Spheroidal Quantum Dots Research Articles

The electronic properties of a single electron in the GaAs/Ga1−xAlxAs oblate spheroidal quantum dot under the finite confinement potential

Quantum Dots, due to their fully quantized electronic states, have contributed to considerable progress in modern science and technology. Here we calculate the wave functions and energy spectrum of an electron confined in an oblate spheroidal quantum dot under the finite barrier potential condition, allowing the tailoring of the various energy states for specific applications. By calculating the electron wave functions outside the dot, we found that an infinite barrier is not a valid approximation for analyzing the optical properties of the structure. The effect of various geometrical and electrical characteristics of the structure, including the eccentricity, effective volume, and the height of barrier potential, is investigated. Additionally, the findings are compared with those found with prolate spheroidal quantum dot. The findings are further validated by comparing them to the exact electron energy level in a spherical quantum under the infinite barrier approximation.

Stationary States of an Electron in a Prolate Spheroidal Quantum Dot

Stationary States of an Electron in a Prolate Spheroidal Quantum Dot

Simultaneous effect of the capped matrix and the geometric factors of CdS/ZnSe spheroidal quantum dots on the linear and nonlinear optical properties

Simultaneous effect of the capped matrix and the geometric factors of CdS/ZnSe spheroidal quantum dots on the linear and nonlinear optical properties

Prolate spheroidal quantum dot: Effect of dot size and eccentricity on confined energy states

We have explored the energy states of an electron trapped in a prolate spheroidal shape CdSe quantum dot (QD) within a finite barrier height, utilizing the Schrodinger equation in a prolate spheroidal coordinate system. The calculation of various eigen energy states have been performed as a function of the QD volume and spheroid eccentricity. Our findings demonstrate that with the increase in both the QD’s volume and the eccentricity, the confinement energy decreases. Furthermore, we discovered that for any given l value, the energy of states corresponding to higher and lower sublevels (m) decreases with an increase in eccentricity. However, the decrease in energy of sublevels with increasing eccentricity varied for different m values. Additionally, a comparison of the energy states of a confined electron in prolate spheroidal and spherical quantum dots revealed that they are located at different positions.

Spheroidal Cesium Lead Chloride-Bromide Quantum Dots and a Fast Determination of Their Size and Halide Content.

Lead halide perovskite (LHP) quantum dots (QDs), with their bright and narrow emission, are promising candidates for LEDs, lasers, and quantum light sources. However, current methods to synthesize monodisperse CsPb(Cl:Br)3 and CsPbCl3 QDs exhibiting multiple sharp absorption resonances are not as well developed compared to CsPbBr3. Furthermore, both quantum confinement and the halide ratio in CsPb(Cl:Br)3 QDs strongly influence the bandgap, making it impossible to optically determine their size. In this work, monodisperse spheroidal CsPb(Cl:Br)3 QDs are synthesized in the 4-10 nm range, at any Cl:Br ratio, with up to five excitonic absorption transitions. Furthermore, in situ spectroscopy was used to cross-correlate the size and composition of these QDs directly to the energy of the first two excitonic absorption transitions. This work therefore provides not only a method for monodisperse CsPb(Cl:Br)3 QDs but also a protocol to determine their size, concentration, and halide ratio, circumventing conventional expensive and time-consuming techniques.

Numerical modeling for computation of confined energy states in oblate spheroidal quantum dots: effect of dot size, eccentricity and surrounding matrix

Numerical modeling for computation of confined energy states in oblate spheroidal quantum dots: effect of dot size, eccentricity and surrounding matrix

Synthesis of Colloidal Quantum Dots with an Ultranarrow Photoluminescence Peak

Localization of exciton wavefunctions away from the inorganic–organic interface is proposed for synthesizing colloidal spheroidal quantum dots (QDs) with an ultranarrow photoluminescence (PL) peak ...

