On-center Impurity Research Articles

Hydrogenic impurity bound polaron in a quantum dot quantum well structure

A variational approach is used within the framework of effective mass approximation to study the binding energy of the hydrogenic impurity in a spherical quantum dot quantum well (QDQW) structure. The electron- and ion-longitudinal-optical (LO) phonon interactions are taken into account in the calculation. The numerical results for the CdS/HgS QDQW structure embedded in an insulator matrix show that the binding energy is sensitive both to the size of the core and the width of the shell. The binding energy decreases with the core radius being increased, and exhibits a maximum with the shell width being increased. The LO phonon effect lowers the binding energy of the on-center impurity and decreases sharply with the shell well-width being increased.

Combination effects of tilted electric and magnetic fields on donor binding energy in a GaAs/AlGaAs cylindrical quantum dot

We have performed a systematic study on the ground-state binding energy of an on-center donor impurity confined in a GaAs/Al0.3Ga0.7As cylindrical quantum dot (QD), subjected to simultaneously applied electric and magnetic fields. The two fields are tilted with respect to the QD growth direction and they are either parallel or perpendicular to each other. All the calculations are based on the potential morphing method which is employed within the framework of the effective-mass approximation. Our results show that when the tilted electric and magnetic fields are parallel, the magnetic shift of the donor binding energy is a monotonic function of the magnetic field strength. On the other hand, when the two fields are perpendicular to each other, the magnetic shift of the donor binding energy varies nonmonotonically with respect to the magnetic field strength, exhibiting a minimum value at a critical magnetic field strength. The position of this minimum value and its dependence on the QD size, its aspect ratio and the orientation of the tilted magnetic field is systematically investigated. Moreover, we discuss in detail the competition effects which appear in the presence of the two fields, showing that the critical line which corresponds to zero shift of the donor binding energy can be manipulated by suitably adjusting the QD size, the aspect ratio and the relative orientation of the two fields.

The electronic properties of a core/shell/well/shell spherical quantum dot with and without a hydrogenic impurity

In this study, we have performed a detailed investigation of the electronic properties of a core/shell/well/shell multilayered spherical quantum dot, such as energy eigenvalues, wave functions, electron probability distribution, and binding energies. The energy eigenvalues and their wave functions of the considered structure have been calculated for cases with and without an on-center impurity. For this purpose, the Schrödinger equation has been numerically solved by using the shooting method in the effective mass approximation for a finite confining potential. The electronic properties have been examined for different core radii, barrier thicknesses, and well widths in a certain potential. The results have been analyzed in detail as a function of the layer thicknesses and their physical reasons have been interpreted. It has been found that the electronic properties are strongly dependent on the layer thicknesses.

Stark effects on bound polarons in polar rectangular quantum wires

The impurity binding energy in a polar rectangular quantum wire under an applied electric field is studied by a variational approach. The electron- and ion-longitudinal-optical (LO) phonon interactions are both taken into account in the calculations. The numerical results for the GaAs rectangular quantum wires show that the binding energies and Stark energy-shift are both sensitive to the size, shape of the wire section, and the position of the impurity. The binding energy increases with decreasing the section area. The LO phonon effect lowers the binding energy of the on-center impurity but raises that of the impurity near the wire surface, and gives a qualitatively similar contribution to the Stark effect.

Binding energy of an off-center shallow donor [formula omitted] in a spherical quantum dot

The binding energy of a negatively charged hydrogenic impurity with on- and off-center positions in a spherical Gaussian quantum dot was calculated with the configuration interaction method. Our calculations show that E b is always positive for on-center impurities with a maximum near to the radius for one-electron stability of the potential well R c . For off-center positions the binding energy can assume negative values within a range of the quantum dot radius, thus indicating the instability of the system.

