The thermodynamic and optical properties of germanium, silicon, diamond and gallium arsenide

Abstract

Measurements of the dispersion curves of the normal modes of vibration, by inelastic neutron scattering techniques, have been used to find the parameters of dipole approximation models to describe the lattice dynamics of germanium, silicon, diamond and gallium arsenide. The model for diamond, which has not previously been published, shows marked differences in the dispersion curves between this material and the other three and these give rise to characteristic differences in the physical properties. The models for all four materials give good agreement with the experimental results and enable other physical properties to be calculated with reasonable confidence in the frequencies of the normal modes computed from the models. Detailed calculations are made of the frequency distribution and its moments, and of the specific heat which is compared with experimental results. The agreement obtained is quite satisfactory for diamond but less so for the other materials. The negative thermal expansion coefficient of these materials at low temperatures is found to arise easily from these models, when they are extended in a simple way to include the central force part of the anharmonicity between nearest-neighbour ions. The infra-red absorption spectra are calculated both by assuming a joint density of states approximation, and also by assuming first- and second-nearest-neighbour interactions to describe the dipole moments. While none of these calculations is able to give a good account of the experimental results, the latter calculation suggests that second-nearest-neighbour interactions are necessary to explain the measured spectra. The calculations for diamond lead to an entirely different interpretation of the critical points in the spectra from that given previously. The Raman spectra of the elements have been calculated including the effects of anharmonicity on the one-phonon part of the spectra. Since the results depend on the orientation of the specimen and the geometry of the experiment a direct comparison with experiment is not possible. Nevertheless the results do suggest that this type of calculation may well be able to provide agreement with more detailed experiments. Critical points are frequently deduced from measurements of the infra-red and Raman spectra. The difficulties both in identifying and in assigning them to the appropriate normal modes are discussed.