Spherical QD Research Articles

Perturbative effects on the optical extinction of GaN/AlN spherical QD in 0–0.5 eV range

Perturbative effects on the optical extinction of GaN/AlN spherical QD in 0–0.5 eV range

Q-BOR–FDTD method for solving Schrödinger equation for rotationally symmetric nanostructures with hydrogenic impurity

An efficient method inspired by the traditional body of revolution finite-difference time-domain (BOR-FDTD) method is developed to solve the Schrödinger equation for rotationally symmetric problems. As test cases, spherical, cylindrical, cone-like quantum dots, harmonic oscillator, and spherical quantum dot with hydrogenic impurity are investigated to check the efficiency of the proposed method which we coin as Quantum BOR-FDTD (Q-BOR-FDTD) method. The obtained results are analysed and compared to the 3D FDTD method, and the analytical solutions. Q-BOR-FDTD method proves to be very accurate and time and memory efficient by reducing a three-dimensional problem to a two-dimensional one, therefore one can employ very fine meshes to get very precise results. Moreover, it can be exploited to solve problems including hydrogenic impurities which is not an easy task in the traditional FDTD calculation due to singularity problem. To demonstrate its accuracy, we consider spherical and cone-like core-shell QD with hydrogenic impurity. Comparison with analytical solutions confirms that Q-BOR–FDTD method is very efficient and accurate for solving Schrödinger equation for problems with hydrogenic impurity

Modeling and characterization of carrier mobility for truncated conical quantum dot infrared photodetectors

In the present paper, a theoretical model for calculating the carrier mobility which is a result of the existence of a truncated conical quantum dots of n-type quantum dot infrared photodetectors (QDIPs) is developed. This model is built on solving Boltzmann’s transport equation that is a complex integro-differential equation describing the carrier transport. The time-domain finite-difference method is used in this numerical solution. The influences of dimensions and density of the QDs for this structure on the carrier mobility are studied. Eventually, the calculated mobility for truncated conical InAs/GaAs QDIP is contrasted to other conical, spherical, and hemispherical QD structures. The model put forward is a generic model that is applicable to various structures of truncated conical QDs devices.

Impurity with two electrons in the spherical quantum dot with Unite confinement potential

Two-electron states in a spherical QD with the hydrogenic impurity located in the center and with a finite height confinement potential barrier are investigated. The effective mass mismatch have been taken into account. The dependence of ground state energy and Coulomb electron-electron interaction energy correction on the QD size is studied. The problem of the state exchange time control in QD is discussed, taking into account the spins of the electrons in the Russell-Saunders approximation. The effect of quantum emission has been shown.

Linear and nonlinear intra-conduction band optical absorption in (In,Ga)N/GaN spherical QD under hydrostatic pressure

Linear, third-order nonlinear and total optical absorption coefficients of intra-conduction band 1s–1p transition with hydrogenic shallow-donor impurity in wurtzite (In,Ga)N/GaN spherical quantum dot are reported. Hydrostatic pressure effect is investigated within the framework of single band effective-mass approximation using a combination of Quantum Genetic Algorithm (QGA) and Hartree–Fock–Roothaan (HFR) method. The results show that the pressure has a great influence on optical absorption coefficients of QDs. A blue-shift of the resonant peak is observed while the maximum of the amplitude of optical absorption coefficients decreases under hydrostatic pressure effect. A good agreement is shown compared with results of the finding.

Relaxation time and impurity effects on linear and nonlinear refractive index changes in (In,Ga)N–GaN spherical QD

By means of a combination of Quantum Genetic Algorithm and Hartree–Fock–Roothaan method, the changes in linear, third-order nonlinear and total refractive index associated with intra-conduction band transition are investigated with and without shallow-donor impurity in wurtzite (In,Ga)N–GaN spherical quantum dot. For both cases with and without impurity, the calculation is performed within the framework of single band effective-mass and parabolic band approximations. Impurity׳s position and relaxation time effects are investigated. It is found that the modulation of the refractive index changes, suitable for good performance optical modulators and various infra-red optical device applications can be easily obtained by tailoring the relaxation time and the position of the impurity.

Pressure-dependent of linear and nonlinear optical properties of (In,Ga)N/GaN spherical QD

Third-order nonlinear intra-conduction band optical properties of (In,Ga)N–GaN spherical quantum dot are investigated. Linear, third-order nonlinear and total absorption coefficients (ACs) of 1p–1d and 1d–1f transitions are computed using a combination of Quantum Genetic Algorithm (QGA) and Hartree–Fock–Roothaan (HFR) method. Hydrostatic pressure effect is examined within the single band effective-mass and the one parabolic band approximations under finite potential barrier. The results show that the hydrostatic pressure has a great impact on the optical properties of QDs. A blue shift of the resonant peak is observed while the maximum of the amplitude of optical absorption coefficients decreases nonlinearly under hydrostatic pressure effect. Two competing parameters are suggested to explain our results. Compared with the finding results, a good agreement is shown.

