Abstract: With the rapid advancement of the photovoltaic and semiconductor industries, the trend towards producing larger diameter (12 inch and above, 1 inch=2.54 cm) silicon single crystal has become increasingly prominent. The Czochralski method, as a predominant technique for silicon single crystal production, is highly emphasized. However, during the growth of large-diameter, high-quality Czochralski silicon single crystals, the enlargement in both crystal diameter and crucible size significantly expands the melt volume, thereby intensifying the complexity of the thermal field, flow field, and stress field. The interaction between vortices, thermal buoyancy, and Coriolis forces induces substantial turbulence and causes fluctuations in the melt's flow velocity and temperature, leading to challenges such as uneven temperature distribution at the solid-liquid interface and complex thermal convection within the melt, which can impact the defect distribution within the silicon crystals. Therefore, how to control process parameters to achieve ideal silicon single crystals with large-diameter is of significant importance. This study established a two-dimensional axisymmetric global numerical simulation model for the preparation of 18-inch crystal silicon rods within a 40-inch thermal field, capable of real-time prediction, dynamic control, and optimization of process parameters to address delays and cost issues in actual production. The model takes into account the increased crucible depth and extended heat conduction path, and incorporates an additional bottom heater alongside the main heater. Using the finite element method, the effects of variations in crystal rotation speed, crucible rotation speed, and gas pressure on the thermal field and silicon single crystal growth were analyzed individually, including shape of solid-liquid interfaces, temperature gradient, value of V/G, oxygen concentration and defect distribution, etc. Through multiple simulation experiments, a set of optimal process parameters was identified: a crystal rotation speed of 15 r/min, a crucible rotation speed of 5 r/min, and a furnace gas pressure of 1 200 Pa, which can make the temperature gradient of solid-liquid interface smaller and the temperature distribution more uniform, effectively avoiding excessive turbulence. Crystal growth experiments and a series of tests show that thesilicon single crystal rods produced with the optimal process parameters obtained from the simulation can increase the crystallization rate to 87.44%. This set of optimal process parameters for the 18-inch silicon single crystal rods (including crystal rotation speed, crucible rotation speed, and furnace pressure) has been precisely optimized based on the complexities of the thermal and flow fields in the growth of large-diameter (12 inches and above) Czochralski silicon single crystals. These parameters are well-suited for large-diameter silicon single crystal growth but may require specific adjustments and validation for smaller diameters (such as 4, 6 or 8-inch), where differences in heat transfer and airflow disturbances must be taken into account. The digital model established in this study can accurately predict and optimize the growth process of large-size Czochralski silicon single crystal, and have practical application prospects.

Key words: silicon single crystal, Czochralski method, two-dimensional axisymmetriy, finite element method, process parameter, numerical simulation, digital model