Rapid prediction of interface morphology and oxygen transportation in crystal growth based on the response surface method

Abstract

In this paper, a two-dimensional (2D) axisymmetric model subjected to the gas shear effect and thermal Marangoni effect is developed. It is highlighted that the growth conditions of pulling rate, gas flow rate, crucible, and crystal rotation rates play important roles in determining the crystal behaviors of interface morphology and oxygen transportation during the crystal growth process. A Kriging-based response surface method (RSM) is proposed to rapidly predict the crystal growth behaviors, indicating that the outputs of interface morphology and oxygen concentration can be predicted by the corresponding input growth conditions. By global sensitivity analysis, the pulling rate is identified as the key factor in determining the interface morphology, while gas flow rate and crucible rotation rate have a greater effect on oxygen transportation. Furthermore, these two inputs with the highest sensitivities are used to construct the response surface and predict unknown oxygen transportation. When compared with the numerical simulations, the presented model proves to be an effective tool for reducing measurement time and improving accuracy in predicting crystal behaviors. Our findings provide important insights into understanding the crystal growth process under different growth conditions and inspire a data-driven method for crystal growth prediction.