Thermal-capillary analysis of Czochralski and liquid encapsulated Czochralski crystal growth. II - Processing strategies

The pseudosteady-state heat transfer model developed in a previous paper is augmented with constraints for constant crystal radius and melt/solid interface deflection. Combinations of growth rate, and crucible and bottom-heater temperatures are tested as processing parameters for satisfying the constrained thermal-capillary problem over a range of melt volumes corresponding to the sequence occuring during the batchwise Czochralski growth of a small-diameter silicon crystal. The applicability of each processing strategy is judged by the range of existence of the solution, in terms of melt volume and the values of the axial and radial temperature gradients in the crystal.