Controlling transport phenomena in the Czochralski crystal growth process

A mathematical formulation and computational techniques are presented to de scribe optimal control and design strategies for the suppression of turbule nt motions in the melt and the minimization of temperature gradients in the crystal in Czochralski crystal growth processes. The methodologies develop ed can be used to test control mechanisms, design parameters, and optimizat ion objectives to determine their effectiveness in improving the processes. They can also be used to effect such improvements by systematically determ ining optimal values of the design parameters. The controls or design param eters considered include applied magnetic fields, temperature gradients alo ng the side wall of the crucible, and crucible and crystal rotation rates. The results show that applied magnetic fields can be very effective in redu cing velocity perturbations in the melt, while side wall temperature gradie nts are less effective and crucible and crystal rotation rates are ineffect ive. The results also show that applied magnetic field and crucible and rot ation rates are ineffective in reducing temperature gradients in the crysta l or in the melt. (C) 2002 Elsevier Science BY. All rights reserved.