Triangular Potential Well Research Articles

Effects of rainbow gravity on an electron confined to a triangular well and a periodic potential

We investigate quantum effects concerning the modification of the background via rainbow gravity on an electron. We employ the nonrelativistic approximation of the Dirac equation to analyze these effects in depth. We initially study the interaction between an electron and a uniform electric field, by exploring confinement of the particle to a triangular potential well. We find systematic alterations in the energy levels reliant on the rainbow parameter ϵ. Additionally, we investigate a particle in a periodic potential resembling a ring. We also find consistent alterations in energy levels due to changes in the background via rainbow functions. As in the previously analyzed scenario, the larger the rainbow parameter, the lower the obtained energy levels. These findings underscore a systematic influence of modified gravity on particle dynamics in quantum scenarios.

A Closed-Form Model for 2-DEG Charge and Surface Potential in N-Polar Gallium Nitride Heterostructures

A closed-form model to calculate the 2-D electron gas (2-DEG) charge density and surface potential in an N-polar GaN/AlGaN heterostructure is presented. The proposed model is developed from the solution of Schrödinger’s equation for a finite triangular potential well. Asymptotic expressions of Airy functions are used to compute an initial value of subband energy. A new, unified expression to update the surface potential due to Poisson’s equation is presented. The modified Fang–Howard (M.F.H.) function is then employed to develop a closed-form correction to the subband energy using first-order perturbation theory. No fitting parameters are used. The results from our model are validated with numerical data for a wide range of bias conditions, channel layer thickness, and spacer layer mole fraction. Finally, the gate capacitance of the heterostructure is evaluated using automatic differentiation and validated against experimental data.

Analytical estimation of lifetime of quasi-bound states in iii-v semiconductors quantum well

The lifetime of electrons in the Quasi Bound States in a quantum well formed by III-V semiconductors has been calculated numerically by several researchers in the past. In this work, we obtain an analytical expression for the lifetime by finding the poles of the scattering matrix in small-width approximation. Airy functions which are solutions of the Schrödinger equation for triangular potentials are expanded asymptotically for large arguments and in power series for small arguments. A scattering problem for the triangular potential well is solved with the help of mixed boundary conditions to derive the expression for the decay width that further gives the net tunneling current from the quantum well. Heterostructures of III-V materials are modeled with triangular wells whose experimental measurements are in close approximation with the theoretical calculations presented in this paper. The analytically calculated decay width in this work is also compared with the reported values by different numerical methods and found in close agreement with them.

Surface Quantum-Dimensional Photocarrier Recombination in <i>CdTe</i> Microcrystals

The scope of the study is the spectra of low-temperature (T = 2K) photoluminescence of a p-CdTe/n-CdS film heterostructure comprising a monolayer of CdTe microcrystals, where a single microcrystalline particle is typically one micron in size. Focus is made on the dominant band of “super-hot” emission appearing in the spectral region located in energy above the fundamental absorption edge of a CdTe bulk crystal. A theoretical model has been developed that assumes the existence of a space-charge layer inside a microcrystal, which leads to the formation of a triangular potential well for an electron near the surface. The anomalous emission band arises as a result of the optical transitions of electrons from near-surface levels of spatial quantization to valence band states.

Dependence of the radiative lifetime on the type-II band offset in GaAsxSb1−x/GaAs quantum dots including effects of photoexcited carriers

In quantum dot (QD) heterostructures that have a type-II band alignment, either the electron or the hole is confined inside the QD. Due to smaller electron–hole overlap in such structures, relatively long radiative lifetimes can be realized, which is beneficial for devices such as intermediate-band solar cells. The use of GaAsxSb1−x/GaAs QDs allows us to control the energy level of the confined state by changing the type-II conduction-band offset (CBO) without the need of changing the QD size. However, the dependence of the radiative lifetime τr on the CBO needs to be considered to achieve optimum device performance. In this work, GaAsxSb1−x/GaAs QDs were grown by molecular beam epitaxy. The amount of deposition was controlled to obtain QDs with approximately the same size even for different values of As composition x, and the carrier lifetime was determined by time-resolved photoluminescence measurements. Since the CBO becomes smaller for larger values of x, a simple model would predict a larger electron–hole overlap for larger x values, and thus, the lifetime should decrease monotonically. However, the experimentally obtained lifetime does not decrease monotonically, which has interesting implications for applications. We explain the observed trend by the effect of photoexcited carriers; a triangular potential well is formed around the QDs in the case of high excitation densities, and thus, electrons are localized near the QDs. We also calculated τr considering the effect of photoexcited carriers to confirm our model, and a similar tendency was obtained.

