Abstract
A model is proposed for a detail three dimensional thermo fluid flow analysis of large silicon crystal growth systems composed of the silicon melt, silicon crystal, and silica crucible, by first solving the coupled not-1inear governing equation for a steady, viscous, laminar flow, using the finite element method. The temperature, presssure, and gravitational fields thus obtained are 'loaded' into the stress sub-model for calculation of stresses to ascertain a 'dislocation-free' crystal grown. The model is particularly suitable for parametric studies to arrive at an optimum design of the system The model also provides options for a 'multiple species transport' analysis and for a more detailed local analysis, such as a boundary layer analysis at the crystal-melt interface, by sub-structuring part of the model. Based on results obtained from the current example, it is also concluded that a large dislocation-free crystal of 300 mm diameter or larger is obtainable functionally by the Czochralski technique, with a room for improvement', and economically using technique presented in this paper.
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