A viscoplastic constitutive equation that coupled a microscopic dislocation density and impurity atoms to a macroscopic plastic deformation was used in a transient finite-element model for predicting the dislocation density generated in undoped and doped crystals grown by using the vertical gradient freeze process. The effects of crystal growth parameters (imposed temperature gradient, crystal diameter, crystal growth rate) upon dislocation generation were also investigated. The numerical results showed that a doped impurity could significantly reduce the dislocation density generated in these crystals. It also showed that the dislocation density was drastically reduced as the crystal diameter and imposed temperature gradient decreased, but the crystal growth rate had almost no effect upon dislocation generation in these crystals.

Finite Element Modeling of Dislocation Reduction in GaAs and InP Single Crystals Grown from the VGF Process. X.A.Zhu, G.Sheu, C.T.Tsai: Finite Elements in Analysis and Design, 2006, 43[1], 81-92