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.

中文翻译：

---

关于硅晶体中生长缺陷的沃龙科夫理论的临界v / G的修正

沃龙科夫（Voronkov）开发了一种有关硅晶体中缺陷的理论。从理论推论出的最重要的特性之一是v / G临界值（v / G）临界值，可以在其中生长出高质量的晶体。根据Voronkov对浓度梯度的解释，我们提出了（v / G）crit的简单表达式，它与浓度梯度成正比。我们用两个物理模型检查了空位和间隙的成对an灭，即部分an灭和最小自由能。两者都是从自由能源的考虑推导出来的。