Accurate wavefunctions for hydrogenic donors in GaAs(Ga,Al)As quantum dots

A simple variational wavefunction is proposed for calculating the energy of nodeless quantum states of a hydrogenic donor located at the centre of a spherical GaAs(Ga,Al)As quantum dot. Energies are calculated for the 1s, 2p and 3d states for a range of values of the radius of the quantum dot. The results are compared to the “exact” energies and for the ground state with the results obtained by using the wavefunction proposed by Porras-Montenegro and Perez-Merchancano [Phys. Rev. B 46 (1992) 9780]. For the range of quantum dot radii of practical interest, it is shown that the proposed wavefunction gives results of good accuracy. For the ground state, the results from the proposed wavefunction for R ≤ 4 are considerably better than those obtained from the wavefunction used by Porras-Montenegro and Perez-Merchancano.     

Simple wavefunction for an impurity in a parabolic quantum dot

A simple variational wavefunction is proposed for calculating the ground-state energy of a hydrogenic donor located at the centre of a spherical parabolic quantum dot. Binding energies are calculated for three values of the parameter which gives the strength of the confining parabolic potential by the proposed wavefunction as well as by a wavefunction used by Xiaoet al. [Superlattices and Microstructures,19, 137 (1996)]. The results are compared to the ‘exact’ energies obtained by numerical integration of the Schrodinger equation. It is shown that the proposed wavefunction gives considerably better results than the wavefunction used by Xiaoet al. in all cases.     

纤锌矿GaN柱形量子点中类氢施主杂质态

在有效质量近似和变分原理的基础上,选取含两个变分参数的波函数,研究了纤锌矿结构的GaN/AlxGa1-xN单量子点中类氢施主杂质体系的结合能随量子点(QD)尺寸以及杂质在量子点中位置的变化,并与以前使用不同尝试波函数的计算结果进行了比较。结果表明:由我们选取的两变分参数波函数得到的结果与前人选取的两变分参数波函数得到的结果相比有所改进,而与选取一个变分参数波函数得到的结果一致。同时我们还计算了体系的维里定理值随量子点半径的变化情况,所得结果与前人工作结果一致,说明本文选取的两变分参数波函数能很好地描述柱形量子点中施主杂质态的运动。     

Diamagnetic susceptibility of hydrogenic donor impurity in low-dimensional semiconducting systems

The binding energies of a hydrogenic donor both in the parabolic and non-parabolic conduction band model within the effective mass approximation have been computed for the low-dimensional semiconducting systems (LDSS) like quantum well, quantum well wire and quantum dot taking GaAs/Al_xGa_1−xAs systems as an example. It is observed that the effect of non-parabolicity is not effective when the system goes to lower dimensionality. The diamagnetic susceptibility of a hydrogenic donor impurity has also been computed in these LDSS in the infinite barrier model. Since no theoretical or experimental works on the diamagnetic susceptibility of LDSS are available in the literature, as a realistic case the diamagnetic susceptibility has been computed in the finite barrier model (x=0.3) for a quantum well and the results are discussed in the light of semiconductor-metal transition.     

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.     

Photoionization cross section of a donor impurity in a two-dimensional anisotropic quantum dot

A system of an electron with a hydrogenic impurity confined in a two-dimensional anisotropic quantum dot has been investigated. We report a calculation for the binding energy of a donor impurity. The important feature of a donor impurity in a two-dimensional anisotropic quantum dot is obtained via an analysis of the binding energy. The photoionization cross section associated with intersubband transitions has been calculated. The results are presented as a function of the incident photon energy. The results show that the photoionization cross section of a donor impurity in a two-dimensional anisotropic quantum dot is strongly affected by the degree of anisotropy and the size of the quantum dot.     

