Relaxation of thermal stresses by dislocation flow and multiplication in the continuous casting of silicon

A semi-analytical model is proposed for simulating thermal stress generation during experimental continuous casting of polycrystalline silicon billets for photovoltaic applications. The geometry is axi-symmetric and the temperature field is formulated using three parameters. The thermoelastic stress source is given by the plane strain approximation. The Alexander and Haasen model, based on the classical Orowan equation, expresses the plastic relaxation and the associated multiplication of dislocations. This set of approximations allows us to discuss separately the influence of the withdrawal rate and of the thermal parameters on the variation along the billet of both the stress and the dislocation density.