Effects of viscosity on the continuous growth of dendritic silicon crystal ribbon

Abstract

This paper investigates the effects of viscosity on the thermal stresses developed in a silicon ribbon during its continuous growth. Kelvin models are used to study the viscous behavior of silicon. A specialization of the general three dimensional model for the plane stress conditions is presented. Results of the numerical studies, based on the assumed constants of the Kelvin models, indicate that the viscosity of silicon reduces peak elastic thermal stresses and does notcause any residual stress in the ribbon. The instability of the numerical solution process is also studied and various alternatives are proposed to avoid divergence of the numerical solution.