Distortion of depth profiles during sputtering: I. General description of collisional mixing

Abstract

The present work concerns collisional mixing which is one of the factors limiting the depth resolution of sputter profiling. A general treatment comprising the effects of recoil implantation and cascade mixing on the distortion of an impurity profile in a bulk matrix is presented. The statistics of the distorting events is shown to be a close analogue to that of the stopping of charged particles in random matter, and describable in terms of the Bothe-Landau theory of energy loss; a general expression is given for the Green's function transforming a given impurity profile into an apparent (or distorted) profile. In the diffusion approximation, the present theory yields a well defined shift and smearing of an impurity profile without introduction of a (more or less arbitrary) effective minimum energy for displacement.