Binding energies of donor impurities in modulation-doped double quantum wells under an electric field

In this study, we have investigated theoretically the binding energies of shallow donor impurities in modulation-doped GaAs/Al_0.33Ga_0.67As double quantum wells (DQWs) under an electric field which is applied along the growth direction for different doping concentrations as a function of the impurity position. The electronic structure of modulation-doped DQWs under an electric field has been investigated by using a self-consistent calculation in the effective-mass approximation. The results obtained show that the carrier density and the depth of the quantum wells in semiconductors may be tuned by changing the doping concentration, the electric field and the structure parameters such as the well and barrier widths. This tunability gives a possibility of use in many electronic and optical devices.     

The effect of hydrostatic pressure on subband structure and optical transitions in modulation-doped quantum well

Within the framework of effective-mass approximation, we have calculated theoretically the effects of hydrostatic pressure and doping concentration on subband structure and optical transitions in modulation-doped GaAs/Al_xGa_1−xAs quantum well for different well widths. The electronic structure of modulation-doped quantum well under the hydrostatic pressure is determined by solving the Schrödinger and Poisson equations self-consistently. The results obtained show that intersubband transitions and the subband energy levels in the modulation-doped quantum well can be significantly modified and controlled by the well width, donor concentration and hydrostatic pressure.     

Intensity-dependent nonlinear optical properties in a modulation-doped single quantum well

In the present work, the changes in the intersubband optical absorption coefficients and the refractive index in a modulation-doped quantum well have been investigated theoretically. Within the envelope function approach and the effective mass approximation, the electronic structure of the quantum well is calculated from the self-consistent numerical solution of the coupled Schrödinger-Poisson equations. The analytical expressions of optical properties are obtained by using the compact density-matrix approach. The numerical results GaAs/Al_xGa_1−xAs are presented for typical modulation-doped quantum well system. The linear, third-order nonlinear and total absorption and refractive index changes depending on the doping concentration are investigated as a function of the incident optical intensity and structure parameters, such as quantum well width and stoichiometric ratio. The results show that the doping concentration, the structure parameters and the incident optical intensity have a great effect on the optical characteristics of these structures.     

Effects of an intense, high-frequency laser field on the intersubband transitions and impurity binding energy in semiconductor quantum wells

Within the framework of effective-mass approximation, using a variational method, the effect of high-frequency laser field on intersubband transitions and the binding energy of shallow-donor impurities in a semiconductor quantum well are investigated. We have found that the increase of the laser-dressing parameter leads to important effects on the electronic and optical properties of a quantum well. This gives a new degree of freedom in various device applications based on the intersubband transition of electrons.     

Geometrical effects on shallow donor impurities in quantum wires

We have studied theoretically the impurity binding energy for wires of different shapes (V-shaped quantum wire (V-QWR) and rectangular wire) with a variational procedure without using any coordinate transformation. The effective potential for V-QWR used in this work consists of a square well potential in the z-direction and full graded well potential in the x-direction. Our results are in good agreement with previous theoretical results, found by the coordinate transformation method. Furthermore, it is shown that the impurity binding energy in quantum wires is sensitive to the geometrical effects.     

Effects of built-in electric field on donor binding energy in InGaN/ZnSnN2 quantum well structures

In_xGa${}_{1?x}$N/ZnSnN₂ quantum well structures are studied in terms of a binding energy of a donor atom. 1s and $2p_{\pm }$ impurity states are considered. The Schrödinger's and Poisson's equations are solved self-consistently. A hydrogenic type wave function to represent each impurity state is assumed. The calculations include band-bending in the potential energy profile introduced by the built-in electric field existing along the structures. The binding energy and the energy of the transition between the impurity states are represented as a function of the quantum well width, the donor position, and the indium concentration. An external magnetic field up to 10 T is included into the calculations to compute the Zeeman splitting. The maximum value of the transition energy is around 30 meV (nearly 7.3 THz) which occurs in a 15-Å In_0.3Ga_0.7N/ZnSnN₂ quantum well. Being strong, the built-in electric field makes the transition energy drop quickly with the decreasing well width. For the same reason, the energy curves are found to be highly asymmetric function of the donor position around the well center. Compared to the bulk value, the transition energy in the quantum well structures enhances nearly two-fold.     

