Ellipsoidal Quantum Dot Research Articles

Biexciton in Prolate Ellipsoidal Quantum Dot: Optical-Magnetic Properties

In this study, we present a theoretical framework for assessing the ground state energy of a biexciton within an ellipsoidal quantum dot subjected to an external magnetic field. Our method involves employing the variational method and the geometrical adiabatic approximation. We calculate the biexciton energy and binding energy, considering their dependence on the magnetic field strength and the small geometrical parameter of the ellipsoidal quantum dot. Our findings reveal an increase in magnetobiexciton energy with the strength of the magnetic field. Additionally, we analyze the biexciton’s magnetization concerning the external magnetic field and the small semiaxis of the ellipsoidal quantum dot. Moreover, we provide an estimation of the magnetobiexciton recombination radiative lifetime in the ellipsoidal quantum dot, which falls within the nanosecond range.

Electron-donor-impurity polarizability in a semiconductor nanostructure under electric field: Geometrical effects in ellipsoidal quantum dots

The features of electron-impurity polarizability in a quantum nanostructure are investigated from the knowledge of allowed electron states coupled to a shallow-donor impurity. The influence of geometry on the carrier confinement and the presence of external probes such as electric fields are explicitly considered. For the sake of illustration, the example of CdS/ZnSe-based prolate ellipsoidal core/shell quantum dot (PECSQD) configuration is chosen. This problem allows to consider a finite confinement potential model, employing both the finite element method and the effective mass approximation. Within this framework, impurity-related energies and associated polarizability for the lowest states were determined as functions of the shell thickness, core dimensions, impurity position, and applied electric field strength - while keeping the shell dimensions fixed. Electron-impurity energies are largely affected by electric field values. Under thinner shell conditions, polarizability shows variations with field strength that include “anomalous” negative values for certain states. Then, the increase in shell thickness causes a significant increment in the polarizabilities, regardless impurity position.

The third-order nonlinear optical susceptibility in an ellipsoidal core-shell quantum dot embedded in various dielectric surrounding matrices

The third-order nonlinear optical susceptibility in an ellipsoidal core-shell quantum dot embedded in various dielectric surrounding matrices

The influence of the electric and magnetic fields on donor impurity electronic states and optical absorption coefficients in a core/shell GaAs/Al$$_{0.33}$$Ga$$_{0.67}$$As ellipsoidal quantum dot

The influence of the electric and magnetic fields on donor impurity electronic states and optical absorption coefficients in a core/shell GaAs/Al$$_{0.33}$$Ga$$_{0.67}$$As ellipsoidal quantum dot

Impact of intense laser Bessel beam on excitonic complexes in ellipsoidal quantum dot

This theoretical study investigates the response of a strongly oblate GaAs ellipsoidal quantum dot to an intense laser field with a Bessel intensity profile at non-resonant extreme violet and simultaneously resonant mid-infrared laser irradiation. Mainly, the linear and nonlinear optical properties of biexcitons in quantum dot are observed. Due to the complexity of the considered particle, all calculations are performed in the framework of the variational method. Biexciton variational function is constructed on the one-particle wave functions, which are correlated with each other by exponents with variational parameters. The biexciton energies for different values of applied intense laser field magnitude on the small geometrical parameter of ellipsoidal quantum dot are calculated. The nonlinear optical properties, including the oscillator strength, third-order nonlinear susceptibility, absorption coefficient, and refractive index change, are evaluated. Numerical results reveal the dependence of the exciton and biexciton energies on the intensity of the laser field and the geometrical parameters of the quantum dot. Additionally, the dependencies of the third-order susceptibility, absorption coefficient, and induced refractive index change on photon energy near the one-photon resonance and two-photon resonance are analyzed. The two-photon absorption coefficient of the biexciton in GaAs ellipsoidal quantum dot is computed, and the spectra of refractive index changes induced by biexciton transitions between ground states are analyzed for different magnitudes of the intense laser field. Biexciton recombination radiative lifetime on the small semiaxis of the ellipsoidal quantum dot for the different values of the laser field influence is estimated. Finally, the visualization of the localization region of biexciton in the ellipsoidal quantum dot is performed.

Relativistic correction of biexciton fine structure in ellipsoidal quantum dots

In the framework of the effective mass approximation the biexciton states have been investigated in the oblate and prolate ellipsoidal quantum dots. To calculate the ground state energy of the biexciton, three-parameters’ variational trial function was utilized. Based on the non-relativistic energy and wave function the lowest-order relativistic correction to the non-relativistic Hamiltonian have been calculated. The relativistic correction energy of the biexciton fine structure have been found to be the order 10−6meV. The relativistic correction approaches zero with increase of the quantum dot sizes. It has been also revealed that the relativistic correction of the biexciton fine structure increases with the increase of size quantization. As a result, the mentioned effect is more pronounced for the case of prolate ellipsoidal quantum dot in the comparison with oblate one.

