Impurity-induced modes of Mg, As, Si, and C in hexagonal and cubic GaN

We present a cluster-model calculation of local vibrational modes in hexagonal GaN using the valence-force model of Keating and Kane with valence-force parameters fitted to Raman and neutron-scattering experiments. We used the scaling-factor approximation to describe the interatomic forces of the central defect atom. For hexagonal GaN:Mg we find three modes at 136, 262, and 656 cm^-1 in good agreement with experiments. For cubic GaN:As the isolated impurity atom gives us local modes at 95, 125, 151, and 250 cm^-1, which were observed as sharp lines in the experiment. For Si and C defects, for which local modes have not yet been reported, a similar choice of scaling factor as for Mg and As leads to modes that strongly hybridize with the host phonons.