Global simulation of a silicon Czochralski furnace

To understand the characteristics of the Czochralski (Cz) furnace for the s ingle-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: 3.5cm, operated in a 10 Torr argon flow environment) is carried out using the finite-element method, The global analysis assumes a pseudost eady axisymmetric state with laminar flow, equilibrium relations at the mel t/silica interface and vapor-liquid chemical equilibrium at the melt/gas in terface, as well as the segregation coefficient of unity at the melt/crysta l interface. Convective and conductive heat transfers, radiative heat trans fer between diffuse surfaces and the Navier-Stokes equations for gas and me lt phases are all combined and solved together, Thus, the velocities and te mperatures obtained are used to calculate the oxygen concentrations. The gl obal analysis code is effectively used to discuss the influences of the Mar angoni effect and a gas guide (or a heat shield) placed between the crucibl e and the crystal. The results indicate that the gas guide reduces the heat er power and changes the melt flow pattern and oxygen transport. The melt f low pattern is strongly dependent on the Marangoni effect and gas flow near the surface, and changes the oxygen concentration significantly. This anal ysis reveals the importance and effectiveness of global analysis. (C) 2002 Elsevier Science B.V. All rights reserved.