On the evaluation of the dopant concentration of a three-dimensional steady-state constant-source diffusion problem

Abstract

In this paper, we consider a three-dimensional steady-state constant-source diffusion problem. On the surface of a half space, the dopant concentration function is prescribed over a circular area and its normal derivative is zero over the remaining part of the boundary. The analytical solution of this problem has been 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. This paper shows that, to be able to evaluate 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 time-evolutions of dopant concentrations and non-constant diffusion coefficients.