Finite element simulation of dislocation generation in doped and undoped GaAs single crystals grown from the melt

Abstract

Dislocations in gallium arsenide (GaAs) single crystals are generated by excessive stresses that are induced during the crystal growth process, and the fabrication and packaging of microelectronic devices/circuits. The presence of dislocations has adverse effects on the performance, lifetime and reliability of the GaAs-based devices/circuits. It is well known that dislocation density can be significantly reduced by doping impurity atoms into the GaAs crystal and/or decreasing the thermal stresses in the crystal during its growth process. A transient finite element model is developed to simulate the dislocation generation in GaAs crystals grown from the melt. A viscoplastic constitutive equation that couples a microscopic dislocation density with a macroscopic plastic deformation is employed to formulate this transient finite element model, where the dislocation density is considered as an internal state variable and the doping impurity is represented by a drag-stress in this constitutive model. GaAs single crystals grown by the vertical gradient freeze process are adopted as an example to study the influences of doping impurity on dislocations generated in the grown crystal. The calculated results show that doping impurity can significantly reduce dislocation generation and produces low-dislocation GaAs crystals.