Binding Energy Of Hydrogenic Impurity Research Articles

Binding energy of hydrogenic impurity states in an inverse parabolic quantum well under static external fields

In the present theoretical study, we investigate the influence of external fields (electric and/or magnetic) on the binding energy of hydrogenic impurities in a GaAs/Ga1-xAlxAs inverse parabolic quantum well, in which the parabolicity depends on the Al concentrations at the well center. Our calculations have been based on the potential morphing method in the effective mass approximation. The systematic theoretical investigation contains results with all possible combinations of the involved parameters, as quantum well width, Al concentrations at the well center, position of the impurity and magnitudes of the external fields.

Bound polaron in a wurtzite nitride semiconductor ellipsoidal quantum dot

The binding energy of a hydrogenic donor impurity in weakly oblate ellipsoidal quantum dot is investigated with a variational method by taking the electron couples with both branches of the mixing properties of the LO and TO polarizations (LO-like and TO-like phonons) due to the anisotropic effect into account. The interaction between impurity and phonons has also been considered to obtain the binding energy of bound polaron. The numerical computation has been performed for wurtzite nitride semiconductor GaN. The results show that the binding energy of bound polaron is reduced by the phonons effect on the impurity states. It indicates that the contribution of LO-like phonon to the binding energy is dominant, and the anisotropic angle and ellipticity influence on the binding energy are small.

Influence of strain on hydrogenic impurity states in a GaN/Al x Ga1−x N quantum dot

Within the effective-mass approximation, we calculated the influence of strain on the binding energy of a hydrogenic donor impurity by a variational approach in a cylindrical wurtzite GaN/AlxGa1−xN strained quantum dot, including the strong builtin electric field effect due to the spontaneous and piezoelectric polarization. The results show that the binding energy of impurity decreases when the strain is considered. Then the built-in electric field becomes bigger with the Al content increasing and the binding energy of hydrogenic donor impurity decreases when the Al content is increasing. For dot height L < 2 nm, the change of the binding energy is very small with the Al content variety.

Shallow impurity binding energy in lateral parabolic confinement under an external magnetic field

We have described the calculation of hydrogenic impurity binding energies in cylindrical GaAs–Ga 1− x Al x As quantum well wires (QWWs) with lateral parabolic confinement in the presence of an axial magnetic field. The numerical calculations of this system have been performed with the use of a variational procedure in the effective mass approximation. We observed sharp changes in binding energy for critical spatial confinement radius and B magnetic field values.

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/AlxGa1−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.

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 rectangular confinement is better than the parabolic and spherical confinements. These results are compared with the existing literature.

The magnetic field dependency of hydrogenic impurity binding energy under inverse lateral parabolic potential

We calculated the magnetic field dependency of hydrogenic donor binding energy in cylindrical quantum wires under inverse lateral parabolic potential. We have worked in the effective mass approximation and variational calculation scheme. We have found there is an abrupt change in binding energy with the magnetic field strength, and the results are compared with square quantum wire binding energies.

Simultaneous effects of pressure and magnetic field on donors in a parabolic quantum dot

The binding energy of shallow hydrogenic impurities in parabolic quantum dots is calculated using a variational approach within the effective mass approximation. The binding energies are worked out for GaAs/Ga 1− x Al x As structures as a function of dot size when the static pressure and the magnetic field are applied simultaneously. The results show that the impurity binding energy (i) increases with the reduction in dot sizes for a given pressure and magnetic field; (ii) decreases for a given dot in the presence of pressure; (iii) increases for a given dot by the influence of magnetic field and (iv) increases for a given dot in the presence of pressure and magnetic field applied simultaneously. The result shows that the ionization energy is purely pressure dependent for dots of size less than an effective Bohr radius. The results are compared with available data in the literature.

Hydrogenic impurity binding energy in self-assembled GaAs∕Ga1−xAlxAs quantum rings

Using a variational approach within the effective mass approximation and adiabatic approximation, the binding energy of the ground state of a hydrogenic impurity positioned in a self-assembled GaAs∕Ga1−xAlxAs quantum ring (QR) is studied. The binding energy is calculated as a function with the size (outer radius, height) of the QR, the Al concentration, and the donor impurity position. The results indicate that the binding energy reaches a peak value when the size (outer radius, height) of the QR decreases to a certain value. The binding energy reaches a maximum for an impurity ion positioned at the midplane perpendicular to the symmetry axis of the QR. In addition, the binding energy becomes large as the Al concentration in GaAs∕Ga1−xAlxAs increases. When shifting the impurity ion from the internal surface of the QR to the external surface, the impurity binding energy increases, then decreases to a certain value, indicating that there is a maximum.

Binding energy of hydrogenic impurity in [formula omitted] multi-quantum-dot structure

In this paper, we perform a theoretical study, using a variational method, of the binding energy of ground state for hydrogenic impurity in the multi-quantum-dot structure. It is found that the binding energy is not only as a function of the size of the system in the x – y plane, but also the barrier thickness and the width of a dot in the z direction. Especially, when the barrier thickness is equal to the width of a dot, there are two peaks in the behavior of the binding energy as a function of the barrier thickness. All these behaviors of the binding energy are determined by the competition between the localization effect of the wave function and the tunneling effect of the wave function due to an increase or decrease in the barrier thickness and the width of a dot. Moreover, we also investigate the behavior of binding energy with different impurity position.

The binding energy of hydrogenic impurity in multilayered spherical quantum dot

The binding energy of a hydrogenic impurity of a multilayered spherical GaAs-(Ga,Al)As quantum dot has been investigated as a function of the barrier thickness and the inner dot thickness for various barrier potentials in the effect of the band non-parabolicity. Within the effective mass approximation, the ground state energy has been calculated using the fourth-order Runge–Kutta method. The ground state binding energy of hydrogenic impurity located at the center of a quantum dot has been studied with a variational approach. We have found that a variation in the binding energy has depended on the geometry of the dot.

