A first-principle model of 300 mm Czochralski single-crystal Si production process for predicting crystal radius and crystal growth rate

The Czochralski (CZ) process is the dominant method for manufacturing large cylindrical single-crystal ingots for the electronics industry. Although many models and control methods for the CZ process have been proposed, they were only tested with small equipment and only a few industrial application were reported. In this research, we constructed a first-principle model for controlling industrial CZ processes that produce 300 mm single-crystal silicon ingots. The developed model, which consists of energy, mass balance, hydrodynamic, and geometrical equations, calculates the crystal radius and the crystal growth rate as output variables by using the heater input, the crystal pulling rate, and the crucible rise rate as input variables. To improve accuracy, we modeled the CZ process by considering factors such as changes in the positions of the crucible and the melt level. The model was validated with the operation data from an industrial 300 mm CZ process. We compared the calculated and actual values of the crystal radius and the crystal growth rate, and the results demonstrated that the developed model simulated the industrial process with high accuracy.