Calculation of local vibrational modes at point defects in semiconductors

We present a simple method to calculate local vibrational modes (LVMs) in cubic semiconductors using the valence-force model of Keating and Kane together with Coulomb forces. The vibration frequencies and amplitudes are obtained from the eigenvalues and eigenvectors of the dynamical matrix, respectively. The valence-force parameters of GaAs were obtained from calculations of the interatomic forces by density-functional theory. The resulting phonon dispersion curves are in agreement with neutron scattering experiments and we present the LVM of A(1) symmetry at the As antisite. We calculated the isotope shift of LVMs for the shallow impurities B, C, N in Si and at Ni impurities in ZnS and present a general relation between the mass dependence of a LVM and the relative vibration amplitude of the impurity.