Anharmonic Keating model for group-IV semiconductors with application to the lattice dynamics in alloys of Si, Ge, and C

A generalization of the Keating model is given which treats anharmonic effects in a much improved manner. The dependence of the bond-stretching and bond-bending force constants on the crystal volume was determined by means of ab initio density-functional calculations, revealing simple universal scaling laws. The resulting anharmonic model was used to investigate optical phonons in disordered alloys of Si, Ge, and C. The calculated Raman spectra agree well with experimental results and are analyzed in terms of microscopic and macroscopic strain as well as confinement effects due to mass disorder.