<i>Ab initio</i>calculation of phonon dispersions in semiconductors

The density-functional linear-response approach to lattice-dynamical calculations in semiconductors is presented in full detail. As an application, we calculate complete phonon dispersions for the elemental semiconductors Si and Ge, and for the III-V semiconductor compounds GaAs, AlAs, GaSb, and AlSb. Our results are in excellent agreement with experiments where available, and provide predictions where they are not. As a byproduct, we obtain real-space interatomic force constants for these materials, which are useful both for interpolating the dynamical matrices through the Brillouin zone, and as ingredients of approximate calculations for mixed systems such as alloys and microstructures. The possibility of studying these systems using the force constants of the pure materials relies on the so-called mass approximation, B i.e., on neglecting the dependence of the force constants upon composition. The accuracy of such an approximation is tested and found to be very good for cationic intermixing in binary semiconductors, while it is less so for anionic substitutions. The situation is intermediate in the case of elemental semiconductors.