Infinite Confinement Potential Research Articles

Combined effects of hydrostatic pressure and temperature on diamagnetic susceptibility, dipole moment and optical band gap properties of Hemi-Quantum Ring: Presence of a single off-center donor atom

In this study, we have investigated the combined influence of hydrostatic pressure and temperature on the electronic and optical properties of an electron and a off-center atom confined in a Hemi Quantum Ring. To analyze the system, we employed the finite difference method, considering the effective mass approximation and an infinite confinement potential. Our study examines the permanent dipole moment and diamagnetic susceptibility under the influence of the donor atom’s position, temperature, and applied hydrostatic pressure in the three directions Rg, Rc and φ0. Our results reveal that the permanent dipole moment increases as the geometric confinement decreases, while the diamagnetic susceptibility exhibits a negative behavior and is influenced by temperature and hydrostatic pressure. Furthermore, we observed that the bandgap and the optical bandgap are sensitive to variations in temperature and the size of the HQR (Hemi Quantum Ring) nanostructure. The study on the combined influence of hydrostatic pressure and temperature on the electronic and optical properties of an electron and an off-center atom confined in a Hemi Quantum Ring has potential real-world applications in the development of electronic and optical devices.

Donor Atom Properties in 2D Ultra-Thin Cylindrical Quantum Dots

The objective of this work is to study theoretically the ground state energy of a donor atom located in a two-dimensional ultra-thin cylindrical nanostructure called nanoflakes for different geometries controlled by the three geometrical parameters, in an infinite confinement potential. The solution of our equations system is based on the 2D finite difference method. Our numerical calculations show that the ground state energy of a donor atom is more important in the small area of the nanoflakes. Moreover, beyond the critical regions, the donor energy becomes stable.

The Effect of a Single Off-Center Shallow Donor Atom on the Binding Energy and Diamagnetic Susceptibility in a GaAs Horn Torus Quantum Dot

In this work, we have studied an electron confined in a GaAs Horn torus quantum dot in the presence of a shallow donor impurity. Using the effective mass approximation and by considering an infinite confinement potential, the Schrödinger equation was calculated by the finite difference method. The electron-impurity binding energy and the diamagnetic susceptibility are studied for different geometric sizes of the Horn torus. In addition, the effect of the radial and angular positions of the shallow donor impurity on the binding energy and the diamagnetic susceptibility are examined. The results show that the binding energy is much higher at small sizes of the nano system. Also, the diamagnetic susceptibility exhibits a symmetric behavior as a function of the angular position of the shallow impurity donor unlike that when the impurity moves radially. The influences of these parameter variants help us to better understand the effects of the size of the quantum dot and the position of the donor impurity, which improve the sensitive of the opto-electronic devices.

Simultaneous effects of hydrostatic pressure and temperature on the electronic spectrum in the presence of a single off-center donor atom in a hemi-quantum ring

This study numerically investigates the electronic and donor atom properties of an electron and off-center donor atom confined in a hemi-quantum-ring (HQR) using the effective mass approximation and an infinite confinement potential. The Schrödinger equation is solved using finite element and difference methods to obtain the system’s eigenenergies and eigenfunctions. The study examines the influence of the electronic spectrum under the simultaneous effects of HQR sizes, temperature, and hydrostatic pressure applied to three directions Rg, Rc, and φ0. Additionally, the influence of donor displacement on binding and donor energies is evaluated. The numerical results show that the electronic and binding energies are highly sensitive to the size of the HQR nanostructure. Furthermore, the study found that the donor atom displacement can control the variation of binding energy and donor energy for different values of hydrostatic pressure and temperature, such as the pressure (temperature) contribution increases (decreases) the binding energy. Also, the hydrostatic pressure (temperature) applied leads to a decrease (increase) of the first four confined state energies and donor energy. The simultaneous influence of geometrical parameters, hydrostatic pressure, and temperature can help improve the efficiency of electronic devices.

