Few-electron semiconductor quantum dots with Gaussian confinement (original) (raw)
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Electronic structure and electron correlation in weakly confining spherical quantum dot potentials
2008
The electronic structure and electron correlations in weakly confining spherical quantum dots potentials are investigated. Following a common practice, the investigation starts with the restricted Hartree-Fock (HF) approximation. Then electron correlation is added in steps in a series of approximations based on the single particle Green's function approach: (i) Second-order Green function (GF) (ii) 2ph-Tamm-Dancoff approximation (TDA) and (iii) an extended version thereof (XTDA) which introduces ground-state correlation into the TDA. The study includes as well Hartree-Fock V (N-1) potential approximation in which framework the Hartree-Fock virtual orbitals are calculated in the field of the N-1 electrons as opposed to the regular but unphysical N-electron field Hartree-Fock calculation of virtual orbitals. For contrast and comparison, the same approximation techniques are applied to few-electron closed-shell atoms and few-electron negative ions for which pertinent data is readily available. The results for the weakly confining spherical quantum dot potentials and the standard atomic systems exhibit fundamental similarities as well as significant differences. For the most part the results of these calculations are in favor of application of HF, GF, and TDA techniques in the modeling of three-dimensional weakly confining quantum dot potentials. The observed differences emphasize the significance of confinement and electronic features unique to quantum dots such as the increased binding of electrons with higher angular momentum and the modified shell filling sequences.
Journal of the Korean Physical Society, 2018
In this work, the ground-state properties of an interacting electron gas confined in a twodimensional quantum dot system with the Gaussian potential υ(r) = V0(1 − exp(−r 2 /p)), where V0 and p are confinement parameters, are determined numerically by using the Thomas-Fermi approximation. The shape of the potential is modified by changing the V0 and the p values, and the influence of the confining potential on the system's properties, such as the chemical energy, the density profile, the kinetic energy, the confining energy, etc., is analyzed for both the non-interacting and the interacting cases. The results are compared with those calculated for a harmonic potential, and excellent agreement is obtained in the limit of high p values for both the non-interacting and the interacting cases.
Electronic structure of one electron confined in three-dimensional quantum dots
Physica B-condensed Matter, 2017
We study the electronic structure of three-dimensional quantum dots with one electron using the canonical formalism. The confining potential is assumed to be spatially isotropic and harmonic. For one electron the energy spectrum, heat capacity and Helmholtz free energy are calculated as a function of temperature and confinement strength. We find that the internal energy for one-electron artificial atoms and the heat capacity are nearly independent of confinement frequency at high temperatures, while at low temperatures the energy-level structure and heat capacity are shown to be strongly dependent on the confinement strength. In addition, the heat capacity decreases less rapidly with increasing confinement frequency at appropriate temperatures and energy levels are almost linear. Also, the Helmholtz-free energy is obtained to test the confinement and stability of the system.
ELECTRONIC STATES OF QUANTUM DOTS
The self-assembled quantum dots are grown on wetting layers and frequently in an array-like-assembly of many similar but not exactly equal dots. Nevertheless, most simulations disregard these structural conditions and restrict themself to simulating of a pure single quantum dot. Moreover, many simulations settle for the linear model with constant instead of the rational eective mass. In this work we argue that the nonlinear model is necessary to correctly capture the interesting part of the spectrum. We advocate the eective one electronic band Hamiltonian with the energy and position dependent eective mass approximation and a finite height hard-wall 3D confinement potential for computation of the energy levels of the electrons in the conduction band. Within this model we investigate the geometrical eects mentioned above on the electronic structure of a pyramidal InAs quantum dot embedded in a GaAs matrix. We find that the presence of a wetting layer may aect the electronic structure...