The energy states of an electron in a spheroidal quantum dot with finite barrier

Abstract The problem of finding an electron wave function and energy spectrum in the prolate spheroidal quantum dot under the finite barrier potential is solved. Furthermore, the electron energy spectrum in the core-shell configuration is investigated. The dependence of the electron energy states on the eccentricity, size of quantum dot, barrier potential, and the shell thickness is studied. The results reveal that the energy of levels with lower m and n values decrease with the increase of eccentricity. This behavior is reversed for higher values of m. Also, for higher n levels, by increasing the eccentricity the energy of levels initially decreases and then increases. It is also observed that the ground and excited states energies increase with increasing the height of barrier potential, and with decreasing the size of the quantum dot. Furthermore, the obtained results for the low eccentricities near zero and for the high barrier potential match with those reported for spherical quantum dot and infinite barrier potential case, respectively. Moreover, in the case of core-shell configuration, the results denote that with increasing the shell thickness, the ground and excited states energies decrease.

Excitons and Biexcitons in Spheroidal Quantum Dots A2B6

In the limit of strong quantum confinement the lower energy states of excitons and biexcitons in spheroidal quantum dots of semiconductors with a fourfold degenerate vertex of the valence band, which are active in the dipole approximation at one- and two-photon excitation, have been considered. The comparative analysis of the order of energy levels of the hole in the potentials of the infinitely deep quantum well and a three-dimensional harmonic oscillator taking into account the axial anisotropy of the quantum dot (QD) shape is carried out. It is shown that the anisotropy of the QD shape can lead to the opposite sign of splitting with respect to angular momentum projection ±3/2, ±1/2 for spatially odd (1P3/2) and even (1S3/2) levels of the hole. At the same time, in the case of the potential of an infinitely deep quantum well, an inversion of the order of 1S3/2 and 1P3/2 levels can be observed at values of the ratio of the effective masses of the light and heavy holes β = mlh/mhh ≈ 0.14. The type of the trial wave functions of the hole for the state 1P3/2 in the potential of an isotropic three-dimensional harmonic oscillator depending on β is proposed. The dependence of the binding energy of excitons in the considered potentials on β is presented and the possibility of formation of various biexcitonic states is considered.

Excitonic binding energy in prolate and oblate spheroidal quantum dots

Excitonic energy is theoretically investigated in a spheroidal quantum dot as a function of an ellipticity parameter χ defined as the semi-axes ratio. The total energy is determined through the variational method using a trial wave function build from exact electron and hole spheroidal functions. For a fixed volume of the dot, it is shown that the total energy varies considerably against the parameter χ in contrast with the binding energy which is weakly dependent on the ellipticity.

Экситоны и биэкситоны в сфероидальных квантовых точках А-=SUB=-2-=/SUB=-B-=SUB=-6-=/SUB=-

AbstractIn the limit of strong quantum confinement the lower energy states of excitons and biexcitons in spheroidal quantum dots of semiconductors with a fourfold degenerate vertex of the valence band, which are active in the dipole approximation at one- and two-photon excitation, have been considered. The comparative analysis of the order of energy levels of the hole in the potentials of the infinitely deep quantum well and a three-dimensional harmonic oscillator taking into account the axial anisotropy of the quantum dot (QD) shape is carried out. It is shown that the anisotropy of the QD shape can lead to the opposite sign of splitting with respect to angular momentum projection ±3/2, ±1/2 for spatially odd (1 P _3/2) and even (1 S _3/2) levels of the hole. At the same time, in the case of the potential of an infinitely deep quantum well, an inversion of the order of 1 S _3/2 and 1 P _3/2 levels can be observed at values of the ratio of the effective masses of the light and heavy holes β = m _lh/ m _hh ≈ 0.14. The type of the trial wave functions of the hole for the state 1 P _3/2 in the potential of an isotropic three-dimensional harmonic oscillator depending on β is proposed. The dependence of the binding energy of excitons in the considered potentials on β is presented and the possibility of formation of various biexcitonic states is considered.

Resonance energy transfer in a dense array of II–VI quantum dots

Forster resonance energy transfer in inhomogeneous dense arrays of epitaxial CdSe/ZnSe quantum dots is demonstrated by time- and space-resolved photoluminescence spectroscopy. The specific feature of this process is the dipole–dipole interaction between the ground exciton levels of small quantum dots and the excited levels of large dots. This interaction brings efficient energy collection and spectral selection of a limited number of emitters. Results of theoretical modeling of optical transitions in spheroidal quantum dots with a Gaussian potential profile agree with the observed features of optical spectra induced by the change of the dominant energy transfer mechanism.