Computation of the oscillator strength and absorption coefficients for the intersubband transitions of the spherical quantum dot

The electronic structure and optical properties of one-electron Quantum Dot (QD) with and without an on-center impurity were investigated by assuming a spherically symmetric confining potential of finite depth. The energy eigenvalues and the state functions of QD were calculated by using a combination of Quantum Genetic Algorithm (QGA) and Hartree–Fock Roothan (HFR) method. We have calculated the binding energy for the states 1s,1p,1d,1f, oscillator strengths, the linear and third-order nonlinear optical absorption coefficients as a function of the incident photon energy and incident optical intensity for the 1s–1p, 1p–1d and 1d–1f transitions. The existence of the impurity has great influence on the optical absorption spectra and the oscillator strengths. Also we found that the magnitudes of the total absorption coefficients of the spherical QD increase for transitions between higher states.

Stability of neutral and negative donor impurity in a semiconductor cylindrical quantum dot

The stability of neutral (D0) and negative charged donor (D−) on- and off-center in anisotropic cylindrical quantum dot (CQD) is studied by use of a variational approach. Two-parameter anisotropic trial wave function which includes electron-correlation effects is utilized, to explore strong and weak confinement regions. A comparison between one and two-parameter trial wave functions results is introduced. The finite barrier height and the CQD dimensions, dependence of the “stability and the binding energy” of the D0 and the D− is obtained. It has been shown that the donor's stability dependent on CQD dimensions and the confinement potential in strong confinement region but in weak confinement region, the stability of D0 and D− is dependent strongly on the quantum dot (QD) radius R. It has been found that the donors D0 and D− off-center are less stable than the on-center impurities, and also the off-center donors more stable in small CQDs. It has shown that the stability of D− depends on the energy of the excess electron.

PHOTOIONIZATION CROSS-SECTION AND OSCILLATOR STRENGTH OF HYDROGENIC IMPURITIES IN ZnS/SiO2 QUANTUM DOTS

In this study, the photoionization cross-section and oscillator strength for the intersubband electronic transitions associated with an on-center impurity in the ZnS / SiO 2 spherical quantum dot have been calculated. The effects of dot radius, the normalized photon energy and the potential barrier height on the cross-section have been investigated. In the calculations, both the infinite and finite confinement cases have been considered.

Electronic structure of Mn-doped III-V semiconductor quantum dots

The electronic structure of GaAs and InAs quantum dots (QDs) containing a single substitutional Mn impurity is investigated in the envelope-function formalism. The Mn impurity in these compounds is known to be a shallow acceptor in the configuration ${d}^{5}+h$ and characterized by a strong antiferromagnetic $sp\text{\ensuremath{-}}d$ exchange interaction between the hole $(h)$ and the Mn ion. Our model for the hole states is based on the Luttinger Hamiltonian and the Coulomb potential with a central-cell correction that accounts for the observed binding energy and the effective $g$ factor in the bulk. The binding energy as well as the exchange contribution is found to increase with decreasing QD size. However, in contrast with the case of spherical nanocrystals (NCs), the binding energy in lens-shaped self-assembled QDs in the low-confinement limit is lower than that in the bulk because of their highly anisotropic shape. With an on-center impurity, NCs retain the bulk ${T}_{d}$ symmetry and the ground state is a $j=3/2$-like ${\ensuremath{\Gamma}}_{8}({T}_{d})$ level. In self-assembled QDs it splits into two doublets: ${\ensuremath{\Gamma}}_{6}$ $(|{j}_{z}|=1/2)$ and ${\ensuremath{\Gamma}}_{7}$ $(|{j}_{z}|=3/2)$ of ${D}_{2d}$, which mix in the presence of in-plane asymmetry, both belonging to ${\ensuremath{\Gamma}}_{5}$ of the reduced symmetry ${C}_{2v}$. The order and the splitting between the doublets depend on the degree of confinement and the strain-induced separation between the light- and heavy-hole valence bands. In lattice-matched GaAs/(Ga,Al)As QDs the ground-state doublet is $|{j}_{z}|=3/2$-like in the low-confinement limit. As the lateral size decreases there is a rapid crossover to a $|{j}_{z}|=1/2$-like ground state in QDs of typical sizes. On the other hand, in strained InAs/GaAs QDs the ground state is always $|{j}_{z}|=3/2$-like and the splitting relatively large. The $sp\text{\ensuremath{-}}d$ coupling with the Mn spin $S=5/2$ finally leads to a splitting of the ground-state doublet into six doubly-degenerate levels. The components are close to one another as the effective exchange parameters are an order of magnitude smaller than in the bulk. Our results thoroughly contradict the previously adopted picture based on treating the confinement potential as a small perturbation to the bulk impurity levels. We also consider the lowest two-hole states: the ground state in InAs/GaAs QDs is a singlet almost uncoupled to the Mn spin. We deduce the zero-field fine structure of the excitonic transitions and compare the results with the recently reported photoluminescence spectra.

