Spheroidal Quantum Dots Research Articles

Adiabatic description of nonspherical quantum dot models

Within the effective mass approximation an adiabatic description of spheroidal and dumbbell quantum dot models in the regime of strong dimensional quantization is presented using the expansion of the wave function in appropriate sets of single-parameter basis functions. The comparison is given and the peculiarities are considered for spectral and optical characteristics of the models with axially symmetric confining potentials depending on their geometric size making use of the total sets of exact and adiabatic quantum numbers in appropriate analytic approximations.

The effect of confining electric potentials on binding energies in a spheroidal quantum dot

Calculations of binding energies due to a hydrogenic impurity located at the centre of a spheroidal quantum dot are presented. The effects of the radius of the quantum dot and of spatially variant electric potential confinement have also been investigated. The shifted parabolic potential and the inverse lateral shifted parabolic potential are compared with the well studied parabolic potential. While the parabolic potential and inverse lateral shifted parabolic potential enhance the binding energy, the shifted parabolic potential attenuates it.

Numerical calculation of electronic states in ellipsoidal finite-potential quantum dots with an off-centered impurity

In this article, the computational procedure to calculate wave-functions and energies of spherical quantum dots with finite barriers and a shallow donor impurity located anywhere inside is extended to prolate spheroidal quantum dots. As in the spherical case, the extension of the procedure fully takes into account polarization effects originating from the dielectric mismatch at the dot surface. Particular attentions are paid to the calculations of self-polarization potential energy so as to overcome the mathematical divergence in the self energy when the sharp step-like dielectric interface is assumed between the dot and the surrounding matrix. In this regard, the so-called three-layer dielectric models, including the novel quasi-harmonic dielectric model, are employed. The procedure is implemented to calculate energy states of a prolate spheroidal quantum dot with a hydrogenic donor impurity located at the polar axis of the dot, held at a finite confining potential. The resulting code is then employed to carry out an illustrative study on the effects of the dielectric mismatch, the impurity location, and the choice of dielectric models to the electronic energy in the dot.

The influence of shape and potential barrier on confinement energy levels in quantum dots

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/SiO2 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.

Energy levels in spheroidal quantum dots with finite barrier heights

The effect of non-sphericity of the quantum dot on the eigenvalues and eigenfunctions hasbeen investigated for the case when the barrier height at the surface is finite. The groundand excited state energies have been calculated variationally for prolate and oblatespheroids as a function of eccentricity of the spheroid. Analytic wavefunctions giving theadmixture of higher angular momentum states have been obtained as a function ofeccentricity.

Polar optical phonons in wurtzite spheroidal quantum dots: theory and application to ZnOand ZnO/MgZnO nanostructures

Polar optical-phonon modes are derived analytically for spheroidal quantum dots withwurtzite crystal structure. The developed theory is applied to freestanding spheroidal ZnOquantum dots and to spheroidal ZnO quantum dots embedded into a MgZnO crystal. Thewurtzite (anisotropic) quantum dots are shown to have strongly different polaroptical-phonon modes in comparison with zincblende (isotropic) quantum dots. Theobtained results allow one to explain and accurately predict phonon peaks in the Ramanspectra of wurtzite nanocrystals, nanorods (prolate spheroids), and epitaxial quantum dots(oblate spheroids).

Optical phonons and resonant Raman scattering in II–VI spheroidal quantum dots

AbstractFirst order and multiphonon resonant Raman scattering processes from confined and interface polar optical phonons in II–VI nanocrystallites are analyzed. Fröhlich interaction between excitons and optical phonons has been considered and general selection rules for the exciton–phonon matrix elements of the scattering processes in the case of spheroidal quantum dots are given. A comparison is made between the Raman selection rules and non‐linear hyper‐Raman selection rules for spherical dots. It is shown that the relative intensities between phonon overtones in II–VI spherical quantum dots can be correctly described in the framework of excitonic model and the optical polar vibrational continuum model satisfying both the mechanical and electrostatic matching conditions at the interface. Detailed discussions of the surface optical phonons are provided in the case of a spherical Quantum‐Dot/Quantum‐Well (QD/QW) heterostructure. Their frequency dependence on the geometry, material parameters, as well as the electron–phonon interaction Hamiltonian are also reported. In addition, the interface optical phonons and the corresponding electron–phonon interaction in nanostructures with prolate and oblate spheroidal geometries and their contribution to the first order scattering process have been studied. This surface‐optical phonon modes are strongly dependent on the nanocrystal geometry and new Raman selection rules are obtained given a plausible explanation for the observed low frequency shoulders present in the spectrum of several II–VI semiconductor nanostructures. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Polar surface vibration strips on GaN/AlN quantum dots and their interaction with confined electrons

The conditions are found for the existence of polar surface vibrational modes on a spheroidal quantum dot. These conditions determine allowed windows in the frequency-surface coordinate plane. The modes found are either truly localized of leaky states. The latter can provide effective energy relaxation of the confined electrons.

Anisotropy effects on the orbital magnetism of electrons in a spheroidal quantum dot

Anisotropy effects in the orbital magnetic susceptibility of electrons in a spheroidal quantum dot are investigated by applying tilted magnetic field with parabolic confinement potential. The results show dramatic phase change; magnetic susceptibility as a function of the electron concentration changes from para- or diamagnetic in the case of anisotropic quantum dot to diamagnetic only in the isotropic case. Temperature, field and tilted angle dependences are also extensively studied.

Electronic structure of quantum dots with two electrons in tilted magnetic fields

The energy levels of a spheroidal quantum dot in tilted magnetic fields are calculated and compared with those for a disk-like dot. The magneto-optical spectrum and the ground state show considerable difference between the two quantum dots. We find that this feature can be understood by considering the magneto-electric hybridization and electron-electron interaction effects on the energy spectrum.