A general approach for calculating melt–solid impurity segregation coefficients based on thermodynamic integration

Abstract

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.