Dynamic piezotronic effect modulated AlGaN/GaN HEMTs with HfZrOx gate dielectric

High electron mobility transistors (HEMTs) based on AlGaN/GaN heterojunctions show promising applications in high-performance power electronics. Having to face the limited device performance caused by electrically unstable issues, high-κ gate dielectric has been brought into HEMTs (forming MOS-HEMTs) to make a breakthrough. Impressively, a high-κ HfZrOx (HZO) dielectric has been proved to enable the HEMTs to exhibit enhanced performances, e.g., higher output performance, lower leakage current, and better surface properties. Additionally, by coupling piezoelectric and semiconductor properties, piezotronic effect also provides a novel approach for optimizing HEMTs with the use of external stress. Here, we present dynamic piezotronic effect of AlGaN/GaN HEMTs with HZO gate dielectric in pulse voltage modes. When the GaN layer is suffered from tensile stress, the DC and pulse output characteristics of the MOS-HEMTs show significantly decreased trends, and the gate leakage current shows a slight increase. Moreover, theoretical analysis based on Crosslight simulation and a self-consistent model shows that the applied tensile stress can effectively improve the energy band height of triangular potential well and affect the energy states of defects. This work not only provides an inspiration for the modulated device performance in dynamic piezotronic effect, but also expands the application prospect of HEMTs in a strain-controlled platform.

A Difference-Microvariation Solution and Analytical Model for Generic HEMTs

An analytical dc model of AlGaN/GaN and AlGaAs/GaAs-based high-electron mobility transistors (HEMTs) is proposed, while the charge accumulated in the barrier layer at high gate biases voltage is taken into account. To break through the bottleneck problem of solving model accurately and efficiently, an improved difference-microvariation (DM) explicit algorithm is developed to solve the complex transcendental equations of Fermi level and surface potential in the physical model, including two important subbands in a triangular potential well. Compared with the existing analytical surface potential-based algorithms, the DM algorithm quantifies the high-order component and obtains a more precise solution. The universality and accuracy of the model and DM solutions are verified against numerical results and experimental data under a wide range of operation region, which proves that the model combined with DM method is expected to become the suitable simulation tools for generic heterojunction HEMTs.

High-order Gundlach resonances at exceptional large voltages: Consequences for determining work functions

We report a combined experimental and theoretical study of Gundlach resonances Un in scanning tunneling spectroscopy at constant current over an exceptional range of energy and number, typically tens of an eV and over thirty in order n. By performing (1) three-dimensional electrostatic calculations, (2) WKB quantum calculations of the current, and (3) one-dimensional solutions of the Schrödinger equation along the perpendicular line from the surface to the tip apex, we provide a theoretical understanding and prediction of the experimental U(n) curve. Unlike commonly assumed, the triangular potential well is not found to be a good approximation for the high-n states. We show that although the spectroscopy mode assures a constant electric field at the tip apex, this leads only for the intermediate resonance states (approximately 2<n<6) to reside in a linear potential between the tip and the surface. Whereas the low lying (n <6) states all lie approximately in the same quantum well, at higher tip-sample distances d and bias voltages V(d), the quantum well is no longer triangular but attains a curvature, which is d dependent. Each high-n state resides in its own well that can be well-approximated by a polynomial of second order. Hence, the range of Un to be analyzed in terms of spectroscopic positions needs to be chosen with great care when deducing surface work functions.

