Delay-based control model for Czochralski growth of high-quality oxides

This paper presents a study to model the Czochralski growth process as a time-varying time delay linear input–output model. It was especially designed for the slow growing of oxide crystals (⩽2 mm/h). Such crystals pose a significant challenge to the control system design because of the delayed effect of the power change on the growth rate. This delay is caused by slow heat-mass transfer and large measurement lag. In this study, controlled perturbations were applied during the growth process to identify the effects of system parameters such as melt level on the time delay. We observed that the time delay rises with the decreasing melt level. For advanced adaptive control system with such time-varying delay, real time process identification is needed. Higher-order autoregressive moving average with exogenous input (ARMAX) model with recursive estimation was considered to represent the growth process with delay in real time. The use of such high-order model and especially its stability for real-time process identification are discussed. Also during these experiments, constraints on the process control to preserve the crystal quality were identified. These experiments were carried out on the growth of high-quality La 3Ga 5.5Ta 0.5O 14 (LGT).