Hydrogen-like donor impurity states in strongly prolate ellipsoidal quantum dot

In the current article, the binding energy and impurity-related photoionization cross-section are investigated for the case of an infinite confinement potential well model using a variational approach for hydrogen-like impurity states in strongly prolate ellipsoidal quantum dot. The binding energy is calculated as a function of ellipsoidal small and large semiaxes and as a function of impurity displacement. The behavior of the oscillator strength for the quantum transitions between the impurity ground state and the first two non-impurity states are considered for different values of incident light angles and geometrical parameters. In the work, we illustrate the results of photoionization cross-section computations depending on the incident photon energy for a range of incident angles and different values of impurity shift. It is revealed that the threshold frequency decreases with the increase of impurity displacement.

Impurity photo-ionization cross section and stark shift of ground and two low-lying excited electron-states in a core/shell ellipsoidal quantum dot

A new investigation on photo-ionization cross section (PICS) of a donor impurity confined in a GaAs/AlGaAs core/shell elliptic quantum dots (CSEQDs) has been performed under electric field (EF) effect. By means of the finite element method (FEM), we have computed the binding energy (BE), oscillator strength Pif and PICS within the framework of the effective mass theory (EMT). Our numerical results reveal that the stark shift is greatly dependent on the strength of the EF, the degree of ellipticity β, and the states of electronic transitions. It can take positive or negative values depending on the situation. In addition, the photo-ionization describing the transition from the donor impurity ground-state (1simp) to one of the conduction sub-band states (1s0, 2s0, and 2p0) is affected by the shape of the quantum dots (QDs) and the EF. We demonstrated that varying internal and external parameters may control the photo-ionization cross-section. These characteristics can be exploited to fabricate optoelectronic devices like QD infrared photodetectors.

Investigation of Biexciton Induced Linear and Nonlinear Refractive Index Changes in Ellipsoidal Quantum Dot

Investigation of Biexciton Induced Linear and Nonlinear Refractive Index Changes in Ellipsoidal Quantum Dot

Bandgap engineering of CdTe/CdSe rod-shaped core/shell and CdTeSe ellipsoidal alloy quantum dots with tunable and intense emission

In this work, core CdTe, core-shell CdTe/CdSe and alloy CdTeSe QDs are synthesized by aqueous solvent. TEM visually shows the rod-shaped core-shell structure with a transverse to longitudinal ratio of 6.5 and the ellipsoidal alloy structure with different crystal planes competing for growth. The XRD and Raman spectra of the three QDs illustrate the characteristics of the internal lattice structure. With the increase of reaction time, CdTe emission maximum (EM) shows a red shift of 84 nm. Stokes shift changes little, and full width half maximum (FWHM) increases slightly. Compared with the CdTe, the red shift of CdTe/CdSe EM is slowly first and then faster, with a total shift of 125 nm. Stokes shift increases obviously. The initial FWHM is larger than CdTe and the widening speed is gradually accelerated. The initial EM of CdTeSe is red shifted compared with CdTe, and the total red shift of EM is 72 nm. Stokes shift increases obviously. The initial FWHM is significantly wider than CdTe. FWHM first decreases and then increases with reaction time. CdTe shows obvious band edge exciton absorbance of photoluminescence excitation (PLE) spectrum between 356 nm and 400 nm. CdTe/CdSe shows double band edge exciton absorption at 354–373 nm and 401–436 nm due to wave function separated of core-shell structure. The PLE spectrum of CdTeSe shows an obvious upward trend at 306–373 nm due to high energy level nonradiation. The average lifetime of CdTe/CdSe increases by 53 ns compared with CdTe due to the spatially separated electrons and holes. The defect state of CdTeSe increases the proportion of fast delay, which is 2 ns shorter than the average lifetime of CdTe. The transition mechanism of core-shell indirect band gap and alloy direct band gap is explained according to the valence bands of each element shown by XPS and the simulation of energy band density of states. The thickness shell and the doping elements can be adjusted to provide rich variation in the optical properties. This provides a more definite direction for the applications of cadmium chalcogenide in the fields of photoelectric devices and biology. • Type I and type II transformation through Rod-shaped core/shell and ellipsoidal alloy QDs. • Tunable emission achieved by adjusting morphology, lattice structure and valence bond connection. • Precise and rich regulation of band gap engineering. • Providing a more definite direction for the applications of cadmium chalcogenide QDs.

