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<p>This study presents a hybrid modeling approach integrating Finite Element Modeling (FEM) and Artificial Neural Networks (ANN) to optimize the Czochralski (CZ) silicon crystal growth process. The FEM model simulates key process parameters, particularly crystal front deflection (∆), under varying crucible and crystal rotation speeds. A dataset of 900 FEM simulations was generated to train, validate, and test the ANN, achieving high prediction accuracy with a mean squared error (MSE) of 0.0025. Findings show that increasing the crystal rotation speed from 2.5 rpm to 7.5 rpm leads to an 18.3-mm rise in ∆ while increasing the crucible rotation speed within the same range reduces ∆ by 9.6 mm. Thermal gap variations show a minor effect on ∆ but significantly impact energy consumption, with a 3.6-kW increase in heater power for a 10-mm rise in gap distance. Melt flow analysis reveals that a crucible speed of 7.5 rpm induces Taylor-Proudman vortices, enhancing thermal uniformity and reducing ∆. The FEM-ANN hybrid model highlights the critical impact of rotation speeds on crystal quality and also provides an efficient and accurate predictive tool for optimizing CZ process parameters, improving crystal quality while minimizing defects and energy consumption.</p>

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FEM-ANN hybrid model for large-scale silicon ingot growth optimization to minimize crystal front deflection

  • 期刊论文

  • 发表日期：

    2025年8月20日

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  • Swami Nath Maurya,
  • Hamza Helal,
  • Li-Shang Lin,
  • Amir Reza Ansari Dezfoli

摘要

This study presents a hybrid modeling approach integrating Finite Element Modeling (FEM) and Artificial Neural Networks (ANN) to optimize the Czochralski (CZ) silicon crystal growth process. The FEM model simulates key process parameters, particularly crystal front deflection (∆), under varying crucible and crystal rotation speeds. A dataset of 900 FEM simulations was generated to train, validate, and test the ANN, achieving high prediction accuracy with a mean squared error (MSE) of 0.0025. Findings show that increasing the crystal rotation speed from 2.5 rpm to 7.5 rpm leads to an 18.3-mm rise in ∆ while increasing the crucible rotation speed within the same range reduces ∆ by 9.6 mm. Thermal gap variations show a minor effect on ∆ but significantly impact energy consumption, with a 3.6-kW increase in heater power for a 10-mm rise in gap distance. Melt flow analysis reveals that a crucible speed of 7.5 rpm induces Taylor-Proudman vortices, enhancing thermal uniformity and reducing ∆. The FEM-ANN hybrid model highlights the critical impact of rotation speeds on crystal quality and also provides an efficient and accurate predictive tool for optimizing CZ process parameters, improving crystal quality while minimizing defects and energy consumption.