The constitutive equation for silicon and its use in crystal growth modeling

A stress analysis that describes the crystal growing process requires a material model that is valid over a wide temperature range and includes dislocation motion and mutliplication. The stresses developed in the growing process could induce residual stresses, changes in dislocation density and buckling into the growing crystals. The dislocation density is introduced as an internal variable in the constitutive model. The stress-strain and dislocation density-strain characteristics of silicon crystals are discussed as a function of temperature, strain rate, and initial dislocation density