Triangular Barrier Research Articles

Tunneling-Induced Decay of Wave Packets Localized Beyond an Asymmetric Potential Barrier

The time behavior of a wave packet, transmitted through a potential barrier, is investigated for all times assuming it to be initially located outside the asymmetric barrier. The survival probability of the initial state, which characterizes the decay of the unstable quantum system in three time domains, is discussed. The presence of initial, exponential, and long-time regimes is a general feature of the decay process. We analytically found the three crucial points of time that separate these regimes. These characteristic times are set by simple formulae, including momentum distribution. It is then shown that the radius of convergence of the cumulant expansion for the survival probability is always small. A long-time behavior of survival probability is described by the asymptotic series whose coefficients decrease with increasing particle energy but at different rates. To be specific, we have examined the exactly solvable model of tunneling through a finite range triangular barrier.

Evidence of Poole-frenkel and Fowler-Nordheim tunneling transport mechanisms in leakage current of (Pd/Au)/Al0.22Ga0.78N/GaN heterostructures

In this report, the gate leakage mechanism for AlGaN/GaN high electron mobility transistors (HEMTs) is consistently analyzed by means of temperature-dependent reverse gate current–voltage characteristics in the temperature range of 60–320 K. The gate leakage current of the AlGaN/GaN HEMT is studied by adjusting the experimental data using Poole–Frenkel (PF), and Fowler–Nordheim (FN) tunneling. In the temperature range of 200–325 K, the reverse bias leakage current is well dominated by a Frenkel-Poole emission model. The scenario describing the PF mechanism assumes that a defect level at φt = 0.45eV could be considered as an intermediate level through which carriers can transit to reach another level attributed to dislocations closer to conduction band. On the other hand, the FN mechanism seems to operate over the entire temperature range of 60–320 K and starts to dominate the gate leakage current due to triangular barrier formation.

Microporous networks of NiMn2O4 as a potent cathode material for electric field emission

The electric field-induced sterling electron emission of NiMn2O4 microporous networks synthesized via the sol-gel auto combustion route was investigated. Some primary characterization techniques such as x-ray diffraction, Fourier-transform infrared spectroscopy, and Raman spectroscopy were performed to confirm the pure crystallinity and metal oxide (Ni–O and Cr–O) stretching vibrations and also to provide a molecular fingerprint of the NiMn2O4 porous network. The distinct field emission (FE) properties of the NiMn2O4 microporous network was observed which was correlated with an electric field induced electron tunneling F–N (Fowler–Nordheim) model from a nearly planner conducting emitter surface with triangular potential-energy barrier approximation. A low turn-on field of 4.15 V µm−1 and threshold field of 5.25 V µm−1 were detected to draw emission current densities of 1 µA cm−2 and 10 µA cm−2 respectively. The local work function (Φ) of 5.509 eV for the NiMn2O4 porous network was computed using density functional theory (DFT) and it exhibits an impressive field enhancement factor (β) of 3381 with good FE current stability. These results demonstrate the potential application of this material for future vacuum micro/nanoelectronics and FE panel display applications.

Carrier transport improvement in ZnO/MgZnO multiple-quantum-well ultraviolet light-emitting diodes by energy band modification on MgZnO barriers

Ultraviolet (UV) light-emitting diodes (LEDs) based on zinc oxide (ZnO) materials have been the subject of many investigations because of their potential applications. In this study, ZnO/MgZnO multiple-quantum-well UV LEDs with graded-composition barriers were developed and numerically analyzed. The simulation results demonstrate that an optimized LED with a Mg composition graded from 24% to 2% in each triangular barrier exhibits the highest internal quantum efficiency (IQE) (88.0%) at 200 A/cm2, showing a 31.3% increase compared with the conventional LED with square barriers. This enhancement is attributed to the modified energy band structures that improve the symmetry in carrier transportation and increase the radiative recombination rate in each ZnO quantum well, thus enhancing the IQE of the device. Additionally, the different band-offset ratios of the MgZnO/ZnO and InGaN/GaN heterojunctions, which lead to the different carrier transport and electroluminescence properties of the ZnO- and GaN-based LEDs, were discussed here, providing researchers new insights into device design of ZnO-based LEDs.

