Numerical simulation of thermal stress distribution in a solidified silicon ingot for solar cells

A three-dimensional (3D) thermo-elastic stress model based on the displacement method was developed to study the thermal stress distribution in the solidified silicon ingot in a directional solidification process. The temperature field was obtained from a 3D global simulation of heat transfer in the furnace. A new coupled model was developed to account for the interaction between the silicon ingot and the quartz crucible. The thermal stresses and deformations of the ingot and the crucible were solved simultaneously in a strictly coupled way. The thermal stresses in the square-shaped ingot and crucible were analyzed. The influence of the thermal expansion coefficient of crucible on the thermal stresses in the ingot and crucible was also investigated. The numerical results show that the crucible has important impact on the thermal stress in the silicon ingot. It is necessary to account for the deformation of crucible in the computation model of thermal stress in the silicon ingot. The material property of a crucible also has important effect on the thermal stress in the ingot. A crucible with large thermal expansion coefficient is beneficial to reduce the thermal stress in the silicon ingot.