Effective Mass Theory Research Articles

The [100] direction strained Ge[formula omitted]Snx nanowires with low Sn contents towards the application of SWIR or MWIR lasers

The band structures of Ge1−xSnx nanowires with low Sn contents at the Γ-valley and L-valley under the [100] direction stress are studied via effective-mass theory, and we find that Ge0.95Sn0.05 and Ge0.92Sn0.08 nanowires can be tuned to direct-bandgap semiconductors even for the stress less than 4 GPa. Moreover, as increasing the stress, the calculations of the optical gain manifest that the z direction peak gain can be enhanced sharply regardless of the diameter and Sn content since more electrons are filled at the Γ-valley. The further research shows that the FCA loss of Ge1−xSnx nanowires can almost be neglected, meanwhile remarkable and positive net peak gain along the z direction can be acquired even though electron concentration is as low as the order of 1018 cm−3, which can overcome the non-negligible FCA loss caused by electron concentration of the order of 1019 cm−3 in Ge or strain-free Ge1−xSnx nanowires.

Modeling Si/SiGe quantum dot variability induced by interface disorder reconstructed from multiperspective microscopy

SiGe heteroepitaxial growth yields pristine host material for quantum dot qubits, but residual interface disorder can lead to qubit-to-qubit variability that might pose an obstacle to reliable SiGe-based quantum computing. By convolving data from scanning tunneling microscopy and high-angle annular dark field scanning transmission electron microscopy, we reconstruct 3D interfacial atomic structure and employ an atomistic multi-valley effective mass theory to quantify qubit spectral variability. The results indicate (1) appreciable valley splitting (VS) variability of ~50% owing to alloy disorder and (2) roughness-induced double-dot detuning bias energy variability of order 1–10 meV depending on well thickness. For measured intermixing, atomic steps have negligible influence on VS, and uncorrelated roughness causes spatially fluctuating energy biases in double-dot detunings potentially incorrectly attributed to charge disorder. Our approach yields atomic structure spanning orders of magnitude larger areas than post-growth microscopy or tomography alone, enabling more holistic predictions of disorder-induced qubit variability.

Efficiency of InN/InGaN/GaN Intermediate-Band Solar Cell under the Effects of Hydrostatic Pressure, In-Compositions, Built-in-Electric Field, Confinement, and Thickness.

This paper presents a thorough numerical investigation focused on optimizing the efficiency of quantum-well intermediate-band solar cells (QW-IBSCs) based on III-nitride materials. The optimization strategy encompasses manipulating confinement potential energy, controlling hydrostatic pressure, adjusting compositions, and varying thickness. The built-in electric fields in (In, Ga)N alloys and heavy-hole levels are considered to enhance the results' accuracy. The finite element method (FEM) and Python 3.8 are employed to numerically solve the Schrödinger equation within the effective mass theory framework. This study reveals that meticulous design can achieve a theoretical photovoltaic efficiency of quantum-well intermediate-band solar cells (QW-IBSCs) that surpasses the Shockley-Queisser limit. Moreover, reducing the thickness of the layers enhances the light-absorbing capacity and, therefore, contributes to efficiency improvement. Additionally, the shape of the confinement potential significantly influences the device's performance. This work is critical for society, as it represents a significant advancement in sustainable energy solutions, holding the promise of enhancing both the efficiency and accessibility of solar power generation. Consequently, this research stands at the forefront of innovation, offering a tangible and impactful contribution toward a greener and more sustainable energy future.

Modeling of light absorption in self-assembled truncated conical quantum dot structures

Quantum Dots have shown a significant potential as a top candidate for infrared photodetection at higher temperatures. In the presented work, a theoretical model for estimating the coefficient of optical absorption of self-assembled truncated conical quantum dot is developed. This model considers both bound-to-continuum and bound-to-bound absorption mechanisms that increase the accuracy of the absorption coefficient estimation. The developed model is based on estimating the bound states by diagonalizing the Hamiltonian matrix, where the density of states is computed using the Non-Equilibrium Greens function and the effective mass theory to obtain the unbound states. The kinetic equation of Green’s function is solved numerically by finite difference method. Besides, the effects of quantum dot size, height, aspect ratio, and density on the coefficient of the optical absorption are investigated. The results of the developed model are contrasted with those of other alternative QD structures where the truncated conical QD structure results in a higher absorption coefficient in infrared range than semispherical and conical QD structures.