Quantum model of the prolate spheroidal Thomson hydrogen atom

In a uniformly charged prolate spheroidal Thomson hydrogen atom the electron states have been investigated. It has been shown from the mathematical point of view that the problem is equivalent to a spheroidal hydrogen atom in a parabolic potential with the cylindrical symmetry. In the framework of adiabatic approximation, the energy of ground state has been calculated. Comparison with the case of uncharged spheroidal quantum dot has been made, and the analytical form of wave function of electron has been also obtained.

Prolate spheroidal quantum dot: Electronic states, direct interband light absorption and electron dipole moment

Excitonic states and direct interband light absorption are considered in prolate spheroidal quantum dot. The problem of finding the one electron wave function and energy spectrum have been solved exactly. Three regimes of size quantization have been considered. Absorption edge dependence on the small semiaxes of the spheroid has been obtained. The probability of the direct interband transitions has been calculated and the selection rules for quantum numbers have been obtained. It has been shown that in prolate spheroidal quantum dot the exact value of the electron ground state with high accuracy coincides with the value of ground state in strongly prolate ellipsoidal quantum dot obtained in the framework of the adiabatic approximation. The dependence of z component of the electron dipole moment has been studied on the small semiaxes of the prolate spheroidal quantum dot.

Oblate spheroidal quantum dot: electronic states, direct interband light absorption and pressure dependence

Exitonic states and direct interband light absorption are considered in an oblate spheroidal quantum dot. The problem of finding the one electron wave function and energy spectrum has been exactly solved. Three regimes of size quantization have been considered. Absorption edge dependence on the small semiaxes of the spheroid and its hydrostatic pressure dependencies have been obtained. It has been shown that the exact value of the electron ground state in the oblate spheroidal quantum dot coincides with high accuracy to the value of ground state in strongly oblate ellipsoidal quantum dot obtained in the framework of the adiabatic approximation. The dependences of the electron ground state energy on the hydrostatic pressure and temperature have been studied.

Erratum to: “Methods for calculating X-ray diffuse scattering from a crystalline medium with spheroidal quantum dots”

Erratum to: “Methods for calculating X-ray diffuse scattering from a crystalline medium with spheroidal quantum dots”

Methods for calculating X-ray diffuse scattering from a crystalline medium with spheroidal quantum dots

Two independent approaches to calculate the angular distribution of X-ray diffusion scattering from a crystalline medium with spheroidal quantum dots (QDs) have been proposed. The first method is based on the analytical solution involving the multipole expansion of elastic strain fields beyond QDs. The second approach is based on calculations of atomic displacements near QDs by the Green’s function method. An analysis of the diffuse scattering intensity distribution in the reciprocal space within these two approaches shows that both methods yield similar results for the chosen models of QD spatial distribution.

Analytical and numerical calculations of spectral and optical characteristics of spheroidal quantum dots

In the effective mass approximation for electronic (hole) states of a spheroidal quantum dot with and without external fields the perturbation theory schemes are constructed in the framework of the Kantorovich and adiabatic methods. The eigenvalues and eigenfunctions of the problem, obtained in both analytical and numerical forms, were applied for the analysis of spectral and optical characteristics of spheroidal quantum dots in homogeneous electric fields.

Analytical and Numerical Calculations of Spectral and Optical Characteristics of Spheroidal Quantum Dots

Analytical and Numerical Calculations of Spectral and Optical Characteristics of Spheroidal Quantum Dots

Spectral and optical characteristics of spheroidal quantum dots

In the framework of effective mass approximation and in strong size quantization regime the absorption coefficients for ensembles of spheroidal quantum dots (SQDs) are analyzed using the eigenvalues and eigenfunctions, calculated by means of Kantorovich and adiabatic methods. The comparison of absorption coefficients for oblate and prolate SQDs with parabolic and non-parabolic dispersion laws reveals different behavior depending on the aspect ratio (ratio of minor to major semiaxis) and the external homogeneous electric fields. The possibility of verification of the considered models is discussed.