Fractional-dimensional Space Approach Research Articles

High precision parabolic quantum wells grown using pulsed analog alloy grading technique: Photoluminescence probing and fractional-dimensional space approach

The designed GaAs/AlGaAs parabolic quantum well (PQW) was grown using a pulsed analog alloy grading (PAAG) technique with molecular beam epitaxy by setting a significantly lower growth rate, growth time variation with growth rate change, and growth interruptions for stabilization of Al source temperature. The growth conditions allowed to achieve high precision parabolic potential of the PQW due to the arrangement of crystalline lattice by migration of group-III atoms and smoothing of interfaces under As overpressure. The structure was probed by scanning transmission electron microscopy and investigated via excitation power and temperature dependent photoluminescence (PL). The origin of the PL spectra lines was corroborated by fractional-dimensional space approach with dimensionality factor varying from 2.46 for confined to 3 for bulk semiconductor radiative transitions. Up to 5 PQW equidistant subbands in conduction and valence bands are observed by filling the states with photoexcited carriers. The PL of the excited PQW states is resolved up to 240 K temperature. The results indicate excellent agreement between luminescent properties of the designed PQW using numerical Schrödinger equation solver and the produced PQW using PAAG technique. It validates the developed PAAG technique as a powerful tool for PQWs growth to tailor a basis for more sophisticated quantum systems for near-infrared to terahertz emitters employing interband and intersubband transitions.

Electron – Phonon interaction to tune pseudocapacitive properties of NiO

Electrochemical properties of two protype NiO nanostructures (coral and flake) were investigated at room temperature. Coral – like nanostructure possesses higher specific capacitance instead of having less surface area. In addition, significant differences have been noticed in the shape of the CV curves. Here, a mechanism of electron transfer across electrode – electrolyte has been proposed to understand these phenomenon on the basis of electron – phonon interaction, analysed by Raman and photoluminescence spectroscopies. Difference in electron – phonon interaction for the two synthesized structures is found to originate from morphological anisotropy that has been illustrated using fractional dimensional space approach.

Properties of many-polaron in fractional dimensional space

Polaron properties such as the binding energy and the effective mass are calculated in the fractional dimensional space approach using the second-order perturbation theory. The effect of carrier density on the static screening correction of the electron–phonon interaction is included in the Hubbard’s local field factor. It is found that the polaron properties decrease with increase in dimension due to quantum confinement. Since the screening of the electron–phonon interaction is enhanced with increase in doping, the polaron properties decrease with increasing density.

Novel method to determine effective length of quantum confinement using fractional-dimension space approach

The binding energy and effective mass of a polaron confined in a GaAs film deposited on an AlxGa1-xAs substrate are investigated, for different film thickness values and aluminum concentrations and within the framework of the fractional-dimensional space approach. Using this scheme, we propose a new method to define the effective length of the quantum confinement. The limitations of the definition of the original effective well width are discussed, and the binding energy and effective mass of a polaron confined in a GaAs film are obtained. The fractional-dimensional theoretical results are shown to be in good agreement with previous, more detailed calculations based on second-order perturbation theory.

Dynamics of free carriers – neutral impurity related optical transitions in Be and Si δ-doped GaAs/AlAs multiple quantum wells: Fractional-dimensional space approach

The dynamics of impurity-related optical transitions in 20 nm wide silicon and beryllium δ-doped GaAs/AlAs multiple quantum wells with various doping levels has been investigated at near liquid helium temperatures. The radiative lifetimes of the free electron-neutral acceptor and the free hole-neutral donor have been identified. The capture cross-sections of the free electrons by neutral Be acceptors were experimentally determined to σ e-Be = 4 × 10 –10 cm, whereas this corresponded to σ h-Si = 2.2 × 10 –8 cm for the free holes by neutral Si donors. The experimentally determined cross-section ratio of σ h-Si /σ e-Be = 55 is close to the estimated 2D value of σ h-D /σ e-A = 64 and remains lower compared to the calculated value for the 3D case of σ h-D /σ e-A = 121.

