Abstract The noncontact crucible (NOC) method has a large and deep low-temperature region in the upper central part of a Si melt to grow a uniform large Si single ingot without contact with the crucible wall. The temperature distribution in the NOC ingot is quite different to that in an ingot grown by the Czochralski (CZ) method because the NOC ingot is grown inside the Si melt. However, the distributions of point defects such as vacancy and interstitial Si atom are not known for the NOC ingot. To clarify the distributions of point defects, a simulation model is proposed to calculate the distribution of point defects in the NOC ingot. The effect of accumulation of diffusion fluxes on the concentrations of both vacancy and interstitial Si atom is considered for NOC growth because these diffusion fluxes are expected to continuously affect such concentrations in the ingot grown with the moving interface under the relatively low temperature gradient inside the melt. This point is one of the large merits of NOC growth. The concentrations of vacancy and interstitial Si atom were also calculated after the dynamic equilibrium pair-annihilation process between the diffused point defects during growth. They were calculated as a function of distance from the growing interface. By selecting the growth conditions, the concentrations of vacancy and interstitial Si atom were found to be very close to each other all over the ingot. The cross point where the concentrations of vacancy and interstitial Si atom were the same was found to strongly depend on G, the temperature gradient in the crystal.

中文翻译：

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考虑扩散通量累积效应的非接触坩埚法在熔体内部生长的硅锭中点缺陷浓度的理论分布

摘要 非接触坩埚（NOC）法在硅熔体的上部中央有一个大而深的低温区域，可以在不与坩埚壁接触的情况下生长均匀的大硅单晶锭。NOC 锭中的温度分布与通过直拉 (CZ) 方法生长的锭中的温度分布完全不同，因为 NOC 锭是在 Si 熔体内部生长的。然而，NOC 锭的点缺陷如空位和间隙硅原子的分布是未知的。为了阐明点缺陷的分布，提出了一种模拟模型来计算NOC铸锭中点缺陷的分布。NOC 生长考虑了扩散通量的积累对空位和间隙 Si 原子浓度的影响，因为这些扩散通量预计会持续影响在熔体内部相对较低的温度梯度下随着移动界面生长的铸锭中的此类浓度. 这一点是 NOC 增长的一大优点。在生长过程中扩散点缺陷之间的动态平衡对湮灭过程之后，还计算了空位和间隙硅原子的浓度。它们被计算为与生长界面的距离的函数。通过选择生长条件，发现整个铸锭中空位和间隙硅原子的浓度彼此非常接近。