ECPM · Computational modelling of electromagnetic control of melt flows and heat/mass transfer during manufacturing of bulk photovoltaic materials

Computational modelling of electromagnetic control of melt flows and heat/mass transfer during manufacturing of bulk photovoltaic materials

The main objective of this project is development of novel computational tools for modelling of various physical phenomena related to bulk growth of photovoltaic materials, as well as to search for the means of electromagnetic control of the growth process. Our computational modelling addresses patterns and instabilities of melt flow, heat and mass transfer, solidification processes, and final distribution of inhomogeneities and dislocations in the grown crystal. The electromagnetic control is established by combining external magnetic fields of different configurations, e.g. DC uniform or cusp, AC rotating or travelling. During the reported year the research was focused on two problems. The first problem is numerical verification and experimental validation of the codes developed for the study of instabilities in Czochralski crystal growth system. Israeli and UK groups succeeded to resolve the disagreements they observed previously when two independent codes were applied to the same benchmark problem. Along with the numerical studies the research group of Prof. Gelfgat at Tel-Aviv University continued experimental studies which resulted in new and more precise experimental data. The latter will be used in forthcoming computations to validate our computational codes. Along with the stability studies we started to develop a time-dependent three-dimensional solver for modelling of the three-dimensional Czochralski process in a whole. At the moment we solve only for simple model flows to check some numerical ideas and newly developed linear solvers. During this year both research groups agreed on the concept of fully 3D solver. Its development can be a topic for our future PhD students and post-doctoral researchers. The second problem is electromagnetic control of convective flows in crystal growth processed by externally imposed time-dependent magnetic fields. We have developed the computational code that studies flow patterns and their instabilities providing calculation of the electromagnetic forces as a set of externally supplied routines. We studied 3D instabilities of a model convection flow, however corresponding convergence studies showed that analytical expressions of electromagnetic forces, usually used in this kind of research, exhibit a strong Gibbs phenomenon and generally cannot be used at large magnetic winding numbers. We started to develop our own code for computation of the forces. The first attempt made by the low-order finite volume method was not fully successful because of the difficulties connected with material properties discontinuities. The second attempt by a higher-order discontinuous Galerkin method was successive and newly developed code will be used in our forthcoming studies. Further advancement of this research strongly depends on the ability of PIs to attract young researchers at the level of PhD and post-doc, as well as to receive necessary funding. Both groups already applied for a joint grant (to British Council) within which the project hopefully will be continued during next two years. We estimate that it will take another year to complete our basic study on the electromagnetic control and two-three years period to develop the first version of the Czochralski 3D code. Application of the codes to the growth of photovoltaic crystals can be started in one-two years. This issue will be discussed with the photovoltaic community at the 16th International Crystal Growth Conference to be held in Beijing, 7-15 August, 2010.

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