Atomic Relaxation of a Junction Profile

Abstract

Nonlinear relaxation of a sharp concentration profile typical in layered semiconductor junctions is investigated using the Path Probability Method (PPM) of irreversible statistical mechanics. We employ the vacancy mechanism for atomic migration and the pair approximation for the statistical treatment. The PPM is a microscopic method, from which we can derive macroscopic parameters. Our results show that at the initial stage of the relaxation of a sharp concentration profile, atoms near the junction may diffuse up against the concentration gradient. More surprisingly, our numerical examples convincingly demonstrate that the atom flux goes up against the local chemical potential gradient near a sharp profile, indicating that in such highly nonlinear regime the usual linear diffusion theory in which the atom flux is linearly proportional to the chemical potential gradient breaks down. It is shown that the cause of the uphill diffusion is the repulsion among different species, which is also the physical origin of the square gradient term.