Two interacting electrons in a vertical quantum dot with magnetic fields

We present a numerical exact calculation for the energy spectra of two electrons in a finite height cylindrical quantum dot in details by a coupled-channel method. The electron correlation energy for various geometry of quantum dots, with and without applied magnetic fields, for singlet and triplet states are investigated. The magnitude of magnetic field for transition of the spin-singlet ground state and the spin-triplet excited state is compared with experimental result. The study shows significant contributions due to the spreading of electron density distribution along the vertical direction. In contrast to the planar circular disk model, the study will be useful for some realistic quantum dots.