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Heat flow in the melt and crucible for crystal growth

University of British Columbia

A magnetic field is imposed on the melt during Czochralski crystal growth to control fluid flow. The influence of an applied magnetic field on heat transfer in a germanium melt has been investigated in this work. In heat-transfer modelling of the Czochralski process, values of thermal conductivity of the crucible material, pyrolytic boron nitride, are required as a function of temperature. The thermal conductivity of a pyrolytic boron nitride crucible material has also been determined in this work. Both the investigation of the influence of the applied magnetic field and the determination of the thermal conductivity have involved experimental temperature measurements and mathematical modelling of heat transfer. The finite element equations for the two-dimensional heat-conduction equation have been derived using the Galerkin method of weighted residuals. They have been validated by comparing the finite element solutions with the corresponding analytical solutions. The finite element results are in excellent agreement with the analytical solutions. A steady-state conduction-dominated mathematical model has been developed to analyze the temperature measurements obtained within the germanium melt in a Czochralski crystal growth configuration with and without an applied magnetic field of 0.099 tesla. The effect of the applied magnetic field on the heat transfer in the melt has been determined by fitting the model-calculated results to the measurements. The effective thermal conductivity of the melt has been found to decrease by a factor of seven due to the magnetic field. The thermal conductivity across a pyrolytic boron nitride crucible plate (through crucible thickness) has been determined from measurements of temperature responses in liquid gallium positioned on both sides of the plate, in conjunction with a transient mathematical model which simulates the thermal responses. By matching the simulated thermal responses with the measurements, the thermal conductivity of the pyrolytic boron nitride crucible plate has been obtained as a function of temperature.

Text

2010-11-17

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http://hdl.handle.net/2429/29991

Materials Engineering

University of British Columbia

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