Deep levels associated with (vacancy, impurity) pairs in covalent semiconductors

A simple theory of deep levels due to vacancies paired with nearest-neighbor $s{p}^3$-bonded substitutional impurities in zinc-blende hosts is presented, and the major chemical trends in such levels in 12 different semiconductors are predicted. The results of these calculations show that when an impurity is complexed with a vacancy, its deep levels in the band gap may be significantly altered in comparison with those of an isolated impurity. Complexing with a vacancy can drive a shallow, isolated impurity level deeper into the band gap, or cause the deep level of an isolated impurity to move across the band gap and become resonant with either the valence or the conduction band. Included in the presented results are predictions for the deep levels produced by the (${\mathrm{As}}_{\mathrm{G}\mathrm{a},}$ $V_{\mathrm{As}}$) vacancy-antisite defect pair in GaAs, which might be associated with the EL2 level in that material.