New model dielectric function and exchange-correlation potential for semiconductors and insulators

Abstract

We propose a new model frequency and wave-vector-dependent dielectric function for systems with an energy gap in their electronic excitation spectrum. The function is homogeneous, isotropic, and causal and satisfies two sum rules relating to particle-number conservation. Moreover, it has an analytic representation, reduces to the Lindhard function in the limit of zero gap, and compares well numerically with the $\ensuremath{\epsilon}(q,\ensuremath{\omega})$ of Si from band-structure calculations. With the model irreducible polarizability, we extend the theory of Singwi et al. [Phys. Rev. B 1, 1044 (1970)] to obtain a one-parameter family of exchange-correlation potentials appropriate for semiconductors and insulators. The existence of a band gap is found to enhance the exchange contributions but reduces the correlation contributions to the exchange-correlation potentials resulting in an overall potential which deepens as the average band gap of the system increases. A band calculation of silicon in the present theory shows a slight improvement of the band gaps over previous work using the metallic exchange-correlation potential.