Symmetric lattice distortions around deep-level impurities in semiconductors: Vacancy and substitutional Cu in silicon

A model based on the electrostatic Hellmann-Feynman theorem and an empirical valence-force potential has been used to study breathing-mode distortions around the vacancy and substitutional Cu in silicon. The calculation of the forces driving the distortion is based on a self-consistent calculation of the charge-density perturbation. In both cases considered, we find an outward breathingmode distortion of the lattice. By using a Kubic-harmonics expansion of the charge density, the structure of the forces can be examined. It is found that the outward breathing-mode distortion is caused mainly by the reduced charge anisotropy around the defect, which is a result of the defectinduced deficiency in the number of valence electrons. Distortion amplitudes and the spatial extension of the distortion fields are also calculated for the fully relaxed lattice.