Diffusion coefficients of carbon, oxygen and nitrogen in silicon melt

The carbon, oxygen and nitrogen are very important light impurities affecting the quality of silicon crystal used in photovoltaic and semiconductor industry. The diffusion coefficients are key parameters in determining the impurity distribution in the melt and crystal. Unfortunately, these parameters are rarely measured by experiments due to challenges of high temperature and complex flow in the melt during crystal growth. Nonetheless, the liquid diffusion coefficients exist as necessary input parameters in the continuum modelling work of mass transport. Here, we first reviewed the liquid state diffusion coefficients used in the continuum models and found out that they are far from consistency. Then, molecular dynamics simulations are employed to calculate the diffusion coefficients and migration barriers of the carbon, nitrogen and oxygen impurities in silicon melt based on various empirical interatomic potentials. The nitrogen diffusivity in silicon melt is reported for the first time. The calculated diffusion coefficients are generally lower than the values used in most continuum models although consistent across different potentials. This discrepancy is discussed in detail.