Magnetic field induced diamagnetic susceptibility of a hydrogenic donor in a GaN/AlGaN quantum dot

The binding energies of a hydrogenic donor in a GaN/AlGaN quantum dot are calculated in the influence of magnetic field. The calculations are carried out using the single-band effective mass approximation within a variational scheme. The magnetic field induced binding energy and diamagnetic susceptibility of the hydrogenic donor are obtained as a function of dot radius. Calculations have been carried out with and without the Zeeman effect through the energy-dependent effective mass. The diamagnetic shift of the hydrogenic donor is found for different dot radii. Our results show that (i) the binding energy is higher for smaller dot radii and the magnetic field effects are predominant for larger dot sizes, (ii) the binding energy is higher when the Zeeman effect is included for all the magnetic fields, (iii) the diamagnetic susceptibility increases with the magnetic field and is not pronounced for smaller dot radii and (iv) the diamagnetic shift has a good influence of larger dot radii.     

The structure of ion-acoustic waves in a low-frequency three-component electron–ion space plasma with two-electron populations

In the present paper, we have studied the binding energy of the shallow donor hydrogenic impurity, which is confined in an inhomogeneous cylindrical quantum dot (CQD) of \(\hbox {GaAs-Al}_{x}\hbox {Ga}_{1-x}\hbox {As}\). Perturbation method is used to calculate the binding energy within the framework of effective mass approximation and taking into account the effect of dielectric mismatch between the dot and the barrier material. The ground-state binding energy of the donor is computed as a function of dot size for finite confinement. The result shows that the ground-state binding energy decreases with the increase in dot size. The result is compared with infinite dielectric mismatch as a limiting case. The binding energy of the hydrogenic impurity is maximum for an on-axis donor impurity.     

Hydrogenic impurity states in zinc-blende InGaN quantum dot

Within the framework of effective-mass approximation, the binding energy of a hydrogenic donor impurity in a zinc-blende (ZB) InGaN/GaN cylindrical quantum dot (QD) is investigated using a variational procedure. Numerical results show that the donor binding energy is highly dependent on impurity position and QD size. The donor binding energy E_b is largest when the impurity is located at the center of the QD. The donor binding energy is decreased when the dot height (radius) is increased.     

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.     

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.     

Hydrogenic donors in doping superlattices: A model calculation

The binding energy and wavefunction of a hydrogenic donor in an effective potential ν(z) = ∣e∣?∣z∣ in a semicondusctor is calculated variationally as a function of the effective electric field ?. Such a potential represents the limit of a doping superlattice in which the donor doping layer is very thin, and it allows the properties of shallow donor states for which the effective potential varies substantially across the wavefunction to be discussed. It is found that substantial variations of the binding energy and wavefunction result for fields which are readily realizable experimentally.     

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.     

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.     

Effect of the parabolic potential on the binding energy of a hydrogenic impurity in a spherical quantum dot

The binding energy of the ground state of a hydrogenic off-center donor in a spherical quantum dot under a parabolic potential is calculated by a variational method within the effective-mass approximation. The parabolic potential is assumed to be a spherically symmetric potential. The location effects of a hydrogenic donor under a parabolic potential on the binding energy of the ground state are studied. It is found that in the case of an on-center donor, the parabolic potential tends to enhance the strength of the Coulomb interaction and the binding energy of the ground state, and in the case of an off-center donor, the effect of the parabolic potential on the binding energy of the ground state is somewhat complicated.     

Optical anisotropy of a donor in ellipsoidal quantum dots

A system of an electron with a hydrogenic impurity confined in anisotropic quantum dots with ellipsoidal shape has been investigated. The linear and nonlinear optical absorptions as well as refractive index changes associated with intersubband transitions has been calculated. The results are presented as a function of the incident photon energy. The results show that the optical properties of a donor in ellipsoidal quantum dots are strongly affected by the anisotropy degree and the dot size. The dot anisotropy is shown to play a fundamental role in determining the dot properties.     

Nonlinear optical properties of an off-center donor in a quantum dot under applied magnetic field

The nonlinear optical properties of an off-center hydrogenic donor in a two-dimensional quantum dot under applied magnetic field are investigated in detail by using the matrix diagonalization method. Based on the computed energies and wave functions, the linear, third-order and total optical absorption coefficients as well as the refractive index changes have been examined between the ground state (L=0) and the first excited state (L=1). The results show that the ion position, the applied magnetic field, the confinement frequency, and the incident optical intensity have an important influence on the nonlinear optical properties of off-center donors.     

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.     

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.     

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.