Crystal growth

The dislocation density in the Gallium Arsenide (GaAs) crystal is generated by the excessive thermal stresses during Czochralski (CZ) growth process. A constitutive equation which couples the dislocation density with the plastic deformation is employed to simulate the dislocation density in the crystal. The temperature distribution in the crystal during growth process is obtained by solving the quasi-steady-state (QSS) heat transfer equation. The thermal stresses induced by the temperature distribution are calculated by finite element method. The resolved shear stress (RSS) in each slip system is obtained by stress transformation. The dislocation motion and multiplication in each slip system are simulated using the constitutive equation and the total dislocation density in the crystal is obtained. The dislocation density is also found to be affected by the growth orientation, growth speed, ambient temperature and the radius of the crystal. The dislocation density in GaAs crystals grown from different growth orientation and crystal radius at various ambient temperatures will be calculated so that the influence of these growth parameters on the dislocation density can be understood. Consequently, one can control the growth parameters to reduce the dislocation density generated in the crystal during the CZ growth process.

Thermal stresses are induced by temperature variations in gallium arsenide(GaAs) crystal growth. The thermal stresses cause plastic deformations by dislocation and dynamic interaction in the crystal. In this study, firstly the temperature distribution in the Czochralski technique (CZ) growth of GaAs crystal is obtained according to the Jordan model. Secondly a visco-plastic response function for the GaAs crystal is developed from the Haasen model. Finally a nonlinear finite element model is employed to simulate the dislocation generation during CZ growth of GaAs crystal.

The generation and multiplication of dislocations in Gallium Arsenide (GaAs) and Indium Phosphide (InP) single crystals grown by the Vertical Gradient Freeze (VGF) process is predicted using a transient crystallographic finite element model. This transient model is developed by coupling microscopic dislocation motion and multiplication to macroscopic plastic deformation in the slip system of the grown crystals during their growth process. During the growth of InP and GaAs crystals, dislocations are generated in plastically deformed crystal as a result of crystallographic glide caused by excessive thermal stresses. The temperature fields are determined by solving the partial differential equation of heat conduction in a VGF crystal growth system. The effects of growth orientations and growth parameters (i.e., imposed temperature gradients, crystal radius and growth rate) on dislocation generation and multiplication in GaAs and InP crystals are investigated using the developed transient crystallographic finite element model. Dislocation density patterns on the cross section of GaAs and InP crystals are numerically calculated and compared with experimental observations. For crystals grown along [001] and [111] orientations, the results show that more dislocations are generated as the temperature gradient, the crystal growth rate and the crystal radius increase. For the same growth process, it shows that the crystal grown along [111] orientation is a favorable growth direction to grow lower dislocation density crystals. All the results show a famous "W" shape and four fold symmetry dislocation density pattern in GaAs and InP crystals grown from both orientations regardless of crystal growth parameters, which agree well with the patterns observed in actual grown crystals. Therefore, this developed crystallographic model can be employed by crystal grower to design an optimal growth parameters and orientations for growing low dislocation density in advanced semiconductor and optical crystals.