Lateral electric field effects on quantum size confinement in cylindrical quantum dot under parabolic potential

Within the effective mass approximation, we investigated theoretically the ground-state energy of a single particle and the binding energy of the neutral donor impurity (D⁰) affected by a lateral electric field in a parabolic quantum dot (QD). The results show that the electron and the hole ground-state energy and the band to band transition energies shift to lower values (red shift) by increasing the field intensity. The quantum Stark shift (QSS) for the electron increases rapidly in the quasi spherical QD (QSQD) by increasing the lateral field, whereas for the hole it increases monotony. In the cylindrical QDs (CQDs), we found that the QSS for electron and hole increase monotonically. The quantum size, lateral electric field and impurity position effect on the binding energy of neutral donor (D⁰) is studied. Unexpected behavior of D⁰ in quantum well limit (QW), the binding energy of D⁰ is increasing (blue shift) with increasing QD radius R$R$ at the presence of a lateral electric field. It appears that for a fixed size of the QD, the off-center binding energy decreases when the impurity ion is displaced from the center to the QD borders, while it is shifted to lower energy with increasing the field.     

Electric field induced nonlinear optical properties of a confined exciton in a ZnO/Zn1−xMgxO strained quantum dot

Electric field induced exciton binding energy as a function of dot radius in a ZnO/Zn_1−xMg_xO quantum dot is investigated. The interband emission as a function of dot radius is obtained in the presence of electric field strength. The Stark effect on the exciton as a function of the dot radius is discussed. The effects of strain, including the hydrostatic and the biaxial strain and the internal electric field, induced by spontaneous and piezoelectric polarization are taken into consideration in all the calculations. Numerical calculations are performed using variational procedure within the single band effective mass approximation. Some nonlinear optical properties are investigated for various electric field strengths in a ZnO/Zn_1−xMg_xO quantum dot taking into account the strain-induced piezoelectric effects. Our results show that the nonlinear optical properties strongly depend on the effects of electric field strength and the geometrical confinement.     

Effects of Electric Field on Electronic States in a GaAs/GaAlAs Quantum Dot with Different Confinements

Binding energies of shallow hydrogenic impurity in a GaAs/GaAlAs quantum dot with spherical confinement, parabolic confinement and rectangular confinement are calculated as a function of dot radius in the influence of electric field. The binding energy is calculated following a variational procedure within the effective mass approximation along with the spatial depended dielectric function. A finite confining potential well with depth is determined by the discontinuity of the band gap in the quantum dot and the cladding. It is found that the contribution of spatially dependent screening effects are small for a donor impurity and it is concluded that the rectangulax confinement is better than the parabolic and spherical confinements. These results are compared with the existing literature.     

Stark-shift of impurity fundamental state in a lens shaped quantum dot

We calculate the Stark effect and the polarisability of shallow-donor impurity located in the centre of lens shaped quantum dot by a variational method and in the effective-mass approximation. Our theoretical model assumes an infinite confinement to describe the barriers at the dot boundaries and the electric field is considered to be applied in the z-direction. The systematic theoretical investigation contains results with the quantum dot size and the strength of the external field. Our calculations reveal that the interval wherein the polarisability varies depends strongly on the dot size.     

Anisotropic exciton Stark shift in hemispherical quantum dots

The exciton Stark shift and polarization in hemispherical quantum dots(HQDs) each as a function of strength and orientation of applied electric field are theoretically investigated by an exact diagonalization method. A highly anisotropic Stark redshift of exciton energy is found. As the electric field is rotated from Voigt to Faraday geometry, the redshift of exciton energy monotonically decreases. This is because the asymmetric geometric shape of the hemispherical quantum dot restrains the displacement of the wave function to the higher orbital state in response to electric field along Faraday geometry. A redshift of hole energy is found all the time while a transition of electron energy from this redshift to a blueshift is found as the field is rotated from Voigt to Faraday geometry. Taking advantage of the diminishing of Stark effect along Faraday geometry, the hemispherical shapes can be used to improve significantly the radiative recombination efficiency of the polar optoelectronic devices if the strong internal polarized electric field is along Faraday geometry.     

