Intrinsic point defect incorporation in silicon single crystals grown from a melt, revisited

Abstract

The so-called Voronkov criterion states that the dominant intrinsic point defect in a silicon single crystal grown from a melt is determined by the ratio of pulling speed over temperature gradient near the melt/solid interface. Above a critical value of this ratio, the crystal is vacancy-rich, while for a ratio below this value, the crystal is interstitial-rich. Applying the Voronkov criterion implies, however, intrinsic point defect diffusivities and/or thermal equilibrium concentrations that can differ strongly from those experimentally determined using self- and metal-diffusion experiments. Furthermore, for a given hot zone, crystal diameter, and length, the thermal gradient itself at the melt/solid interface is a function of the pulling speed, so that the criterion in principle can be replaced by one for the thermal gradient only. There is also experimental evidence, based on crystal detaching experiments, that the growing crystal is always vacancy-rich at the solid/melt interface. In the present paper, the validity of the Voronkov criterion is critically reviewed and the impact of stress, in particular on intrinsic point defect thermal equilibrium concentrations, is taken into account and discussed. It is shown that the temperature and stress gradient near the melt-solid interface have an important impact on the intrinsic point defect incorporation and on the formation of grown-in defects that can be observed in the as-grown and thermally treated crystal. It is also likely that both types of intrinsic point defects can be present in supersaturation in different temperature windows during crystal pulling, leading to the observed coexistence of vacancy and self-interstitial clusters in the as-grown crystal. It is shown that, when taking into account stress effects, there is no need to assume intrinsic point defect diffusivities and thermal equilibrium concentrations that are different from those determined, e.g., from self- and metal-diffusion experiments and from ab initio calculations.