Numerical Simulation Of Heat, Momentum And Mass Transport In The Melt Of Czochralski Silicon Single Crystal

Single crystal silicon is an important raw material of semiconductor devices and integrated circuits, it has a significant effect on the development of information technology. Czochralski crystal growth, associated with the process of momentum, heat and mass transfer, is an important method of producing single crystal silicon. The momentum, heat and mass transfer of the melt in the crucible have a direct effect on silicon quality. In order to improve the quality of single crystal silicon, it is necessary to understand the characteristics of momentum, heat and mass transfer in the silicon melt within the crucible during Czochralski growth process.The characteristics and regularities of momentum, heat and mass transfer of silicon melt in the crucible with an additional partition were investigated under different boundary conditions. The physical and mathematical model of momentum, heat and mass transfer in the Czochralski method silicon melt were established. The silicon melt was assumed incompressible Newtonian fluid, the Boussinesq approximation was applicable, and the flow was steady, two-dimensional axisymmetric. Finite volume method was used for numerical simulation. By using the low-Reynolds numberκ-εturbulence model, the effects of different partition sizes and locations, crystal and crucible rotation rates, thermal boundary conditions of crucible side wall on the flow fields, temperature fields and oxygen concentration fields were analyzed. The results show that:With the partition height becomes shorter, silicon melt flow gets weaker; the contours of temperature near melt-crystal interface is more dense, more flat; the average oxygen concentration at the melt-crystal interface increases, the radial distribution of oxygen concentration at the melt-crystal interface is more uneven. Increasing the distance between the partition and crucible axis, melt flow gets weaker; the contours of temperature near melt-crystal interface is more dense, more flat; the average oxygen concentration at the melt-crystal interface decreases, the radial distribution of oxygen concentration at the melt-crystal interface tends to more uneven.The effect of crystal rotation rate on the whole melt flow is not significant, and the effect of crystal rotation rate on the whole melt flow becomes further weakened because of the existence of the partition. However, the centrifugal force caused by crystal rotation can greatly influence the melt flow, heat transfer and oxygen concentration near the melt-crystal interface.With the increase of crystal rotation rate, melt flow becomes stronger; the contours of temperature near melt-crystal interface is more sparse; the average oxygen concentration at the melt-crystal interface increases, the radial distribution of oxygen concentration at the melt-crystal interface tends to more uniform.The effect of crucible rotation rate on the whole melt flow is significant. With the increase of crucible rotation rate, the whole melt flow becomes weaker; the contours of temperature near melt-crystal interface is more dense, more flat; the average oxygen concentration at the melt-crystal interface decreases, the radial distribution of oxygen concentration at the melt-crystal interface tends to more uniform.The features of the whole melt flow fields, temperature fields and oxygen concentration fields are silimar when the thermal boundary condition of the crucible side wall is the first thermal boundary condition or the second thermal boundary condition. With the increase of maximal temperature difference between side wall of crucible and melt-crystal interface or with the increase of heat flux of crucible side wall, the whole melt flow becomes stronger; the average oxygen concentration at the melt-crystal interface increases, the radial distribution uniformity of oxygen concentration at the melt-crystal interface has little changes.