Exciton and donor binding energies in quantum-well wires and quantum dots a fractional-dimensional space approach

A simple method for calculating the free-exciton binding energies in the fractional-dimensional-space model for single-quantum-well structure has been extended to quantum-well wires and quantum dots, in which the real anisotropic system is modelled through an effective isotropic environment with a fractional dimension. In this scheme, the fractional-dimensional parameter is chosen via an analytical procedure and involves no ansatz. We calculated the ground-state binding energies of excitons and donors in quantum-well wires with rectangular cross sections. Our results are found to be in good agreement with previous variational calculations and available experimental measurements. We also discussed the ground-state exciton binding energy changing with different shapes of quantum-well wires,     

Binding energy of impurity states in an inverse parabolic quantum well under magnetic field

 We have investigated the effects of the magnetic field which is directed perpendicular to the well on the binding energy of the hydrogenic impurities in an inverse parabolic quantum well (IPQW) with different widths as well as different Al concentrations at the well center. The Al concentration at the barriers was always x_max=0.3. The calculations were performed within the effective mass approximation, using a variational method. We observe that IPQW structure turns into parabolic quantum well with the inversion effect of the magnetic field and donor impurity binding energy in IPQW strongly depends on the magnetic field, Al concentration at the well center and well dimensions.     

Simultaneous effects of pressure and temperature on donors in a GaAlAs/GaAs quantum well

The ground state and a few excited state energies of a hydrogenic donor in a quantum well are computed in the presence of pressure and temperature. The binding energies are worked out for GaAs/ Ga_1−xAl_xAs structures as a function of well size when the pressure and temperature are applied simultaneously. A variational approach within the effective mass approximation is considered. The results show that for a constant applied pressure, an increase in temperature results in a decrease in donor impurity binding energy while an increase in the pressure for the same temperature enhances the binding energy. When the pressure and temperature are applied simultaneously the binding energy decreases as the well width increases. In all the cases, it is observed that there is an increase in the binding energy due to the decrease in the quantum well size and in the dielectric constant whereas the effects of temperature on the effective mass are minimal.     

Interband transitions in a spherical quantum layer in the presence of an electric field: Spherical rotator model

The interband transitions in a spherical GaAs quantum layer in the presence of an arbitrarily directed electric field are studied theoretically within the framework of the rigid spherical rotator model. The problem is solved under the assumption that the external field is a perturbation. Within the framework of the dipole approximation an expression for the interband absorption coefficient is obtained, and the absorption threshold frequency is determined. The corresponding selection rules are derived. A comparison with the case of quantum transitions in a spherical quantum layer in the presence of a radial electric field is performed.     

Barrier height effect on binding energies of shallow hydrogenic impurities in coaxial GaAs/ AlxGa1−xAs quantum well wires under a uniform magnetic field

The ground state binding energies of axial hydrogenic impurities in a coaxial cylindrical quantum well wire are reported as a function of the barrier height and the radius of wire in the presence of a uniform magnetic field applied parallel to the wire axis. The quantum well wire (QWW) is assumed to be an infinitely long cylinder of GaAs material surrounded by Al_xGa_1−xAs (for finite case and vacuum for infinite case). Binding energy calculations were performed with the use of a variational procedure in the effective mass approximation. We observed that the binding energy is sensitive to well radius only for both larger R$R$ values and small magnetic fields. We also compared the infinite and finite case binding energies and showed that increasing the Al concentration in the finite barrier case, binding energies are increased as expected. Our results are in good agreement and complementary with the previous theoretical works.     

