<p>The Czochralski (Cz) process is a crucial method for producing high-quality single-crystal silicon for semiconductor applications. This study introduces a Monte Carlo-finite element (MC-FE) optimization model to enhance Cz puller performance by refining five key parameters: crystal rotation speed, crucible rotation speed, insulation thermal conductivity, melt level, and thermal gap. A finite element model has been developed to incorporate conduction, convection, and radiation heat transfer, with a segregated solver employed to simulate silicon ingot growth. The MC-FE optimization reduced the objective function from 1.0 to 0.13 with an 87% improvement, achieving a flatter crystal front with maximum deflection decreasing from − 36.0 to − 10.4 mm. The optimized process increased the melt temperature from 1442 to 1517 °C at a 10 mm crystal length, enhancing thermal gradient stability. The <i>V</i>/<i>G</i> ratio, important for defect minimization, was flattened from a steep drop of 0.205 to 0.098 mm/min·K to a more uniform 0.185 to 0.158 mm/min·K range. Optimized parameters, including an increased crystal rotation speed of 9 RPM and a reduced thermal gap of 10 mm, contributed to a well-defined hot–cold thermal zone separation that supports stable crystal growth. These findings demonstrate the effectiveness of MC-FE optimization in improving the efficiency and quality of large-scale silicon crystal growth in semiconductor manufacturing.</p>

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Process parameter optimization in Czochralski growth of silicon ingots: a Monte Carlo-finite element coupled model

  • Amir Reza Ansari Dezfoli,
  • Swami Nath Maurya,
  • Zary Adabavazeh,
  • Yi-Jen Huang

摘要

The Czochralski (Cz) process is a crucial method for producing high-quality single-crystal silicon for semiconductor applications. This study introduces a Monte Carlo-finite element (MC-FE) optimization model to enhance Cz puller performance by refining five key parameters: crystal rotation speed, crucible rotation speed, insulation thermal conductivity, melt level, and thermal gap. A finite element model has been developed to incorporate conduction, convection, and radiation heat transfer, with a segregated solver employed to simulate silicon ingot growth. The MC-FE optimization reduced the objective function from 1.0 to 0.13 with an 87% improvement, achieving a flatter crystal front with maximum deflection decreasing from − 36.0 to − 10.4 mm. The optimized process increased the melt temperature from 1442 to 1517 °C at a 10 mm crystal length, enhancing thermal gradient stability. The V/G ratio, important for defect minimization, was flattened from a steep drop of 0.205 to 0.098 mm/min·K to a more uniform 0.185 to 0.158 mm/min·K range. Optimized parameters, including an increased crystal rotation speed of 9 RPM and a reduced thermal gap of 10 mm, contributed to a well-defined hot–cold thermal zone separation that supports stable crystal growth. These findings demonstrate the effectiveness of MC-FE optimization in improving the efficiency and quality of large-scale silicon crystal growth in semiconductor manufacturing.