Global Simulation On Effect Of Thermophysical Properties On Silicon Single Crystal Czochraski Growth Processes

The Czochralski (CZ) crystal growth is one of the most important methods of producing single crystals from the melt. In single crystal growth of silicon, it is important to acquire correct knowledge about momentum, heat and mass transfers in the crystal growth furnace and then to control them, because the quality of crystals is closely related to the transport phenomena in the furnace. Numerical simulation is one of the methods to understand the phenomena in the furnace. In the numerical simulation, the determination of thermophysical properties is very important. To understand the effect of the thermophysical properties on the transport phenomena in the CZ furnace for the single-crystal growth of silicon, a set of global analyses of momentum, heat and mass transfer in small CZ furnaces (crucible diameter: 7.2 cm, crystal diameter: 3.5 cm, operated in a 10 Torr argon flow environment) is carried out using the finite-element method. The global analysis assumes a pseudosteady axisymmetric state with laminar flow. Convective and conductive heat transfers, radiative 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 concentrations. The results show that the various thermophysical properties have different effect on the heater power, the melt flow pattern and oxygen transport. The temperature coefficient of surface tension, thermal conductivity and emissivity of melt give significant effects on the flow pattern, heater power, and shape of the crystal/melt, temperature gradient and oxygen transport. However, effects of the density, viscosity of the melt and heat of fusion on silicon single crystal Czochralski growth processes are very small. The increase in λm enchances conductive heat transfer from the crucible to the crystal, and leads to reduction in the heater power, the maximum temperature difference between the crucible wall and crystal/melt interface, and leads to increase in the temperature gradient on the crystal/interface. In addition, such an enhancement of heat transfer through the melt renders the melt/crystal interface shape less convex towards the melt. The increase in (-γT) intensifies the surface-tension-driven convection. The accelerated melt flow increases the efficiency of heat transport from the crucible to the crystal, and consequently, the enhanced heat transfer requires a reduction in the heater power. The melt/crystal interface shape becomes more convex towards the melt as (-γT) increases. The heater power decreases as the heat of fusion increases. The heat of fusion has small effects on the melt flow pattern and oxygen transport.