Excited-states of hydrogenic-like impurities in InGaN–GaN spherical QD: Electric field effect

By means of a traditional Ritz variational method within the effective-mass and single parabolic band approximations, the excited-states energy with and without the existence of the impurity is performed. Externally applied electric field and system radius effects are considered in wurtzite (In,Ga)N–GaN spherical quantum dot with finite potential barrier. The normalized binding energy is also reported. Compared to the previous theoretical findings, a good agreement is shown.

Impurity binding energy of lowest-excited state in (In,Ga)N–GaN spherical QD under electric field effect

External electric field effect on the lowest-excited state in wurtzite (In,Ga)N–GaN spherical quantum dot is considered. By means of a traditional Ritz variational method within the effective-mass approximation and finite potential barrier, the lowest-excited state energy with and without the presence of the impurity is investigated. The normalized binding energy under electric field effect is also performed. Our numerical results are compared with the previous theoretical findings and show a good agreement with those concerning especially the ground-state for different semiconductors materials and different QDs-shapes.

Interband absorption and excitonic states in narrow band InSb spherical quantum dots

Interband transitions in the ensemble of weakly interacting narrow band spherical InSb QD have been investigated by dipole approximation. Dispersion law of electrons and light holes has been considered in the framework of Kane's model, which is similar to the relativistic one. Transitions from light hole and heavy hole bands to conduction band are considered. Selection rules for the transitions have been mentioned. Exciton consisting of heavy hole and electron is described in the frame of adiabatic approximation. It is shown that analogous to the case of electron, which has the standard dispersion law, heavy hole is in the effective spherical symmetric oscillating field. Meanwhile the exciton shift in absorption spectra is more significant than in the case of standard dispersion law of electron due to the non-parabolicity of electron dispersion.

The hydrostatic pressure and temperature effects on a hydrogenic impurity in a spherical quantum dot

The combined effects of the hydrostatic pressure and temperature on the binding energy, ΔE (transition energy), the oscillator strength and the third-order susceptibility of third harmonic generation (THG) of a hydrogenic impurity in a spherical QD, in the presence of the external electric field, have been investigated by means of the perturbation approach within the framework of effective-mass approximation. It is found that the binding energy, ΔE (transition energy), the oscillator strength and the third-order susceptibility of third harmonic generation (THG) of the hydrogenic impurity are affected by the confinement strength, the electric field, pressure and temperature.

Nonlinear optical properties of a D− system in a spherical quantum dot

The nonlinear optical properties of a D− system confined in a spherical quantum dot represented by a Gaussian confining potential are studied. The great advantage of our methodology is that the model potential possesses the finite height and range. Calculations are carried out by using the method of numerical diagonalization of Hamiltonian matrix within the effective-mass approximation. We calculate the linear, third-order nonlinear and total optical absorption coefficients under the density matrix formalism. Numerical results for GaAs−Ga1−xAlxAs QDs are presented. Our results show that the optical absorption coefficients in a spherical QD are much larger than their values for GaAs quantum wells. It is found that optical absorptions are strongly affected not only the confinement barrier height, dot radius, the electron–impurity interaction but also the position of the impurity.

Optical absorption of a hydrogenic impurity in a disc-shaped quantum dot

Using the perturbation method and the effective-mass approximation, we studied a hydrogenic impurity confined in a disc-shaped quantum dot with a parabolic potential in the presence of an electric field. Both the electric field and the confinement effects on the transition energy and the oscillator strength were investigated. Based on the computed energies and wave functions, the linear, the third-order nonlinear and the total optical absorption coefficients were also calculated. The results show that the optical absorption coefficients obtained in a disc-shaped parabolic QD can reach the magnitude of 10 4 / cm , which is 1–2 orders of magnitude higher than that in the case of a spherical parabolic QD. We found that the transition energy, the oscillator strength, the linear, the third-order nonlinear and the total optical absorptions of the hydrogenic impurity in a disc-shaped QD dependent strongly on the confinement strength, and the applied electric field intensity.

Correlation energy in a triplet state of a two-electron spherical quantum dot

Correlation energies in the (1s-1p) triplet state of a two-electron spherical QD with square-well potential confinement are estimated for dots of different radii. The results are presented taking GaAs dot as an example. Our results show that the correlation energies are i) negative in a triplet state in contrast to the singlet state, ii)approaches zero as the dot size approaches infinity, and iii) the "fictitious crossing" of the singlet and triplet state energies at a particular dot size is explained on the basis of Hund's rules.

