Diffusion from a Plane, Finite Source into a Second Phase with Special Reference to Oxide-Film Diffusion Sources on Silicon

A model is set up for the diffusion from a source of finite thickness into an adjacent second phase of semi‐infinite extent. With the principal assumption of no diffusion in or out of the system, a solution is obtained for the diffusion profile in the second phase. It is also assumed that the diffusion coefficients are independent of concentration, but segregation at the inter‐phase boundary is taken into account and so also, to a first approximation, is the possibility of precipitation or reaction at the interface. The model predicts a change in the profile from an ERFC to Gaussian shape depending on whether the diffusion length in the source is much less than or much greater than its thickness, i.e., as the diffusion time increases.