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 had been known for over half a century. Due to the complexity of the solution, it seemed that nobody had ever used it for the direct evaluation of the dopant concentration in the half space. It was shown here that, in order to be able to evaluate it directly, the prescribed boundary function had to be expressed as a power series. It could be used as a special case 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