Exciton complexes in low dimensional transition metal dichalcogenides

We examine the excitonic properties of layered configurations of low dimensional transition metal dichalcogenides (LTMDCs) using the fractional dimensional space approach. The binding energies of the exciton, trion, and biexciton in LTMDCs of varying layers are analyzed, and linked to the dimensionality parameter α, which provides insight into critical electro-optical properties (relative oscillator strength, absorption spectrum, exciton-exciton interaction) of the material systems. The usefulness of α is highlighted by its independence of the physical mechanisms underlying the confinement effects of geometrical structures. Our estimates of the binding energies of exciton complexes for the monolayer configuration of transition metal dichalcogenides suggest a non-collinear structure for the trion and a positronium-molecule-like square structure for the biexciton.

Effective length of quantum confinement and polaron effect in a GaAs film

The polaron confined in a GaAs film deposited on AlxGa1-xAs substrate are investigated in the framework of the fractional-dimensional space approach. We propose a new approach to define the effective length of quantum confinement. Limitations of the definition of original effective well width are discussed. The dimension and the binding energy of a polaron confined in a GaAs film deposited on Al0.3Ga0.7As substrate are obtained and investigated.

Polaron binding energy and effective mass in the GaAs film

The binding energy and effective mass of a polaron in a GaAs film deposited on the Al0.3Ga0.7As substrate are studied theoretically by using the fractional-dimensional space approach. Our calculations show that the polaron binding energy and mass shift decrease monotonously with increasing the film thickness. For the film thicknesses with Lw ≤ 70Å and the substrate thicknesses with Lb ≤ 200Å, the different values of the substrate thickness influence the polaron binding energy and mass shift in the GaAs film. The polaron binding energy and mass shift increase monotonously with increasing the substrate thickness. For the film thickness with Lw ≥ 70Å or the substrate thicknesses with Lb ≤ 200Å, the different values of the substrate thickness have no significant influence on the polaron binding energy and mass shift in the GaAs film deposited on the Al0.3Ga0.7As substrate.

The polaron in a GaAs film deposited on AlxGa1−xAs influenced by the thickness of the substrate

The binding energy and the effective mass of a polaron confined in a GaAs film deposited on the AlxGa1−xAs substrate for different aluminum concentration at different values of film thickness are studied theoretically by using the fractional–dimensional space approach. Analytical expressions allowing a very simple estimation of the corresponding polaron binding energy and mass shift are found. The numerical results for the polaron binding energy and mass shift as functions of the substrate thickness in the GaAs film deposited on the AlxGa1−xAs substrate structure are obtained. It is shown that the polaron binding energy and mass shift for different aluminum concentration at different values of film thickness exhibit a maximum.

Fractional-dimensional space approach for the polaron in a GaAs film deposited on AlxGa1−xAs substrate

Within the framework of the fractional-dimensional space approach, the binding energy and the effective mass of a polaron confined in a GaAs film deposited on the AlxGa1−xAs substrate for different aluminum concentration at different values of substrate thickness are investigated. Analytical expressions allowing a very simple estimation of the corresponding polaron binding energy and mass shift are found. As functions of the film thickness, the numerical results for the polaron binding energy and mass shift in the GaAs film deposited on the AlxGa1−xAs substrate structure are obtained. Our calculations show that the polaron binding energy and mass shift both have their maxima in a GaAs film deposited on the AlxGa1−xAs substrate. It is shown that the polaron binding energy and mass shift for different aluminum concentration have a maximum at a certain film thickness for the sample with a given substrate thickness.

