Crystallographic finite element modeling for dislocation generation in semiconductor crystals grown by VGF process

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.