Prediction of quantum dot characteristics through universal scaling relations

Abstract

We derive scaling relations for the electrochemical potential and addition energy of 2D quantum dots charged with N electrons. In the derivation we apply the Thomas-Fermi theory for the harmonic model of a quantum dot in the effective mass approximation. We demonstrate that the resulting scaling relations yield excellent agreement with measured chemical potentials and addition energies for both lateral and vertical quantum dots. Moreover, we show that the scaling relation has predictive power in estimating the confinement strength and the number of electrons trapped in the quantum dot.

Energies and densities of electrons confined in elliptical and ellipsoidal quantum dots

“…The total energy of the 3D dot's electrons, E p = E ee + E V , is calculated in the same way as in the 2D case of section 3.2. The variational condition (17) and its corollary (18) hold in the present case as well.…”

“…III.B. The variational condition(17) and its corollary (18) hold in the present case as well.Direct evaluation of the integral for EV , as in Eq. (16), in the present case of uniform electron density, Eq.…”

“…This immediately leads to Eq. (17). AUTHOR SUBMITTED MANUSCRIPT -JPCM-107305.R1 AUTHOR SUBMITTED MANUSCRIPT -JPCM-107305.R1…”

“…Treatments of the full TF equation incorporating edge effects for such systems as axially symmetric 2D quantum dots, planar metallic surfaces, metal clusters and 3D parabolically confined electrons can be found, e.g. in [6,[15][16][17][18].…”