Analytical solutions were presented for Fick’s one-dimensional diffusion equation in a semi-infinite medium with an exponentially decaying initial impurity concentration profile and various boundary conditions. The properties of the solution for a constant surface concentration were discussed in more detail. The theoretical results were applied to the diffusion of N which had been incorporated by laser melting. The diffusion coefficient of N in Si near to its melting point was estimated to be of the order of 10-6 cm2/s. This result confirmed previously reported high diffusion coefficients for N in Si.

G.J.Willems, H.E.Maes: Journal of Applied Physics, 1993, 73[7], 3256-60