Three methods of quality evaluation based on the thermo-elastic, thermo-plastic and thermo-creep theories were established to investigate the quality of multi-crystalline silicon ingots. The thermal field in a directional solidification furnace was obtained with a 2D transient global model of heat transfer. The Von Mises stress, the accumulated plastic strain and the dislocation density were calculated to evaluate the ingot quality by the thermo-elastic, thermo-plastic and thermo-creep methods, respectively. Research was carried on in the crystal growing and the ingot annealing process. Simulation results indicate that in the crystal growing process, the low quality region distributions calculated by these methods match well with each other. The thermo-elastic method was recommended for its high computing efficiency. While in the ingot annealing process, the low quality region distributions obtained with these methods vary from each other. The real low quality region distribution in the ingot may between that calculated from the thermo-plastic and thermo-creep methods in this stage.

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Fig. 1 Crystal quality distribution in the ingot in crystal growing process: (a) Von Mises stress calculated by thermo-elastic method (MPa), (b) accumulated plastic strain calculated by thermo-plastic method, (c) dislocation density calculated by thermo-creep method (cm^-2).

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1. Quantitative analysis of the cover effects on crystal growth in the industrial directional solidification process for silicon ingots