Dielectric screening approach to the average band gap of semiconductors

Abstract

In Phillips' spectroscopic theory of semiconductors, the covalency and ionicity is derived empirically from the average band gap between the highest valence and lowest conduction bands. In this paper a theoretical expression for the average band gap is derived in terms of a moment expansion of the microscopic dielectric matrix. For 15 semiconductors the dielectric constant and the average band gap are calculated. The values of the dielectric constant for most materials are within 15% of the experiment. The calculated values of the average band gap agree within 5% with the values given by Phillips. For ZnTe, InSb and GaSb the discrepancies are maximum 33% for the dielectric constant and 16% for the band gap. This is due to strong spin-orbit interaction which has not been taken into account in the calculation.