First-principle calculation of electrons charge density in the diamond–structure semiconductor crystals

Abstract

A computational study of the total electrons charge density in the diamond-structure semiconductor crystals has been performed. In a typical modern electronic structure calculation, the charge density is obtained from a certain density functional, however, the charge density in this work was obtained from first principles. It is assumed that the one-electron Bloch functions for the crystals will not very seriously differ from the wave functions in the atomic systems, therefore, they are represented by the well known normalized Slater atomic orbital for multi-electron atoms and ions. Since the spherical harmonics are expressed in the spherical coordinate system, all the calculations are done in this system. The wave functions and the total electron charge densities are calculated along the [l00], [010], and [00l] directions for the state k=0. The atomic system of units is used throughout the calculations. i.e. distances are expresPsed in unit of the Bohr radius, and charges in unit of the electronic charge. It has been found that in each crystal, the total electrons charge density along the [100] and [010] directions are equal, however, the charge densities at a given distance from the center of the cell along [001] and [100] directions are not exactly equal; the density along [100] been always higher. This shows that the potentials arising from the electrons are not spherically symmetric. The results are presented and discussed