Energies and densities of electrons confined in elliptical and ellipsoidal quantum dots
Abstract
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.
- Authors:
-
- 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
- Univ. of Southern California, Los Angeles, CA (United States). Dept. of Physics and Astronomy
- Publication Date:
- Research Org.:
- Argonne National Laboratory (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)
- OSTI Identifier:
- 1352650
- Alternate Identifier(s):
- OSTI ID: 1287745
- Grant/Contract Number:
- AC02-06CH11357; AC-02-06CH11357
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Physics. Condensed Matter
- Additional Journal Information:
- Journal Volume: 28; Journal Issue: 39; Journal ID: ISSN 0953-8984
- Publisher:
- IOP Publishing
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Thomas–Fermi theory; nanoclusters; quantum dots; self-consistent field
Citation Formats
Halder, Avik, and Kresin, Vitaly V. Energies and densities of electrons confined in elliptical and ellipsoidal quantum dots. United States: N. p., 2016.
Web. doi:10.1088/0953-8984/28/39/395302.
Halder, Avik, & Kresin, Vitaly V. Energies and densities of electrons confined in elliptical and ellipsoidal quantum dots. United States. https://doi.org/10.1088/0953-8984/28/39/395302
Halder, Avik, and Kresin, Vitaly V. Tue .
"Energies and densities of electrons confined in elliptical and ellipsoidal quantum dots". United States. https://doi.org/10.1088/0953-8984/28/39/395302. https://www.osti.gov/servlets/purl/1352650.
@article{osti_1352650,
title = {Energies and densities of electrons confined in elliptical and ellipsoidal quantum dots},
author = {Halder, Avik and Kresin, Vitaly V.},
abstractNote = {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.},
doi = {10.1088/0953-8984/28/39/395302},
journal = {Journal of Physics. Condensed Matter},
number = 39,
volume = 28,
place = {United States},
year = {Tue Aug 09 00:00:00 EDT 2016},
month = {Tue Aug 09 00:00:00 EDT 2016}
}
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Works referencing / citing this record:
Donor Impurity-Related Optical Absorption in GaAs Elliptic-Shaped Quantum Dots
journal, January 2017
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- Journal of Nanomaterials, Vol. 2017