Control of multi-zone resistive heater in low temperature gradient BGO Czochralski growth with a weighing feedback, based on the global dynamic heat transfer model

The global heat transfer in a crystallization setup has been optimized to develop a strategy of control over a three-zone heater in the BGO Czochralski process, in order to provide invariable thermal conditions near the solid-liquid interface in the stage of a constant-diameter crystal growth. The functional related to the exactness of the heat balance condition at the crystallization front, i.e., the Stefan problem, was chosen as the target function. The optimization yielded unexpected results. The temperature of the lower heater should be lowered, relative to that of the middle heater, with increasing crystal length, whereas the temperature of the upper heater is to be raised. These recommendations were incorporated into a dynamic model of the oxide Czochralski process with a weighing control and into the control loop of the temperature regulators of a crystallization setup. A comparison of results of the time-dependent simulation with the real growth process confirmed that the new control strategy minimizes the deviation of the solid-liquid interface from the prescribed one, significantly decreases variations of interface shape during the process, and enables growth of high-quality crystals.