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Modeling of electronic structure for dome-shaped quantum dots

A Hamiltonian operator in assessing the energy levels and wavefunctions of quantum dots (QDs) was proposed. The finite element method was used to solve the numerical Schrödinger equation for envelope function in the effective mass approximation. Within this model, we have investigated QDs with different geometries (cone, lens and dome-shaped dot). While it is easy to attain stability for conical QDs, it is difficult with lens QDs. Strain and mole-fraction effects are also studied. Our results coincide with the experimental one.