Linear and nonlinear optical absorption coefficients in InGaN/GaN quantum wells: Interplay between intense laser field and higher-order anharmonic potentials

This computational investigation delves into the electronic and optical attributes of InGaN/GaN nanostructures subjected to both harmonic and anharmonic confinement potentials, coupled with the influence of a nonresonant intense laser field (ILF). The theoretical framework incorporates higher-order anharmonic terms, specifically quartic and sextic terms. The solutions to the Schrödinger equation have been computed employing the finite element method and the effective mass theory. Moreover, linear and third-order nonlinear optical absorption coefficients are derived via a density matrix expansion. Our analysis reveals the feasibility of manipulating electronic and optical properties by adjusting confinement potential parameters, system attributes, and laser field intensity. In addition, the ILF induces remarkable modifications, characterized by reduced resonance peak amplitudes and a blue shift in absorption coefficients. Intriguingly, regardless of potential harmonicity, the impact of incident electromagnetic intensity is notably more pronounced in the absence of the ILF. These findings hold significant promise for advancing theoretical predictions, providing valuable insights into the intricate interplay between confinement potentials, laser fields, and their effects on electronic and optical behaviors within nanostructures.

Computational investgation of the optical properties of GaAs/Ga0.7Al0.3 Core/Shell Thin Film for optoelectronic Applications: under tuned external field and impurity effects

This study provides valuable insights into the optical properties of GaAs/Ga0.7Al0.3As core/shell quantum disks, including optical transitions, oscillator strength, linear optical absorption coefficient, and refractive index. We investigate these properties by employing the finite difference method. The Schrödinger equation has been solved within the effective-mass theory. However, our results reveal that adjustments in core/shell radii and electric field direction induce red-shifted resonance peaks, accompanied by improved magnitudes. Furthermore, strategically placing impurities within the core–shell region substantially enhances these optical properties. These discoveries carry the potential to catalyze groundbreaking progress and unveil fresh opportunities for technological innovation in the realm of nanostructured semiconductor devices.

Combined Effects of Intense THz Laser Field and Applied Electric Field on Binding Energy of Exciton in GaAs/GaAlAs Finite Spherical Quantum Dot

This paper describes the combined effects of intense THz laser field and electric field on the ground state binding energy of heavy hole excitons confined in GaAs/ GaAlAs spherical finite quantum dots. The formulation is based on the model of “laser dressed potential” which combines Coulomb interaction and field effect in only one potential as reported in the literature. The calculation is performed by using the variational method in the framework of the single band effective mass theory. Our results show that (i) the laser field increases the electron and hole confinement energy that form the exciton in the QD until they reach a maximum, then they become almost constant for an intense laser field, (ii)the electric field and the laser field lowers the binding energy for all quantum dot radii making the exciton stabilized and clustered near the center of the dot, and iii)the laser field increases the spatial extension of exciton but the electric field decreases it linearly.

Tuning the Photoluminescence Anisotropy of Semiconductor Nanocrystals.

Semiconductor nanocrystals are promising optoelectronic materials. Understanding their anisotropic photoluminescence is fundamental for developing quantum-dot-based devices such as light-emitting diodes, solar cells, and polarized single-photon sources. In this study, we experimentally and theoretically investigate the photoluminescence anisotropy of CdSe semiconductor nanocrystals with various shapes, including plates, rods, and spheres, with either wurtzite or zincblende structures. We use defocused wide-field microscopy to visualize the emission dipole orientation and find that spheres, rods, and plates exhibit the optical properties of 2D, 1D, and 2D emission dipoles, respectively. We rationalize the seemingly counterintuitive observation that despite having similar aspect ratios (width/length), rods and long nanoplatelets exhibit different defocused emission patterns by considering valence band structures calculated using multiband effective mass theory and the dielectric effect. The principles are extended to provide general relationships that can be used to tune the emission dipole orientation for different materials, crystalline structures, and shapes.

