Gray-box modeling of 300 mm diameter Czochralski single-crystal Si production process

Abstract More than 95% of 300 mm diameter single-crystal silicon ingots, the raw material for semiconductors, are produced by Czochralski process. The demand improving yield, throughput, and control performance has been increasing. present study developed a gray-box model that can predict controlled variables from manipulated with higher accuracy conventional first-principle (Zheng et al., 2018), aiming at realizing predictive proposed used statistical to temperature gradient crystal solid–liquid interface G cry , which was constant in model. length melt as input . prediction compared using real process data obtained during production four ingots. results demonstrated reduced root mean square errors radius, growth rate, heater 94.1%, 62.7%, 70.6% on average, respectively.