Asymptotic analysis of some two-dimensional diffusion problems
M. G. Meere, John R. King, T. G. Rogers · Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences · 1995
Abstract In this paper we discuss two-dimensional surface source and implant problems for a substitutional-interstitial diffusion model. We present asymptotic solutions in the limit of the surface concentration of impurity (or peak concentration of the implant) being far greater than the equilibrium vacancy concentration. Using leading order composite solutions we plot contours of constant impurity concentration. Some of these contours differ markedly from those of the corresponding linear problem, having the ‘bird’s beak’ shape which is frequently observed in experiments. We also discuss a two-dimensional surface source problem for a vacancy model.