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<p>Achieving precise thermal uniformity across wafers in vertical diffusion furnaces is essential for high-quality semiconductor processing. This study presents a coupled finite-element–Monte-Carlo (FE-MC) framework for optimizing heater geometry and power distribution to minimize temperature non-uniformity during dry oxidation. A three-dimensional FE model was developed to simulate the heat transfer in a vertical batch furnace containing 50 silicon wafers. The optimization parameters were the lengths of four side heaters (<i>H₁–H₄</i>) and a power scaling factor (<i>W</i>) that was applied to the middle heaters. Monte Carlo iterations were used to perturb the heater configuration and evaluate the objective function. The initial configuration produced a temperature deviation Φ of 65&#xa0;°C, which was reduced to 29.2&#xa0;°C after 196 accepted optimization steps. Experimental validation was performed using an empty furnace equipped with thermocouples, and the results demonstrated 92% agreement with the simulation results. Post-optimization results showed improved radial uniformity, and the range of wafer temperatures was reduced from 966 to 1017&#xa0;°C to 983–1010&#xa0;°C. The findings confirm that the FE-MC methodology is an accurate and efficient design tool for thermal optimization in batch furnace systems.</p>

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Thermal Uniformity Enhancement in Vertical Diffusion Furnaces Using MonteCarlo-Guided Finite Element Modeling

  • 期刊论文

  • 发表日期：

    2026年2月25日

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  • Shang-Kuo Yang,
  • Amir Reza Ansari Dezfoli

摘要

Achieving precise thermal uniformity across wafers in vertical diffusion furnaces is essential for high-quality semiconductor processing. This study presents a coupled finite-element–Monte-Carlo (FE-MC) framework for optimizing heater geometry and power distribution to minimize temperature non-uniformity during dry oxidation. A three-dimensional FE model was developed to simulate the heat transfer in a vertical batch furnace containing 50 silicon wafers. The optimization parameters were the lengths of four side heaters (H₁–H₄) and a power scaling factor (W) that was applied to the middle heaters. Monte Carlo iterations were used to perturb the heater configuration and evaluate the objective function. The initial configuration produced a temperature deviation Φ of 65 °C, which was reduced to 29.2 °C after 196 accepted optimization steps. Experimental validation was performed using an empty furnace equipped with thermocouples, and the results demonstrated 92% agreement with the simulation results. Post-optimization results showed improved radial uniformity, and the range of wafer temperatures was reduced from 966 to 1017 °C to 983–1010 °C. The findings confirm that the FE-MC methodology is an accurate and efficient design tool for thermal optimization in batch furnace systems.