Nonlinear two-dimensional impurity diffusion in semiconductors: A quasi-linear numerical analysis

A two-dimensional numerical simulation program is proposed which enables the concentration profiles of diffused dopants in semiconductors to be calculated. This program takes the nonlinear phenomena typical of high concentrations into account; however, since the corresponding nonlinear diffusion model is made quasi-linear by means of a suitable transformation of the variable, it becomes almost as easy and efficient as a linear numerical simulation program. The numerical algorithm developed is based on the finite difference Alternating Direction Implicit (ADI) method proposed by Peaceman and Rachford. As a practical application, the two-dimensional doping profiles of arsenic into silicon are calculated for a predeposition process and for a drive-in process following an ion implantation.