Binding energy and diamagnetic susceptibility of an on-center hydrogenic donor impurity in a spherical quantum dot placed at the center of a cylindrical nano-wire

The binding energy and diamagnetic susceptibility of an on-center hydrogenic donor impurity in an InAs spherical quantum dot placed at the center of a GaAs cylindrical nano-wire have been investigated using finite element method in the framework of the effective mass approximation. The binding energy and diamagnetic susceptibility are calculated as a function of the dot radius, nano-wire radius and nano-wire height. The results show that as the dot radius increases (I) for a dot radius smaller than some critical value, the effect of the spherical confinement on the energy levels becomes negligible and the energies remain constant, for a dot radius larger than some specific value, the energy levels decrease (II) the ground and the first excited state binding energies increase, reach a maximum and then decrease (III) the ground state diamagnetic susceptibility increases, reach a maximum and then decreases (IV) the first excited state diamagnetic susceptibility increases, indicating two maxima and then decreases. The effects of the nano-wire dimensions on the binding energy and diamagnetic susceptibility have also been studied. We found that the binding energy and diamagnetic susceptibility decrease reach a minimum value and then increase as the nano-wire radius increases. Finally we found that as the height of the nano-wire increases the ground state binding energy decreases, reaches a minimum value and then increases but the first excited state binding energy decreases and reaches a constant value.     

Diamagnetic susceptibility of a laser dressed donor in a quantum well

The binding energy of laser dressed donor impurity is calculated under the influence of a magnetic field in a quantum well. The binding energy of the ground state of a donor is investigated, within the single band effective mass approximation, variationally for different concentrations at the well centre. The effect of laser and magnetic fields on diamagnetic susceptibility of the hydrogenic donor is reported. The Landau energy levels of electrons in the quantum well as a function of magnetic field are reported. The results show that the diamagnetic susceptibility (i) decreases drastically as intensity of the laser field increases (ii) increases with the magnetic field strength (iii) decreases as the Al-concentration decreases and (iv) a variation of increase in binding energy is observed when non-parabolicity is included and this effect is predominant for narrow wells. Our results are in good agreement with previous investigations for other heterostructures in the presence of laser intensity.     

Magnetic-field effect on the diamagnetic susceptibility of hydrogenic impurities in quantum well-wires

We have studied the magnetic field effects on the diamagnetic susceptibility and binding energy of a hydrogenic impurity in a quantum well-wire by taking into account spatially dependent screening. Using the effective-mass approximation within a variational scheme, binding energy and diamagnetic susceptibility of donor are obtained as a function of the magnetic field, length of the square quantum well-wire for different impurity positions. It is shown that the magnetic field effects on diamagnetic susceptibility can be more important for donors in quantum well-wires over a large range of wire dimensions.     

The binding energy of a hydrogenic impurity in self-assembled double quantum dots

The binding energy of a hydrogenic impurity in self-assembled double quantum dots is calculated via the finite-difference method. The variation in binding energy with donor position, structure parameters and external magnetic field is studied in detail. The results found are: (i) the binding energy has a complex behaviour due to coupling between the two dots; (ii) the binding energy is much larger when the donor is placed in the centre of one dot than in other positions; and (iii) the external magnetic field has different effects on the binding energy for different quantum-dot sizes or lateral confinements.     

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.     

Role of a uniform magnetic field on the energy spectrum of a single donor in a core/shell spherical quantum dot

Using the variational approach within the framework of the effective-mass approximation (EMA), the binding energy of a centred hydrogenic donor impurity in a CdSe/ZnTe core/shell spherical quantum dot (CSSQD) in the presence of an external magnetic field was investigated. In this model, we have taken into account the effect of the radial dependence of the dielectric constant and of the electron effective mass. Our numerical results show a remarkable influence of the nanodot spatial parameters and of the external magnetic field strength on the shallow donor binding energy.     

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.     

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.     

Combined effects of electric and magnetic fields on confined donor states in a diluted magnetic semiconductor parabolic quantum dot

A variational formalism for the calculation of the binding energies of hydrogenic donors in a parabolic diluted magnetic semiconductor quantum dot is discussed. Results are obtained for Cd Mn Te/Cd Mn Te structures as a function of the dot radius in the presence of external magnetic and electric fields applied along the growth axis. The donor binding energies are computed for different field strengths and for different dot radii. While the variation of impurity binding energy with dot radii and electric field are as expected, the polarizability values enhance in a magnetic field. However, for certain values of dot radii and in intense magnetic fields the polarizability variation is anomalous. This variation of polarizability is different from non- magnetic quantum well structures. Spin polaronic shifts are estimated using a mean field theory. The results show that the spin polaronic shift increases with magnetic field and decreases as the electric field and dot radius increase.     

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.     

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.     

