Effects of disorder on the vibrational properties of SiGe alloys: Failure of mean-field approximations

The vibrational properties of Si1/2{Ge}1/2$ alloys are studied using first principles interatomic force constants. The effects of disorder are either simulated using large supercells or treated at the mean-field level by the coherent-potential approximation. The latter approach fails not only to reproduce the details of the Raman spectra due to the local atomic environment, but even to predict the three-mode behavior of this alloy. Supercell calculations, on the contrary, are in good agreement with observed Raman spectra and shed light on the microscopic mechanisms responsible for their detailed features.