Data-Driven Cz–Si Scale-Up under Conditions of Partial Similarity

Abstract

In Cz–Si growth, the shape of the solid–liquid interface and the v/G ratio significantly impact crystal quality. This study utilizes a data-driven approach, employing multilayer perceptron (MLP) neural networks and Bayesian optimization, to investigate the scale-up process of Cz–Si under conditions of partial similarity. The focus is on exploring the influence of various process and furnace geometry parameters, as well as radiation shield material properties, on the critical measures of crystal quality. Axisymmetric CFD modeling produces 340 sets of 18D raw data, from which 14-dimensionless derived data tuples are generated for the design and training of the MLP. The best MLP obtained demonstrates the ability to accurately assess the complex nonlinear dependencies among dimensionless numbers derived from CFD data and, on the output side, interface deflection and v/G. These relationships, crucial for scale-up, are successfully generalized across a wide range of parameters.