The intensity and direction of the electric field effects on off-center shallow-donor impurity binding energy in wedge-shaped cylindrical quantum dots

• In the effective mass approximation, the finite difference method is adopted. • Electric field effect on donor binding energy in a wedge quantum dot is obtained. • The geometrical parameters effects (radius, height and opening) have been affected. • The six confined electronic states dependent on dot shape have been examined. Taking into account an infinite confinement potential, including the influence of external electric field applied in different directions, we have systematically examined the different factors that lead to changes in the ground state binding energy between the hydrogen impurity and the electron, which are confined in a wedge-shaped cylindrical quantum dot (WSCQD) of radius R , height H and azimuthal angle θ m . The resolution of the Schrödinger equation in three dimensions is achieved by the numerical finite difference method. The binding energy is calculated for several quantum dot geometry, various electric field direction, and different position of the impurity located on the first rectangular surface or inside the WSCQD. We have obtained that the direction of the electric field has an important influence on the binding energy of the off-center impurity. We have discussed in detail the weak effect of the radial electric field in the critical value of the WSCQD azimuthal angle θ m = 76.20 ∘ for R = 30 nm and H = 50 nm. The competition between the different effects, such as the electric field direction, the impurity position, and the no-symmetry of the WSCQD, on the electron-impurity distance, is physically interpreted in this paper. To make a more self-contained work, the finite confinement potential effects have also been discussed. Calculations have also been validated by using the finite element method.

Size Effect of Hemi-Toroidal Quantum Dot on the Electronic Properties in the Presence of an Off-Center Hydrogenic Shallow Donor Impurity

We have studied the electronic properties in presence of an off-center hydrogenic shallow donor impurity confined in GaAs semiconductor quantum dot with toroidal geometry by considering the infinite confinement potential. This study has been performed within the parabolic band and the effective mass approximations in the presence of an off-center donor impurity. Three-dimensional Schrödinger equations are discretized using the finite difference method on a mesh containing Nr*Nθ*Nφ nodes. The numerical results of the analytical calculations demonstrate that the variation of the geometrical and torus radii (Rg and Rc) has a remarkable effect on the donor energy and the average electron-impurity distance, which is quite remarkable in small hemi-Toroidal quantum dot. On the other hand, we've demonstrated that the donor atom's position has a considerable impact on their energy. Furthermore, our numerical results show that the geometrical radius and donor atom's position significantly affect the electron impurity binding energy.

Impact of Applied Temperature and Hydrostatic Pressure on the Off-Center Donor Spectrum in Spherical Quantum Dot

Within the effective mass approximation and the infinite confinement potential, this work focused on studying the electronic properties of spherical quantum dot (SQD) nanostructure through the finite difference method. The effects of shallow donor impurity position, temperature (T), and hydrostatic pressure (P) on the binding energy, the electron spatial extension <re> and the average electron-impurity distance <rD-e> in a SQD have been evaluated. Our findings show that the binding energy increases as a function of hydrostatic pressure and decreases with the temperature effect. However, the binding energy presents very clear maximum around the spherical nanostructure center depending on the impurity position. For higher SQD, the impact of externals perturbations (P and T) on the electron spatial extension are more significant. The distance <re> decreases with the augmentation of hydrostatic pressure when the impurity is near the center, which is conversely when the impurity is near the edge. In addition, applying the hydrostatic pressure and temperature leads to decreasing and increasing the average distance <rD-e>, respectively.

Hydrostatic pressure and temperature effects on spectrum of an off-center single dopant in a conical quantum dot with spherical edge

In this paper we have studied the spectrum of an off-center donor impurity confined in the GaAs conical quantum dot with spherical edge surrounded by finite and infinite confinement potential. By considering the effective mass approximation and using the finite difference and elements method, we have obtained the eigenenergies and the eigenfunctions of the nanosystem. The hydrostatic pressure and temperature effects as well as the displacement of the donor on the binding energy are investigated. Within the confinement effect, the variation of the dot angle and the radius of the conical quantum dot on the electron-donor properties are evaluated. The numerical findings show that the binding energy is very sensitive to the position of the impurity and the size of the conical quantum dot (radius and dot angle). The position of the donor impurity leads to control the way of the variation of the binding energy versus the conical angle. The study includes the effects of hydrostatic pressure and temperature. It is noted that the binding energy increases with hydrostatic pressure and decreases with temperature. Additionally, the results show that the diamagnetic susceptibility increases with the conical angle and decreases with the dot radius. Therefore, it has an effective influence on the small radius of the quantum cone. In addition, we have examined extensively the possible effect due to change of the geometric angle and different position of impurity on the permanent dipole moment created by the electron and the ionized atom. Our results indicate that the spectrum of the impurity is strongly related to the impurity positions and the dot angle of the nanodot. These different influences allow a good understanding of the spectrum of these nanoparticles, and facilitate the fabrication of new optoelectronic devices.

