Analytical model for the out-diffusion of an exponentially decaying impurity profile. Application to nitrogen in silicon

Abstract

Analytical solutions of Fick’s one-dimensional diffusion equation for a semi-infinite medium with an exponentially decaying initial impurity concentration profile and different boundary conditions are presented. The properties of the solution for a constant surface concentration are discussed more extensively. The theoretical results are applied to the diffusion of nitrogen incorporated in silicon by laser melting. The diffusion coefficient of nitrogen in silicon near its melt temperature is estimated to be of the order of 1×10−6 cm2/s. This confirms the recently reported high diffusion coefficient values for nitrogen in silicon.