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Shape and Size Dependent Electronic Properties of GaAs/AlGaAs Quantum Dots

We have theoretically investigated the effect of shape anisotropy and size on electronic structure of GaAs/AlGaAs quantum dots (QDs). The quantum dot is modeled by anisotropic parabolic confinement potential in the plane perpendicular to the growth direction while the confinement along the growth direction is modeled as quantum well potential. The Luttinger Hamiltonian formulation has been used to account for the valence subband mixing. The electronic structure is calculated by numerical diagonalization of Luttinger Hamiltonian using the harmonic oscillator basis functions. The calculations for hole energies and transition energies have been carried out over wide range of size and shape of QDs. The results show that transition energy of QDs decreases with the height of QDs. Significant variation in the hole energy is observed with the change in anisotropy. We also observe that shape anisotropy and mixing have significant effect on the energy states.