The optical gain of GaAs1−x−y N x Bi y nanowires under the [100] direction uniaxial stress

Based on the 16-band effective-mass theory, the band structures and optical gain of GaAs1−x−y N x Bi y nanowires under [100] direction uniaxial stress are investigated. Our calculations indicate, as the increase of stress, the first gain peak position can be redshifted to optical communication band even though nitrogen and bismuth contents are less than 0.05, and we almost obtain pure optical gain along z-direction due to the strong inhibition of optical gain along x-direction. Moreover, GaAs1−x−y N x Bi y nanowires with high nitrogen contents and large diameters are apt to be adjusted to 1310–1550 nm under the proper stress.

Transmission of a position-dependent mass system through a soft Coulomb potential

This research delves into the fascinating transmission characteristics of a system with variable mass, confined by a Coulomb-like potential. By utilizing an analytic approach to transmission probability, we were able to unveil the intriguing features that are observed experimentally in a specially designed two-dimensional lattice. This lattice was engineered to manipulate itinerant electrons through entanglement, resulting in variable masses as they traverse the lattice. To build our model system, we utilized the displacement operator approach to the position-dependent effective mass theory. This allowed us to investigate the effects of different configurations of leads, system geometries and lattice deformations on the transmission characteristics of the system. The resulting data showed that the model system was highly sensitive to these parameters, which led to various interesting features. First, we observed Andreev-like reflections, which occur when a particle is reflected as a hole, resulting in the transfer of both energy and charge. Another feature was reflectionless transmission, in which the transmission probability of a particle is close to unity, and almost no reflection occurs. We also observed complete localization of charge carriers, where the transmission probability is effectively zero, indicating that the charge carriers are completely confined within the lattice. Our findings demonstrate the remarkable versatility of the effective mass approach in the modeling of physical systems. By unraveling the intricate relationships between system parameters and transmission probability, we have gained new insights into the behavior of itinerant charge carriers in lattice structures. These insights may guide the design and development of novel electronic devices with enhanced performance and functionality.

Interface and electromagnetic effects in the valley splitting of Si quantum dots

The performance and scalability of silicon spin qubits depend directly on the value of the conduction band valley splitting (VS). In this work, we investigate the influence of electromagnetic fields and the interface width on the VS of a quantum dot in a Si/SiGe heterostructure. We propose a new three-dimensional theoretical model within the effective mass theory for the calculation of the VS in such heterostructures that takes into account the concentration fluctuation at the interfaces and the lateral confinement. With this model, we predict that the electric field is an important parameter for VS engineering, since it can shift the probability distribution away from small VSs for some interface widths. We also obtain a critical softness of the interfaces in the heterostructure, above which the best option for spin qubits is to consider an interface as wide as possible.

The optical gain of dilute bismuth GaAs nanowires under the joint uniaxial stresses

Combining the effective-mass theory with valence-band anticrossing model, the electronic structures and optical gain of dilute bismuth (Bi) GaAs nanowires under the uniaxial stresses are studied. The calculations manifest the band gap of GaAs1−xBix nanowires will be lowered with increasing bismide composition and [100] direction uniaxial stress, which can cause the red shift of optical gain peaks of nanowires. Moreover, it is found that, although almost pure optical gain along z direction can be obtained via applying single [100] direction stress, the first gain peaks are hard to be tuned to the optimal optical communication band, which makes it possible to impose another small uniaxial stress along [001] direction simultaneously to further redshift the gain peaks, and the ultimate results prove that the effect under the joint uniaxial stresses is remarkable. Our investigations mean that GaAs1−xBix nanowires is suitable for optoelectronic devices in optical communication band through appropriate modulated methods.

