Related Experiment Video
Updated: Mar 16, 2026
Resonance Fluorescence of an InGaAs Quantum Dot in a Planar Cavity Using Orthogonal Excitation and Detection
Published on: October 13, 2017
Energies and densities of electrons confined in elliptical and ellipsoidal quantum dots
Avik Halder1,2, Vitaly V Kresin2
1Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439, USA.
Abstract:
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. The 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). An interesting feature is that the eccentricity of the electron droplet is not the same as that of its confining potential well.
Related Concept Videos
02:45The Quantum-Mechanical Model of an Atom
03:21The Energies of Atomic Orbitals
02:43Quantum Numbers
02:28Electronic Structure of Atoms
An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum...
01:09Electron Behavior
Electrons Orbit the Nucleus
Electrons are found in specific locations outside of the nucleus. The shell in which an electron resides indicates the general energy level of the electron: those closer to the nucleus have less energy,...
00:54Electron Behavior
Electrons are negatively charged subatomic particles that are attracted to an orbit around the positively-charged nucleus of an atom. They reside in locations that are associated with energy levels called shells and are further organized into sub-shells and orbitals within each shell.
Electrons Orbit the Nucleus
Electrons are found in specific locations outside of the nucleus. The shell in which an electron resides indicates the general energy level of the electron: those closer to the...