Exciton effects on the refractive index and optical absorption in wurtzite quantum wells via a fractional-dimensional space approach

The optical refractive index changes and absorption coefficients of quantum wells (QWs) are theoretically investigated with considering exciton effects within the framework of the fractional-dimensional space approach. The exciton wave functions and bound energies are obtained as a function of spatial dimensionality, and the dimension increases with the well width increasing. Then optical properties are obtained by using the compact-density matrix approach and an iterative method. Numerical results are presented for wurtzite ZnO/MgxZn1−xO QWs. The calculated results show that the changes of refractive index and absorption coefficients are greatly enhanced due to the quantum confinement of exciton. And the smaller the QW width (dimension) is, the larger influence of exciton on the optical properties will be. Furthermore, the exciton effects make the resonant peaks move to a lower energy. In addition, the optical properties are related to the QW width, the incident optical intensity and carrier density.

Excitonic binding energies in non‐polar GaN quantum wells

AbstractWe use a fractional dimensional space approach to calculate the excitonic binding energies in non‐polar GaN/AlGaN quantum wells (QWs) as a function of well width. We investigate the influence of the conduction band to valence band offset ratio on the excitonic binding energies. Because the exciton energy is mainly dominated by he eectron sngle‐particle staes, the calculated binding energies increase strongly with increasing conduction band offset, but the fractional increase in energy remains smaller than that found in previous studies of GaAs/AlGaAs structures, and is also smaller than binding energies deduced from recent experimental analysis of a ‐plane GaN/Al0.18Ga0.82N QWs. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Impurity-related photoluminescence line shape asymmetry in GaAs/AlAs multiple quantum wells: Fractional-dimensional space approach

The optical transitions in 20 nm wide silicon and beryllium δ-doped GaAs/AlAs multiple quantum wells with various doping levels were investigated at different excitation intensities. A fractional dimensionality model was used to describe the free hole-donor and free electron-acceptor transitions in the quantum wells. The measured photoluminescence spectra from samples of different doping level related to donor-impurity or acceptor-impurity induced effects in the photoluminescence lineshape, were compared within the framework of these model calculations. Both experimentally and theoretically it was shown that acceptor and donor related optical transitions and photoluminescence line shapes were related to the difference in the effective masses of holes and electrons. This effect also leads to a difference in the photoluminescence spectra in which the luminescence band for the donor related spectrum is narrower in comparison to the acceptor related spectrum.

Impurity-induced Huang–Rhys factor in beryllium δ-doped GaAs/AlAs multiple quantum wells: fractional-dimensional space approach

This paper reports the observation of phonon sidebands in the photoluminescence spectra of Be acceptor-doped GaAs/AlAs multiple quantum wells. The intensity and energetic positions of the sideband lines are investigated experimentally for several quantum wells having various doping concentrations and photoluminescence excitation intensities. Theoretical analysis of a sideband-related lineshape, considering their energy position and impurity-induced spectra, has shown that phonon satellites can be attributed to free-electron–Be acceptor transitions involving longitudinal optical phonons of the GaAs—the host material of the studied quantum wells. The Huang–Rhys factor which determines the distribution of luminescence intensities between the phonon replicas and the main no-phonon peak was examined both experimentally and theoretically by varying the quantum well width. Thus, it has been found that this factor increases monotonically from 0.052 to 0.11 as the width of the quantum well decreases from 20 nm to 5 nm. The dependence of the Huang–Rhys factor on the width of the quantum well for a free-to-acceptor recombination was calculated applying the fractional-dimensional space approach. The proposed model adequately describes the experimentally determined dependence of the Huang–Rhys factor.

Exciton and donor binding energies in quantum-well wires and quantum dots a fractional-dimensional space approach

A simple method for calculating the free-exciton binding energies in the fractional-dimensional-space model for single-quantum-well structure has been extended to quantum-well wires and quantum dots, in which the real anisotropic system is modelled through an effective isotropic environment with a fractional dimension. In this scheme, the fractional-dimensional parameter is chosen via an analytical procedure and involves no ansatz. We calculated the ground-state binding energies of excitons and donors in quantum-well wires with rectangular cross sections. Our results are found to be in good agreement with previous variational calculations and available experimental measurements. We also discussed the ground-state exciton binding energy changing with different shapes of quantum-well wires.

