Modification of the critical v/G of the Voronkov’s theory on the grown-in defects in Si crystals

Abstract

Voronkov developed a theory on the grown-in defects in Si crystals. One of the most important properties deduced from the theory is the critical value of v/G, (v/G)crit, where high-quality crystals can be grown. According to Voronkov’s explanation on the concentration gradients, we proposed a simple expression of (v/G)crit, which is proportional to the concentration gradient. We examined pair annihilation of vacancies and interstitials with two physical models, namely, a partial annihilation and a free-energy-minimum. Both were deduced from free energy considerations.