Non-Fickian microscopic diffusion at interfaces and in thin films

This paper investigates the consequences of a random walk diffusion based on the multidimensional tensorial extension of the adjacency matrix concept on the dopant distribution at the interfaces and in thin films. The random walk concept used here provides a rigorous method of counting all possible random walk paths in an arbitrary 2D and 3D domain and avoids the conceptual inconsistencies of the conventional random walk´s treatment of the so called reflective barrier. The new approach leads to a new phenomenon of a depleted sub-barrier region characterized by a non-zero asymptotic relative gradient at the barrier instead of the vanishing gradient predicted by the conventional treatment. The depleted region extends over only several diffusional jump distances. In restricted diffusion domains in 2D and 3D geometries the depletion at the interface or in the corners is much stronger than in the one-dimensional case. The effects in 2D geometries are illustrated specifically on isolation structures in SOI films