Electronic edition ISSN 1574-0579

Three-dimensional numerical comparison between two traveling magnetic field inductorcoil designs: Bitter coil versus winding coil on melt convection and front shape during silicon directional solidification

Abdallah Nouri^1, - Brahim Hiba^1, - Kader Zaidat^2, - Lakhdar Hachani^1}

¹ Laboratoire Physique des Matériaux, Université Amar Telidji de Laghouat, BP 37G, Laghouat, 03000, Algérie
² SIMaP-EPM PHELMA, University of Grenoble Alpes, BP75, 38402 Saint Martin d'Hères Cedex, France

Abstract
For photovoltaic (PV) applications, one way to lower the cost of multicrystalline (MC) solar wafers is to use inexpensive feedstock silicon, i.e. the metallurgical solar grade silicon (metallurgical SoG-Si), rather than polysilicon. The solidification process can be improved by adding electromagnetic stirring (EMS) to the silicon melt, as in our case, using a traveling magnetic field (TMF). For this purpose, understanding how the magnetohydrodynamic (MHD) melt flow topology develops during the process is crucial for selecting the most suitable TMF-induced convection configuration, since this will ultimately result in a higher-quality MC silicon crystal. The focus of this work is to numerically analyze how the designs of the Bitter coil, i.e. TMF inductor, affect melted silicon flow topology and the solidification front shape in a vertical directional solidification furnace equipped with a crucible of cylindrical geometry. For the same tubular TMF inductor, two designs were compared: the current design (as a Bitter coil) and the proposed design (as a winding coil). A three-dimensional numerical model was developed and implemented in the COMSOL Multiphysics software to simulate the coupling between the silicon melt hydrodynamics, the electromagnetic effect generated by the TMF inductor, and the heat transfer throughout the furnace with the solidification process by modelling the two phases present (i.e. the solid and liquid phases of silicon). The numerical results supported by the experimental measurements and analyses have shown that the design of the real Bitter coil leads to a loss of axisymmetric MHD melt flow. However, a symmetric flow configuration towards the vertical XZ-plane was obtained which can be subsequently destabilized by the progress of the solidification front. As a result, instead of having a clearly concave or convex front shape-depending on whether the TMF configuration is downward or upward, a front shape inclined toward one side of the ingot was observed. On the other hand, as a solution to avoid this undesirable situation, the winding coil design produces an axisymmetric melt MHD flow as a toroidal flow configuration with a central axis of symmetry and a perfect concave or convex interface shape. Therefore, this result can change the quality of the silicon final ingot by affecting the segregation of impurities close to the interface and the crystal structure morphology evolution. Tables 2, Figs 12, Refs 19.