Ab initio calculation of local vibrational modes by the Green’s function method. Application to GaAs:C and GaN:As

Abstract

We present an ab initio technique for the calculation of vibrational modes at deep defects in semiconductors outside and inside the host-phonon bands. The dynamical matrix is calculated using density-functional theory in the local density approximation. In the results presented here all interatomic harmonic forces up to the eleventh nearest neighbour of a particular atom of the perturbed or unperturbed crystal are included. The Green’s function method is used to obtain the difference of the density of phonon states between the perturbed and the perfect crystal. This technique is applied to calculate the split-off mode at the C impurity at As site in GaAs and its isotope shifts, which are in good agreement with Raman scattering experiments. It is demonstrated that the impurities generate resonances and localized modes inside the host-phonon bands. The resonances arise at specific energies of the density of phonon states of the perfect crystal which are practically independent of the chemical nature of the defect, whereas the localized modes show distinct impurity or ligand isotope shifts. Our calculations of GaAs and cubic GaN lead to the assignment of a number of low energy Raman-scattering peaks between 7.2 meV and 31.0 meV, observed at a layer of cubic GaN on a GaAs substrate, to resonances inside the phonon bands of GaAs and GaN.