Electronic and formation energies for deep defects in narrow-gap semiconductors

We consider the charged states of certain deep defects in the narrow-gap semiconductors mercury cadmium telluride, mercury zinc telluride, and mercury zinc selenide. We predict the values of the deep-defect energy levels and also the formation energy of the defects. For each charged state we include the effect of relaxation. We consider substitutional and interstitial anions and cations as well as vacancies. We use Green's-function techniques throughout and adapt the Haldane-Anderson model to consider the effects of different charged states. By use of a pseudopotential we generalize the ideal vacancy model so as to be able to consider relaxation. As always, chemical trends were predicted with considerably more accuracy than the absolute location of the energy levels. Formation energies, involving differences, were predicted with an accuracy similar to that of chemical trends. The more negatively charged the impurity, the higher the energy except that the vacancy energy did not depend strongly on the charge. Typical charge-state energy shifts of defect levels are about twice that caused by relaxation effects. Formation energies for defects in the same material and at the same site were quite similar while the formation energy for different charged states could vary considerably. If one considered only native defects, self-interstitials had the lowest formation energy while for antisites and vacancies the results were similar.