Binding energy of an off-center hydrogenic donor in a spherical Gaussian quantum dot

The energy levels of an off-center hydrogenic donor confined by a spherical Gaussian potential have been calculated as a function of the potential radius for different donor position by exact diagonalization method. The results have clearly demonstrated the so-called quantum size effect. The binding energy is dependent on the dot radius R, the impurity ion distance D, and the confining potential depth V₀.     

Binding energy of a screened donor in a spherical quantum dot with a parabolic potential

A wavefunction is proposed for calculating the ground-state energy of a screened donor in a spherical quantum dot under a parabolic potential by a variational method. The donor is taken to be at the center of the quantum dot. Results are presented for four values of the screening parameter by the proposed wavefunction as well as for the hydrogenic donor case by a wavefunction used by Xiao et al.. To assess the accuracy of the results, ‘exact’ energies are also obtained by numerical integration of the Schrödinger equation. It is shown that the proposed wavefunction gives very good results in all cases including the hydrogenic donor case.     

Finite-difference calculation of donor energy levels in a spherical quantum dot subject to a magnetic field

The ground and excited states of a donor impurity at the center of a spherical quantum dot subject to a magnetic field are calculated within the effective-mass approximation. The barriers are infinitely high and the differential equation is solved by combining the finite-difference method with the Richardson extrapolation. The binding and transition energies are more accurate than the available variational values, and excellent agreement is found with the hydrogen atom. The transition energies for a medium-size quantum dot are given.     

A bound polaron in a spherical quantum dot

The binding energy of a bound polaron in a spherical quantum dot has been investigated by using the variational method. The influence of LO and SO phonons have taken into consideration. Result shows that the phonon contribution to the binding energy is dependent on the size of the quantum dot as well as the position of the impurity in the quantum dot. Numerical calculation on the ZnSe quantum dot shows that such contribution is about 5% to 20% of the total binding energy. Received: 13 October 1997 / Revised: 4 March 1998 / Accepted: 26 May 1998     

Effects of electric field and hydrostatic pressure on donor binding energies in a spherical quantum dot

The binding energies of a hydrogenic donor in a GaAs spherical quantum dot in the Ga_1−xAl_xAs matrix are presented assuming parabolic confinement. Effects of hydrostatic pressure and electric field are discussed on the results obtained using a variational method. Effects of the spatial variation of the dielectric screening and the effective mass mismatch are also investigated. Our results show that (i) the ionization energy decreases with dot size, with the screening function giving uniformly larger values for dots which are less than about 25 nm, (ii) the hydrostatic pressure increases the donor ionization energy such that the variation is larger for a smaller dot, and (iii) the ionization energy decreases in an electric field. All the calculations have been carried out with finite barriers and good agreement is obtained with the results available in the literature in limiting cases.     

Lifetime of resonant state in a spherical quantum dot

This paper calculates the lifetime of resonant state and transmission probability of a single electron tunnelling in a spherical quantum dot (SQD) structure by using the transfer matrix technique. In the SQD, the electron is confined both transversally and longitudinally, the motion in the transverse and longitudinal directions is separated by using the adiabatic approximation theory. Meanwhile, the energy levels of the former are considered as the effective confining potential. The numerical calculations are carried out for the SQD consisting of GaAs/InAs material. The obtained results show that the bigger radius of the quantum dot not only leads significantly to the shifts of resonant peaks toward the low-energy region, but also causes the lengthening of the lifetime of resonant state. The lifetime of resonant state can be calculated from the uncertainty principle between the energy half width and lifetime.     

Exciton related optical absorption in a spherical quantum dot

An exciton in a spherical quantum dot is studied analytically within the effective mass approximation. A parabolic confinement under an electric field is considered. The linear and nonlinear optical absorption coefficients are calculated within the density matrix formalism. No assumptions are made about the strength of the confinement. It is shown how the competing mechanisms of the Coulomb interaction, the confinement and the applied static electric field affect the optical absorption.     

Control of electron correlations in a spherical quantum dot

Spherical quantum dots containing several electrons are considered for different values of the total spin. Numerical calculations are carried out using the quantum path-integral Monte Carlo method. The dependence of the electron correlations on the dimensionless control quantum parameter q associated with the steepness of the confinement potential is studied. The quantum transition from a Wigner crystal-like state (i.e., from the regime of strongly correlated electrons) to a Fermi-liquid state (“cold” melting) driven by the parameter q is studied in detail. The behavior of the radial and pair correlation functions, which characterize quantum delocalization of the electrons, is considered.     

Confined states of a positronium in a spherical quantum dot

Confined states of a positronium (Ps) in the spherical quantum dot (QD) are theoretically investigated in three size-quantization (SQ) regimes: strong, weak and intermediate. In the strong SQ regime, analytical expressions for the wave functions (WFs) and energy of the electron-positron pair are obtained. In the weak SQ regime, the Ps energy and binding energy are analytically calculated. To calculate the Ps energy in the intermediate SQ regime, variational and numerical methods are used. It is shown that, in the corresponding limits, the results obtained by variational method agree with those obtained in the strong and weak SQ regimes.     

Double detected spin-dependent quantum dot

We study the dynamics of a spin-dependent quantum dot system, where an unsharp and a sharp detection scenario is introduced. The back-action of the unsharp detection related to the magnetization, proposed in terms of the continuous quantum measurement theory, is observed via the von Neumann measurement (sharp detection) of the electric charge current. The behavior of the average electron charge current is studied as a function of the unsharp detection strength γ$\gamma$, and features of measurement back-action are discussed. The achieved equations reproduce the quantum Zeno effect. Considering magnetic leads, we demonstrate that the measurement process may freeze the system in its initial state. We show that the continuous observation may enhance the transition between spin states, in contradiction with rapidly repeated projective observations, when it slows down. Experimental issue, such as the accuracy of the electric current measurement, is analyzed.     

