Intense laser field effects on the electron Raman scattering in a strained InGaN/GaN quantum well

The differential cross-section for an intersubband electron Raman scattering process in a strained InGaN/GaN quantum well in the presence of an intense laser field is studied. In the effective-mass approximation, the electronic structure is calculated by taking into account the effects of spontaneous and piezoelectric polarization fields on the confinement potential. Effects of laser field strength, indium composition and the well width on the differential cross-section of the strained quantum well are investigated. Results show that the position and the magnitude of the peaks of emission spectra considerably depend on the laser field strength as well as structural parameters.     

Photoionization cross-section and binding energy of donor impurities in GaAs, Ge and Si quantum wires with infinite barriers

Within the effective-mass approximation, we have investigated the binding energies of donor impurities as a function of the wire dimensions and the photoionization cross-section for a hydrogenic donor impurity placed on the center of the quantum well-wire as a function of the normalized photon energy in the GaAs, Ge and Si quantum wires with infinite barriers. The calculations are performed by the variational method based on a two-parametric trial wave function. The results show that the impurity binding energy and the photoionization cross-section depend strongly on both wire dimensions and material parameters.     

Pressure induced optical absorption and refractive index changes of a shallow hydrogenic impurity in a quantum wire

Pressure induced binding energy of a hydrogenic impurity in an InAs/GaAs quantum wire is investigated. Calculations are performed using Bessel functions as an orthonormal basis within a single band effective mass approximation using variational method. Photoionization cross-section of the hydrogenic impurity in the influence of pressure is studied. The total optical absorption and the refractive index changes as a function of normalized photon energy between the ground and the first excited state in the presence of pressure are analyzed. The optical absorption coefficients and the refractive index changes strongly depend on the incident optical intensity and pressure. The occurred blue shift of the resonant peak due to the pressure gives the information about the variation of two energy levels in the quantum well wire. The optical absorption coefficients and the refractive index changes are strongly dependent on the incident optical intensity and the pressure.     

Electronic Raman scattering in double semi-parabolic quantum wells

The differential cross-section for electronic Raman scattering in double semi-parabolic quantum wells of typical GaAs/AlxGa1-x As is investigated numerically with the effective-mass approximation. The dependence of the differential cross-section on structural parameters such as the barrier width and the well widths is studied. Our results indicate that the electronic Raman scattering is affected by the geometrical size and can be negligible in the symmetric double-well case.     

Hydrostatic pressure on optical absorption and refractive index changes of a shallow hydrogenic impurity in a GaAs/GaAlAs quantum wire

The effect of hydrostatic pressure on the binding energy of a hydrogenic impurity in a GaAs/GaAlAs quantum wire is discussed. Calculations have been performed using Bessel functions as an orthonormal basis within a single band effective mass approximation. Pressure induced photoionization cross section of the hydrogenic impurity is investigated. The total optical absorption and the refractive index changes as a function of normalized photon energy between the ground and the first excited state in the presence of pressure are analysed. The optical absorption coefficients and the refractive index changes strongly depend on the incident optical intensity and the pressure.     

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.     

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.     

Comparison of external electric and magnetic fields effect on binding energy of hydrogenic donor impurity in different shaped quantum wells

The effects of external electric and magnetic fields on the ground state binding energy of hydrogenic donor impurity are compared in square, V-shaped, and parabolic quantum wells. With the effective-mass envelope-function approximation theory, the ground state binding energies of hydrogenic donor impurity in InGaAsP/InP QWs are calculated through the plane wave basis method. The results indicate that as the quantum well width increases, the binding energy changes most fast in SQW. When the well width is fixed, the binding energy is the largest in VQW for the donor impurity located near the center of QWs. For the smaller and larger well width, the electric field effect on binding energy is the most significant in VQW and SQW, respectively. The magnetic field effect on binding energy is the most significant in VQW. The combined effects of electric and magnetic fields on the binding energy of hydrogenic donor impurity are qualitative consistent in different shaped QWs.     

Far infrared impurity absorption in a quantum well

We have calculated the energy and lineshape of the 1s → 2p_x,y transition for a hydrogenic impurity located in a quantum well. Due to the dependence of the transition energy on the impurity location, the absorption lineshape is very sensitive to the doping profile. The spectrum, in general, exhibits two peaks, arising from impurities located near the center and the edges of the well.     

