Global Simulation On Effect Of Cusp Magnetic Field On Silicon Single Crystal Czochraski Growth Processes

The growth of large diameter single crystal silicon is one of the active branches in silicon material research and production. It is known from experiments that the shape of the growth interface, the temperature distribution and the oxygen concentration are sensitive to the melt motion. In order to understand the effects of the strength of a cusp magnetic field on the transport phenomena in the CZ furnace for the single-crystal growth of silicon, a set of global numerical simulations in a CZ furnace (crucible diameter: 7.2cm, crystal diameter: 3.5cm, operated in a 10 Torr argon flow environment) is carried out using the finite-element method. It is assumed that the flow was pseudosteady axisymmetric laminar in both the melt and the gas, the melt is incompressible and a constant temperature is imposed on the outer wall of the CZ furnace. Convective and conductive heat transfers, radiant heat transfer between diffuse surfaces and the Navier–Stokes equations for gas and melt phases are all combined and solved together. Thus, the velocities and temperatures obtained are used to calculate the oxygen concentration.The results show that the silicon melt flow is suppressed by the cusp magnetic field. With the increasing of magnetic field strength, two toroidal roll cells are found in the melt pool. The one in the upside of the melt pool is driven by both the Lorentz and Marangoni force, the other by both the Lorentz force and buoyancy.The increase in magnetic field strength depresses the efficiency of heat transfer from the crucible to the crystal, and consequently leads to increase in the heater power, the maximum temperature difference between the crucible wall and crystal-melt interface, and increase in the temperature gradient on the crystal-melt interface except when the strength of magnetic field is 0.05T. In addition, such an enhancement of magnetic field strength leads the crystal-melt interface shape less convex towards the melt except when the strength of magnetic field is 0.05T and 0.1T.As the melt flow is suppressed, the maximum oxygen concentration is increasing and the minimum oxygen concentration is reducing. The average oxygen concentration along the melt-crystal interface reduces when the strength of magnetic field is less than 1.0T. With the increasing of the magnetic field strength, the oxygen motion becomes diffusion-controlled.