Nonlinear optical rectification of a hydrogenic impurity in a disc-like quantum dot

An investigation of the nonlinear optical rectification of a hydrogenic impurity, which is in a two-dimensional disc-like quantum dot (QD) with parabolic confinement potential, has been performed by using the perturbation method in the effective mass approximation. Both the electric field and the confinement effects on the energy are investigated in detail. The results are presented as a function of the incident photon energy for the different values of the confinement strength and the electric field. It is found that the nonlinear optical properties of hydrogenic impurity states in a disc-like QD are strongly affected by the confinement strength and the electric field.     

Electron Raman scattering of a hydrogenic impurity in a disc-shaped quantum dot

We have carried out the theoretical calculation of the differential cross section for the electron Raman scattering process associated with a hydrogenic impurity in a disc-shaped quantum dot (QD). We consider the impurity states confined in a disc-shaped QD with parabolic potential in the presence of an external electric field. Effects of the electric field and the confinement strength on the differential cross section are investigated. We make a comparison about the Raman intensity between with and without the Coulomb interaction. We found that the differential cross section of the hydrogenic impurity in a disc-shaped QD dependent strongly on the confinement strength, the external electric field intensity and the Coulomb interaction.     

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.     

The polaron effect on the binding energy of a shallow donor impurity in quantum-well wires in an electric field

Using a variational technique, the effect of electron-longitudinal optical (LO) phonon interaction on the ground and the first few excited states of a hydrogenic impurity in a semiconductor quantum wire of rectangular cross section under an external electric field is studied theoretically for the impurity atom doped at various positions. The results for the binding energy as well as polaronic correction are obtained as a function of the size of the wire, the applied uniform electric field and the position of the impurity. It is found that the presence of optical phonons changes significantly the values of the impurity binding energies of the system. Taking into account the electron–LO phonon interaction the 1s→2p_y and 1s→2p_z transition energies are calculated as a function of applied electric field for different impurity positions.     

The nonlinear optical rectification of an ellipsoidal quantum dot with impurity in the presence of an electric field

We have performed theoretical calculation of second-order nonlinear optical rectification (OR) coefficient in a typical GaAs/AlGaAs QD with ellipsoidal confinement potential in the presence of an impurity and an applied electric field. Using an appropriate coordinate transformation and the perturbation theory, we have investigated the OR coefficient as a function of incident photon energy. Calculation results show that the values of OR coefficient increase with an increase of applied electric field. However, the values decrease with increases in confinement strength and ellipticity constant. Additionally, the presence of a donor impurity shifts the OR coefficient peak positions to higher energies (blueshift), contrary to that of an acceptor impurity.     

External electric field, hydrostatic pressure and conduction band non-parabolicity effects on the binding energy and the diamagnetic susceptibility of a hydrogenic impurity quantum dot

Electric field, hydrostatic pressure and conduction band non-parabolicity effects on the binding energies of the lower-lying states and the diamagnetic susceptibility of an on-center hydrogenic impurity confined in a typical GaAs/Al_xGa_1−xAs spherical quantum dot is theoretically investigated, by direct diagonalization of the Hamiltonian. To this end, the effect of band non-parabolicity has been performed, by means of the Luttinger-Kohn effective mass equation. Binding energies and diamagnetic susceptibility of the hydrogenic impurity are computed as a function of the dot size, external electric field strength and hydrostatic pressure, with considering the edge-band non-parabolicity. Results show that the external electric field and the hydrostatic pressure have an obvious influence on the binding energies and the diamagnetic susceptibility of the impurity.     

External electric field effects on the electronic and hydrogenic impurity states in ellipsoidal and semi-ellipsoidal quantum dots

In the effective mass approximation, energy eigenvalues of an electron confined in ellipsoidal and semi-ellipsoidal quantum dots, with and without hydrogenic impurity, under the influence of an external electric field have been investigated, using the matrix diagonalization method. The lower-laying states of the electron as functions of the electric field strength, the dot size and its geometry are calculated. Our results show that the electronic states are strongly affected by the applied electric field, the size and the geometry of the dot.     

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.     

Linear and Nonlinear Optical Absorptions of a Donor Impurity in Spherical Quantum Dots

An investigation of the optical properties of a hydrogenic donor in sphericalparabolic quantum dots 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 confinement strength. These results show the effects of the quantum size and the impurity on the optical absorption coefficient of a donor impurity quantum dot.     

Electric and magnetic field effects on the binding energy of a hydrogenic impurity in quantum well wires with different shapes

In this work, we directly calculate the ground state energies for an electron in quantum well wires (QWWs) with different shapes in the presence of applied electric and magnetic fields using the finite difference method. Then, we study the ground state binding energy of a hydrogenic impurity with a variational approach. We obtain the binding energy for QWWs consisting of the combinations of square and parabolic well potential. Our results indicate that the impurity binding energy depends strongly on the structural confinement and also, on the applied electric and magnetic field.     

Electronic and Shallow Impurity States in Semiconductor Heterostructures Under an Applied Electric Field

With the use of variational method to solve the effective mass equation, we have studied the electronic and shallow impurity states in semiconductor heterostructures under an applied electric field. The electron energy levels are calculated exactly and the impurity binding energies are calculated with the variational approach. It is found that the behaviors of electronic and shallow impurity states in heterostructures under an applied electric field are analogous to that of quantum wells. Our results show that with the increasing strength of electric field, the electron confinement energies increase, and the impurity binding energy increases also when the impurity is on the surface, while the impurity binding energy increases at first, to a peak value, then decreases to a value which is related to the impurity position when the impurity is away from the surface. In the absence of electric field, the result tends to the Levine＇s ground state energy （-1/4 effective Rydberg） when the impurity is on the surface, and the ground impurity binding energy tends to that in the bulk when the impurity is far away from the surface. The dependence of the impurity binding energy on the impurity position for different electric field is also discussed.     

