Optimization of the melt/crystal interface shape and oxygen concentration during the Czochralski silicon crystal growth process using an artificial neural network and a genetic algorithm

Abstract

The melt/crystal interface shape and oxygen concentration during the Czochralski silicon crystal growth process significantly influence the crystal quality. In this paper, an optimization system with the combination of an artificial neural network and a genetic algorithm is proposed to optimize the growth parameters during the growth process. Flattening the melt/crystal interface and reducing the oxygen concentration along the interface were chosen as the optimization targets. Two important growth parameters, the crystal rotation rate and crucible rotation rate, were chosen as optimization variables. First, a global heat and mass transfer model was developed to simulate the crystal growth process and then tested with experimental data. The verified heat and mass transfer model was then used to train an artificial neural network with the aim of rapidly assessing the complex nonlinear dependence of the interface shape and oxygen concentration on the growth parameters. The trained neural network combined with a genetic algorithm was then used to obtain the optimal growth parameters. Both deflection of the melt/crystal interface and the oxygen concentration along the interface decreased after optimization. Finally, the optimal growth parameters were checked in the heat and mass transfer model to evaluate the performance of the optimization system. The proposed method will also be useful for optimization of other crystal growth processes.