Electronics states of interdiffused quantum dots

We have developed a three-dimensional model for electronic states calculation of interdiffused quantum dots (QDs) with arbitrary shape by solving the BenDaniel-Duke’s equation in momentum space domain. The proposed model features several advantages such as automatic solution to the Fick’s diffusion equation, a relatively compact and efficient Hamiltonian matrix, and natural representation of a large array of QDs. Without considering the interdiffusion effect, our model yields good agreement with our references of $\mathrm{InAs}∕\mathrm{GaAs}$ QDs ground state energy calculation. We analyze the interdiffusion effect in QDs with various shapes of theoretical and practical interest like spherical, cubical, pyramidal, and lens shaped. We study the effect of QD size and aspect ratio to the blueshift profile due to interdiffusion. We found a similar blueshift profile in these QDs at almost any size that can be well approximated by $\mathrm{sech}\left(x\right)$ function. This model will serve as a valuable tool for QD band gap engineering based on the interdiffusion technique.