Unraveling conditions for W-shaped interface and undercooled melts in Cz-Si growth: A smart approach

In Cz-Si growth, concave and W-shaped solid-liquid interfaces and undercooled melts are primary contributors to the degradation of crystal quality, particularly structure loss, defect generation, non-uniform dopant distribution, and crystal twisting, making their avoidance crucial. We employed a classification tree machine learning approach to investigate the importance of 15 process and furnace design parameters and their critical ranges for the formation of various types of W-shaped interfaces and undercooled melts at different scales, both in dimensional and dimensionless forms, and across a wide range of process conditions. Moreover, symbolic regression was used to predict minimal melt temperature based on the aforementioned inputs. Training data were obtained by CFD modeling. The classification tree for combined output identified the Grashof, Reynolds for crystal, and Stefan numbers, along with the percentage of silicon solidified, as the most decisive inputs. Symbolic regression for the temperature of undercooled melt highlighted crucible diameter, pulling rate, and the power of the bottom heater as key parameters.