The multilayered spherical quantum dot under a magnetic field

The binding energy of an impurity located at the center of multilayered spherical quantum dot (MSQD) is reported as a function of the dot and barrier thickness for different alloy compositions under the influence of a magnetic field. Within the effective mass approximation, the binding energy has been calculated using the fourth order Runge-Kutta method without magnetic field. A variational approach has been employed if a magnetic field is present. The binding energy in MSQD with equal dot and barrier thickness is calculated. It is shown that the binding energy in MSQD differs from that of a single quantum dot. Also, the geometry is dominant on the binding energy for thin MSQDs, but the magnetic field becomes more effective for thick MSQDs.     

Energy levels of a spherical quantum dot in a confining potential

Using an exact analytical method, we obtain the ground state and the excited states wave functions as well as the corresponding eigenvalues of a spherical quantum dot in the presence of a confining potential which is a combination of linear, Coulomb and quadratic terms. Next, we investigate the quantum dot energy as the potential coefficients are changed. Our study reveals that considering such a confining potential leads to results which are in good agreement with experimental results.     

Nonlinear optical properties of a hydrogenic donor quantum dot

A investigation of the nonlinear optical properties of a hydrogenic donor in a disc-like parabolic quantum dot has been performed by using the matrix diagonalization method. The optical absorption coefficient between the ground (L=0) and the first excited state (L=1) have been examined based on the computed energies and wave functions. The results are presented as a function of the incident photon energy for the different values of the incident optical intensity and the confinement strength. We found the total optical absorption coefficient is strongly affected by the incident optical intensity and the confinement strength.     

Bound polaron in a spherical quantum dot under an electric field

A variational approach is used to study the ground state of a bound polaron in a spherical quantum dot under an external electric field. The binding energy of the hydrogenic impurity state is calculated by taking the interaction of an electron with both the confined longitudinal optical phonons and the surface optical phonons into account. The interaction between impurity and longitudinal optical phonons has also been considered to obtain the binding energy of a bound polaron. It shows that the polaron effects give significant corrections to the binding energy and its Stark energy shift. The external electric field increases the phonon contributions to the binding energy.     

Donor binding energies and spin-orbit coupling in a spherical quantum dot

The ground state and a few excited state energies of a hydrogenic donor in a spherical quantum dot (GaAs in a GaAlAs matrix) are computed. While the 1s and the 2s-state energies behave normally for dots of all radii, the 2p₀ and 2p_± states are unbound for most of the radii of interest. It is predicted that a semiconductor quantum dot with a hydrogenic donor will exhibit photoconductivity for a low threshold wavelength ∼12 μm. The spin-orbit coupling gives a contribution of the order of 10⁻⁵ meV for both 2p₀ and 2p_± states.     

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 − Ga_1 − xAl_xAs 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.     

The effects of cup-like and hill-like parabolic confining potentials on photoionization cross section of a donor in a spherical quantum dot

A theoretical investigation of the effects of hill-like and cup-like parabolic confiningelectric potentials on photoionization cross section (PCS) in a spherical quantum dot ispresented. The hill-like and the cup-like parabolic potentials are superimposed on aninfinite spherical square well (ISSW) potential. As the cup-like parabolic potentialintensifies, the peak of the PCS becomes redshifted for the s → ptransition, and becomes blueshifted for the p → d, d → f (andso forth) transitions. The hill-like parabolic potential, on the contrary, blueshiftspeaks of the PCS for s →p transitions, while it redshifts those oftransitions between higher states as it intensifies. Consequently, the two potentialsdiscriminate between transitions involving the ground state and those involving higherstates.     

Role of a uniform magnetic field on the energy spectrum of a single donor in a core/shell spherical quantum dot

Using the variational approach within the framework of the effective-mass approximation (EMA), the binding energy of a centred hydrogenic donor impurity in a CdSe/ZnTe core/shell spherical quantum dot (CSSQD) in the presence of an external magnetic field was investigated. In this model, we have taken into account the effect of the radial dependence of the dielectric constant and of the electron effective mass. Our numerical results show a remarkable influence of the nanodot spatial parameters and of the external magnetic field strength on the shallow donor binding energy.     

Diploe-allowed optical absorption of an exciton in a spherical parabolic quantum dot

A investigation of the linear and nonlinear optical properties of an exciton in a spherical parabolic quantum dot has been performed by using the matrix diagonalization method. The optical absorption coefficients between the ground state (L=0,π=+1) and the first excited state (L=1,π=-1) have been examined based on the computed energies and wave functions. The results are presented as a function of the incident photon energy for the different values of the incident optical intensity and the confinement strength. We found the optical absorption coefficient is strongly affected by the incident optical intensity and the confinement strength.     

Spin magnetic moment current of impurity electron in a spherical quantum dot

Current of the spin magnetic moment of an electron coupled with hydrogen-like impurity, placed in the center of a spherical quantum dot, is studied. Confinement potential of the quantum dot is approximated by rectangular infinitely high walls. S-states of electron for both positive and negative values of total energy are considered. Dependences of spin magnetic moment current of electron on the radial variable for different values of dot radius are obtained. It is shown that for quantum dots with large radius, due to weakening of size-quantization effect, corresponding curves approach each other.