Silicon ingot diameter modeling in Czochralski process and its dynamic simulation

Silicon wafers are manufactured by cutting an ingot into the same thickness. The Czochralski process is a representative method for making an ingot. During manufacture, the ingot diameter is affected by the Pull speed and heat transfer amount. Therefore, controlling the ingot manufacturing process involves controlling the ingot diameter related to pull speed and controlling the heater power supply to maintain the pull speed within the allowable range. The modeling of ingot diameter can be established by the ingot pull speed change based on an understanding of the mechanism of heat transfer, and the calculation of the heat transfer amount between all the parties of the crystal growth furnace according to the energy balance equations. Comparing the simulation results with real process results, the step change of the heater showed 1st or 2nd process dynamics at all points with a time delay of 18 minutes, which was similar to that of the real process. Furthermore, the pull speed step change exhibited a 5 min time delay from the test spot, which confirmed the relation between the integral and process properties. This result is similar to the real process, too. With a specific ingot length, the temperature in each point of the furnace in the real process was similar to these simulation results.