Dynamic global simulation of the Czochralski process. II. Analysis of the growth of a germanium crystal

For pt.I see ibid., p.65-76, 1997. The time-dependent Czochralski growth of a germanium crystal is analyzed, using the numerical scheme developed in a previous paper. Heat transfer by conduction and diffuse grey radiation is taken into account in the overall furnace, together with all the transient effects induced by the growth of the crystal. Convection in the melt is not considered. The inverse problem of the pulling of the top-end cone and body of a crystal of an imposed shape is solved at first. A real transient behavior is observed during the shouldering process. On the basis of these results, perturbations of heater power or pull rate are applied. Calculations demonstrate large differences in the short term system responses to these two input parameters. Simulations are carried out for 2 and 4 cm/h nominal pull rates, demonstrating the sensitivity of the system dynamics (and the crystal radius) to the operating conditions. An example illustrating the effect of combined heater power and pull rate perturbations is also analyzed. Results indicate the possibility to maintain an unchanged crystal radius, while modifying the solid-liquid interface position, showing how the model can be used to develop control strategies.