Development of the VGF Crystal Growth Recipe: Intelligent Solutions of Ill‐Posed Inverse Problems using Images and Numerical Data

Abstract

Development of the Vertical Growth Freeze crystal growth process is a typical example of solving the ill‐posed inverse problem, which violates one or more of Hadamard's well‐posedness criteria of solution existence, uniqueness, and stability. In this study, different data‐driven approaches are used to solve inverse problems: Reduced Order Modelling method of Proper Orthogonal Decomposition with Inverse Distance weighting (ROM POD InvD), an approximation method of Kriging and Artificial Neural Networks (ANN) employing images, combination of images and numerical data and solely numerical data, respectively. The ≈200 training data are generated by Computational Fluid Dynamics (CFD) simulations of the forward problem. Numerical input data are related to the temperatures and coordinates in 10 characteristic monitoring points in the melt and crystal, while the image input data are related to the interface shape and position. Using the random mean squared error as a criterion, the Kriging method based on images and numerical data and the ANN method based on numerical data are able to capture the system behavior more accurately, in contrast to the ROM POD InvD method, which is based solely on images.

Numerical Simulation of CdTe Crystal Growth Using the Vertical Gradient Freeze Technique Assisted by Axial Low-Frequency Oscillations of the Melt

“…The impressive achievements of the VGF method for production of perfectly structured GaAs crystals with a diameter of up to 200 mm are associated with the implementation of a multi-crucible configuration of the growth installation [1]. In this installation, despite the low growth rate of the VGF process, it was possible to implement a highly profitable industrial process [2]. However, these achievements are inextricably linked with an increase in the chemical purity of the starting material to a purity of 7-8N [3][4][5].…”

Decision Tree-Supported Analysis of Gallium Arsenide Growth Using the LEC Method

“…In recent years, the advancement of artificial intelligence has led to the utilization of machine learning techniques for the enhancement of crystal growth processes. Specifically, artificial neural networks (ANNs) have found application in the optimization of crystal growth, e.g., as documented in references [27][28][29][30][31]. Additionally, decision trees (DTs) and random forests have been employed for the analysis of multi-parameter crystal growth [32][33][34].…”

Numerical Simulation of CdTe Crystal Growth by VGF Technique Assisted by Axial Low-Frequency Oscillations of the Melt

“…The impressive achievements of the VGF method for production of perfect structure GaAs crystals with a diameter of up to 200 mm are associated with the implementation of a multi-crucible configuration of the growth installation [1]. In this installation, even despite the low growth rate of the VGF process, it was possible to implement a highly profitable industrial process [2]. However, these achievements are inextricably linked with an increase in the chemical purity of the starting material to a purity of 7-8N [3][4][5].…”