Polaron and conduction band non-parabolicity effects on the binding energy, diamagnetic susceptibility and polarizability of an impurity in quantum rings

By employing a variational approach, we have investigated the effect of conduction band non-parabolicity (NP) on the binding energy ( E b ) and the susceptibility diamagnetic ( χ d i a ) of a donor impurity confined in wurtzite G a N / G a 1 − x A l x N quantum rings (QRs) with finite confinement potential in the presence of an electric field ( F ) applied in the z – direction. The combined effect of conduction band NP and interaction between electron-bulk longitudinal optical (LO) phonon on the E b and the χ d i a are also investigated in the case of infinite confinement potential. It is illustrated that the E b decreases progressively with F , particularly for large height ( H ) or for small radial thickness ( Δ R ) of QR, and the polaronic correction to the E b increases slightly with the increase of the electric field. In the case of infinite potential, the combined effects of NP and polaron leads to a more enhancement on the E b and χ d i a particularly for an on-center donor impurity. In addition, we have examined the dependence of the polarizability ( α p ) on the sizes of QR and the electric field with and without polaron effect. It is shown that the α p increases (decreases) with H (applied the electric field) and it is nearly insensitive to the polaron effect for the strong confinement. Our findings show also that the polaronic effect tends to decrease the α p , especially for thick QR. • The polaron effect enhances the binding energy and the diamagnetic susceptibility. • The binding energy and the diamagnetic susceptibility increases with the non-parabolicity effect. • Polaron effect tends to decrease the polarizability especially for larger quantum rings. • Polarizability decreases with increasing electric field especially for thick quantum rings.

On the electronic states in lens-shaped quantum dots

Using the effective mass and parabolic band approximations, we determine analytically the energies of the fundamental and lowest states of a confined electron in paraboloidal quantum lens with infinite confinement potential. Consistent with the axial symmetry, when the separation constant is different of zero the states are twice degenerate. The method has been applied to investigate the evolution of the gap energies of some alloys versus the dot size. The electron localization has also been investigated by using finite element calculations. The method developed in this work could be useful to investigate more deeply the lens-shaped quantum dot.

HYDROGENIC IMPURITY BINDING ENERGY IN GaAs QUANTUM RINGS

Using a variational approach within the effective-mass approximation, we investigate the ground-state binding energy of a donor impurity in the GaAs quantum rings (QR) in the infinite confinement potential. A trial wave function with two variational parameters is used in the calculation. The binding energy as a function of the QR structure parameters and the impurity position is investigated. The results indicate that the binding energy decreases gradually as the QR structure parameters increase in the infinite confinement potential. In addition, the binding energy of the impurity exhibits a maximum as the impurity position moves along the symmetry axis of the QR from the bottom of the QR to the top. The impurity binding energy firstly increases and then decreases as the impurity moves from the internal surface of the QR to the external surface, indicating that there is a maximum.

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>100Å, and the impurity is located at center. Moreover, a two parameter trial wave function model gives higher values of diamagnetic susceptibility, except for χz (GaAs).

The diamagnetic susceptibilities of donors in quantum wells with anisotropic effective mass

The diamagnetic susceptibility of a hydrogenic donor placed in Si, Ge and GaAs quantum wells with infinite confinement potential which have different effective mass anisotropy parameters ( γ = m ⊥ / m ∥ ) has been investigated as a function of the well sizes. The binding energies of the donor have also been computed using a trial wave function with two parameters in the framework of the effective mass approximation. It has been observed that the diamagnetic susceptibility of the donor in the anisotropic materials converges rapidly to the bulk limit as the well size increases.

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.

