Calculation of compositional dependence of stresses in GaInAs/GaAs strained multilayer heterostructures

Abstract

A theoretical model was proposed to calculate the stress in strained multilayer heterostructures. In this model, each composed crystal layer is divided into many imaginary thin layers. The face force, moment and strained balance were considered over all the imaginary thin layers with coherent interfaces. The accurate bending moment for multilayer heterostructures was derived by expanding Davidenkov's expression of a two-phase composite layer, and it was used in the model. Using this model, the stresses at 25°C were calculated for both the GaInAs/GaAs strained multilayer heterostructure and the GaInAs/GaAs single layer heterostructure, and were compared with each other. In this calculation, the relative thickness of GaInAs layers in the GaInAs/GaAs strained multilayer heterostructure is set up to be equal to that of the GaInAs layer in the GaInAs/GaAs single layer heterostructure. The stress in both the structures was calculated over the entire GaInAs layer composition range. The relative stress in the GaInAs/GaAs bottom heterointerface of the multilayer heterostructure is smaller than that in the GaInAs/GaAs heterointerface of the single layer heterostructure especially for In-rich GaInAs. However, the absolute stress in the GaInAs layer at the bottom heterointerface of the multilayer heterostructure is larger than that in the GaInAs layer at the heterointerface of the single layer heterostructure over the entire GaInAs composition range. The difference between the stresses of both heterostructures increases as the thickness of the GaInAs layer increases. The total thickness of GaInAs layers in the multilayer heterostructure corresponding to a constant interfacial relative stress decreases as the Ga composition in the GaInAs layers decreases and it abruptly decreases when the Ga composition is smaller than 0.4. The relative stress in the GaInAs/GaAs bottom heterointerface of the multilayer heterostructure decreases as the thickness of the GaAs barrier layer increases, but the absolute stress in the GaInAs layer at the GaInAs/GaAs bottom heterointerface of the multilayer heterostructure increases as the thickness of the GaAs barrier layer increases. The effect of the thickness of the GaAs barrier layer on the relative and absolute stresses increases as the thickness of the GaInAs layers increases. These results imply that misfit dislocations due to the interfacial total stress are more easily introduced into the single layer heterostructure than into the multilayer heterostructure, and the band structure due to the absolute stress is more easily transformed in the multilayer heterostructure than in the single layer heterostructure.