A Model to Predict Contact Resistance During Contact Solidification in Ribbon Growth on Substrate Process

Abstract

Ribbon Growth on Substrate (RGS) has emerged as a promising method for growing multicrystalline silicon wafer directly on a substrate for photovoltaic applications. In this method, the wafer forms as a substrate contacts molten silicon for a controlled period of time. Due to the surface roughness, a thin layer of air is trapped at the interface of the substrate and molten silicon, leading to a contact resistance to heat transfer. The interfacial heat transfer plays an important role in determining the subcooling rate and nucleation, which defines the structural characteristics of the wafer. The contact resistance has been identified as an important phenomenon that affects solidification at the interface. It is dependent on many factors such as the roughness and wetting of the substrate as well as the substrate pre-heating temperature. Quantitative knowledge of the interfacial heat transfer resistance is essential for control of the solidification process. A mathematical model is presented for quantification of the interfacial heat transfer resistance during the initial stage of the solidification for RGS process. A three dimensional unit cell is constructed to represent the contact geometry and interface characteristics. The surface roughness, the mean trapped air layer between the substrate and the liquid, the parameters of area density and the radius of contact spots will be included in the geometry of the unit cell. A microscale heat transfer model is developed to describe conduction and radiation across the interface to quantify the contact heat transfer resistance as a function of surface roughness, morphology and preheating temperatures of the substrate. The contact resistance is incorporated into a heat transfer model and predicts the temperature variation with time in the substrate during the initial stage of contact. The presented model provides a valuable tool to predict the effect of various process parameters and substrate surface roughness on wafer growth during the RGS process.