Entanglement and entropy squeezing in the system of two qubits interacting with a two-mode field in the context of power low potentials

We study the dynamics of two non-stationary qubits, allowing for dipole-dipole and Ising-like interplays between them, coupled to quantized fields in the framework of two-mode pair coherent states of power-low potentials. We focus on three particular cases of the coherent states through the exponent parameter taken infinite square, triangular and harmonic potential wells. We examine the possible effects of such features on the evolution of some quantities of current interest, such as population inversion, entanglement among subsystems and squeezing entropy. We show how these quantities can be affected by the qubit-qubit interaction and exponent parameter during the time evolution for both cases of stationary and non-stationary qubits. The obtained results suggest insights about the capability of quantum systems composed of nonstationary qubits to maintain resources in comparison with stationary qubits.

Origin and evolution of ultraflat bands in twisted bilayer transition metal dichalcogenides: Realization of triangular quantum dots

Using a multiscale computational approach, we probe the origin and evolution of ultraflatbands in moir\'e superlattices of twisted bilayer MoS$_2$, a prototypical transition metal dichalcogenide. Unlike twisted bilayer graphene, we find no unique magic angles in twisted bilayer MoS$_2$ for flatband formation. Ultraflatbands form at the valence band edge for twist angles ($\theta$) close to 0$^\circ$ and at both the valence and conduction band edges for $\theta$ close to 60$^\circ$, and have distinct origins. For$ \theta$ close to 0$^\circ$, inhomogeneous hybridization in the reconstructed moir\'e superlattice is sufficient to explain the formation of flatbands. For $\theta$ close to 60$^\circ$, additionally, local strains cause the formation of modulating triangular potential wells such that electrons and holes are spatially separated. This leads to multiple energy-separated ultraflatbands at the band edges closely resembling eigenfunctions of a quantum particle in an equilateral triangle well. Twisted bilayer transition metal dichalcogenides are thus suitable candidates for the realisation of ordered quantum dot array.

Entanglement, photon statistics and Wehrl entropy for a time-dependent qubit–field system in the presence of phase decoherence effect

We investigate the effect of qubit motion in terms of speed and acceleration on the variation in dynamic behavior of Wehrl entropy, second order correlation function and qubit–field entanglement. We consider three different coherent states of low-power potential (CSLPP) through the value of its exponent, specifically, the infinite-square, triangular, and harmonic potential wells. The relationship between the photon statistics quantified by the second order correlation function and nonclassical correlation of the qubit–field system is explored as the system evolves. The results show that the proposed scheme is very sensitive to the value of the exponent for both a moving and a stationary qubit. A high correlation between the qubit and CSLPP field is achieved by a proper choice of exponent, qubit speed, and acceleration.

Dramatically improved electron transport performance by a deep triangular potential well in organic field-effect transistors

Overcoming the intrinsic properties of organic molecules to achieve high device performance, particularly for electron transport, is a challenge in the field of organic semiconductor device physics. Energy-band engineering in modern inorganic electronics has been introduced in organic electronics. Here, we utilized Al2O3 and PbO metal-oxide layers as dielectric modification layers and fabricated high-quality organic heterojunction films with large band bending and sharp interfaces. The large band bending indicated a deeper triangular potential well, which can confine more electrons and form a high carrier density organic two-dimensional electron gas. A sharp heterojunction interface can reduce interface carrier transport scattering and crystal lattice defects and can retain uniform interfacial electronic structures. These two features of organic heterojunctions are the key factors to realize energy-band engineering in organic electronics. By using these heterojunction films as active layers in organic field-effect transistors, the transistors exhibited a high electron mobility of approximately 8 cm2 V−1 s−1. Therefore, we demonstrated the feasibility and solutions of energy-band engineering in organic electronics, and provided a novel strategy to improve device performance.

Imaging of Plasmonic Eigen Modes in Gold Triangular Mesoplates by Near-Field Optical Microscopy

We investigated the spectral and spatial characteristics of plasmons induced in chemically synthesized triangular gold nano- and microplates by aperture-type scanning near-field optical microscopy. Near-field transmission images taken at plasmon resonance wavelengths showed two-dimensional oscillating patterns inside the plates. These spatial features were well reproduced by the square moduli of calculated eigen functions confined in the two-dimensional triangular potential well. From the irreducible representations of the eigen functions, it was found that both the out-of-plane modes and in-plane modes were clearly visualized in the near-field images. We compared near-field transmission images of a triangular nanoplate to those of a truncated one with a similar dimension and revealed that the fine details of the geometrical shape of the apex on the plate strongly influence the experimentally observed eigen mode structures. We also performed near-field transmission measurements of micrometer-scale triangu...

