Global simulation of a silicon Czochralski furnace

Abstract

To understand the characteristics of the Czochralski (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, equilibrium relations at the melt/silica interface and vapor–liquid chemical equilibrium at the melt/gas interface, as well as the segregation coefficient of unity at the melt/crystal interface. 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 global analysis code is effectively used to discuss the influences of the Marangoni effect and a gas guide (or a heat shield) placed between the crucible and the crystal. The results indicate that the gas guide reduces the heater power and changes the melt flow pattern and oxygen transport. The melt flow pattern is strongly dependent on the Marangoni effect and gas flow near the surface, and changes the oxygen concentration significantly. This analysis reveals the importance and effectiveness of global analysis.