| The steady-state growth of semiconductor crystals from the melt is modeled via a computational scheme for the prediction of the final dislocation density and residual stresses in the crystal after growth. Two types of growth techniques are examined in this thesis; one is Czochralski (CZ) growth of the solid cylindrical boule, the other is edge-defined film-fed growth (EFG) of the circular cylindrical thin shell.; By applying the Alexander-Haasen constitutive law in the computational model, the high temperature creep behavior and dislocation dynamics of the grown materials can be appropriately described. More detailed and comprehensive formulations, especially considering the boundary conditions of traction rates at the crystal-melt interface, have also been derived. A nonlinear finite element scheme for CZ crystals and a direct integral method for EFG crystals are developed to solve these problems.; For CZ crystals, the steady-state temperature and interface shape are simulated at first by incorporating the Stefan boundary condition in the classical heat transfer problem on solidification. Then, the dislocation multiplication and stress relaxation of the isotropic and cubic anisotropic materials are evaluated. From the computed results, the crystal-melt interface shape is taken to have the most dominant effect on dislocation density and stresses. In addition, other effects such as the growth condition, initial dislocation density and stresses at interface, crystalline anisotropy and also growth orientation have been investigated.; For EFG crystals, both the thermoelastic and thermal viscoplastic models have been implemented. The influence of temperature profiles, growth rates and initial conditions at interface have been studied. The possibility of geometrical nonlinearities in the context of the thermoelastic model has also been considered. Conditions have been established to validate the use of the simpler thermoelastic analysis as compared to the nonlinear thermal viscoplastic model. |
