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

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 degrees 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<middle dot>K to a more uniform 0.185 to 0.158 mm/min<middle dot>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.