Two-step strain analysis of self-assembled InAs/GaAs quantum dots

Strain effects on optical properties of self-assembled InAs/GaAs quantum dots grown by epitaxy are investigated. Since a capping layer is added after the self-assembly process of the quantum dots, it might be reasonable to assume that the capping layer neither experiences nor affects the induced deformation of quantum dots during the self-assembly process. A new two-step model is proposed to analyse the three-dimensional induced strain fields of quantum dots. The model is based on the theory of linear elasticity and takes into account the sequence of the fabrication process of quantum dots. In the first step, the heterostructure system of quantum dots without the capping layer is considered. The mismatch of lattice constants between the wetting layer and the substrate is the driving source for the induced elastic strain. The strain field obtained in the first step is then treated as an initial strain for the whole heterostructure system, with the capping layer, in the second step. The strain from the two-step analysis is then incorporated into a steady-state effective-mass Schrodinger equation. The energy levels as well as the wavefunctions of both the electron and the hole are calculated. The numerical results show that the strain field from this new two-step model is significantly different from models where the sequence of the fabrication process is completely omitted. The calculated optical wavelength from this new model agrees well with previous experimental photoluminescence data from other studies. It seems reasonable to conclude that the proposed two-step strain analysis is crucial for future optical analysis and applications.