DENSITY OF STATES OF QUANTUM DOTS AND CROSSOVER FROM 3D TO Q0D ELECTRON-GAS

An isolated quantum dot is modelled by a potential box with delta-profiled, penetrable potential walls embedded in a large outer box with infinitely high potential walls which represent the work function with respect to a vacuum. We calculate the energies E and the density of states of the electron gas in the quantum dot as functions of the strengths of the potential walls of the inner box. As the strengths of the opposite potential walls increase pairwise from small to large values, the density of states shows smooth crossover from the three-dimensional E1/2 form to the quasi-two-dimensional (Q2D) staircase and further down to the Q1D sawtooth and the delta-function peaks of the Q0D electron gas.