Vibrational properties of amorphous Si and Ge

Calculations of the vibrational density of states and the Raman and infrared spectra have been performed for random-network, microcrystalline, and polymorph structures of Si and Ge. The polymorphs considered include Si III, Ge III, and two clathrate structures. The calculations are based on simple semiempirical forms for interatomic interactions and Raman and infrared activities. The results for some representations of the random network compare favorably with experimental measurements on amorphous Si and Ge. The apparent similarity of the vibrational densities of states of amorphous Si and Ge to those of diamond cubic Si and Ge is explained by a study of the form of the density of states for nearest-neighbor central forces. There is an interesting relationship to a simple tight-binding theory of the electronic density of states in this limit. The variations of infrared and Raman activities in different parts of the spectrum are discussed. Numerical calculations for energy-loss spectra in neutron scattering are also presented. A simple model explains the oscillation of intensity between the high- and low-frequency parts of the spectrum as the scattering vector increases.