Spectroelectrochemistry of hollow spherical CdSe quantum dot assemblies in water

The hollow spherical CdSe QD assemblies were synthesized via a sonochemical approach that utilizes β-cyclodextrin as a template reagent in aqueous solution. The hollow nanospheres have an average diameter of 70 nm and are found to consist of an assembly of monodispersed 5 nm sized CdSe quantum dots. Following an electrochemical reaction with persulfate ions, strong electrogenerated chemiluminescence (ECL) was observed from the CdSe nanoassemblies suspended in an aqueous solution of pH ⩽ 7.95. The study indicates that the morphology of the 70 nm nanoassembly plays an important role in generating the stable ECL since individually dispersed quantum dots did not exhibit any significant ECL. The unique ECL intensity and stability of the synthesized spherical nanoassemblies could allow for potential sensor applications of CdSe quantum dots in water.

Two-photon absorption processes in semiconductor quantum dots

The two-photon absorption process is a nonlinear phenomenon that shows very low optical efficiency in bulk semiconductors. For this reason the detection of these processes becomes very difficult from the experimental point of view. Nevertheless, when dealing with semiconductor QD's with few nanometer radii, these transitions are enhanced and the detection is possible. In this contribution we present analytical calculations for the absorption coefficient in CdSe spherical QD's subjected to these second order processes, as a function of the characteristic dot parameters. The intensities of the absorption peaks, as well as the statistical treatment involving QD's ensembles, are also reported.

Temperature Dependence of the Effective Coefficient of Auger Recombination in 1.3 μm InAs∕GaAs QD Lasers

Semiconductor laser heterostructures containing five and ten sheets of InAs/GaAs QDs on GaAs substrates, with an emission wavelength of ∼1.3 μm, have been studied. Dependences of the nonradiative lifetime and effective Auger coefficient in QDs are obtained from an analysis of temperature and current dependences of the efficiency of spontaneous radiative recombination. The zero-threshold Auger recombination channel in QDs is shown to dominate at low (below 200 K) temperature, whereas at higher temperatures the quasithreshold channel becomes dominant. The effective 3D Auger coefficient is estimated in the approximation of a spherical QD, and a good agreement with the experimental data is obtained.

Interface optical phonons in spherical quantum-dot/quantum-well heterostructures

Interface optical phonons are studied in the case of a spherical quantum-dot/quantum-well (QD/QW) heterostructure by applying a dielectric continuum approach. The prototypical case is a QD/QW of CdS/HgS in the form of spherical shell of HgS embedded on a spherical CdS QD, a kind of structure intensively investigated in the latter times. We also assume the QD/QW hetrerostructure surrounded by a host material which is modeled in the form of an infinite dielectric medium which does not participate of the polar optical vibrations. The possible interface phonon modes (CdS-and HgS-SO phonons), the corresponding frequencies and the electron-phonon interaction Hamiltonian are reported. A detailed discussion is made of the SO phonons fundamental characteristics and of the strength of the electron-phonon interaction.

Exciton states and optical transitions in colloidal CdS quantum dots: Shape and dielectric mismatch effects

We present a theoretical investigation of electron-hole and exciton energy spectra as well as oscillator strengths of optical transitions in colloidal CdS quantum dots (QD's) with spherical and tetrahedral shape. The Coulomb potential energy of the electron-hole system is treated taking into account the dielectric mismatch at the QD boundaries. Calculation of electron-hole energy spectrum and Coulomb potential energy in tetrahedral QD's is carried out using the finite difference method. It is shown that the bulk Coulomb potential energy with the dielectric constant of QD leads to lower exciton energy levels as compared to the Coulomb potential, which includes electron-hole interaction and self-action energies. The Coulomb potential changes the electron-hole pair energies without dielectric confinement contributions in such a way that the exciton ground state becomes active for optical transitions in dipole approximation for both tetrahedral and spherical QD's while the lowest electron-hole pair energy level is active for tetrahedral and passive for spherical QD's. The exciton binding energy in both types of QD's is enhanced by a factor of 2 in the presence of the dielectric mismatch. It is proven that the inclusion of the real QD shape and dielectric mismatch is important not only for the quantitative analysis but also for the qualitative description of optical properties of colloidal CdS QD's.

Renormalized Schr�dinger Equation for Excitons in Graded Quantum Dot

A simple method for calculating the ground-state energy of excitons confined in spherical quantum dots is presented. The exciton trial wave function is taken as a product of the ground-state wave functions of the unbound electron and hole in the QD, with a correlation function that depends only on electron-hole separation. A renormalized Schrodinger equation for the correlation function is deduced by using the variational principle. Both the differential equations for the unbound electron (hole) wave function in the QD and for the correlation function are solved numerically by means of the trigonometric sweep method. The ground state binding energies of an exciton in a GaAs-(Ga, Al)As spherical QD as a function of the dot radius are calculated for the models of square-well, soft-edge-barrier and double-step potentials.