COMPUTER MODELING OF HEAT-TRANSFER IN CZOCHRALSKI SILICON CRYSTAL-GROWTH

A finite element quasi-steady state modelling of heat transfer during the growth of a silicon single crystal by the Czochralski (CZ) method is presented. Computations are performed for a comprehensive geometrical model of an actual CZ puller, accounting for detailed radiation heat exchange and introducing a reviewed set of temperature dependent thermophysical properties. The implemented problem solving procedure goes through the recursive scaling of the power yield in order to guarantee the melt/crystal/gas tri-junction temperature matches the melting one. An effective, time saving, numerical scheme is employed for the coupled convergence of both melt/crystal interface location and temperature distribution. Many different growth conditions are simulated for analyzing the sensitivity of the heat flow pattern versus changes of pull rate, gas convection and material properties. The results stress the strong influence of growth rate on the phase change interface deflection, while the input of a correct melt emissivity value is shown to be imperative for working out reliable predictions of the crystal thermal field. The computed temperatures are compared with the corresponding thermographic data collected by means of an infrared imaging system, allowing a satisfactory validation of the adopted mathematical model.