(Invited) A Density Functional Theory Study of the Effect of Pressure on the Formation and Migration Enthalpies of Intrinsic Point Defects in Growing Si Single Crystals

Abstract

The dependences of the formation enthalpy (Hf) and the migration enthalpy (Hm) of the self-interstitial I and the vacancy V in single crystal Si on hydrostatic pressure and on internal pressure were studied by calculating the formation energies and relaxation volumes. Density functional theory calculations were used with 216-atom supercells and with special attention for the convergence of the calculations. The obtained Hf and Hm were used to describe the impact of thermal stress on the critical pulling speed over thermal gradient ratio Γ0crit as defined in the Voronkov criterion. A nearly linear relation between Γ0crit (in 10-3 cm2min-1K-1) and σ0 (in MPa) was obtained, described by Γ0crit 1.509 - 0.023σ0. The impact of thermal stress on Γ0crit is opposite to that of hydrostatic pressure and makes the growing Si crystal more vacancy-rich. It is important to take into account the impact of stress on the generation of intrinsic point defects in developing future large diameter defect-free crystals.