Point-defect equilibrium during diffusion of purely substitutional impurities into elemental crystals

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Abstract
Diffusion of exclusively substitutional solutes (B) into elemental metallic or semiconducting matrices via exchanges with vacancies (V) is treated by starting from a quasichemical reaction which includes impurity-vacancy pairs (BV) as a third species, i.e., BV⇄B+V. This approach enables us to answer the question whether during foreign-atom penetration the vacancy concentration of the host crystal remains in thermal equilibrium. Within the present concepts a distinction can be made between the BV-controlled and the V-controlled mode of the vacancy mechanism. It is shown that commonly the former case, in which vacancy equilibrium persists, is realized. In the V-controlled case the B incorporation is limited by the removal of excess isolated vacancies originating from dissociation of BV pairs. Conditions for the appearance of this diffusion mode are pointed out. We also discuss the role of dislocations as vacancy sinks, the validity of the mass-action law associated with the above reaction, and a possible influence of self-interstitials.