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 hexago nal GaN using the valence-force model of Keating and Kane with valence-forc e parameters fitted to Raman and neutron-scattering experiments. We used th e scaling-factor approximation to describe the interatomic forces of the ce ntral defect atom. For hexagonal GaN:Mg we find three modes at 136, 262, an d 656 cm(-1) in-good agreement with experiments. For cubic GaN:As the isola ted impurity atom gives us local modes at 95, 125, 151,and 250 cm(-1), whic h 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 f actor as for Mg and As leads to modes that strongly hybridize with the host phonons.