Modelling of the phonon strain shift coefficients in Si_1-xGe_x alloys

In the Raman spectrum of epitaxial Si_1-xGe_x alloys, the composition effect, that determines the three mode peak position, is superimposed to the phonon shift caused by strain. Therefore, the experimental spectra interpretation remains not straightforward, unless vibrational properties calculations of such systems are available. In this paper, reticular dynamic calculations within a modified Keating model, the Anharmonic Keating, are discussed. A new set of model parameters is introduced, providing simple and predictive supercell calculations to investigate accurately the three Raman-active phonon modes in Si_1-xGe_x alloys. The recalculated AK model is successfully employed to model the zone centre Raman-active phonon modes of relaxed and hydrostatically stressed Si_1-xGe_x alloys. The results of the calculations are in quantitative agreement with experimental data reported in literature.