Lattice distortion associated with isolated defects in semiconductors

Abstract

A semi-empirical tight-binding (TB) method is used to investigate the lattice relaxation around isovalent impurities and its effect on the vibrational properties of semiconductors. In terms of the revised Hartree-Fock atomic-term values, this technique provides simple analytical expressions for the change in the impurity-host bond energy and suggests a computationally efficient and reasonable method to estimate the bond-length distortions. Numerical calculations for the symmetric lattice relaxations are reported for eighty cases of impurity-host systems in nineteen elemental and compound semiconductors. For GaAs: In, InAs: Ga, GaP:As, GaAs: P, ZnSe: Te and ZnTe: Se, the results are found to be in good agreement with the recent extended X-ray absorption fine structure (EXAFS) data and, in other cases, the bond-length distortions are seen to be compatible with the theoretical values reported by Martins and Zunger (1984). In almost all the systems studied here the calculated relaxation parameter ε lies in the range 0˙5 ≤ ε < 1˙0, a result which is considerably closer to the value suggested by Bragg (1920), rather than ε = 0 which is commonly used in the virtual-crystal approximation. Simply using the ratio of the effective hybrid energies for the ‘host-host’ to the “impurity-host” {δ ≅ |kε_h|/|k'ε_h'|} systems, the present method reasonably predicts the nature (δ > 1 outward and δ < 1 inward) and the magnitude of the bond relaxation. By considering appropriate distortions, the frequencies of the impurity modes in the dilute limit of mixed II–VI and III–V compounds are derived and the results are compared and discussed with the existing optical experiments and full lattice dynamical (Green's function) calculations.