Numerical modeling of carbon distribution and precipitation during directional solidification of photovoltaic silicon

Abstract

Numerical modeling is used to investigate carbon distribution and precipitation in directional solidification of multicrystalline silicon. Computations are performed for samples of 6 cm in diameter grown in a Vertical Bridgman Freezing (VGF) system starting from silicon feedstock with different grades of contamination in carbon. The value of the unknown reaction rate coefficient governing the carbon precipitation in the silicon melt was estimated in the present work by comparing the numerically computed concentration profiles to the experimental results taken from the literature. Numerical results show that the growth rate has a significant influence on the interface deflection, melt convection and carbon precipitation. It is found that the silicon samples grown from the melts of low carbon contamination (<1018at/cm3) exhibit low content in SiC precipitates, even if they are solidified at high growth rates (1–2 cm/h). The samples with high initial carbon contamination (5·1018at/cm3) should be solidified at much lower rates (0.2 cm/h) in order to avoid the formation of SiC precipitates.