Calculation of local vibrations at deep centers in semiconductors

A theoretical treatment of local vibrational modes applied to intrinsic defects in GaAs is presented. The dynamics of the perfect and imperfect lattice are described with the help of the valence force model of Kane and the Coulomb interaction is included explicitly. The interatomic forces of the host crystal and at the defect are determined by using the self-consistent density functional theory applied to a supercell containing 54 atoms. The force constants due to various displacements of the nearest neighbours of an atom are used to determine the valence force parameters. They are used to calculate the dynamical matrix of the perfect crystal from which we obtain the phonon dispersions curves. They are in good agreement with the experiments. In case of a defect we calculate the dynamical matrix of 280 vibrating atoms around the defect and determine the local vibrational modes and resonances and their spatial extent in both optical and acoustical branches of the crystal phonons. The results for the As-antisite and the vacancies in GaAs are compared with Raman scattering and optical absorption experiments at intrinsic defects in GaAs. The formation entropies of these defects are also calculated.