A perturbative approach to the valence charge density in tetrahedrally bonded semiconductors

An equation for the charge density in term of the dielectric matrix of the crystal is used to study the valence charge density distribution in covalent and and partially ionic semiconductors. Through a perturbation expansion of the dielectric matrix in terms of the ion pseudopotential, we can write the valence charge density as a series of powers of the pseudopoptential. The linear term arises from the diagonal elements of the dielectric matrix and represents the superposition of spherical charge distributions around each atom. The non linear term, due to the off-diagonal elements, is responsible of the heaping up of charge between the ions and describes the covalent part of the chemical bond. This term give also reason of the nonzero intensities of the 'forbidden' reflections (222) and (442).