A 3-dimensional steady-state constant-source diffusion problem was considered. On the surface of a half space, the dopant concentration function was prescribed over a circular area while its normal derivative was zero over the remaining part of the boundary. The analytical solution of this problem had been known for over half a century. However, due to the complexity of the solution, it had never been used for the direct evaluation of the dopant concentration in the half-space. It was shown here that, in order to ensure direct evaluation, the prescribed boundary function had to be expressed as a power series. It could be used, in special cases, to verify numerical diffusion models which considered the time-evolution of dopant concentrations and non-constant diffusion coefficients.

On the Evaluation of the Dopant Concentration of a Three-Dimensional Steady-State Constant-Source Diffusion Problem. G.Fu, T.Cao, L.Cao: Materials Letters, 2005, 59[24-25], 3018-20