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Stability of Thermocapillary Convection in the Float-Zone Process for the Manufacturing of Semiconductor Crystals

Some of the most challenging eigenvalue problems arise in the stability analysis of solutions to parameter-dependent nonlinear partial diierential equations. Surface tension gradients along the free boundary of the oat-zone in crystal growth give rise to a stationary thermocapillary convection. Loss of stability leads to undesirable material imperfections. Stability analyses employing both energy and linearized theory are employed. In each case complex, large, and sparse generalized eigenvalue problems have to be solved. Methods for their solution are proposed and the numerical results are compared to experimental results.