Quasi-normal modes in a symmetric triangular barrier

Quasi-normal modes (QNMs) of the massless scalar wave in 1 + 1 dimensions are obtained for a symmetric, finite, triangular barrier potential. This problem is exactly solvable, with Airy functions involved in the solutions. Before obtaining the QNMs, we demonstrate how such a triangular barrier may arise in the context of scalar wave propagation in a tailor-made wormhole geometry. Thereafter, the Ferrari-Mashhoon idea is used to show how bound states in a well potential may be used to find the QNMs in a corresponding barrier potential. The bound state condition in the exactly solvable triangular well and the transformed condition for finding the QNMs are written down. Real bound state energies and complex QNMs are found by solving the respective transcendental equations. Numerical integration of the wave equation yields the time domain profiles for scalar waves propagating in this wormhole geometry which illustrate the quasi-normal ringing. Estimates relating the size of the wormhole throat (in units of solar mass) with the QNM frequencies are stated and discussed. Finally, we show how the effective potential and the QNMs for scalar perturbations of the Ellis-Bronnikov wormhole spacetime can be reasonably well-approximated using a properly parametrised triangular barrier.

Laboratory Experiments on an Internal Solitary Wave over a Triangular Barrier

Laboratory experiments were conducted to investigate the evolution of interfacial internal solitary waves (ISWs) incident on a triangular barrier. ISWs with different amplitudes were generated by gravitational collapse. The ISW energy dissipation and turbulence processes were calculated as waves passed over the triangular barrier. Experimental results showed that ISWs were reflecting back off the triangular barrier, and shoaling ISWs led to wave breaking and mixing when waves propagated over the obstacle. Wave instability created the dissipation of energy as it was transmitted from waves to turbulence. The rate of ISW energy dissipation, the maximum turbulent dissipation, and the buoyancy diffusivity linearly increased with the increase in the incident wave energy.

Spectral characterization of a Rh(110) photocathode: Band structure interpretation

The spectral dependence of the mean transverse energy and quantum efficiency of photoemission from a single-crystal Rh(110) photocathode are determined at 300K using the solenoid scan technique and a sub-picosecond laser-based UV radiation source tunable from 3.0-5.3eV (235-410nm). The tunable UV radiation is generated by sum frequency mixing the second and third harmonics of a front-end, 2W, 28MHz repetition rate, femtosecond Yb:KGW laser with signal and idler radiation from nonlinear-fiber continuum-seeded optical parametric amplification. The measured properties of the Rh(110) photocathode are well explained by a one-step photoemission simulation employing the dispersion of the emitting Σ1 and Σ2 bulk band states evaluated by fully relativistic (including spin-orbit coupling) Ab initio density functional theory methods and an exact quantum solution for transmission through and over a triangular barrier that is extended into the transverse dimension. The inclusion of the joint density of states (bulk crystal and vacuum) in the simulation accounts for the observed spectral dependence of both the mean transverse energy and the quantum efficiency of the photoemission process. The consequent demonstrated base line for the evaluation of photocathode emission properties using Ab initio methods will allow for the development of screening tools to select promising (ultra)low emittance solid-state photocathodes.

Electron emission produced by strong field laser radiation

The well-established Fowler-Nordheim-Schottky field emission theory is modified for strong electric fields E produced by pulsed laser radiation. The derivation of the electron tunneling probability through the triangular potential barrier is re-examined and simplified for an effective solution. This probability is studied only for strong fields, when the wavelength of the electrons is much larger than the barrier width. It is calculated for ten channels of electron emission; the emission decreases very sharply for channels with high numbers.

Effect of magnetic field on Goos-Hänchen shifts in gaped graphene triangular barrier

We study the effect of a magnetic field on Goos-Hänchen shifts in gaped graphene subjected to a double triangular barrier. Solving the wave equation separately in each region composing our system and using the required boundary conditions, we then compute explicitly the transmission probability for scattered fermions. These wavefunctions are then used to derive the Goos-Hänchen shifts in terms of different physical parameters such as energy, electrostatic potential strength and magnetic field. Our numerical results show that the Goos-Hänchen shifts are affected by the presence of the magnetic field and depend on the geometrical structure of the triangular barrier.