Spontaneous Exciton Collapse in a Strongly Flattened Ellipsoidal InSb Quantum Dot

Electronic and excitonic states in an InSb strongly flattened ellipsoidal quantum dot (QD) with complicated dispersion law are theoretically investigated within the framework of the geometric adiabatic approximation in the strong, intermediate, and weak quantum confinement regimes. For the lower levels of the spectrum, the square root dependence of energy on QD sizes is revealed in the case of Kane’s dispersion law. The obtained results are compared to the case of a parabolic (standard) dispersion law of charge carriers. The possibility of the accidental exciton instability is revealed for the intermediate quantum confinement regime. For the weak quantum confinement regime, the motion of the exciton's center-of-gravity is quantized, which leads to the appearance of additional Coulomb-like sub-levels. It is revealed that in the case of the Kane dispersion law, the Coulomb levels shift into the depth of the forbidden band gap, moving away from the quantum confined level, whereas in the case of the parabolic dispersion law, the opposite picture is observed. The corresponding selection rules of quantum transitions for the interband absorption of light are obtained. New selection rules of quantum transitions between levels conditioned by 2D exciton center of mass vertical motion quantization in a QD are revealed. The absorption threshold behavior characteristics depending on the QDs geometrical sizes are also revealed.

Non-Linear Optical Properties of Biexciton in Ellipsoidal Quantum Dot.

We have presented a theoretical investigation of exciton and biexciton states for the ground and excited levels in a strongly oblate ellipsoidal quantum dot made from GaAs. The variational trial wave functions for the ground and excited states of the exciton and biexciton are constructed on the base of one-particle wave functions. The energies for the ground and excited levels, depending on the ellipsoidal quantum dot’s geometrical parameters, are depicted in the framework of the variational method. The oscillator strength of the transition from exciton to biexciton states for ground and excited levels is investigated as a function of the ellipsoidal quantum dot’s small and large semiaxes. The third-order optical susceptibilities of ground and excited biexcitons around one-photon and two-photon resonances are calculated as a function of the photon energy. The dependences of third-order optical susceptibilities for the ground and excited levels on the photon energy for different values of the ellipsoidal quantum dot’s semiaxis are revealed. The absorption coefficients in the ellipsoidal quantum dot, both for ground and excited states of exciton and biexciton, are calculated. The absorption coefficients for the ground level of exciton and biexciton for the fixed value of the large semiaxis and for the different values of the small semiaxis are determined. Finally, the two-photon absorption coefficient of the biexciton in the GaAs ellipsoidal quantum dot is computed.

Magnetobiexciton in strongly oblate ellipsoidal quantum dot

The theoretical investigation of biexciton in ellipsoidal quantum dot in the presence of the magnetic field is done in the framework of the variational method. The dependencies of the energy and the binding energy for the magnetobiexciton on the magnetic field are calculated. It is shown, that the magnetobiexciton energy increases with the increase of the magnetic field magnitude. The optical transition energy of the magnetobiexciton is calculated as a function of the magnetic field and the large semiaxis. The recombination energy, defined as a difference between the total energies of the initial and final states after recombination, is computed. The magnetization as a function of magnetic field and small semiaxis is calculated. Finally, the recombination radiative lifetime of the magnetobiexciton is estimated and shown that it is of the order of nanoseconds.

Binding and Recombination Energies of Quasi-One-Dimensional Excitonic Complexes in Ellipsoidal Quantum Dot

In the framework of the effective mass approximation, negative and positive trions, exciton, and biexciton states are investigated in strongly prolate ellipsoidal quantum dots by the variational method. Since the ellipsoidal quantum dot has a prolate character, all excitonic complexes are considered quasi-one-dimensional. As in such a system, the analytical solution does not exist for the many-particle problem, it is solved by the variational method. The trial variation functions based on the one-particle wave functions are used to construct the wavefunctions for the excitonic complexes. The energy spectrum, binding, and recombination energies dependent on the geometrical parameters of the ellipsoidal quantum dots are calculated for the excitons, negative and positive trions, and biexcitons. The radiative lifetime of exciton complexes in ellipsoid is estimated.

Quantum Beat of Excitons in the Prolate Ellipsoidal Quantum Dots

In this paper, renormalized wavefunction method was applied to study quantum beats of excitons in the InGaAs/InAlAs prolate ellipsoidal quantum dots (QDs). The obtained results show that, without the pump laser, the exciton absorption intensity is just a smooth curve. In contrast, when the system is illuminated by a strong pump laser resonating with two exciton levels, the oscillation behavior of exciton absorption intensity, which is known as quantum beats of excitons, is observed. That result can be interpreted as an indirect consequence of the Pauli exclusion principle leading to a splitting of the electron levels, which forms two close exciton levels, and if two excitons are excited coherently, the interference of these two excitons will finally form a quantum beat. The study also shows that the geometry shape of the QDs has strong influence on the properties of quantum beats. Changing the period of quantum beats in particular or optical properties in general in QDs thus becomes more flexible through changing their geometry shapes. This is one interested advantage of the ellipsoidal QDs and is expected to increase their applicability more than the spherical QDs.