The temperature dependence of the interband critical points in silicon within afractional-dimensional space approach

The fractional-dimensional space approach (FDSA) is used to analyse the temperaturedependence of direct interband transitions in Si. The critical point (CP) parameters areobtained. The results obtained by the FDSA show general or even better agreement withthe theoretical calculation than the standard treatment. In the temperature range of20–450 °C, the results obtained by FDSA indicate that the excitonic effects can be ignored, and theCP can be treated as a band character. Our research shows that the FDSA provides a goodway to derive basic information on relevant physical quantities from the observed opticalspectra, and it has the advantages of directness, flexibility, and sensitivity, which enable usto obtain the CP parameters efficiently without ambiguity. This method is especiallyuseful in the cases where the limitations of the standard treatment are serious.

Oxide overlayer effect on the measurement of the parameters of interband critical point: A fractional-dimensional space approach*

The fractional-dimensional space approach and analysis of spectroscopic ellipsometry are used to study an oxide overlayer effect on the measurement of the parameters of interband critical point (CP) of Si by a Si-SiO＿2 model. There sults of the calculation show that the oxide overlayer effect can influence the calculated CP parameters derived from an optical spectrum by decreasing t he ampl itude and dimensionality, and increasing the lifetime broadening. Moreover, the effect is enhanced with increasing thickness of the overlayer. However, this eff ect on threshold energy is shown to be very small and can be ignored.

Composition dependence of the interband critical points in Si1−xGex alloys: A fractional–dimensional space approach

The fractional–dimensional space approach is used to analyze the compositional dependence of direct interband transitions in Si1−xGex. The pertinent critical point (CP) parameters are obtained, and a CP structure, identified as E1′, is found. With regard to the CP energy, general agreement with the results obtained by the standard treatment is achieved. The other CP parameters, such as dimensionality, lifetime broadening, and amplitude, directly show an effect of a residual oxide overlayer. Our research shows that the fractional–dimensional space approach has the advantages of directness, flexibility, and sensitivity which provide a straightforward and rapid analysis of critical points, especially useful for deformed optical spectra.

Fractional-dimensional polaron corrections in asymmetric GaAs-Ga 1− xAl xAs quantum wells

Polaron effects in asymmetric GaAs-Ga 1− x Al x As quantum wells (QWs) are investigated within the framework of the fractional-dimensional space approach and by using second-order perturbation theory. A well-width dependence of the polaron corrections with a dip and a peak is obtained for both symmetric and asymmetric QWs. The dip and the peak occur in the case of asymmetric QWs for larger well widths than in the case of symmetric QWs. An enhancement of the contrast between the dip and the peak of the polaron energy shift is found for the case of asymmetric QWs. These results show the convenience of using asymmetric QWs instead of symmetric ones in any experimental attempt of detecting the dip and the peak of the polaron energy shift.

On the virial theorem value and scaling of Coulomb‐bound states in semiconductor heterostructures: effects of magnetic fields

We have used the variational procedure and the fractional-dimensional space approach to study the effects of applied magnetic fields (perpendicular to the interfaces) in the virial theorem value and scaling of the shallow-donor binding energies versus quantum-sized donor Bohr radius in GaAs–(Ga,Al)As semiconductor quantum wells. In the fractional-dimensional space approach, one may show, under certain approximations, that the virial theorem value equals two and the scaling rule for the donor binding energy versus Bohr radius is hyperbolic for GaAs–(Ga,Al)As wells. In contrast, calculations within the variational scheme show that the scaling of the donor binding energies with a quantum-sized Bohr radius is, in general, non-hyperbolic and that the virial theorem value is non-constant. We conclude with a comparison with previous theoretical studies with respect to exciton states.