Darken's equation and other diffusion relations in the light of atomistic kinetic concepts

Abstract

The atomistic kinetic approach of the DOCC sites concept (meaning, very simplified, that the dopant migration in solids progresses via sites which are suitable for occupation by dopant corpuscles summarized as dopant-occupiable sites, i.e. DOCC sites) is here used as a basis on which several diffusion models are thoroughly analysed. Since it is able to cover all effects determining dopant migrations, so that it may be valid in general, it proves other statements on dopant transport to be incorrectly formulated. Following this conception, Darken's equation leads to a link between the Fickian diffusion coefficient of an ideal solution and the activity coefficient of the non-ideal solution, which has up to now been ignored. Contrasting with Darken's hypothesis, Einstein's relation between the Fickian diffusion coefficient and the mobility of dopant particles proves true even in cases of non-ideal solutions. The supposed vacancy wind effect and the diffusion of dopant-defect pairs as molecule-like joined complexes are shown to be physically unrealistic. Orlowski's dopant flux formula proves false. Roth's and Plummer's model on oxidation-enhanced diffusion in silicon is shown to involve incorrectnesses.