Microscopic calculation of the lattice dynamics of germanium using pseudo-atoms

Abstract

The phonon frequencies of germanium are calculated using a quantum-mechanical dynamical matrix and the pseudo-atom expression for the change in charge density. A model pseudo-atom is constructed from Phillips' bond charge model with the dimensions of the bond charge taken from the static crystal: each pseudo-atom moves rigidly with its ion and is taken to consist of a central part and half of each adjacent bond charge. Without exchange-correlation (XC) effects, the calculated phonon spectrum is unsatisfactory with several acoustic modes being unstable. Several modifications of the model are tried but do not rectify this. An expression for the energy contribution caused by the XC effects is derived using perturbation theory. It is shown that it introduces a strong force attracting the two halves of the bond charge together. This force stabilises the acoustic modes and gives results in reasonable agreement with experiment and which are comparable with some of the results of more complicated methods. The flat behavior of the TA modes is not reproduced. The amount of computation required is small and the method is compared with the usual methods of calculation. The implications of the treatment of the XC effects is discussed and so are some possible improvements to the model pseudo-atom.