Czochralski (CZ) silicon is widely utilized as a crucial substrate material in the semiconductor industry. As an effective and cost-efficient approach, numerical simulation has been widely used to study heat transfer and heat loss for improving crystal quality and reducing heat losses. Regarding numerical models, the traditional 2D model simplifies the CZ furnace axisymmetrically and the previous 3D models often neglect the full coupling between the thermal and electric fields in the heating system. In this work, a 3D global thermal-electric full coupling model for CZ silicon growth is established. Based on the novel 3D model, the 3D distribution characteristics of heat transfer and Joule heat in the CZ furnace are investigated. Further, by comparisons between novel 3D and traditional 2D models, the limitations of the traditional 2D model on simulating the distribution of thermal fields, heating system Joule heat, furnace heat losses, and furnace heat flow network are systematically investigated. The results indicate that the heater Joule heat exhibits a nonuniform distribution and the furnace temperature displays a nonaxisymmetric profile in the novel 3D model, which cannot be captured by the traditional 2D model. Additionally, the traditional 2D model underestimates the total heat loss and overestimates both temperature and its gradient within the silicon melt. This study evaluates the limitations of the traditional 2D model of CZ silicon growth in simulating heat transfer and heat loss, thereby facilitating more effective application of numerical simulation to promote high-quality and low-cost crystal growth.
Qi et al. (Thu,) studied this question.