Electronic states in quantum dots with ellipsoidal symmetry

Dvoyan, K. G.; Kazaryan, É. M.; Petrosyan, L.

doi:10.1016/j.physe.2005.03.021

Cited by 64 publications

(19 citation statements)

References 13 publications

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“…In the theoretical works, it is customary to assume a spherical shape for the Quantum Dot (QD). Since deformation of spherical shape during QD growth is unavoidable, QD with an ellipsoidal shape represents a better approach to the actual problems [8][9][10]. In most of the investigations the dot is held at infinitely large potential and the emphasis is put upon the dependence of physical properties of the enclosed particles on the ellipticity.…”

Section: Introductionmentioning

confidence: 99%

“…The effects of finite barrier confinement potential on the electronic structures of SQD have been investigated [11,12], but except the work reported by Dvoyan [9], almost all the research on EQD have been performed with infinite confinement potential. Studies of the hydrogenic impurity states in various confined systems, such as Quantum Wells [13,14], Quantum Well Wires [15,16] and QD's [17][18][19], initiated by Bastard [20,21], have also become subjects of vast investigations in the last decade.…”

Section: Introductionmentioning

confidence: 99%

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Binding energy of a hydrogenic donor impurity in an ellipsoidal finite‐potential quantum dot

Barati

Rezaei

Vahdani

2007

Physica Status Solidi (b)

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In this article, the binding energy of a hydrogenic donor impurity in weakly oblate Ellipsoidal Quantum Dot (EQD), using the perturbation theory within the framework of effective mass approximation, is investigated. In this regard, the binding energies of 1S, 2S and 2P 0 states for GaAs/Al x Ga 1-x As structures, as functions of the dot radius and ellipticity constant, are calculated. Results show that variations of binding energies of a hydrogenic impurity with respect to the dot dimension are similar to the case of Spherical Quantum Dot (SQD). In addition, it is found that the binding energy is inversely proportional to the ellipticity constant. This behavior is more profound for 2P 0 state, where, depending on the dot's dimensionality and ellipticity, the binding energy may become negative.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Binding energy of a hydrogenic donor impurity in an ellipsoidal finite‐potential quantum dot

Barati

Rezaei

Vahdani

2007

Physica Status Solidi (b)

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“…In all simulations, the imposed upper limit of n is set to N = 100. Unless otherwise specified, all analytical results and illustrative plots are based on the calculation of the self-polarization energies of 1000 unit charges (in atomic unit) uniformly distributed (in terms of the ξ-dependent distance) along the line segment OP with two endpoints O = (0, 0, 0) and P = (26,24,18). Furthermore, when the numerical solution is involved, the number of sublayers used to discretize the transition layer is set to L = 1000.…”

Section: Illustrative Numerical Experimentsmentioning

confidence: 99%

“…This extension may be needed since, for example, realistic quantum dots might be neither perfect spheres nor perfect spheroids, while it has been shown that a small change in the external shape of a QD may strongly influence the energy spectrum and other characteristics of such a semi-conductor structure [21][22][23][24]. On the other hand, in the hybrid solvation models for bio-molecular simulations, for non-spherical or non-spheroidal bio-macromolecules, from computational point of view, it may be more beneficial to adopt ellipsoidal cavities that can conform closely to the irregular shapes of the bio-molecules.…”

Section: Introductionmentioning

confidence: 99%

Three-layer dielectric models for generalized Coulomb potential calculation in ellipsoidal geometry

Xue

Deng

2011

Phys. Rev. E

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This paper concerns a basic electrostatic problem: How to calculate generalized Coulomb and self-polarization potentials in heterogeneous dielectric media. In particular, with simulations of ellipsoidal semi-conductor quantum dots and elongated bio-macromolecules being its target applications, this paper extends the so-called three-layer dielectric models for generalized Coulomb and self-polarization potential calculation from the spherical and the spheroidal geometries to the tri-axial ellipsoidal geometry. Compared to the simple step-like dielectric model, these threelayer dielectric models can overcome the mathematical divergence in the self-polarization energy by employing continuous radial dielectric functions. More specifically, in this paper, the novel quasi-harmonic three-layer dielectric model for the ellipsoidal geometry is first discussed, and the explicit analytical series solutions of the corresponding electrostatic problem are obtained in terms of the ellipsoidal harmonics. Then, a robust numerical procedure working for general three-layer dielectric models is developed. The key component of the numerical method is to subdivide the transition layer of the underlying three-layer model into multiple sublayers, and then in each one of them approximate the select dielectric function of the transition layer by one of the quasi-harmonic functional form rather than simply by a constant value as one would normally do. As the result, the numerical method has no numerical divergence.

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“…Optical properties of spheroidal QDs have been studied in 11,12,13,14 . Recently the liquid phase epitaxy technique is used to create ellipsoidal QDs 15,16 .…”

Section: Introductionmentioning

confidence: 99%

Magneto-Absorption in Ellipsoidal Quantum Dot

Dvoyan

Evoyan

Kazaryan

et al. 2012

Int. J. Mod. Phys. Conf. Ser.

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The absorption of light in ellipsoidal quantum dot in the presence of a magnetic field is discussed using perturbation theory. Also the same problem is discussed using the normal modes. Quantum dot absorption coefficient is calculated -as well as threshold frequency of absorption -as a function of applied magnetic field. Theoretical results are compared with experimental data obtained by magneto-luminescence method in In 0.53 Ga 0.47 As quantum dot (M.

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Electronic states in quantum dots with ellipsoidal symmetry

Cited by 64 publications

References 13 publications

Binding energy of a hydrogenic donor impurity in an ellipsoidal finite‐potential quantum dot

Binding energy of a hydrogenic donor impurity in an ellipsoidal finite‐potential quantum dot

Three-layer dielectric models for generalized Coulomb potential calculation in ellipsoidal geometry

Magneto-Absorption in Ellipsoidal Quantum Dot

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