Real-space Green’s-function approach applied to the phonon spectra of isolated impurities

It is shown how the real-space Green’s-function approach to the calculation of densities of state for large systems can be used in studying the behavior of isolated impurities on crystals. The local Green’s function associated with the impurity configuration can be obtained by coupling the impurity configuration with the Green’s function of the host lattice surrounding the impurity configuration. The case of substitutional Si in GaAs illustrates the approach. The unusual case of isolated oxygen in GaAs is studied in detail. It is shown that the picture of oxygen forming isolated Ga₂O molecules needs modification in that interactions with all four nearest-neighbor sites must be included to reproduce the experimental spectrum. Sources of the individual peaks in the multiplets are identified and the appearance of a transient four-component multiplet is explained. © 1996 The American Physical Society.