Numerical simulations of thermo-mechanical stresses during the casting of multi-crystalline silicon ingots

Silicon is an important semiconductor substrate for manufacturing solar cells. The mechanical and electrical properties of multi-crystalline silicon (mc-Si) are primarily influenced by the quality of the feedstock material and the crystallization process. In this work, numerical calculations, applying finite element analysis (FEA) and finite volume methods (FVM) are presented, in order to predict thermo-mechanical stresses during the solidification of industrial size mc-Si ingots. A two-dimensional global model of an industrial multi-crystallization furnace was created for thermal stationary and time-dependent calculations using the software tool CrysMAS. Subsequent thermo-mechanical analyses of the silica crucible and the ingot were performed with the FEA code ANSYS, allowing additional calculations to define mechanical boundary conditions as well as material models. Our results show that thermal analyses are in good agreement with experimental measurements. Furthermore we show that our approach is suitable to describe the generation of thermo-mechanical stress within the silicon ingot.