Effects of an electric field on the confined hydrogen impurity states in a spherical parabolic quantum dot

In this paper, we studied the effects of an electric field on a hydrogenic impurity confined in a spherical parabolic quantum dot using nondegenerate and degenerate perturbation methods. The binding energies of the ground and three low-excited states are calculated as a function of the confinement strength and as a function of the intensity of an applied electric field. Moreover, we computed the oscillator strength and the second-order nonlinear optical rectification coefficient based on the computed energies and wave functions. The results show that the electric and optical properties of hydrogenic impurity states are strongly affected by the confinement strength and the applied electric field.     

Electronic states of coupled quantum dot-ring structure under lateral electric field with and without a hydrogenic donor impurity

A detailed investigation of the lateral electric field effect on single electron states in coupled quantum dot-ring structure has been systematically studied for cases with and without an on-center hydrogenic donor impurity. The single electron energy spectrum has been found using the effective mass approximation and an exact diagonalization technique. The electron ground state's probability density has been examined for different values of the confinement energies and depth of dot confinement relative to the bottom of the quantum ring and barrier thickness. The energy level's dependence on the electric field strength has been studied considering the effects of mentioned parameters of the structure and hydrogenic donor impurity.     

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.     

Double donor in a spherical quantum dot

We present a variational calculation for the ground state of the double donor in a spherical GaAs–Ga_1–x Al _x As quantum dot. The binding energies for the ionized and neutral centres are calculated for several barrier height values as a function of the radius of the dot. Compared with a square well structure, there is a stronger confinement and a larger binding energy for the double donors in a spherical quantum dot.     

Simultaneous effects of dielectric mismatch and electric field on the electronic properties in Si nanodots

By using the finite element method within the effective mass approximation, the effects of both dielectric confinement and electric field on the shallow-donor binding energy and polarizability in spherical Si quantum dots are investigated. It is found that: (i) the ground state binding energy is significantly increased by the dielectric mismatch at the dot interface, (ii) in the freestanding nanodot the competition between the electric field, polarization charges induced at interfaces and impurity position determines the symmetry of the electron probability distribution; (iii) the donor polarizability decreases with electric field strength and this effect is more pronounced for large dielectric mismatches. Therefore, the electronic properties of the nanocrystals could be tuned by proper tailoring of the surrounding medium dielectric constant as well as by varying the electric field. The normalized binding energy of an on-center hydrogenic donor is also been estimated and the results are in good agreement with the previous reported values.     

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.     

Electric field and impurity effects on optical property of a three-dimensional quantum dot: A combinational potential scheme

The present study seeks to scrutinize the optical properties of an ellipsoidal quantum dot (EQD) containing an electron in the presence of an external electric field and a donor (acceptor) impurity. In this regard, the perturbation theory is used and for different values of the confinement strength and the electric field, the linear, nonlinear and total absorption coefficients are calculated as functions of the incident photon energy. The oscillator strength between the ground and first excited states in the EQD is also calculated in terms of the confinement strength. The results show that the optical properties of an EQD decrease with increases in the ellipticity constant and electric field.     

The role of the electron-hole coulomb interaction in quantum confined stark effect

The luminescence peak energy and tunneling lifetime of an exciton in a semiconductor quantum well with a small valence band offset in the presence of a perpendicular electric field is calculated by generalizing the variational approach of quantum confined Stark effect normally used for systems of GaAs/AlGaAs quantum wells. At a finite electric field, the electron-hole Coulomb interaction provides additional confinement to each of the carriers and significantly enhances the Stark shift and the exciton lifetime against field ionization. Numerical results are presented for ZnSe/Zn_1−xMn_xSe heterostructures studies in recent experiments.     