CALCULATION OF ELECTRONIC STRUCTURE OF A SPHERICAL QUANTUM DOT USING A COMBINATION OF QUANTUM GENETIC ALGORITHM AND HARTREE–FOCK–ROOTHAAN METHOD

The electronic structure of Quantum Dot (QD), GaAs/Al x Ga 1-x As , has been investigated by using a combination of Quantum Genetic Algorithm (QGA) and Hartree–Fock–Roothaan (HFR) method. One-electron system with an on-center impurity is considered by assuming a spherically symmetric confining potential of finite depth. The ground and excited state energies of one-electron QD were calculated depending on the dot radius and stoichiometric ratio. Expectation values of energy were determined by using the HFR method along with Slater-Type Orbitals (STOs) and QGA was used for the wavefunctions optimization. In addition, the effect of the size of the basis set on the energy of QD was investigated. We also calculated the binding energy for a dot with finite confining potential. We found that the impurity binding energy increases for the finite potential well when the dot radius decreases. For the finite potential well, the binding energy reaches a peak value and then diminishes to a limiting value corresponding to the radius for which there are no bound states in the well. Whereas in previous study, in Ref. 40, for the infinite potential well, we found that the impurity binding energy increases as the dot radius decreases.

Photoionization cross section and intersublevel transitions in a one- and two-electron spherical quantum dot with a hydrogenic impurity

A detailed investigation of the optical properties of a spherical quantum dot (QD) containing one and two electrons has been performed for cases with and without a hydrogenic impurity. First, the photoionization cross section of both ${D}^{0}$ and ${D}^{\ensuremath{-}}$ impurities in the QD has been calculated for an on-center impurity. Second, the intersublevel optical absorption and oscillator strength between the ground and excited states have been examined based on the computed energies and wave functions. The full numeric matrix diagonalization technique has been employed in determining sublevel energy eigenvalues and their wave functions. The Poisson-Schr\odinger equations have been solved self-consistently in the Hartree approximation. In addition, quantum-mechanical many-body effects have been investigated in the local density approximation. The results are presented as a function of quantum dot radii and photon energies.

INVESTIGATION OF ELECTRONIC STRUCTURE OF A QUANTUM DOT USING SLATER-TYPE ORBITALS AND QUANTUM GENETIC ALGORITHM

In this study, electronic properties of a low-dimensional quantum mechanical structure have been investigated by using Genetic Algorithm (GA). One- and two-electron Quantum Dot (QD) systems with an on-center impurity are considerable by assuming the confining potential to be infinitely deep and spherically symmetric. Linear combinations of Slater-Type Orbitals (STOs) were used for the description of the single electron wave functions. The parameters of the wave function of the system were used as individuals in a generation, and the corresponding energy expectation values were used for objective functions. The energy expectation values were determined by using the Hartree-Fock-Roothaan (HFR) method. The orbital exponent ζi's and the expansion coefficient ci's of the STOs were determined by genetic algorithm. The obtained results were compared with the exact result and found to be in a good agreement with the literature.

Oscillator strengths for the intersubband transitions in a CdS–SiO2 quantum dot with hydrogenic impurity

In this study, we have calculated the oscillator strengths for intersubband electronic transitions associated with an on-center impurity in a spherical quantum dot. Numerical calculations have been performed for both infinite confinement case and for different finite confining potential values in a spherical CdS/SiO2 quantum dot. Also, for comparison purpose, oscillator strengths for a spherical ZnS/SiO2 quantum dot with an infinite confinement potential are evaluated.

