| 초록 |
The optimization of the crystal surface temperature distribution is performed for the single crystal growth in the Czochralski process. In our optimization problem, we seek an optimal solution in the sense that the index of the crystal quality is maximized while the growth rate is also maximized. The objective function is formulated by considering the distribution of the von Mises stress and the radial uniformity of the temperature distribution in the crystal. As the single crystal growth rate, the heat transfer rate at the crystal-melt interface toward the crystal phase is considered. In order to solve the optimization problem with the equality constraints described by partial differential equations, we apply variational calculus and solve the coupled partial differential equations by the iterative numerical scheme proposed in this work. The optimal distributions of the crystal surface temperature obtained in this work may provide an insight for the optimal design of thermal surroundings. |