Hypertension pulmonaire

Semiconductor CdTe:Te films were deposited by means of rf sputtering on glass substrates. The excess of Te gave place to a high number of Cd-vacancies (VCd) producing p-type CdTe films. The density of carriers produced a high strength surface electric field which allowed obtain the bandgap value employing modulated transmittance spectroscopy. The obtained bandgap value of 1.40 ± 0.01 eV was confirmed by absorption spectroscopy measures. The density of holes is so high that bandgap renormalization is observed. Photoluminescence (PL) measurements were carried out with the down-converted 883.2 nm (1.403 eV) line of the 441.6 nm wavelength of a He-Cd laser. This energy allows to produce a resonant excitation of the CdTe:Te films, in such a way that electrons from the conduction band (CB) can be just excited to the valence band (VB). The resonant excitation produced a PL spectrum of band to band electron-hole recombination showing discrete energy emissions that follow the pattern of oscillations corresponding to the Airy model for a quantum triangular potential well. The average width of signals of the higher energy oscillations is 12 ± 3 μeV and separation between energy levels is of the order of 12 ± 3 μeV.

Airy pattern on narrow photoluminescence spectrum of band to band recombination in CdTe:Te thin films

Semiconductor CdTe:Te films were deposited by means of rf sputtering on glass substrates. The excess of Te gave place to a high number of Cd-vacancies (VCd) producing p-type CdTe films. The density of carriers produced a high strength surface electric field which allowed obtain the bandgap value employing modulated transmittance spectroscopy. The obtained bandgap value of 1.40 ± 0.01eV was confirmed by absorption spectroscopy measures. The density of holes is so high that bandgap renormalization is observed. Photoluminescence (PL) measurements were carried out with the down-converted 883.2nm (1.403eV) line of the 441.6nm wavelength of a He-Cd laser. This energy allows to produce a resonant excitation of the CdTe:Te films, in such a way that electrons from the conduction band (CB) can be just excited to the valence band (VB). The resonant excitation produced a PL spectrum of band to band electron-hole recombination showing discrete energy emissions that follow the pattern of oscillations corresponding to the Airy model for a quantum triangular potential well. The average width of signals of the higher energy oscillations is 12 ± 3μeV and separation between energy levels is of the order of 12 ± 3μeV.

A novel analytical model for scattering limited electron transport in nano-dimensional InAlAs/InGaAs heterostructure for cryogenic applications

This paper models the scattering limited electron transport in a nano-dimensional In0.52Al0.48As/In0.53Ga0.47As/InP heterostructure. An analytical model for temperature dependent sheet carrier concentration and carrier mobility in a two dimensional electron gas, confined in a triangular potential well has been developed. The model accounts for all the major scattering process including ionized impurity scattering and lattice scattering. Quantum mechanical variational technique is employed for studying the intrasubband scattering mechanism in the two dimensional electron gas. Results of various scattering limited structural parameters such as energy band-gap and functional parameters such as sheet carrier concentration, scattering rate and mobility are presented. The model corroborates the dominance of ionized impurity scattering mechanism at low temperatures and that of lattice scattering at high temperatures, both in turn limiting the carrier mobility. Net mobility obtained taking various scattering mechanisms into account has been found in agreement with earlier reported results, thus validating the model.

Atmospheric pressure-MOVPE growth of GaSb/GaAs quantum dots

This study focuses on the growth of GaSb/GaAs quantum dots (QD) using an atmospheric pressure MOVPE system. For the best uncapped dots, the average dot height, base diameter and density are 5nm, 45nm and 4.5×1010cm−2, respectively. Capping of GaSb QDs at high temperatures caused flattening and formation of thin inhomogeneous GaSb layer inside GaAs resulting in no obvious QD PL peak. Capping at low temperatures lead to the formation of dot-like features and a wetting layer (WL) with distinct PL peaks for QD and WL at 1097nm and 983nm respectively. Some of the dot-like features had voids. An increase in excitation power caused the QD and WL peaks to shift to higher energies. This is attributed to electrostatic band bending leading to triangular potential wells, typical of type-II alignment between GaAs and strained GaSb. Variable temperature PL measurements of the QD sample showed the decrease in the intensity of the WL peak to be faster than that of the QD peak as the temperature increased.

