Self- and foreign-atom diffusion in semiconductor isotope heterostructures. I. Continuum theoretical calculations

Dopant diffusion experiments in semiconductors yield the mobility of the element of interest and information about the possible mechanisms of atomic diffusion. In many cases the diffusion is described on the basis of Fick's law of diffusion, but this treatment is often too simple. In this paper, dopant diffusion in semiconductors is treated systematically on the basis of diffusion-reaction equations. Predictions on the shape of dopant-diffusion profiles that develop under specific experimental conditions are derived. It is illustrated that the charge states of the point defects involved in the diffusion process strongly affect the shape of the dopant profile under electronically extrinsic conditions. The relation between the shape of the dopant profile and the underlying mechanism of atomic diffusion, and between the apparent dopant diffusion coefficient and the point defect mediating the diffusion process is explained. With the advance in epitaxial deposition techniques and the availability of isotopically enriched elements, semiconductor isotope heterostructures can be grown, which are highly appropriate for studying the impact of dopant diffusion on self-diffusion. The modeling of the simultaneous diffusion of self- and dopant atoms in semiconductor isotope heterostructures is described and the advances resulting from this new diffusion approach compared to conventional diffusion studies that treat self- and dopant diffusion separately, are highlighted. This paper aims to serve as a useful guide to understand and accurately model the diffusion of dopants and their impact on self-diffusion in semiconductors.