Theory of impurity vibrations due to isolated interstitials and interstitial-substitutional pair defects in semiconductors.

Abstract

Dynamical properties of isolated interstitials and ``interstitial substitutional'' pair defects in semiconductors are reported with use of the well-known Green's-function technique. To make the problem amenable to calculations, we exploit the symmetry properties of the defect environment and assume the interstitial site to be tetrahedral. For the isolated-impurity case, the perturbation is restricted to the impurity interacting with the host lattice atoms up to and including second-nearest neighbors. Similar to the substitutional-impurity vibrations, the contribution of the nearest-neighbor interactions to the dynamical properties of interstitials in semiconductors is found to be appreciable. For light defects (e.g., ${\mathrm{Li}}_{\mathrm{int}}$ in Si and CdTe), a single dimensionless nearest-neighbor perturbation parameter \ensuremath{\tau} has provided the isotopic frequency shifts of localized vibrational modes, in excellent agreement with the observed optical data. To explain the observed isotopic shifts of inband resonance modes due to heavier impurities (e.g., $^{63}\mathrm{Cu}$, $^{65}\mathrm{Cu}$ in Si, etc.) the effect of second-nearest-neighbor impurity-host interaction is found to be important. Finally, the calculated force-constant changes due to isolated substitutional and interstitial impurities are used to understand the ``interstitial-substitutional'' pair defect vibrations in Si and CdTe.