Lattice dynamics and isotope effects in isotopically enriched semiconductors with diamond structure

We have investigated the isotope effects on the thermodynamic properties of the isotope-enriched diamond structures; namely, lattice parameter, elastic moduli, and Raman shift. Using phenomenological models in lattice dynamics we developed simple theoretical expressions for the effects of the isotope concentrations on lattice parameter, elastic moduli, and Raman shift in general forms both in the quasiharmonic approximation and taking into account the zero-point motion in the long wavelength limit. Qualitative and even quantitative agreement to experimental data is obtained by fitting harmonic and anharmonic force constants for diamond and germanium. We deduce isotope effects on crystals as truly quantum effects decreasing as temperature increases. Most importantly, we have shown the effectiveness of a simple model with a small number of variables in describing the bulk properties of diamond-type crystals