Transient analysis of the cooling process and influence of bottom insulation on the stress in the multicrystalline silicon ingot

Directional solidification is one of the most popular techniques for massive production of multicrystalline silicon. After growth and annealing, the ingot is cooled down by a designed cooling process, which is initialized by descending bottom insulation, and then is controlled both by power ramp-down rate and by motion of the bottom insulation. Thermal stress is piled up during cooling, and associated crystal defects, such as dislocation and micro-cracks, may generate and propagate in the ingot. In the paper, transient modeling is applied to study the effect of bottom insulation on the cooling process. Temperature, velocity and thermal stress fields are obtained with linear, parabolic and sinusoidal motions of the insulation. The measured and predicted temperatures at two points of the ingot are found consistent. Distributions of von Mises stress in the ingot at different cooling time are obtained, and the maximum von Mises stresses are presented as a function of the cooling time. Specifically, dislocation-free regions, evaluated by the critical resolved shear stress model, at certain cooling time, and area fractions of the regions as a function of the cooling time are proposed. The linear motion is further discussed with different moving rates, considering its wide applications in the current industry and convenient realization in control.