Optical properties of a magneto-donor in a quantum dot

The optical-absorption spectra associated with transition between the ground state of a hydrogenic donor impurity to the second conduction levels in the presence of a magnetic field has been calculated for spherical CdSe quantum dot (QD) with infinite potential confinement, using a variational method and a perturbation method within the effective-mass approximation. We have found that as a consequence of the scaling laws, the absorption coefficient varies systematically as a function of QDs size. The application of the magnetic field may hinder the absorption coefficient of an on-center impurity and displace the threshold energy towards high energy if γ > 1 / R 2 and towards low energy if γ < 1 / R 2 for the 1s–2p − transition. For all values of the magnetic field, the threshold energy of the transition 1s–2p + is displaced towards high energy.

The binding energy of hydrogen-like impurity in quantum dots with convex bottom in magnetic field

Within the framework of effective mass approximation and variational method, the electronic and impurity states in spherical quantum dots with convex bottom in magnetic field are calculated. Calculations are carried out both for on-center and off-center impurities. The impurity binding energy dependencies on radius, measure of convexity of quantum dot bottom, impurity position and magnetic field induction are obtained for the Ga 1 - x Al x As / Ga 1 - y Al y As system.

Hydrostatic pressure effects on the donor impurity‐related photoionization cross‐section in cylindrical‐shaped GaAs/GaAlAs quantum well wires

AbstractUsing a variational method the binding energy has been calculated for a shallow donor impurity and the donor‐related photoionization cross‐section in 1D and 0D GaAs low‐dimensional systems. The dependence on the binding energy and the photoionization cross‐section for a hydrogenic donor impurity in the finite potential model are discussed and the results are presented as a function of the radius, polarization of the photon, applied hydrostatic pressure, and photon energy. The calculations for the pressure effects are performed both in the direct and indirect GaAs gap regime. Calculations are presented for an on‐axis (on‐center) impurity in the wire (in the dot). (© 2004 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Size effect on low-lying energy spectra of an electron magnetic quantum ring

We present numerical results for the low-lying spectra of an electron confined in a magnetic quantum ring where the magnetic fields are zero inside the ring and constant elsewhere. Low-lying spectra for both on-center Coulomb acceptor and donor impurities, with qualitative aspects different from those without impurities doped, are also discussed.

Effect of the dielectric-constant mismatch and magnetic field on the binding energy of hydrogenic impurities in a spherical quantum dot

Within the effective mass approximation and variational method the effect of dielectric constant mismatch between the size-quantized semiconductor sphere, coating and surrounding environment on impurity binding energy in both the absence and presence of a magnetic field is considered. The dependences of the binding energy of a hydrogenic on-center impurity on the sphere and coating radii, alloy concentration, dielectric-constant mismatch, and magnetic field intensity are found for the GaAs–Ga 1− x Al x As–AlAs (or vacuum) system.

Impurity effect on low-lying spectra in a two-electron quantum dot with parabolic confinement

Using an exact numerical diagonalization scheme, we calculated the low-lying spectra of a two-electron quantum dot with a confined parabolic potential in the presence of a Coulomb impurity at the center under a perpendicular homogeneous magnetic field. Numerical results show that for the low spectra of on-center acceptor impurity, the orbital angular momentum L-transition and/or spin angular momentum S-transition takes place in the ground state, which is qualitatively the same as the case without impurity, while for the low-lying spectra of on-center donor impurity, there are no ground state transitions and the energy spectra are completely different.

Numerical method forNelectrons bound to a polar quantum dot with a Coulomb impurity

A numerical method is proposed to calculate the Frohlich Hamiltonian containing N electrons bound to polar quantum dot with a Coulomb impurity without transformation to the coordination frame of the center of mass and by direct diagonalization. As an example to demonstrate the formalism of this method, the low-lying spectra of three interacting electrons bound to an on-center Coulomb impurity, both for accepter and donor, are calculated and analyzed in a polar quantum dot under a perpendicular magnetic field. Taking polaron effect into account, the physical meaning of the phonon-induced terms, both self-square terms and cross terms of the Hamiltonian are discussed. The calculation can also be applied to systems containing particles with opposite charges, such as excitons.