skip to main content


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

Here, we consider a droplet of electrons confined within an external harmonic potential well of elliptical or ellipsoidal shape, a geometry commonly encountered in work with semiconductor quantum dots and other nanoscale or mesoscale structures. For droplet sizes exceeding the effective Bohr radius, the dominant contribution to average system parameters in the Thomas– Fermi approximation comes from the potential energy terms, which allows us to derive expressions describing the electron droplet’s shape and dimensions, its density, total and capacitive energy, and chemical potential. Our analytical results are in very good agreement with experimental data and numerical calculations, and make it possible to follow the dependence of the properties of the system on its parameters (the total number of electrons, the axial ratios and curvatures of the confinement potential, and the dielectric constant of the material). One interesting feature is that the eccentricity of the electron droplet is not the same as that of its confining potential well.
 [1] ;  [2]
  1. Argonne National Lab. (ANL), Argonne, IL (United States). Materials Science Division; Univ. of Southern California, Los Angeles, CA (United States). Dept. of Physics and Astronomy
  2. Univ. of Southern California, Los Angeles, CA (United States). Dept. of Physics and Astronomy
Publication Date:
Grant/Contract Number:
AC02-06CH11357; AC-02-06CH11357
Accepted Manuscript
Journal Name:
Journal of Physics. Condensed Matter
Additional Journal Information:
Journal Volume: 28; Journal Issue: 39; Journal ID: ISSN 0953-8984
IOP Publishing
Research Org:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); National Science Foundation (NSF)
Country of Publication:
United States
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Thomas–Fermi theory; nanoclusters; quantum dots; self-consistent field
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1287745