Dynamics of liquid-encapsulated czochralski growth of gallium arsenide: Comparing model with experiment

The dynamic thermal-capillary model developed previously [Derby, Atherton, Thomas and Brown, J. Sci. Computing 2 (1987) 297] is extended to model a low-pressure, liquid-encapsulated Czochralski system for growth of GaAs in an axial magnetic field that is strong enough that convective heat transport is unimportant. The model includes thermal conduction in all phases, a model for semi-transparent radiation through the B₂O₃ encapsulant and diffuse-gray radiation between the crystal, crucible and melt. Numerical simulations of seeding and growth are compared directly to experimental growth using a Hamco CG-800 puller modified for GaAs growth and equipped with a superconducting magnet capable of producing an axial magnetic field of up to 5 kG. The crystal shape predicted by the simulations is in semiquantitative agreement with the experiment. The calculations also predict optimum operating strategies for producing constant-diameter crystals, including the transients associated with seeding and shouldering the crystal.