Rashba spin-orbit interaction effects on thermal and magnetic properties of parabolic GaAs quantum dot in the presence of donor impurity under external electric and magnetic fields

Based on the effective mass approximation, the magnetic and thermal properties of parabolic GaAs quantum dot have been investigated in the presence of Rashba Spin-Orbit interaction (RSOI), donor impurity and applied magnetic and electric fields. The exact diagonalization method has been used to solve the Hamiltonian of an electron confined in a quantum dot (QD) and obtain the eigenenergies and the binding energy of the donor impurity as a function of various QD physical parameters. We have shown the dependence of the average statistical energy, magnetization, magnetic susceptibility and heat capacity of the donor impurity in the QD on: the Rashba interaction parameter, the magnetic and electric fields, confining frequency, and temperature. The results reveal that these parameters can tune the magnetic properties of the GaAs quantum dot and flip the sign of magnetic susceptibility from negative (diamagnetic) to positive (paramagnetic) type material.     

The magnetoexciton binding energy dependency on aluminium concentration in cylindrical quantum wires

A calculation of the binding energy of an exciton confined in cylindrical quantum wires of GaAs surrounded by (Ga, Al) As in the presence of a uniform magnetic field is reported as a function of wire radius, potential height and magnetic field strength, using effective mass approximation and variational approach techniques. For larger magnetic field strength and aluminium (Al) concentration values, the binding energies get larger as expected and are found to be in good agreement with previous theoretical reports. However, we also observed a shift in the binding energy maxima position to smaller wire radii with increasing magnetic field strength and Al concentration.     

The electric field effect on binding energy of hydrogenic impurity in zinc-blende GaN/AlxGa1−xN spherical quantum dot

Within the framework of effective mass approximation, the binding energy of a hydrogenic donor impurity in zinc-blende GaN/Al_xGa_1−xN spherical quantum dot (QD) is investigated using the plane wave basis. The results show that the binding energy is highly dependent on impurity position, QD size, Al content and external field. The binding energy is largest when the donor impurity is located at the centre of the QD and the binding energy of impurity is degenerate for symmetrical positions with respect to the centre of QD without the external electric field. The maximum of the donor binding energy is shifted from the centre of QD and the degenerating energy levels for symmetrical positions with respect to the centre of QD are split in the presence of the external electric field. The binding energy is more sensitive to the external electric field for the larger QD and lower Al content. In addition, the Stark shift of the binding energy is also calculated.     

Simultaneous effects of temperature and pressure on diamagnetic susceptibility of a shallow donor in a quantum antidot

The effect of temperature and pressure, simultaneously, on the diamagnetic susceptibility and binding energy of a hydrogenic donor impurity at the center of a GaAs/Ga_1−xAl_xAs quantum antidot is studied within the effective mass approximation. For this goal, we first analytically solve the Schrödinger equation to obtain wavefunctions and energy levels. Then, using the electronic states, we can calculate the diamagnetic susceptibility. The results obtained from the present work reveals that (i) the diamagnetic susceptibility increases with increasing pressure, (ii) the diamagnetic susceptibility decreases by increasing temperature, (iii) the value of 〈r²〉 decreases with increasing pressure due to the quantum confinement, and (iv) an increase in the pressure enhances the binding energy for a constant temperature.     

The diamagnetic susceptibility of hydrogenic donor in two-dimensional semiconductors with anisotropic effective mass of carriers

In this study, the effects of quantum confinement and effective mass anisotropy parameter on the diamagnetic susceptibility of a hydrogenic donor placed in GaAs, Si, and Ge quantum wells with infinite confinement potential are investigated in the effective mass and parabolic band approximations by using two and one parameter trial wave functions. It is observed that the diamagnetic susceptibility of a hydrogenic donor in anisotropic quantum wells is essentially equal to the transverse diamagnetic susceptibility part when well widths are larger than L > 100 Å, and the impurity is located at center. Moreover, a two parameter trial wave function model gives higher values of diamagnetic susceptibility, except for χ_z (GaAs).     

Effects of concentration on magnetization in a diluted magnetic semiconductor quantum dot

The donor bound spin polaron in a Cd_1?xMn_xTe quantum dot is investigated theoretically. Spin polaronic shifts are estimated using a mean field theory. Magnetization is calculated for various concentrations of Mn²⁺ ions with the dot sizes. The lowest binding energies in a diluted magnetic semiconductor of a Cd_1?xMn_xTe quantum dot are also estimated. Using the effective mass approximation, calculations are presented with and without spatial dependent effective masses. It is found that (i) the lowest binding energy decreases with the dot radius (ii) position dependent mass gives larger binding energy for smaller dots (iii) the ionization energy becomes more when spin interaction energy is included (iv) variation of increase in ionization energy is sharper for smaller dots with increase in concentration and (v) the magnetization of Mn subsystem increases when concentration of Mn²⁺ ions increases and it has appreciable changes for smaller dots.     

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.     

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。     

Built-in electric field effect on hydrogenic impurity in wurtzite GaN/AlGaN quantum dot

The binding energy of a hydrogenic donor impurity in a wurtzite (WZ) GaN/AlGaN quantum dot (QD) is investigated, including the strong built-in electric field effect due to the spontaneous and piezoelectric polarizations. Numerical results show that the strong built-in electric field induces an asymmetrical distribution of the donor binding energy with respect to the center of the QD. The donor binding energy is insensitive to dot height when the impurity is located at the right boundary of the QD with large dot height.