CALCULATION OF STRESSES IN GAAS/SI STRAINED HETEROSTRUCTURES

A theoretical model was proposed to calculate the stress in the GaAs/Si and GaAs/graded GaAs-Si/Si strained heterostructures. In this model, each composed crystal layer is divided into many imaginary thin layers. The face force, moment and strain balance were considered over all the imaginary thin layers with coherent interfaces. This model is established under accurate consideration of the difference between crystalline parameters such as the lattice constant and thermal expansion coefficient of composed crystal layers. Using this mode, the stress in the GaAs/Si and GaAs/graded GaAs-Si/Si strained heterostructures was calculated at 370 and 25-degrees-C. In the Si layer, the tensile stress is near the GaAs/Si interface and the compressive stress is near the bottom of the Si layer. In the GaAs layer, the compressive stress is near the GaAs/Si interface and it decreases as the thickness of the GaAs layer increases. The total stress at the GaAs/Si interface increases as the thickness of the GaAs layer increases and it decreases as the thickness of the Si layer increases. The total stress at the GaAs/Si interface has a maximum point for the thickness of the GaAs and Si layers. The share of the total stress at the heterointerface depends strongly on the structure such as the thicknesses of the GaAs and Si layers. The curvature radius of the GaAs/Si heterostructures decreases as the thickness of the GaAs layer increases. The stress in the GaAs layer decreases by adding a GaAs-Si graded layer between the GaAs and Si layers, and it decreases as the thickness of the graded layer increases. The tangential and perpendicular lattice constants in the GaAs/graded GaAs-Si/Si were calculated using this model. The misfit dislocation terms were added to the calculation model, and the stress and curvature radius were calculated for the GaAs/Si heterostructures with misfit dislocations only in the heterointerface. The misfit dislocation density was determined to obtain the GaAs/Si heterostructure with no curvature. The curvature radius changes from positive to negative as the misfit dislocation density increases.