The influence of shape and potential barrier on confinement energy levels in quantum dots
Journal of Applied Physics, 2010
The influence of the shape of silicon quantum dots embedded in an amorphous silica matrix on the quantum confinement energy levels, as well as that of the Si/ SiO 2 potential barrier, are studied. The energy levels are computed using both the infinite and finite rectangular quantum well models for spherical quantum dots and the infinite rectangular quantum well for prolate spheroidal quantum dots. The results are compared with each other and also with the experimental activation energies obtained from the temperature dependence of the dark current. These activation energies are identified with the differences between the quantum confinement energies, subject to the selection rules. The finite rectangular quantum well model takes into account the experimental value of the finite potential barrier and the matrix-to-dot electron mass ratio. The energy levels are smaller than those for the infinite rectangular quantum well case; they decrease when the potential barrier decreases and the mass ratio increases. Different aspects of the models are discussed. All the errors are less than about 4%. The spheroidal shape lifts the degeneracy on the magnetic quantum number. The energy levels can decrease or increase with eccentricity as a consequence of the different quantum confinement effects along the major and minor axes. The supplementary information on the magnetic quantum number is beneficial for optical applications.
Journal of Physics: Condensed Matter, 2007
The problem of two electrons in a three-dimensional quantum dot with Gaussian confinement is investigated for the singlet pairing by a variational method with a very simple wavefunction containing only a single parameter and a Jastrow-like factor, which is shown to yield fairly good results for deep confining potentials. The calculation is also performed for a few realistic semiconductor quantum dots and the phase diagrams for the two-electron singlet states are obtained for these materials. The pair density function is calculated for several parameter values and its peak positions are obtained as a function of the confinement length and the depth of the potential to study the behaviour of the electron-pair size. The size of the bound pair of electrons is also obtained by directly calculating the average distance between the two electrons in three different ways and compared with the pair correlation results. It is furthermore shown that, other properties remaining the same, the two-electron energy and the electron-pair size depend crucially on the effective electronic mass and the dielectric constant of the material. Finally, the ways of improving the wavefunction are also indicated.
Correlation studies in weakly confining quantum dot potentials
International Journal of Quantum Chemistry, 2008
We investigate the electron correlation in few-electron closed-shell atomic systems and similarly in few-electron quantum dots under weak confinement. As usual we start with restricted Hartree-Fock (HF) calculations and add electron correlation in steps in a series of approximations based on the single particle Green's function approach: (i) second-order Green function (GF); (ii) 2ph-Tamm-Dancoff approximation (TDA); and (iii) an extended version thereof which introduces groundstate correlation into the TDA. Our studies exhibit similarities and differences between weakly confined quantum dots and standard atomic systems. The calculations support the application of HF, GF, and TDA techniques in the modeling of three-dimensional quantum dot systems. The observed differences emphasize the significance of confinement and electronic features unique to quantum dots, such as the increased binding of electrons with higher angular momentum and thus-compared to atomic systems-modified shell-filling sequences.
Near-threshold properties of the electronic density of layered quantum dots
Physical Review B, 2012
We present a way to manipulate an electron trapped in a layered quantum dot based on nearthreshold properties of one-body potentials. We show that potentials with a simple global parameter allows the manipulation of the wave function changing its spatial extent. This phenomenon seems to be fairly general and could be implemented using current quantum-dot quantum wells technologies and materials if a proper layered quantum dot is designed. The layered quantum dot under consideration is similar to a quantum-dot quantum well device, i.e consists of a spherical core surrounded by successive layers of different materials. The number of layers and the constituent material are chosen to highlight the near-threshold properties.
Simulation of quantum dots (QDs) in the confinement regime
International Journal of Applied Science and Engineering Research, 2012
The ground state confinement energy and its associated wavelength as a function of radius for three different semiconductor quantum dots (QDs) were calculated using the Brus equation. The experimental observation of the size dependence on the band gap energy is in good agreement with the theoretical models for the semiconductor nanocrystals considered. The confinement of electrons in semiconductor quantum dots increases dramatically with decrease in its size (radius) and shows exponential dependence on wavelength of light emitted.
Two-Electron Resonances in Quasi-One Dimensional Quantum Dots with Gaussian Confinement
International Journal of Theoretical Physics, 2015
We consider a quasi one-dimensional quantum dot composed of two Coulombically interacting electrons confined in a Gaussian trap. Apart from bound states, the system exhibits resonances that are related to the autoionization process. Employing the complex-coordinate rotation method, we determine the resonance widths and energies and discuss their dependence on the longitudinal confinement potential and the lateral radius of the quantum dot. The stability properties of the system are discussed.