Impurity-related intraband absorption in coupled quantum dot-ring structure under lateral electric field

The effects of a lateral electric field on intraband absorption in GaAs/GaAlAs two-dimensional coupled quantum dot-ring structure with an on-center hydrogenic donor impurity are investigated. The confining potential of the system consists of two parabolas with various confinement energies. The calculations are made using the exact diagonalization technique. A selection rule for intraband transitions was found for x-polarized incident light. The absorption spectrum mainly exhibits a redshift with the increment of electric field strength. On the other hand, the absorption spectrum can exhibit either a blue- or redshift depending on the values of confinement energies of dot and ring. Additionally, electric field changes the energetic shift direction influenced by the variation of barrier thickness of the structure.     

Influence of the image charge effect on the hydrogen-like impurity-bound polaron in a spherical quantum dot in the presence of an electric field

We have investigated the influence of an external electric field on the binding energies and polaronic shifts of the ground and some first few excited states of a hydrogenic impurity in a spherical quantum dot by taking into account the image charge effect. By using Landau–Pekar variational method the general analytical expression is obtained for the impurity bound-polaron energies. It has been numerically identified the conditions (electric field, nominal radius of quantum dot, etc.) in which the bound-polaron states can be existence in GaAs quantum dot. We have shown that the polaronic shifts in the binding energy of 1s-like state are the same in cases with and without image charge effect while they for 2s-like state are not coincide and have different monotonic behavior versus confinement potential. Electron–phonon interaction lifts the degeneracy of the 2px-, 2py-, and 2pz-like states of a donor impurity and reduces their binding energies.     

Sum frequency generation in the spherical quantum dots in the presence of applied electric field and spin–orbit interaction

The sum-frequency generation (SFG) is theoretically studied in a quantum dot (QD) through the framework of the effective-mass approximation and compact density matrix approach. QD is spherical with the parabolic potential confinement, under applied electric field and in the presence of Rashba spin-orbit interaction (SOI). Using the computed energies and eigenkets, the second-order susceptibility of SFG has been also calculated as a function of radius of QD, spin–orbit interaction strength and the applied electric field. The effects of Rashba SOI strength, radius of QD and the applied electric field on the second-order of susceptibility coefficient are considered.     

Spectrum and Binding Energy of an Off-Center Hydrogenic Donor in aSpherical Quantum Dot

Off-center impurity effects in a spherical quantum dot are theoretically studied by degenerate perturbation method in strong confinement. The energy levels and binding energies are computed for the typical GaAs material as function of the donor position. The numerical results show the quantum size effect. We note that the energy levels and binding energies are not onlyrelated to the position of donor and the strength of confinement,but also related to the fold of degenerate states. We can see obviously that gaps will appear among the degenerate states and the splitting of energy levels and binding energies will appear as the position of the impurity is shifted away off the center.     

A Negative Donor Center Trapped by a Spherical Quantum Dot

The properties of the low-lying states of a negative donor center trapped by a spherical quantum dot, which is subjected to a parabolic potential confinement, are investigated in the absence of magnetic field. The calculations have been performed by means of the exact diagonalization of the Hamiltonian matrix within the effective-mass approximation. We find that there is only one bound state the D^- center in a spherical parabolic quantum dot in the absence of magnetic field. The binding energy of the ground state is obtained as a function of the dot size. Moreover, the critical confined potential radius value at which the negative donor center changes from unbound to bound is obtained.     

Impurity-related electronic properties in quantum dots under electric and magnetic fields

This paper presents a systematic study of the ground-state binding energies of a hydrogenic impurity in quantum dots subjected to external electric and magnetic fields.The quantum dot is modeled by superposing a lateral parabolic potential,a Gaussian potential and the energies are calculated via the finite-difference method within the effectivemass approximation.The variation of the binding energy with the lateral confinement,external field,position of the impurity,and quantum-size is studied in detail.All these factors lead to complicated binding energies of the donor,and the following results are found:(1) the binding energies of the donor increase with the increasing magnetic strength and lateral confinement,and reduce with the increasing electric strength and the dot size;(2) there is a maximum value of the binding energies as the impurity placed in different positions along the z direction;(3) the electric field destroys the symmetric behaviour of the donor binding energies as the position of the impurity.     

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.