Effect of thin gate dielectrics on DC, radio frequency and linearity characteristics of lattice‐matched AlInN/AlN/GaN metal–oxide–semiconductor high electron mobility transistor

In this paper, the authors present a polarisation dependent analytical model for DC, radio frequency (RF) and linearity characteristics of a proposed lattice-matched AlInN/AlN/GaN metal–oxide–semiconductor high electron mobility transistor (MOSHEMT). The developed model includes charge controlled analysis derived from triangular potential well approximation along with the spontaneous and piezoelectric polarisation effects. The model accurately predicts the threshold voltage, two-dimensional electron gas sheet charge density, drain current, transconductance and cut-off frequencies for different samples of gate dielectric materials such as SiO2, HfO2 and Al2O3 over a full range of gate and drain bias. A detailed analysis of the linearity characteristics by investigating the key figure-of-merit metrics such as second-order voltage intercept point, third-order voltage intercept point, third-order input intercept point and third-order intermodulation distortion are performed for different gate dielectric thicknesses of 5, 7 and 10 nm. The accuracy of the model results is verified against Silvaco Technology Computer Aided Design numerical simulation results and found to be satisfactory. It is observed that by careful tuning the device parameters such as dielectric constant and dielectric thickness, lattice-matched AlInN/AlN/GaN MOSHEMT can considerably improve the device performance and suitable for high performance low distortion RF applications.

Sensitivity of resonant tunneling diode photodetectors

We have studied the sensitivity of AlGaAs/GaAs double barrier resonant tunneling diode photodetectors with an integrated GaInNAs absorption layer for light sensing at the telecommunication wavelength of λ = 1.3 μm for illumination powers from pico- to microwatts. The sensitivity decreases nonlinearly with power. An illumination power increase of seven orders of magnitude leads to a reduction of the photocurrent sensitivity from SI = 5.82 × 103 A W−1 to 3.2 A W−1. We attribute the nonlinear sensitivity–power dependence to an altered local electrostatic potential due to hole-accumulation that on the one hand tunes the tunneling current, but on the other hand affects the lifetime of photogenerated holes. In particular, the lifetime decreases exponentially with increasing hole population. The lifetime reduction results from an enhanced electrical field, a rise of the quasi-Fermi level, and an increased energy splitting within the triangular potential well. The non-constant sensitivity is a direct result of the non-constant lifetime. Based on these findings, we provide an expression that allows us to calculate the sensitivity as a function of illumination power and bias voltage, show a way to model the time-resolved photocurrent, and determine the critical power up to which the resonant tunneling diode photodetector sensitivity can be assumed constant.

Field enhancement factors and self-focus functions manifesting in field emission resonances in scanning tunneling microscopy

Field emission (FE) resonance (or Gundlach oscillation) in scanning tunneling microscopy (STM) is a phenomenon in which the FE electrons emitted from the microscope tip couple into the quantized standing-wave states within the STM tunneling gap. Although the occurrence of FE resonance peaks can be semi-quantitatively described using the triangular potential well model, it cannot explain the experimental observation that the number of resonance peaks may change under the same emission current. This study demonstrates that the aforementioned variation can be adequately explained by introducing a field enhancement factor that is related to the local electric field at the tip apex. The peak number of FE resonances increases with the field enhancement factor. The peak intensity of the FE resonance on the reconstructed Au(111) surface varies in the face-center cubic, hexagonal-close-packed, and ridge regions, thus providing the contrast in the mapping through FE resonances. The mapping contrast is demonstrated to be nearly independent of the tip–sample distance, implying that the FE electron beam is not divergent because of a self-focus function intrinsically involved in the STM configuration.