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 and its normal derivative was zero over the remaining part of the boundary. The analytical solution of this problem was known for over half a century. Due to the complexity of the solution, it seems that nobody has ever used it on the direct evaluation of the dopant concentration in the half space. It was shown that, to be able to evaluate it directly, the prescribed boundary function has to be expressed by a power series. It may be used as special cases to verify numerical diffusion models, which consider 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