Toward a Universal Czochralski Growth Model Leveraging Data‐Driven Techniques

Abstract

The Czochralski (Cz) method is widely employed for growing crystalline semiconductors from low‐vapor‐pressure materials. Although furnace designs vary depending on the material, shared hot‐zone components, such as crucibles, supports, heaters, insulation, and radiation shields‐indicate the potential for a universal Cz furnace model. This study focuses on Cz furnaces that utilize resistance heating. Data‐driven techniques including Decision Trees (DT), Symbolic Regression (SR), Artificial Neural Networks (ANN), and Shapley Additive exPlanations (SHAP) are applied to investigate the relationships between furnace design, process parameters, and crystal quality during bulk crystal growth across a range of materials and scales. DT and SR are employed for their interpretability, ANN for its predictive accuracy, and SHAP to enhance model transparency by quantifying feature importance. The analysis explores the correlation between solid–liquid interface deflection, the Voronkov criterion, and 21 input parameters describing furnace geometry, gas composition, crystal and radiation shield thermophysical properties, and growth conditions. The training dataset consists of 632 computational fluid dynamics (CFD) simulations of Cz growth involving silicon, germanium, gallium antimonide, and indium antimonide. Feature engineering using DTs is performed to reduce input dimensionality. The results demonstrate the feasibility of generating a universal Cz growth model that utilizes machine learning techniques to optimize performance across diverse grown materials, furnace configurations, and production scales.