Surface phonons and surface reconstructions of ZnS structure crystals

Abstract

Abstract We present surface phonon calculations for the (111), (110) and (100) surfaces of ZnS structure crystals with special emphasis lying on Si and GaAs. In our potential model we treat short range interactions within a force constant model. Additionally, we take into account long range forces arising from dipole moments, which are induced dynamically on an atom by a displacement of the atom itself or its nearest neighbors. Surface phonons and resonances are calculated by a Green function method yielding the exact solution of the equation of motion for the semi-infinite crystal. We give a comparison of our results to helium time-of-flight and EELS measurements for Si and GaAs. Allowing for changes of the surface layer force constants and dipole parameters we investigate the possibility of a surface phonon softening. Setting up models for the surface parameters we find characteristic features connected with the short range forces and the long range dipole interactions. Relating these soft modes to phase transitions causing surface reconstructions we find evidence for many experimentally observed surface structures. We discuss in detail surface reconstructions of silicon, namely the (2 × 1) and (7 × 7) structures of the (111) surface.