Computational simulations of Ribbon-Growth on substrate for photovoltaic silicon wafer

Abstract

Computational simulations of horizontal ribbon growth on substrate (RGS), used for production of silicon wafers for photovoltaic applications, have been made based on FLUENT-based solutions of the fundamental governing equations of mass, momentum and energy. A conservation equation for the liquid volume fraction, along with a solidification model, is used in addition to find the phase distributions. Validations of both the melt flow and solidification components of the computational model are made by comparing with available data on Czochralski bulk process and vertical ribbon growth process, with good agreements for these components. This provides the basis for validity of the method for silicon melt flow and solidification processes, including the RGS. The pull speed and the heat extraction rates are varied to find the optimum production conditions during RGS. The pull speed can be directly input in the current model, and shows the effects of decreased residence time at high pull speeds. At intermediate heat extraction rates, the solidification dynamics can lead to disruptions in the melt flow on the substrate, leading to inhomogeneous solidification conditions. A test matrix involving the pull speed and the heat extraction rate shows that a pull speed of less than 0.1 m/s and heat extraction rate of greater than 100 W/cm 2 are the necessary conditions for achieving complete and stable solidification over a length scale of 0.8 m in the current configuration. These numbers translate to 2 kJ/m 2 as the minimum necessary enthalpy flux during stable RGS.