Quantum states of interacting electrons in a real quantum dot

We present an exact diagonalization method that allows the electronic states of interacting electrons in a quantum dot to be calculated from first principles, without making assumptions about the shape of the confining potential, the dimensionality of the problem or the exact nature of the electronic states. The electrostatic potential of the entire device is calculated and the subband structure determined numerically to allow the full three-dimensional electron motion to be included in the calculation. Exact diagonalization of the many-body Hamiltonian then determines the states of the electrons in the dot within the effective-mass approximation. The screening due to the gate electrodes is also taken into account. This method may be used for a range of device geometries, but here we calculate the low-lying levels of a cylindrically symmetric, electrostatically confined quantum dot to better than 0.1%. Results for the ground-state energy and the far-infrared absorption spectrum are presented and the physical effects of the electron motion in the perpendicular direction and the screening are discussed.