| 초록 |
The optimization of the crystal surface temperature distribution is performed for the single crystal growth in the Czochralski process. In the optimization problem, we seek an optimal solution in the sense that the crystal quality in terms of point defects and the radial uniformity are maximized. In order to solve the optimization problem with the equality constraints described by partial differential equations, the variational principle is used. Based on the calculus of variations and the method of Lagrange multiplier, the Euler-Lagrange equations are derived and solved by the numerical method. In order to to handle the inequality constraints, the penalty function method is applied. The optimal distributions of the crystal surface temperature obtained in this work may provide an insight for the optimal design of thermal surroundings such as the thermal shield configurations and the heater/cooler positions. |
