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

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

“…Lee et al [12] and Zhang et al [13] constructed models whose input and output are T h and v p . Zheng et al [14] developed a first-principle model to compute r cry and v g from P , v p , and v c for a process to produce 300 mm diameter singlecrystal silicon ingots, and showed that the model simulated r cry and v g with high accuracy using real process data.…”

“…Thus, the objective of the present study is to develop a model to accurately estimate the three controlled variables (r cry , v g , and T h ) from the three manipulated variables of the CZ process. As pointed out by Zheng et al [14], the prediction performance of the conventional lumped-parameter models is limited when applied to 300mm ingots. To realize the high prediction accuracy of r cry and v g , they proposed to divide the heater, the crucible, and the shield into three parts.…”

“…

More than 95% of 300 mm diameter single-crystal silicon ingots, the raw material for semiconductors, are produced by the Czochralski process. The demand for improving yield, throughput, and control performance has been increasing.The present study developed a gray-box model that can predict controlled variables from manipulated variables with higher accuracy than the conventional first-principle model (Zheng et al, 2018), aiming at realizing model predictive control of the Czochralski process. The proposed gray-box model used a statistical model to predict the temperature gradient of the crystal at the solid-liquid interface G cry , which was constant in the first-principle model.

…”

“…The present study developed a gray-box model that can predict controlled variables from manipulated variables with higher accuracy than the conventional first-principle model (Zheng et al, 2018), aiming at realizing model predictive control of the Czochralski process. The proposed gray-box model used a statistical model to predict the temperature gradient of the crystal at the solid-liquid interface G cry , which was constant in the first-principle model.…”

Hydrodynamics and heat exchange of crystal pulling from melts. Part I: Experimental studies of free convection mode

“…Studies have been carried out for models of different level and purpose aimed at solving this complex problem based on the theory of similarity. Physical [9-14, 29, 36] and numerical [9,14,[20][21][22][23][24][25][26][27][29][30][31][32][33][34][35][36][37][38][39][40][41] simulation are widely used and permanently improved. Global numerical models have been developed in recent years [25][26][27][33][34][35][36][37][38][39][40][41] as an attempt to calculate complex conjugate heat and mass exchange in growth chambers.…”