Si Crystal Growth from a Melt: the Secrets Behind the v/G Criterion

摘要

The so called v/G criterion defines a critical value of the ratio of the pulling rate v over the thermal gradient G at the melt solid interface. For a ratio larger than this critical value, the crystal is vacancy-rich while for values below the critical value, the crystal is interstitial-rich. When the ratio is equal to the critical value, the crystal would be defect free or made of "perfect silicon". The expression for the critical ratio is analyzed and it is shown that thermal stress at the melt/solid interface and doping have an important effect. Furthermore, DFT calculations suggest that near the melt/solid interface the formation energy of the intrinsic point defects is lower than in the bulk. This would lead to thermal equilibrium concentrations of vacancies and self-interstitials that are considerably higher than in the bulk of the crystal. It is illustrated how the v/G criterion can be further refined by taking into account these effects.