Impurity-related optical response in a 2D and 3D quantum dot with Gaussian confinement under intense laser field

ABSTRACT

Using the two-dimensional (2D) diagonalisation method, the impurity-related electronic states and optical response in a 2D quantum dot with Gaussian confinement potential under nonresonant intense laser field are investigated. The effects of a hydrogenic impurity on the energy spectrum and binding energy of the electron and also intersubband optical absorption are calculated. The obtained numerical results show that the degeneracies of the excited electron states are broken and the absorption spectrum exhibits a redshift with the values of the laser field. The findings indicate a new degree of freedom to tune the performance of novel optoelectronic devices, based on the quantum dots and to control their specific properties by means of intense laser field and hydrogenic donor impurity. Using the same Gaussian confinement model, the electronic properties of a confined electron in the region of a spherical quantum dot are studied under the combined effects of on-centre donor impurity and a linearly polarised intense laser radiation. The three-dimensional problem is used to theoretically model, with very good agreement, some experimental findings reported in the literature related to the photoluminescence peak energy transition.     

Optical properties of a hydrogenic impurity in a confined Zn1−xCdxSe/ZnSe spherical quantum dot

The effect of longitudinal optical phonon field on the ground state and low lying-excited state energies of a hydrogenic impurity in a Zn_1−xCd_xSe/ZnSe strained quantum dot is investigated for various Cd content using the Aldrich-Bajaj effective potential. We consider the strain effect considering the internal electric field induced by the spontaneous and piezoelectric polarizations. Calculations have been performed using Bessel function as an orthonormal basis for different confinement potentials of barrier height. Polaron induced photoionization cross section of the hydrogenic impurity in the quantum dot is investigated. We study the oscillator strengths, the linear and third-order nonlinear optical absorption coefficients as a function of incident photon energy for 1s-1p and 1p-1d transitions with and without the polaronic effect. It is observed that the potential taking into account the effects of phonon makes the binding energies more than the obtained results using a Coulomb potential screened by a static dielectric constant and the optical properties of hydrogenic impurity in a quantum dot are strongly affected by the confining potential and the radii. It is also observed that the magnitude of the absorption coefficients increases for the transitions between higher levels with the inclusion of phonon effect.     

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.     

Electron–phonon effect on the ground-state binding energy of hydrogenic impurity in quantum-well wire in presence of an electric field

The hydrogenic impurity binding energy in rectangular quantum well wire including both barriers of finite height and an applied electric field are studied. The polaron effects on the ground-state binding energy in electric field are investigated by means of Landau-Pekar variation technique. The results for the binding energy as well as polaronic correction are obtained as a function of the size of the wire, the applied electric field and the position of the impurity. Our calculations are compared with previous results in quantum wires of comparable dimensions.     

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.     

Optical non-linearities associated to hydrogenic impurities in InAs/GaAs self-assembled quantum dots under applied electric fields

Abstract

The effects of the hydrogenic impurity on the electron-related non-linear optical processes in a InAs/GaAs dome-shaped quantum dot with a wetting layer under applied electric fields are studied within the density-matrix formalism. The one-electron energy levels and wave functions are calculated using the effective mass approximation and the finite element method. The non-linear optical absorption, relative refractive index change and non-linear optical rectification associated with interlevel transitions are calculated under a strong probe field excitation for both in-plane and z-polarisation of the incident light. According to our results as the electric field increases the absorption and dispersion peaks decrease and exhibit red shift. Hydrogenic impurity located at the origin induces a blue shift in the optical responses. For the optical absorption coefficient the peaks magnitude is enhanced by the impurity presence independent of the electric field strengths, whereas the non-linear optical rectification is larger in the case with impurity only for zero applied electric field.     

The nonlinear optical rectification of a confined exciton in a quantum dot

An exciton in a disc-like quantum dot (QD) with the parabolic confinement, under applied electric field, is studied within the framework of the effective-mass approximation. The nonlinear optical rectification between the ground and the first-excited states has been examined through the computed energies and wave functions in details for the excitons. The results show that the optical rectification susceptibility obtained in a disc-like QD reach the magnitude of 10⁻² m/V, which is 3-4 orders of magnitude higher than in one-dimensional QDs. It is found that the second-order nonlinear optical properties of exciton states in a QD are strongly affected by the confinement strength and the electric field.     

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.     

Phonon effect on binding energies of impurity states in cylindrical quantum wires of polar semiconductors under an electric field

Phonon effect on hydrogenic impurity states in cylindrical quantum wires of polar semiconductors under an applied electric field is studied theoretically by a variational approach. The binding energies are calculated as functions of the transverse dimension of the quantum wire, and the donor-impurity position under different fields. The electron–phonon interaction is considered in the calculations by taking both the confined bulk longitudinal optical phonons and interface optical phonons as well as the impurity-ion–phonon coupling. The numerical results for the CdTe and GaAs quantum wires are given and discussed as examples. It is confirmed that the electron–phonon interaction obviously reduces both the binding energy and the Stark energy-shift of the bound polarons in quantum wires.