Modeling of incorporation of O, N, C and formation of related precipitates during directional solidification of silicon under consideration of variable processing parameters

Abstract

An axisymmetric time-dependent model of the melt region is presented for the diffusive and convective heat and O, N and C transfer as well as the formation of SiO 2, Si 3N 4 and SiC precipitates during crystallization of multi-crystalline silicon ingots. The species model considers different feedstock qualities, the evaporation of SiO from the free melt surface, the incorporation of carbon via CO from the gas atmosphere into the melt, the dissolution of the Si 3N 4 crucible coating by the silicon melt, a carbon flux into the melt resulting from carbon contamination of the Si 3N 4 coating and the segregation effect by the moving phase boundary. Beside the development of the species transfer model a detailed parameter variation is shown. The numerical results were compared with experimental findings obtained with a laboratory scale crystal growth facility, wherein Si-ingots with a diameter of 6 cm and a height of 4–5 cm were directionally solidified. It will be demonstrated that the species model can describe the experimental results.