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