Impurity optical absorption in parabolic quantum well

Optical absorption in GaAs parabolic quantum well in the presence of hydrogenic impurity is considered. The absorption coefficient associated with the transitions between the upper valence subband and donor ground state is calculated. The impurity ground state wave function and energy are obtained using the variational method. Dependence of the absorption spectra on impurity position in quantum well was investigated. It is shown, that along with quantum well width decrease the absorption threshold shifts to higher frequencies. Results obtained within frames of parabolic approximation are compared with results for rectangular infinite-barrier quantum well case. The acceptor state → conduction band transitions considered as well.     

Limitations of variational methods for hydrogenic systems

Theoretical methods that give good approximations of the behaviours of hydrogen-like impurity states in semiconductors in uniform external magnetic fields are by now well established. With variational methods in mind the sizes of the determinants that give sufficiently accurate energies greatly depend on the quality of the wave functions chosen as these affect the rapidity of the series convergence. The recently developed hybrid functions enable hydrogenic energies to be calculated up ton=7 using fairly small determinants. However, it has emerged that there is a restricted region of variational parameters which maintains the numerical symmetry of the hamiltonian matrix elements for each group of states. Although each such parameter regime appears to narrow as the magnetic quantum number increases, the accuracies of the calculated eigenvalues remain satisfactory.     

Electron and donor-impurity-related Raman scattering and Raman gain in triangular quantum dots under an applied electric field

The differential cross-section of electron Raman scattering and the Raman gain arecalculated and analysed in the case of prismatic quantum dots with equilateral trianglebase shape. The study takes into account their dependencies on the size of the triangle,the influence of externally applied electric field as well as the presence of an ionizeddonor center located at the triangle’s orthocenter. The calculations are made within theeffective mass and parabolic band approximations, with a diagonalization scheme beingapplied to obtain the eigenfunctions and eigenvalues of the x-y Hamiltonian. The incidentand secondary (scattered) radiation have been considered linearly-polarized along they-direction, coinciding with the direction of theapplied electric field. For the case with an impurity center, Raman scattering with theintermediate state energy below the initial state one has been found to show maximumdifferential cross-section more than by an order of magnitude bigger than that resultingfrom the scheme with lower intermediate state energy. The Raman gain has maximum magnitudearound 35 nm dot size andelectric field of 40 kV/cm forthe case without impurity and at maximum considered values of the input parameters for thecase with impurity. Values of Raman gain of the order of up to 10⁴cm^-1 are predicted in bothcases.     

Simultaneous Effects of HydrostaticPressure and Conduction Band Non-parabolicity on BindingEnergies and Diamagnetic Susceptibility of a Hydrogenic Impurityin Spherical Quantum Dots

Simultaneous effects of conduction band non-parabolicity and hydrostatic pressure on the binding energies of 1S, 2S, and 2P states along with diamagnetic susceptibility of an on-center hydrogenic impurity confined in typical GaAs/Al_xGa_1-xAs spherical quantum dots are theoretically investigated using the matrix diagonalization method. In this regard, the effect of band non-parabolicity has been performed using the Luttinger-Kohn effective mass equation. The binding energies and the diamagnetic susceptibility of the hydrogenic impurity are computed as a function of the dot radius and different values of the pressure in the presence of conduction band non-parabolicity effect. The results we arrived at are as follows: the incorporation of the band edge non-parabolicity increases the binding energies and decreases the absolute value of the diamagnetic susceptibility for a given pressure and radius; the binding energies increase and the magnitude of the diamagnetic susceptibility reduces with increasing pressure.     

External electric field and hydrostatic pressure effects on the binding energy and self-polarization of an off-center hydrogenic impurity confined in a GaAs/AlGaAs square quantum well wire

Based on the effective-mass approximation within a variational scheme, binding energy and self-polarization of hydrogenic impurity confined in a finite confining potential square quantum well wire, under the action of external electric field and hydrostatic pressure, are investigated. The binding energy and self-polarization are computed as functions of the well width, impurity position, electric field, and hydrostatic pressure. Our results show that the external electric field and hydrostatic pressure as well as the well width and impurity position have a great influence on the binding energy and self-polarization.     

