The electronic structures of three-dimensional quantum dots described by parabolic and nonparabolic confinements are calculated using spin-density-functional theory. For representative cases we determined the electron-number-dependent capacitive energy, the energy required to add an additional electron to a quantum dot, by self-consistent solution of the equations using a finite difference method with preconditioned conjugate gradient minimization. Shell-filling and spin configuration effects are identified, as found in electronic structure of the atoms. The peak positions of the capacitive energy at the number of electrons $N=2\mathrm{}$, 6, and 12 for the cylindrical symmetric quantum dot are in good agreement with experimental data.

• Received 30 September 1997

DOI:https://doi.org/10.1103/PhysRevB.57.9035