Shallow impurity states and transition energies in cylindricalGaAs–Ga0.6Al0.4As quantum well wires under applied magnetic fields

In this work, using the effective-mass approximation within a variational approach, we have studiedthe behaviour of the binding and transition energies of a donor shallow impurity in a cylindricalGaAs–Ga0.6Al0.4As quantum well wire (QWW) as a function of the wire radius, the impurityposition and the applied magnetic field. The QWW is of infinite lengthwith a finite radial confining potential and the magnetic field is appliedparallel to the wire axis. In our calculations we have considered the 1s-,2p ± - and3p ± -like impurity states. We have found that for the 1s-like state the impurity binding energyincreases with the magnetic field for impurity positions close to the centre of the wire,but diminishes for on-edge impurities, highlighting the competition between thegeometrical and magnetic confinement. Also, we have observed that the energy of the2p ± - and3p ± -like excited states is greater than the energy of the electron ground state without thepresence of the impurity for small radius of the QWW, a result which is more pronouncedfor higher magnetic fields. Our results are in good agreement with previous theoreticalreports, with lower binding and transition energies than those which use infiniteconfinement potential, as expected.

Excited states and infrared transition energies of a donor impurity in cylindrical GaAs–Ga0.6Al0.4As quantum well wires under the action of an applied magnetic field

We report a calculation of the binding and transition energies for a donor shallow impurity in a cylindrical GaAs–Ga0.6Al0.4As quantum well wire (QWW) as a function of the wire radius, the impurity position, and an applied magnetic field. The model considers an infinite length QWW with a finite radial confining potential and the presence of a uniform magnetic field applied parallel to the wire axis. The 1s-, 2p+-, 2p−-, 3p+-, 3p−-like impurity states are considered using the effective-mass approximation within the variational approach. We have found that for the 1s-like state the impurity binding energy increases with the magnetic field for impurity positions close to the center of the wire, but diminishes for on-edge impurities highlighting the competition between the geometrical and magnetic confinement. Also, our results shows that the 2p+-, 2p−-, 3p+-, 3p−-like excited states are not bounded in QWW with small radius, radius which diminishes with the applied magnetic field. We have observed that for high magnetic fields the localization of the wave function in the radial direction is higher for smaller values of the principal quantum number n. Our results are in good agreement with previous theoretical reports, with lower binding and transition energies than those which use infinite confinement potential, as expected.

Hydrogenic impurities in graded GaAs–(Ga,Al)As quantum-well wires in an electric field

The electric field dependence of polarizability and binding energy of shallow-donor impurities in graded quantum-well wires is calculated by a variational method and in the effective-mass approximation. We have considered a finite confinement model and the results are compared with that of infinite confinement potential. Our calculations have revealed the dependence of the impurity binding and polarizability on the field direction in the graded quantum-well wire.

Magnetic field dependence of the binding energy of shallow donors in GaAs quantum-well wires

Using a variational procedure within the effective-mass approximation we have calculated the binding energies of shallow-donor impurities in cylindrical GaAs quantum-well wires, in an axial magnetic field and an infinite confinement potential. In contrast to the previous results in quantum wells, we have found that, in the magnetic field, the impurity binding energy may be increased or decreased as a function of the impurity location in the quantum wire. On the basis of analysis of the variation of the binding energy with magnetic field strength, a method is proposed for experimentalists to confirm the presence of a shallow donor in the vicinity of the wire boundary.

Magnetopolaron effect in CdTe cylindrical quantum dot

This study analyzes the role of the magnetic field and the polaron effect on the binding energy of shallow donor impurities in a cylindrical quantum dot (QD), where the magnetic field is applied in the axial direction. The interactions of carrier charges (electron and ion) with the confined longitudinal optical phonons as well as the side surface and top surface optical phonons are considered. Calculations are made using the effective-mass approximation within the variational approach for an infinite confinement potential at all surfaces of the system. Results are obtained as a function of the dot sizes (radius and height) and the donor impurity position for several magnetic field strengths. Emphasis is put on the dependence of the polaronic correction on the magnetic field and the impurity position. The presented results can be useful to control the spatial distribution of the donor center in the QD.

A Mathematical Model for the Spectrum of a Two-Dimensional Schrödinger Equation with Magnetic Field under Dirichlet Boundary Conditions

We have investigated the spectrum of the Schrödinger equation with magnetic field and infinite confinement potential. The eigenvalues represent energies of the electrons in this structure. Based on numerical results and realizing the symmetry of the group Z2 × Z2 we give a mathematical model for the spectral curves and prove the existence of solutions for complex values of the wavevectors.