Tailoring optoelectronic properties of InGaN-based quantum wells through electric field, indium content, and confinement shape: A theoretical investigation

This paper conducts a comprehensive theoretical examination of the electronic and optical responses, including linear and nonlinear optical responses, of an InGaN-based quantum well with a variable inverted parabolic confinement potential. This examination takes into account the effects of applied vertical electric fields, variable indium content, different confinement shapes, and sizes. The Schrödinger equation is solved numerically using the finite element method and the effective mass theory. The results indicate that both the electrical and optical properties of the system are highly influenced by these factors. Additionally, it is found that by carefully selecting these factors, the total optical absorption coefficient, total refractive index, and linear complex optical susceptibility of the system can be precisely controlled. This study makes a valuable theoretical contribution to the understanding of how electromagnetic radiation interacts with matter and can be applied to help explain the absorption and scattering properties of III-nitride materials, used in the active regions of various devices such as solar cells, photodetectors, and modulators, as well as in the design stages of them.

Spin-Orbit and Zeeman Effects on the Electronic Properties of Single Quantum Rings: Applied Magnetic Field and Topological Defects.

Within the framework of effective mass theory, we investigate the effects of spin-orbit interaction (SOI) and Zeeman splitting on the electronic properties of an electron confined in GaAs single quantum rings. Energies and envelope wavefunctions in the system are determined by solving the Schrödinger equation via the finite element method. First, we consider an inversely quadratic model potential to describe electron confining profiles in a single quantum ring. The study also analyzes the influence of applied electric and magnetic fields. Solutions for eigenstates are then used to evaluate the linear inter-state light absorption coefficient through the corresponding resonant transition energies and electric dipole matrix moment elements, assuming circular polarization for the incident radiation. Results show that both SOI effects and Zeeman splitting reduce the absorption intensity for the considered transitions compared to the case when these interactions are absent. In addition, the magnitude and position of the resonant peaks have non-monotonic behavior with external magnetic fields. Secondly, we investigate the electronic and optical properties of the electron confined in the quantum ring with a topological defect in the structure; the results show that the crossings in the energy curves as a function of the magnetic field are eliminated, and, therefore, an improvement in transition energies occurs. In addition, the dipole matrix moments present a non-oscillatory behavior compared to the case when a topological defect is not considered.

Ultrafast hole relaxation dynamics in quantum dots revealed by two-dimensional electronic spectroscopy

Elucidating the population dynamics of correlated electron-hole pairs (bound excitons) in semiconducting quantum dots (QDs) is key for developing our fundamental understanding of nanoscale photophysics as well as for the optimal design of devices, such as lasers. For decades, it was assumed that holes did not contribute to band edge bleach signals in QDs. Here, we employ two-dimensional electronic spectroscopy to monitor electron and hole dynamics in both CdSe and CdSe/CdS/ZnS QDs to probe electron and hole dynamics. Based on a combination of time and frequency resolution, we observe a previously unresolved bleaching signal in CdSe QDs on timescales faster than 30 fs due to hole cooling. Atomistic semiempirical pseudopotential calculations are used to rationalize the order of magnitude difference in the observed hole dynamics in CdSe and CdSe/CdS/ZnS QDs. This picture advances our understanding of QD excitonics past the prevailing continuum effective mass theories generally used to describe QD electronic structure and dynamics.

Excitons in metal halide perovskite nanoplatelets: an effective mass description of polaronic, dielectric and quantum confinement effects.

A theoretical model for excitons confined in metal halide perovskite nanoplatelets is presented. The model accounts for quantum confinement, dielectric confinement, short and long range polaron interactions by means of effective mass theory, image charges and Haken potentials. We use it to describe the band edge exciton of MAPbI3 structures surrounded by organic ligands. It is shown that the quasi-2D quantum and dielectric confinement squeezes the exciton radius, and this in turn enhances short-range polaron effects as compared to 3D structures. Dielectric screening is then weaker than expected from the static dielectric constant. This boosts the binding energies and radiative recombination probabilities, which is a requisite to match experimental data in related systems. The thickness dependence of Coulomb polarization and self-energy potentials is in fair agreement with sophisticated atomistic models.

