Virtual experiments of Czochralski growth of silicon using machine learning: Influence of processing parameters on interstitial oxygen concentration

Abstract

For a process development, it is crucial to know the influence of each process parameter on the process result. However, it is difficult to gauge the influence by experimentally changing only one parameter value owing to constraints of the combination of the parameter values and experimental costs. Machine learning models can predict results that will be obtained under conditions that have not been considered for the experiment. Utilizing a virtual experiment based on a machine learning model, we evaluated the influence of process parameters on the interstitial oxygen (Oi) concentration in Czochralski-grown Si crystals. A dataset for the parameter analysis was constructed, wherein the crucible rotation rate and/or Ar flow rate were systematically changed while maintaining the other parameters at the reference value of an experimental datum. Thereafter, the dataset was input into a neural network model that had been trained with 450 ingot data; consequently, the corresponding Oi concentration was obtained. The evaluated results were consistent with the scientific knowledge previously studied: Oi concentration increases with increasing crucible rotation rate and decreasing Ar flow rate. Furthermore, the two-parameter analysis illustrated a nonlinear relationship between the parameters quantitatively. These approaches demonstrating the Czochralski growth of Si in this study are useful in other crystal growth processes as well.