Study on the usage of a commercial software (Comsol-Multiphysics®) for dislocation multiplication model

Elaboration of silicon ingots for photovoltaic application in Directional Solidification furnace leads to formation of dislocations mainly due to thermoelastic stresses, which impact photovoltaic conversion rate. Several research teams have created numerical simulation models using home-made software in order to study dislocation multiplication and predict the dislocation density and residual stresses inside ingots after elaboration. In this study, the commercial software Comsol-Multiphysics is used to calculate the evolution of dislocation density during the ingot solidification and cooling. Thermo-elastic stress, due to temperature field inside the ingot during elaboration, is linked to the evolution of the dislocation density by the Alexander and Haasen model (A&H model). The purpose of this study is to show relevance of commercial software to predict dislocation density in ingots. In a first approach, A&H physical model is introduced for a 2D axisymmetric geometry. After a short introduction, modification of Comsol (R) software is presented in order to include A&H equations. This numerical model calculates dislocation density and plastic stress continuously during ingot solidification and cooling. Results of this model are then compared to home-made simulation created by the teams at Kyushu university and NTNU. Results are also compared to characterization of a silicon ingot elaborated in a gradient freeze furnace. Both of these comparisons shows the relevance of using a commercial code, as Comsol (R) to predict dislocations multiplication in a silicon ingot during elaboration. (C) 2016 Elsevier B.V. All rights reserved.