The Czochralski (CZ) method is the dominant technique to produce bulk single crystals of a wide range of electronic and photovoltaic silicon. The argon flow, acting as a protective environment, has significant effects on the generation and transportation of the impurities in the furnace. The coupled transport at the gas and melt interface then influences the levels of the main impurities in the melt and crystal, such as oxygen and carbon. Therefore, a precise simulation of the argon flow is essential to understand the relevant heat and mass transport in CZ-Si crystal growth and to improve the quality of the growing crystal.

It is well-known the argon convection is compressible flow involving low fluid speed (low Mach number) but intensive density variations because of the large temperature differences within the CZ-Si furnace. In this regime, Boussinesq approximations for incompressible flow are unsuitable because of its small temperature difference and density variation constraints. It’s better to use full compressible flow solver. However, compressible flow solvers also have the stiffness problem caused by the disparity of time scales between the mean flow and the acoustic wave. To overcome these difficulties, we solve the acoustically filtered equations of viscous, low-speed compressible flow by the finite-element method for argon flow in CZ-Si crystal growth. Global simulations of coupled heat and mass transport are performed for the CZ-Si furnace. Thermal and velocity boundary conditions are fully coupled between the argon gas, silicon melt and solid parts. Transport of oxygen and carbon in argon gas and silicon melt are calculated simultaneously by considering several chemical reactions at the interfaces. The flow results show the acoustically filtered equations are reliable and easy to handle for the argon flow with a large temperature difference in CZ-Si furnace. The results of oxygen and carbon concentration also show good agreement to experimental data.

To clarify the transport mechanisms of argon flow, the effects of gas flow rate and outlet location are also investigated by a series of global simulations. It is found the amount of impurities carried away by the argon flow increases with the increase in the argon flow rate. Adjustment of the outlet location can change the purge flow pattern, and then carry out the impurities in the furnace efficiently. The present numerical model and results demonstrate a method to analyze and control the gas convection and mass transport in CZ-Si crystal growth.

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