Finite element modeling for dislocation generation in semiconductor crystals grown from the melt

Dislocations in Gallium Arsenide (GaAs) and Indium Phosphide (InP) 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 and InP-based devices/circuits. It is well known that dislocation density can be significantly reduced by doping impurity atoms into the GaAs and InP crystal and/or decreasing the thermal stresses in these crystals during their growth process. In order to reduce the dislocation density generated in the GaAs and InP crystals, the influence of crystal growth parameters and doping impurity atoms on the dislocations reduction in GaAs and InP crystals has to be understood. Therefore, a transient finite element model was developed to simulate the dislocation generation in GaAs and InP 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 and InP single crystals grown by the vertical gradient freeze (VGF) process were adopted as examples to study the influences of doping impurity and growth parameters on dislocations generated in these grown crystal. The calculated results show that doping impurity can significantly reduce dislocation generation and produces low-dislocation-density or dislocation free GaAs and InP single crystals. It also shows that the dislocations generated in GaAs and InP crystals increase as the crystal diameter and imposed temperature gradient increase, but do not change or increase slightly as the crystal growth rate increases. Therefore, this finite element model can be effectively used by crystal growers to select acceptable levels of doping impurity, crystal diameter, temperature gradient, and growth rate to produce the lowest dislocation density in GaAs and InP crystals through a thorough numerical investigation using this developed finite element model.