Interband transitions in a narrow-band spherical InSb quantum layer in the presence of an electric field

The interband transitions in a narrow-band InSb quantum spherical layer are studied theoretically within the framework of the spherical rotator model. The electron and light-hole dispersions are described using the two-band Kane approximation, while for heavy holes the standard dispersion is considered. The absorption coefficients for transitions between conduction and lighthole, heavy-hole bands are calculated. The selection rules and threshold absorption frequencies are determined. It is shown that in the presence of a weak electric field the selection rules and threshold absorption frequencies for dipole transitions are modified.     

On the binding energies of excitons in polar quantum well structures in a weak electric field

The binding energies of excitons in quantum well structures subjected to an applied uniform electric field by taking into account the exciton longitudinal optical phonon interaction is calculated. The binding energies and corresponding Stark shifts for Ⅲ-Ⅴ and Ⅱ-Ⅵ compound semiconductor quantum well structures have been numerically computed. The results for GaAs/A1GaAs and ZnCdSe/ZnSe quantum wells are given and discussed. Theoretical results show that the exciton-phonon coupling reduces both the exciton binding energies and the Stark shifts by screening the Coulomb interaction. This effect is observable experimentally and cannot be neglected.     

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.     

Impurity binding energies in quantum dots with parabolic confinement

We present an effective numerical procedure to calculate the binding energies and wave functions of the hydrogen-like impurity states in a quantum dot (QD) with parabolic confinement. The unknown wave function was expressed as an expansion over one-dimensional harmonic oscillator states, which describes the electron's movement along the defined z-axis. Green's function technique used to obtain the solution of Schredinger equation for electronic states in a transverse plane. Binding energy of impurity states is defined as poles of the wave function. The dependences of the binding energy on the position of an impurity, the size of the QD and the magnetic field strength are presented and discussed.     

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.     

Photoionization and binding energy of a donor impurity in a quantum dot under an electric field: Effects of the hydrostatic pressure and temperature

Using the perturbation approach, we have calculated the donor impurity related photoionization cross-section in a quantum dot under different temperature and hydrostatic pressure conditions. Our calculation have revealed the dependence of the photoionization cross-section on the confinement strength, temperature and hydrostatic pressure.     

Simultaneous effects of temperature and pressure on the donor binding energy in a V-groove quantum wire

The influence of temperature and pressure, simultaneously, on the binding energy of a hydrogenic donor impurity in a ridge GaAs/Ga_1−xAl_xAs quantum wire is studied using a variational procedure within the effective mass approximation. The subband energy and the binding energy of the donor impurity in its ground state as a function of the wire bend width and impurity location at different temperatures and pressures are calculated. The results show that, when the temperature increases, the donor binding energy decreases for a constant applied pressure for all wire bend widths. Also, the binding energy increases by increasing the pressure for a constant temperature for all wire bend widths. In addition, when the temperature and pressure are applied simultaneously the binding energy decreases as the quantum wire bend width increases. On the whole, it is deduced that the temperature and pressure have important effects on the donor binding energy in a V-groove quantum wire.     

The effects of temperature and hydrostatic pressure on the photoionization cross-section and binding energy of shallow donor impurities in quantum dots

Using a variational approach, we have calculated the hydrostatic pressure and temperature effects on the donor impurity related photoionization cross-section and impurity binding in GaAs/GaAlAs quantum dots. Our calculations have revealed the dependence of the photoionizaton cross-section and the impurity binding on temperature and hydrostatic pressure.     

The effect of intense laser field on the Electronic Raman Scattering of shallow donor impurities in quantum dots

The laser-field dependence of energy levels and donor-related Electronic Raman Scattering is investigated by a quasi-analytical approach. The differential cross section involved in this process is calculated as a function of secondary radiation photon energy. We find that the laser field amplitude and confinement strength have an important influence on the Raman scattering. And the transitions between lower electronic energy states are more sensitive to the laser field.