Solar cell efficiencies are generally governed by the concentration and type of impurities, and the density and electrical activity of extended defects such as grain boundaries and dislocations [1]. Dislocations have been identified as one of the most efficiency-relevant defect centers in crystalline silicon for photovoltaic [2]. The requirement for an increase of solar cell efficiencies necessitates a reduction of the crystal dislocations. Therefore, the dislocations generated by thermal stress during crystal growth have to be effectively suppressed for the production of highly efficient solar cells.
    Many optimization studies have been performed to reduce dislocations by controlling the cooling process. However, the results are not consistent. Slow cooling was suggested for obtaining low dislocation density in GaP/Si heterostructures [3] and in SiGe layers grown by liquid phase epitaxy [4]. Fast cooling was suggested for obtaining low dislocation density in Pb [5] and Si crystal growth [6] from the melt. This discrepancy shows that the effect of the cooling process on the multiplication of dislocation is complex and different for different materials, growth furnaces, and growth processes.
   To better understand the relationship between the cooling rate and dislocation, it is essential to study the effect of the cooling process on the increase of dislocations from the perspective of activation of slip systems, since the generation of dislocations mainly originate from the activation of slip systems.
   The results show that the cooling rate has a large effect on the activation of slip systems. In the [001] growth direction, a slow cooling rate either weakly activates 4-fold symmetric slip systems or does not activate them at all. In contrast, a fast cooling rate strongly activates the 4-fold symmetric slip systems. In the [111] growth direction, a slow cooling rate weakly activates the three 3-fold symmetric slip systems, while a fast cooling rate strongly activates the three 3-fold symmetric slip systems. The differences of the activation of the slip systems between the slow and fast cooling rates mainly cause the differences in dislocation and residual stress. Irrespective of the crystal growth direction, it is mainly the radial flux that causes the difference between the fast and slow cooling rates. Therefore, the most effective method for reducing dislocation during the cooling process is to decrease the radial flux.

References
[1] C. Häβler, G. Stollwerck,W. Koch,W. Krumbe, A. Müller, D. Franke, T. Rettelbach, Adv. Mater. 13 (23) 2001.
[2] H. El Ghitani, M. Pasquinelli and S. Martinuzzi, J. Phys. III 3 (1993) 1941.
[3] M. Tachikawa, H. Mori, J. Crystal Growth 183 (1998) 89.
[4] A.M. Sembian, F. Banhart, M. Konuma, J. Weber, S.M. Babu, P. Ramasamy, Thin Solid Films 372 (2000) 1.
[5] G.R. Blackwell, I.A. Bucklow, J. Phys. Chem. Suppl. (1967) 115.
[6] S. Nakano, X. J. Chen, B. Gao, K. Kakimoto, J. Crystal Growth 318 (2011) 280-282.

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