Effect of conduction band parabolicity on the spectrum and binding energy of a hydrogenic impurity in GaAs spherical quantum dots

The energy levels and binding energies of a hydrogenic impurity in GaAs spherical quantum dots with radius R are calculated by the finite difference method. The system is assumed to have an infinite confining potential well with radius R, which can be viewed as a hard wall boundary condition. The parabolicity of the conduction band profile for GaAs material can be viewed as a parabolic potential well. The energy levels and binding energies are depended dramatically on the radius of the quantum dot and the parabolic potential well. The results show that parabolic potential can remarkably alter the energy level ordering and binding energy level ordering of hydrogenic impurity states for the quantum dot with a smaller radius R.     

Hydrogenic impurity states in zinc-blende GaN/AlN coupled quantum dots

Based on the effective-mass approximation, we have calculated the donor binding energy of a hydrogenic impurity in zinc-blende (ZB) GaN/AlN coupled quantum dots (QDs) using a variational method. Numerical results show that the donor binding energy is highly dependent on the impurity position and coupled QDs structural parameters. The donor binding energy is largest when the impurity is located at the center of quantum dot. When the impurity is located at the interdot barrier edge, the donor binding energy has a minimum value with increasing the interdot barrier width.     

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.     

Linear and Nonlinear Optical Properties of Spherical Quantum Dots:Effects of Hydrogenic Impurity and Conduction Band Non-Parabolicity

Simultaneous effects of an on-center hydrogenic impurity and band edge non-parabolicity on intersubband optical absorption coefficients and refractive index changes of a typical GaAs/Al x Ga 1 x As spherical quantum dot are theoretically investigated,using the Luttinger-Kohn effective mass equation.So,electronic structure and optical properties of the system are studied by means of the matrix diagonalization technique and compact density matrix approach,respectively.Finally,effects of an impurity,band edge non-parabolicity,incident light intensity and the dot size on the linear,the third-order nonlinear and the total optical absorption coefficients and refractive index changes are investigated.Our results indicate that,the magnitudes of these optical quantities increase and their peaks shift to higher energies as the influences of the impurity and the band edge non-parabolicity are considered.Moreover,incident light intensity and the dot size have considerable effects on the optical absorption coefficients and refractive index changes.     

Dielectric mismatch effect on the photoionization cross section and intersublevel transitions in GaAs nanodots

A theoretical study of the electronic states in a spherical quantum dot with and without a hydrogenic impurity is performed within the effective mass approximation taking into account the dielectric mismatch effect. By considering the joint action of the quantum confinement and polarization charges, the photoionization cross section for an on-center donor and intersublevel optical absorption are investigated. We found that: i) the subband energies increase while the 1s and 2p impurity levels decrease when the dielectric mismatch between the dot and its environment enhances; ii) the dielectric mismatch has a significant effect on the peak position and magnitude of the photoionization cross section so that the behavior of this quantity can indicate the material in contact with the nanostructure; iii) the absorption spectrum is less sensitive to the environment dielectric properties but it significantly depends on the dot radius as well as on the impurity presence. The possibility of tuning the resonant energies by using the combined effect of the quantum confinement and dielectric mismatch between the dot and the surrounding medium can be useful in designing new optoelectronic devices.     

Conduction Band-Edge Non-Parabolicity Effects on Impurity States in （In,Ga）N/GaN Cylindrical QWWs

In this paper, the conduction band-edge non-parabolicity （NP） and the circular cross-section radius effects on hydrogenie shallow-donor impurity ground-state binding energy in zinc-blende （ZB） InGaN/GaN cylindrical QWWs are reported. The finite potential barrier between （In,Ga）N web and CaN environment is considered. Two models of the conduction band-edge non-parabolicity are taking into account. The variational approach is used within the framework of single band effective-mass approximation with one-parametric 1S-hydrogenic triaJ wave-function. It is found that NP effect is more pronounced in the wire of radius equal to effective Bohr radius than in large and narrow wires. Moreover, the binding energy peak shifts to narrow wire under NP effect. A good agreement is shown compared to the findings results.