Considerations on the limitations of the growth rate during pulling of silicon crystals by the Czochralski technique for PV applications

In this contribution numerical modeling was used to investigate the limitations of the growth speed during pulling of silicon crystals by the Czochralski technique with weights of up to 300 kg in crucibles with up to 26" diameter for PV applications. It will be shown that in a first approximation there is a linear dependence of the deflection of the solid-liquid interface on the pull speed. It is confirmed by the modeling results that the phenomenon of the so-called crystal twisting, where the crystal loses its cylindrical shape, is mainly limiting the pull speed. In all calculated cases it occurs obviously with higher probability if the deflection of the solid-liquid interface exceeds 2 cm. Other factors like thermal stress in the crystal or the requirement to achieve a completely vacancy rich material are not limiting the pull speed. Further, it is shown that the pull speed limit for growing a 210 mm crystal without twisting can be increased up to 1.8 mm/min by using an optimized active crystal cooler. In order to increase the pull speed further two generic measures are proposed: (i) increase of heat removal through the crystal and (ii) lowering the temperature at crucible bottom. It will be shown that both measures can lead to a decrease of the interface deflection for a given pull speed. This means that there is the potential to increase the pull speed further to 2 mm/min and beyond before crystal twisting will take place. This enhancement of the pull speed corresponds to an increase of the productivity of the Cz process in the optimized puller by 54% compared to the original one without active crystal cooler.