Energy spacing in charging a quantum dot: The effect of the electron-electron interactions

Recent experiments on quantum dots have shown that by adding one electron at a time to a quantum dot the energy spacings 'are rather uniform and decrease slightly' as the number of electrons increases (Ashoori et al 1993 Phys. Rev. Lett. 71 613). By applying the scaled Kohn-Sham equations to a cylindrical quantum dot system, we show that this is due to the effect of the electron-electron interactions. The interactions, especially the Coulomb interaction, cause a significant redistribution of the electronic charge density which is determined by the effect of the boundary condition of the quantum dot in minimizing the total energy of the system. To ensure that the effect of the electron-electron interactions is independent of the specific potential used in defining the quantum dot, two model potentials (a constant potential and a potential that is harmonic in the radial part) are considered.