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<p>The ever-growing demand for semiconductors, fueled by advancements in integrated circuits (ICs), necessitates innovative approaches for efficient and high-quality growth of large-scale silicon single crystals using the Czochralski (CZ) method. In this context, machine learning emerges as a transformative tool to predict and optimize the complex, nonlinear CZ silicon growth process. A novel hybrid finite element method–machine learning (FEM-ML) model is proposed to enhance the accuracy of thermal stress predictions. The FEM simulation, incorporating 3D Navier–Stokes and thermal elastic stress equations, was used to evaluate the effects of four key process features: insulation thermal conductivity (0.184–0.736 W/m·K), melt level (448–672&#xa0;mm), crucible rotation speed (1–7.5&#xa0;rpm), and crystal rotation speed (7.5–12.5&#xa0;rpm). Then, machine learning analyses including LASSO regression for feature selection and regression decision trees for predictive modeling, achieving a high coefficient of determination (<i>R</i><sup>2</sup> &gt; 0.97) through tenfold cross-validation is employed. Results identified insulation thermal conductivity as the most significant factor, accounting for 75.4% of predictive performance, while melt level had negligible impact. Individual Conditional Expectation (ICE) results highlighted non-linear dependencies, such as the sharp increase in thermal stress with crucible rotation speeds up to 2.4&#xa0;rpm. The hybrid model demonstrated superior performance in capturing key parameter interactions and predicting thermal stress distributions. This work underscores the potential of hybrid FEM-ML approaches for addressing complex industrial challenges in crystal growth.</p>

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Data-driven approach for optimizing the Czochralski process and predictive modeling: A finite element and machine learning analysis

  • 期刊论文

  • 发表日期：

    2025年5月19日

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

摘要

The ever-growing demand for semiconductors, fueled by advancements in integrated circuits (ICs), necessitates innovative approaches for efficient and high-quality growth of large-scale silicon single crystals using the Czochralski (CZ) method. In this context, machine learning emerges as a transformative tool to predict and optimize the complex, nonlinear CZ silicon growth process. A novel hybrid finite element method–machine learning (FEM-ML) model is proposed to enhance the accuracy of thermal stress predictions. The FEM simulation, incorporating 3D Navier–Stokes and thermal elastic stress equations, was used to evaluate the effects of four key process features: insulation thermal conductivity (0.184–0.736 W/m·K), melt level (448–672 mm), crucible rotation speed (1–7.5 rpm), and crystal rotation speed (7.5–12.5 rpm). Then, machine learning analyses including LASSO regression for feature selection and regression decision trees for predictive modeling, achieving a high coefficient of determination (R2 > 0.97) through tenfold cross-validation is employed. Results identified insulation thermal conductivity as the most significant factor, accounting for 75.4% of predictive performance, while melt level had negligible impact. Individual Conditional Expectation (ICE) results highlighted non-linear dependencies, such as the sharp increase in thermal stress with crucible rotation speeds up to 2.4 rpm. The hybrid model demonstrated superior performance in capturing key parameter interactions and predicting thermal stress distributions. This work underscores the potential of hybrid FEM-ML approaches for addressing complex industrial challenges in crystal growth.