A numerical study of field-aided diffusion

Abstract

A numerical method for determining the effect of the internal electric field on the diffusion of impurity ions in semiconductors is described. The model of the diffusion process is defined by the flux equations, the continuity equations and Gauss' law. Due to the complexity of this model, there is no known analytical solution. However, the system of nonlinear equations is solved numerically using an iteration technique. Diffusion profiles are presented for boron diffusing in silicon at 1100°C for various values of surface concentration C 0. These profiles are compared to the complementary error function which is the correct solution neglecting the internal electric field. The impurity profiles are also compared to those obtained by solving an approximate diffusion equation derived by using the concept of a concentration dependent “effective” diffusion coefficient. It is shown that the influence of the electric field on the motion of the impurities is a strong function of the surface concentration. For high values of C 0, the impurity profile becomes exponential. The accuracy of the solutions obtained by solving the approximate diffusion equation depends on both the value of C 0 and the diffusion time.