Impurity photo-ionization cross section and stark shift of ground and two low-lying excited electron-states in a core/shell ellipsoidal quantum dot

A new investigation on photo-ionization cross section (PICS) of a donor impurity confined in a GaAs/AlGaAs core/shell elliptic quantum dots (CSEQDs) has been performed under electric field (EF) effect. By means of the finite element method (FEM), we have computed the binding energy (BE), oscillator strength Pif and PICS within the framework of the effective mass theory (EMT). Our numerical results reveal that the stark shift is greatly dependent on the strength of the EF, the degree of ellipticity β, and the states of electronic transitions. It can take positive or negative values depending on the situation. In addition, the photo-ionization describing the transition from the donor impurity ground-state (1simp) to one of the conduction sub-band states (1s0, 2s0, and 2p0) is affected by the shape of the quantum dots (QDs) and the EF. We demonstrated that varying internal and external parameters may control the photo-ionization cross-section. These characteristics can be exploited to fabricate optoelectronic devices like QD infrared photodetectors.

Impact of pressure on the resonant energy and resonant frequency for two barriers Ga1−xAlxAs/GaAs nanostructures

We study the effect of hydrostatic pressure on resonant frequency (ν 1) and its associated lifetime (τ 1), and energy (E1) for electrons tunneling through GaAs-AlGaAs two-barrier nanostructure (TBNS). The effective mass mismatch for well and barrier materials is considered using the effective mass theory. Pressure and the Al content, which mainly affect the barrier height and consequently the TBNS’s, are found to have a significant impact on resonant lifetime, resonant frequency, and resonant energy. The current study shows that the resonance lifetime, resonant frequency, and energy are strongly influenced by the barrier thickness and well width. When comparing the results of this study to the data from the experiment, good agreements are found. The GaAs-AlGaAs TBNS’s electronic devices are controlled mainly by the hydrostatic pressure.

Enhanced Light Emission from Type-II Red InGaN/GaNSb/GaN Quantum-Well Structures

Electronic and optical properties of type-II InGaN/GaNSb/GaN quantum-well (QW) structures are investigated by using the multiband effective mass theory for potential applications in red light-emitting diodes. The heavy-hole effective mass around the topmost valence band is not affected much by the insertion of the GaNSb layer, and the optical matrix elements are greatly increased by the inclusion of the GaNSb layer in the InGaN/GaN QW structure. As a result, the type-II InGaN/GaNSb/GaN QW structure shows a much larger emission peak than the conventional type-I QW structure owing to the decrease in spatial separation between electron and hole wavefunctions, in addition to the reduction of the effective well width. It is also observed that the In content in InGaN well can be significantly reduced for the type-II QW structure with a large Sb content, compared to that for the type-I QW structure.

The effects of the dielectric screening, temperature, magnetic field, and the structure dimension on the diamagnetic susceptibility and the binding energy of a donor-impurity in quantum disk

Through the present work, we investigated the dielectric screening, temperature and applied magnetic field on donor-impurity diamagnetic susceptibility and binding energy in quantum disk (QDisk) made out of GaAs. Moreover, the influence of the position, hydrostatic pressure, temperature, and magnetic field on the dielectric screening function and the diamagnetic coefficient are also reported. The calculations are performed within the effective-mass theory using variational approach considering an infinite potential barrier. Our results reveal that the variation of QDisk's dimension, temperature, magnetic field and pressure have a considerable impact on diamagnetic susceptibility and binding energy, diamagnetic coefficient (DC) and dielectric screening. It is found that the magnetic field increase the diamagnetic susceptibility and binding energy while the temperature and dielectric screening reduce the diamagnetic susceptibility and improve the binding energy. We hope that the present work exhibits a modest contribution for further theoretical research on GaAs-based nanostructures.