Dependence of the diffusion coefficient on the fermi level: Zinc in gallium arsenide

Abstract

The experimental variation of the diffusion coefficient D with Zn concentration Cs has been determined at 1000, 900, 800, and 700°C from radioactive Zn65 diffusion profiles by a Boltzmann-Matano analysis. With interstitial Zn as the dominant diffusing species and its concentration controlled by the interstitial-substitutional equilibrium in which the singly ionized interstitial donor reacts with a neutral Ga vacancy to form a singly ionized substitutional acceptor and two holes, the effective diffusion coefficient is described by D=D*Cs2p2[1+(Cs2p)(dpdCs)], where p is the hole activity coefficient. The term D* equals 2DiK1pAs414, where Di is the interstitial diffusion coefficient, K1 the reaction equilibrium constant, and pAs4 the As4 pressure. The relationship between p and the Fermi level Ef is given by p=(Ap)exp(EfkT), where A is a constant dependent only on temperature and p is the hole concentration. This derivation for D has extended previous analyses to include both the built-in field and the nonideal behavior of holes which occurs when the impurity level broadens into an impurity band and merges with the valence band to form impurity-band tails at high Zn concentrations. The observed nonmonotonic dependence of the Zn diffusion coefficient on its concentration is a consequence of the nonideal behavior of holes at high concentrations. Quantitative comparison of D with the experimental concentration dependence has permitted the determination of p and Ef as functions of the hole concentration. © 1967 The American Physical Society.