Silicon Single Crystal Growth from a Melt: On the Impact of Dopants on the v/G Criterion

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The so called v/G criterion defines a critical value Γ0crit of the ratio Γ 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 self-interstitial-rich. When the ratio is equal to the critical value, the crystal would be defect free or made of so called “perfect silicon”. The basic analytical 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 on the Γ0crit value. Furthermore, DFT calculations suggest that near the melt-solid interface the formation energy of the intrinsic point defects is lower than in the bulk of the crystal. This would lead to thermal equilibrium concentrations of vacancies and self-interstitials at the free surface and most probably also at the melt-solid interface that are considerably different from those in the bulk. It is illustrated how the v/G criterion can be further refined by taking into account these effects.