Steady-state thermal-solutal diffusion in a float zone

Abstract A model is presented for a float zone established in a thin vertical sheet. In a coordinate system translating with the heater, the equations describing the steady, two-dimensional diffusion of solute in the melt, and diffusion of heat in the feed material and the product crystal are discussed. Heat transfer between the system (melt, feed and product) and the surrounding environment (including the heating source) is assumed to take place via both convection and radiation. Given the translation velocity, the heater and the ambient temperature profiles, and material properties, asymptotic solutions for the temperature and concentration profiles and the melting, solidifying and melt/gas interfacial shapes are developed in the limit of small aspect ratio (zone half-width/length). Results of a parametric investigation are presented and compared to both numerical and experimental observations. The physical mechanisms involved in the formation of the zone configuration are discussed for both the pure and binary systems of Si and GeGa, respectively.