Evaluation of numerical simulation of constitutional supercooling during heavily Boron-Doped silicon crystal growth using Cz method

Using the Czochralski (Cz) method, it has been established that heavily doped silicon (Si) single crystals with impurities such as boron (B) can negatively impact the quality of grown crystals due to morphological instabilities such as cellular growth caused by constitutional supercooling for doping higher than 1 x 1019 cm-3. To produce high-quality heavily doped Si single crystals, constitutional supercooling must be prevented during growth. In this study, we used a three-dimensional numerical simulation to predict constitutional supercooling during the growth of heavily B-doped Cz-Si single crystals, considering the transport of B in the melt and the segregation effect. We compared the numerically predicted constitutional supercooling region with experimental data to assess its accuracy and found that the cellular growth region observed in the experiment was in good agreement with the region of constitutional supercooling predicted by the simulation. Moreover, we considered the effects of different pulling rates and crystal lengths during the growth process on constitutional supercooling, and the limitations of numerical modelling.