Diffusion with Interstitial-Substitutional Equilibrium. Zinc in GaAs

Abstract

The diffusion of an impurity existing in a substitutional-interstitial equilibrium in an extrinsic semiconductor is considered. The dependence of the effective diffusion coefficient $D$ on the impurity concentration can be simplified by assuming that the concentrations of the substitutional species and electrical carriers are nearly equal and that the diffusion of the substitutional species can be neglected. Then $D$ is shown to vary as the first, second, or third power of the impurity concentration depending on the charge states of the substitutional and interstitial species. Universal calculated results are presented for these three cases for a constant surface concentration and semi-infinite medium. The results are used to explain the anomalous diffusion of zinc in GaAs, for which the model predicts that $D$ should vary as the square of the concentration. Six available diffusion profiles at 1000°C can be fit using a single parameter, and the small temperature dependence of available diffusion profiles is in accordance with the theory. The interstitial zinc concentration is estimated to be several orders of magnitude below that of the substitutional zinc.