A general approach for calculating melt-solid impurity segregation coefficients based on thermodynamic integration
A general approach for calculating melt-solid impurity segregation coefficients based on thermodynamic integration
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DOI：
10.1063/5.0051245
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发表时间：
2021-07-14
影响因子：
3.2
通讯作者：
Liu, Lijun
中科院分区：
文献类型：
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作者：
Luo, Jinping;Cheng, Yunjie;Liu, Lijun
硅晶化过程中杂质在熔体-固相界面的平衡偏聚是决定晶体中杂质浓度和分布的关键因素。不幸的是，由于熔体中存在复杂的输运物理，这种性质很难通过实验测量。在这里，使用Tersoff家族的经验势模型，我们描述了一个热力学集成框架计算间隙氧和替代碳在硅中的偏析系数。热力学积分使用一个理想的气体参考状态的杂质原子被证明是一个有效的和方便的途径，用于评估在固相和液相中的杂质化学势。我们发现，偏析系数被捕获以及替位碳杂质，而它是显着低估间隙氧。后者的差异部分归因于定性不正确的硅固液密度比预测的经验原子间势。
The equilibrium segregation of impurities at the melt-solid interface during silicon crystallization is a key factor in determining the impurity concentration and distribution in the crystal. Unfortunately, this property is difficult to measure experimentally due to the presence of complex transport physics in the melt. Here, using the Tersoff family of empirical potential models, we describe a thermodynamic integration framework for computing the interstitial oxygen and substitutional carbon segregation coefficients in silicon. Thermodynamic integration using an ideal gas reference state for the impurity atoms is shown to be an efficient and convenient pathway for evaluating impurity chemical potentials in both solid and liquid phases. We find that the segregation coefficient is captured well for substitutional carbon impurity while it is significantly underestimated for interstitial oxygen. The latter discrepancy is partially attributed to the qualitatively incorrect silicon solid-to-liquid density ratio predicted by the empirical interatomic potential.