Numerical analysis of constitutional supercooling in heavily doped silicon crystals grown using the Czochralski method

In the growth of silicon single crystal using the Czochralski method, heavy doping using species such as B, P, and As increases the probability of the deterioration of the crystal quality. This is attributed to morphological instability at the growth interface in the crystal because of constitutional supercooling occurring near the growth interface. Therefore, it is necessary to control constitutional supercooling during growth to stabilize the growth of heavily doped Si single crystals. In this paper, we proposed a new approach to predict the formation and distribution of constitutional supercooling based on a three-dimensional numerical model accounting for heat and mass transport, including the segregation effects of the dopants. The dependency of the growth rate, dopant type, and dopant concentration on the formation of constitutional supercooling was evaluated using this approach. Furthermore, the way to suppress constitutional supercooling was discussed through the example of the effect of crystal rotation rate.