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 C_{s} has been determined at 1000, 900, 800, and 700°C from radioactive ^{65}Zn diffusion profiles by a BoltzmannMatano analysis. With interstitial Zn as the dominant diffusing species and its concentration controlled by the interstitialsubstitutional 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^{*}C_{s}^{2}γ_{p}^{2}[1+(C_{s}2γ_{p})(dγ_{p}dC_{s})], where γ_{p} is the hole activity coefficient. The term D^{*} equals 2D_{i}K_{1}p_{As4}^{14}, where D_{i} is the interstitial diffusion coefficient, K_{1} the reaction equilibrium constant, and p_{As4} the As_{4} pressure. The relationship between γ_{p} and the Fermi level E_{f} is given by γ_{p}=(Ap)exp(E_{f}kT), 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 builtin 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 impurityband 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 γ_{p} and E_{f} as functions of the hole concentration.
 Publication:

Physical Review
 Pub Date:
 October 1967
 DOI:
 10.1103/PhysRev.162.660
 Bibcode:
 1967PhRv..162..660C