Magnetic Effect on Thermocapillary Flow of Silicon Melt in an Annulus

Abstract

Thermocapillary convection plays a crucial role in various processes, including the formation of crystals from a molten state. Recent studies have established that the oscillatory flow of the molten material during crystal growth is a significant contributor to the formation of undesirable micro-inhomogeneities. The oscillatory flow can cause uneven distribution of solute and impurities, leading to localized variations in crystal composition and structure. This article discusses the possibility of controlling bidirectional thermocapillary flow, which is one of the sources of inhomogeneity in produced crystals, using an external magnetic field. The model examined in this study is a shallow annulus filled with silicon melt. This research investigates the effects of the annular space and the magnetic field on the thermocapillary process. The mathematical model, formulated as partial differential equations, was solved using the finite-volume method. The results show the formation of hydrothermal waves with different azimuthal modes (m = 6, 4, and 3) corresponding, respectively, to the annular space R = 0.8, 0.7, and 0.6. Stronger magnetic fields attenuate the instabilities and reduce the vertical temperature gradient, transforming the isotherms into concentric circles, thereby improving the homogeneity of the crystals.