On the role of thermal gradient related stress in intrinsic defect formation during single crystal silicon growth from the melt

Abstract

The incorporation of intrinsic point defects during silicon crystal growth from the melt is discussed using recent data for intrinsic point defect thermal equilibrium and diffusivity. It is shown that the impact of compressive stress on the thermal equilibrium concentration and diffusivity of vacancies and self-interstitials should be taken into account. An analytical expression is derived to quantify the relation between crystal diameter and the critical pull rate window to grow defect free crystals. The results are compared with published experimental data on grown-in defect formation for crystal diameters ranging from 1 to 40cm. It is shown that both the thermal stress due to the axial thermal gradient at the melt/solid interface and the silicon yield stress at high temperature play a crucial role. An empirical expression is proposed to describe the dependence of the thermal gradient on pulling rate.