Γ and X to their experimental values is found to lead to dielectric constants in good agreement with the measured values. This suggests that the band-gap underestimate may be due more to the LDA than to a discontinuity in the exchange-correlation potential.