Numerical analysis of effect of thermal stress depending on pulling rate on behavior of intrinsic point defects in large-diameter Si crystal grown by Czochralski method

Abstract

We analyzed the effects of thermal stress and pulling rate on the behavior of intrinsic point defects in a silicon (Si) single crystal grown by the Czochralski (Cz) method using a numerical approach. The thermal equilibrium concentration of the intrinsic point defects (vacancy, V, and self-interstitial Si atom, I) was simulated as a function of thermal stress, which was obtained via ab -initio calculations. Furthermore, the point defect dynamics in the crystal were solved within a framework of a two-dimensional (2D) axisymmetric steady-state global heat and mass transport model of Si crystal growth by the Cz method. The numerical simulations revealed that both magnitude and distribution of the thermal stress depend on the pulling rate. Moreover, they impact the formation and distribution of intrinsic point defects in a growing Si single crystal.