Modeling Semiconductor Crystal Growth Under Electromagnetic Fields
Growth of semiconductor single crystals under electric and magnetic fields is of interest to increase and better control of crystal growth rate, to suppress and control the adverse effect of natural convection and to obtain better mixing in the growth melt (liquid solution) for better crystal uniformity, which all are favorable conditions for a prolonged growth of high quality crystals. To this end, in parallel to well-designed experiments, modeling is essential to shed light on various aspects of these growth processes and also to better understand the transport phenomena involved. In this article the models developed over the years, mostly based on Professor Gerard Maugin’s well-known contributions to “electromagnetic interactions”, are briefly presented for “solution growth” conducted under electric and magnetic fields. Basic and constitutive equations of a binary electromagnetic continuum mixture are specialized for two important solution growth techniques—Liquid Phase Electroepitaxy (LPEE) and Travelling Heater Method (THM). As an application, an LPEE growth of GaAs bulk crystals under a strong static magnetic field is considered. Experimental results, that have shown that the growth rate under an applied static magnetic field is also proportional to the applied magnetic field and increases with the field intensity level, are predicted from these models. The contribution of a third-order material constant in LPEE is also predicted from these models. The prediction of increasing growth rate in THM growth under rotating magnetic fields from modeling was verified by experiments.
The financial support provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canada Research Chairs (CRC) Program is gratefully acknowledged.
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