Light hole states in a strained quantum dot: Numerical calculation and phenomenological models

Starting from the numerical solution of the 6-band \textbf{k.p} description of a lattice-mismatched ellipsoidal quantum dot situated inside a nanowire, including a spin Zeeman effect with values appropriate to a dilute magnetic semiconductor, we propose and test phenomenological models of the effect of the built-in strain on the heavy hole, light hole and exciton states. We test the validity and the limits of a description restricted to a ($\Gamma_8$) quadruplet of ground states and we demonstrate the role of the interactions of the light-hole state with light-hole excited states. We show that the built-in axial strain not only defines the character, heavy-hole or light-hole, of the ground state, but also mixes significantly the light-hole state with the split-off band's states: Even for a spin-orbit energy as large as 1 eV, that mixing induces first-order modifications of properties such as the spin value and anisotropy, the oscillator strength, and the electron-hole exchange, for which we extend the description to the light-hole exciton. CdTe/ZnTe quantum dots are mainly used as a test case but the concepts we discuss apply to many heterostructures, from mismatched II-VI and III-V quantum dots and nanowires, to III-V nanostructures submitted to an applied stress and to silicon nanodevices with even smaller residual strains.

On the Optical Stark Effect of Excitons in InGaAs Prolate Ellipsoidal Quantum Dots

In this paper, we study the exciton absorption spectra in InGaAs prolate ellipsoidal quantum dots when a strong pump laser resonant with electron quantized levels is active. Our obtained results by renormalized wavefunction theory show that, under suitable conditions, the initial exciton absorption peak is split into two new peaks as the evidence of the existence of the three-level optical Stark effect of excitons. We have suggested an explanation of the origin of the effect as well as investigating the effect of pump field energy, size, and geometric shape of the quantum dots on effect characteristics. The comparison with the results obtained in the spherical quantum dots implies the important role of geometric shape of the quantum structures when we examine this effect.

Theoretical Investigation of Different Types of Trion States in GaAs Ellipsoidal Quantum Dot

Using the variational method, various types of mixed two-dimensional coupled negative and positive trions in a GaAs strongly oblate ellipsoidal quantum dot in the intermediate quantization mode were investigated. The trial wave function for the positive and negative trions is constructed on the basis of a single-particle wave function obtained in the framework of the adiabatic approximation. The dependences of the binding energy of the trion states and of the recombination of all types of trions on the geometric parameters of an ellipsoidal quantum dot are obtained. The radiative lifetime of various types of positive and negative trions is estimated for the intermediate quantization mode.

Binding energies and photoionization cross-sections of donor and acceptor impurities in inverted core/shell ellipsoidal quantum dots: Effects of magnetic field, ellipsoid anisotropy and impurity position

Within the framework of the effective-mass approximation and by using a variational and perturbation approach, the binding energies and photoionization cross-sections of donor and acceptor impurities in an inverted core/shell ellipsoidal spherical quantum dot under an applied magnetic field have been studied. We have calculated the binding energies of both donor and acceptor impurities as a function of the core and shell sizes and shapes with different impurity positions under the applied magnetic field. In addition, the corresponding photoionization cross-section is calculated. Our results show that the binding energy of the acceptor impurity is larger than that of the donor impurity, and both of them with different impurity positions and quantum ellipsoid anisotropies will exhibit a nonmonotonic change. The peak value of the photoionization cross-section will reach a maximum with the increasing ratio R1/R2. It is found that the applied magnetic field can be an effective means of enhancing the photoionization cross-section of an impurity state in such core/shell quantum dot system.

Anisotropy dependence of the optical response in an impurity doped quantum dot under intense laser field

In the present work, we are interested in calculating anisotropy dependence of the optical response in an ellipsoidal quantum dot with a hydrogenic impurity in the presence of high-frequency intense laser field within the framework of the effective mass approximation. The effects of the anisotropy of the system and laser field intensity on the energy levels and the respective impurity binding energies are calculated. It is shown that the electrostatic interaction between the electron and the impurity atom becomes the weakest when the structure has a spherical symmetry and in contrast to the 1s-like state, the binding energy of the 2pz-like state increases with the laser field intensity for all values of the anisotropy parameter considered. The results show that the anisotropy degree plays a fundamental role in determining the optical response of the ellipsoidal quantum dot.