Phonon-induced quadrupole potential in diamond-type semiconductors

Abstract

Two models of covalent crystals, the shell model and the bond charge model, are used to calculate the quadrupole component of the valence charge distortion brought about by displacement of an atom from its equilibrium position. On the basis of the shell model it appears that the sources of the quadrupole extend over a considerable region around the displaced atom. In the extreme case of germanium the radius of the region exceeds four nearest neighbour distances, and there are over 200 atoms within the region. The value of the quadrupole parameter is found to be about four times bigger than suggested elsewhere. In the framework of Phillips' bond charge model with variable magnitude of the bond charge, the quadrupole parameter turns out to be much smaller. It is suggested that this may be due to the fact that in the bond charge model the sources of the quadrupole are limited to the immediate neighbourhood of the displaced atom.