| A theoretical and computational model is developed, using the finite element method, to analyze the thermal stresses and defects, specifically dislocation density, in single crystal semiconductors grown from the melt. The model is based on the Alexander and Haasen dislocation model. This model is a microstructural based constitutive model developed for elemental semiconductors loaded in a single slip orientation. It consists of a set of scalar equations, which incorporate dislocation density as a state variable and relates the plastic deformation in the crystal to the movement and multiplication of dislocations, coupling inelastic deformation with dislocation density.; In this work the Alexander and Haasen model is expanded and generalized to account for the kinematics of crystal plasticity and the sphalerite structure of compound semiconductors. The generalized model permits the modeling of both single slip and multiple slip configurations. It also accounts for the latent hardening due to slip system interactions.; The computational model includes a radial return algorithm for integrating the constitutive equations and a consistent tangent matrix for solving the nonlinear system of equations resulting from the finite element discretization. A Lagrangian based interpolation scheme is used along with a time step variation to model the evolution of the material and the growth of the finite element mesh at the solid/liquid interface. Result for the model specialized for InP are presented. |