EFFECT OF MAGNETIC FIELDS ON BINDING ENERGY OF IMPURITY STATES IN A SEMIMAGNETIC PARABOLIC QUANTUM DOT

Using a variational approach, the binding energy of shallow hydrogenic impurities in a semimagnetic parabolic quantum dot is calculated within the effective mass approximation. The binding energy is computed for Cd 1-x in Mn x in Te / Cd 1-x out Mn x out Te structures as a function of the dot size in an external magnetic field. The results show that the impurity binding energy (i) increases with the reduction in dot sizes (ii) decreases when the magnetic field is increased for a given dot and (iii) increases to a maximum value at 100 Å and then decreases as the size of the dot increases beyond 100 Å for a realistic model. Spin polaronic shifts are estimated using a mean field theory. These results are compared with the existing literatures.

Hydrogenic donor states in wurtzite InGaN/GaN coupled quantum dots

The binding energies of the hydrogenic impurity in wurtzite InGaN coupled quantum dots (QDs) are calculated by means of a variational method, considering the strong built-in electric field induced by 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 coupled QDs. When the impurity is located in the center of the left dot, the donor binding energy is largest and insensitive to the barrier height of the wurtzite InGaN coupled QDs.

Binding Energy of an Off-Center Hydrogenic Donor Impurity in a Finite Confining Potential Quantum Well

Low dimensional semiconductor heterostructures such as quantum wells, wires, boxes, and dots have gained a great importance in the last two decades due to their fundamental properties and their wide range of applications. Special care has been given to investigate these quantum systems in the presence of shallow impurities [1{9]. The problem of calculating the binding energy of hydrogenic impurity in a quantum well has been considered in the pioneering work of Bastard [10]. He studied the case of center and ofi-center impurity but in an inflnite conflning potential quantum well. He applied a variational approach that was based on modifying the exact wave function of an inflnite quantum well by adding a term that represents the hydrogenic impurity. The resulting trial wave function depends on one variational parameter. The case of flnite conflning potential quantum well was dealt with by using a similar approach by Chaudhuri and Bajaj [11] and Elabsy [12]. Jia-Lin Zhu [13] and Greene and Bajaj [14, 15] applied more complicated variational methods. However, in all these treatments the case of a

Intense laser field effects on the binding energy of impurities in semiconductors

Nonperturbative, accurate variational results for the binding energy of a shallow hydrogenic impurity in a bulk semiconductor irradiated by a high-frequency, intense laser field are presented. It is pointed out that variational results found with $1s$ and $2s$ atomic trial wave functions presented in previous works on this subject are incorrect because these wave functions do not allow the stretching of the electronic cloud along the polarization direction. This is corrected here by choosing appropriate trial wave functions for the ground and first excited states, which resemble those for the $(1s)\ensuremath{\sigma}$ states of the ${{\mathrm{H}}_{2}}^{+}$ molecular ion. Special attention is paid to the limit of large values for the laser-dressing parameter ${\ensuremath{\alpha}}_{0}$, where our model furnishes almost exact results. In this limit, we found that the binding energy tends to $\ensuremath{-}1∕4\phantom{\rule{0.3em}{0ex}}{\mathrm{Ry}}^{*}$ with the increase of ${\ensuremath{\alpha}}_{0}$. Then, impurity stability against ionization is expected, which is in contrast to previous works.

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

Abstract 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 AlxGa1−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 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.

Hydrostatic-pressure effects on the donor binding energy in GaAs–(Ga, Al)As quantumdots

The binding energy of shallow hydrogenic impurities in a spherical quantum dot underisotropic hydrostatic pressure is calculated using a variational approach withinthe effective mass approximation. The binding energy is computed as a functionof hydrostatic pressure, dot size and impurity position. The results show thatthe impurity binding energy increases with the pressure for any position of theimpurity. Also, we have found that the binding energy depends on the location of theimpurity and the pressure effects are less pronounced for impurities on the edge.

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.

THE EFFECTS OF QUANTUM CONFINEMENT ON THE BINDING ENERGY OF HYDROGENIC IMPURITIES IN A SPHERICAL QUANTUM DOT

The binding energy of a shallow hydrogenic impurity of a spherical quantum dot confined by harmonic oscillator-like and by rectangular well-like potentials, using a variational procedure within the effective mass approximation, has been determined. The calculations of the binding energy of the donor impurity as a function of the system geometry, and the donor impurity position have been investigated. The binding energy of shallow donor impurity depends not only on the quantum confinements but also on the impurity position. Our results reveal that (i) the donor binding energy decreases as the dot size increases irrespective of the impurity position, and (ii) the binding energy values of rectangular confinement are larger than the values of parabolic confinement and (iii) the rectangular confinement is better than the parabolic confinement in a spherical quantum dot.

Binding energy of impurity states in a parabolic quantum dot in a strong magnetic field

AbstractThe binding energies of shallow hydrogenic impurities in parabolic quantum dots are calculated using a variational approach within the effective mass approximation. Results are obtained for CdMnTe/CdMnTe structures as a function of the dot radius in an external magnetic field. The results show that the impurity binding energy (i) increases with the decrease in dot radius, (ii) decreases when the magnetic field is increased for a given dot and (iii) increases to a maximum value at 90 Å and then decreases as the size of the dot increases beyond 90 Å in the finite barrier case. This feature is different from non magnetic quantum well structures. Spin polaronic shifts are estimated using a mean field theory. The results show that the shifts are ≤1 meV in the zero‐field case and still smaller in a magnetic field. This shift not only decreases in a magnetic field but also decreases when the dot radius increases. (© 2005 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)