Calculations of impurity atom diffusion through a narrow diffusion mask opening

Relaxation methods have been used to solve a mixed boundary value problem arising in the fabrication of junction transistors: impurity atom diffusion through a narrow diffusion mask opening. This particular problem is encountered in the fabrication of very narrow diffused p-n junctions. It is shown that the depth of a very narrow junction cannot always be determined from an elementary one-dimensional analysis of this diffusion process. If the width of a diffusion mask opening is less than two impurity atom diffusion lengths, the junction depth becomes geometry dependent. Normalized graphs are presented to illustrate the impurity atom distribution resulting from this particular geometric configuration.