Finite element modeling of dislocation reduction in GaAs and InP single crystals grown from the VGF process

Dislocations in gallium arsenide (GaAs) and indium phosphide (InP) crystals are generated by thermal stresses induced during their solidification process of crystal growth. High dislocation density in these crystals will reduce the performance and reliability of the GaAs- and InP-based microelectronic and photonic devices/circuits. It has been known that doping impurity atoms into GaAs and InP crystals during their solidification process can significantly reduce dislocation densities generated in these crystals. A viscoplastic constitutive equation that couples a microscopic dislocation density and impurity atoms with a macroscopic plastic deformation is employed in a transient finite element model for predicting the dislocation density generated in the undoped and doped GaAs and InP crystals grown by the vertical gradient freeze (VGF) process. The effects of crystal growth parameters (i.e., imposed temperature gradient, crystal diameter, and crystal growth rate) on dislocation generation are also investigated. The numerical results show that doping impurity can significantly reduce the dislocation density generated in these crystals. It also shows that dislocation density reduces drastically as the crystal diameter and imposed temperature gradient decrease, but the crystal growth rate has almost no effect on dislocation generation in these crystals.