Improving the performance of the condenser fan in a subway train against the effects of crosswind flow by placing barriers

In this paper, the effect of crosswind flow and barrier placement on the performance of the condenser fan in a subway train is investigated. In addition, the amount of heat transfer on the condenser tubes is also analyzed. At different velocities of the train, variations in the velocity profile and drag force are determined for various geometries including triangular, rectangular, symmetric triangular barriers, and a barrier with parallel lines outside of the fan. Navier–Stokes, energy equations, and k– ω turbulence model have been used for the numerical modeling of the turbulent and incompressible flow. The results show that due to the created vortices behind the triangular and rectangular barriers, a negative velocity on the outflow of the fan is observed. Also, the symmetric triangular barrier minimizes the rotational flow on the top of the fan, and parallel paths have the most impact on the improvement of the fan's performance due to the elimination of all rotating flows. Finally, variations in temperature on the condenser tubes in the presence of barriers that are placed in the middle gap between the holes on the top of the condenser tubes are determined. These barriers move the crosswind flow toward the condenser tubes and decrease the output air temperature of the condenser.

Evaluation of photocathode emission properties in an electron gun: one-step photoemission from bulk band to vacuum states

A one-step photoemission analysis is developed, using the exact one-dimensional quantum solution for transmission over and through a triangular barrier presented by Forbes and Deane (2011 Proc. R. Soc. A 467 2927), to evaluate the emission properties of a photocathode in an electron gun. The analysis, which employs transverse momentum conservation in electron emission, includes the physical attributes (density of states and energy-momentum dispersion) of both the bulk band emission states and the recipient vacuum states in its evaluation of the mean transverse energy and relative quantum efficiency of the emitted electrons.

Improved carrier injection and confinement in InGaN light-emitting diodes containing GaN/AlGaN/GaN triangular barriers**Project supported by the National Key Research and Development Program of China (Grant Nos. 2017YFB0403100 and 2017YFB0403101), the National Natural Science Foundation of China (Grant Nos. 61404114, 61504119, and 11004170), the China Postdoctoral Science Foundation (Grant No. 2017M611923), and the Jiangsu Planned Projects for Postdoctoral Research Funds, China

In this study, an InGaN lighting-emitting diode (LED) containing GaN/AlGaN/GaN triangular barriers is proposed and investigated numerically. The simulation results of output performance, carrier concentration, and radiative recombination rate indicate that the proposed LED has a higher output power and an internal quantum efficiency, and a lower efficiency droop than the LED containing conventional GaN or AlGaN barriers. These improvements mainly arise from the modified energy bands, which is evidenced by analyzing the LED energy band diagram and electrostatic field near the active region. The modified energy bands effectively improve carrier injection and confinement, which significantly reduces electron leakage and increases the rate of radiative recombination in the quantum wells.

Performance Improvement of UV Light-Emitting Diodes With Triangular Quantum Barriers

Triangular quantum barriers have been designed and investigated in this work to improve the performances of AlGaN-based ultraviolet light-emitting diodes (UV-LEDs). The results show that the designed LED with triangular quantum barriers has been enhanced by 63.6% in light output power, while the efficiency droop has been reduced to 14.8% at an injection current of 180 mA, compared with the conventional LED with a stationary component Al <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.15</sub> Ga <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.85</sub> N barriers. Further research shows that the improvements of the proposed structure are due to the enhanced hole injection efficiency and the suppressed electron overflow as well as the decreased electrostatic field in the active region.

Suppressed polarization effect and enhanced carrier confinement in InGaN light-emitting diodes with GaN/InGaN/GaN triangular barriers

In this study, with the objective of lowering the polarization without degrading the carrier confinement in the active region, an InGaN light-emitting diode with GaN/InGaN/GaN triangular (GIGT) quantum barriers (QBs) was proposed and studied systematically. When traditional GaN QBs were replaced by the GIGT QBs, the output power at 150 mA rose from 82.05 to 155.99 mW, and the efficiency droop was decreased from 51.0% to 16.5%. Simulation results indicated that these improvements could result from the effectively suppressed polarization field in the quantum wells and the markedly enhanced carrier confinement in the active region because of the appropriately modified energy band structure.

InGaAs-based planar barrier diode as microwave rectifier

In this report, we proposed and simulated a new planar nonlinear rectifying device fabricated using InGaAs substrate and referred to as a planar barrier diode (PBD). Using an asymmetrical inverse-arrowhead-shaped structure between the electrodes, a nonuniform depletion region is developed, which creates a triangular energy barrier in the conducting channel. This barrier is voltage dependent and can be controlled by the applied voltage across the PBD, thus resulting in nonlinear diode-like current–voltage characteristics; thus it can be used as a rectifying device. The PBD’s working principle is explained using thermionic emission theory. Furthermore, by varying the PBD’s geometric design, the asymmetry of the current–voltage characteristics can be optimized to realize superior rectification performance. By employing the optimized structural parameters, the obtained cut-off frequency of the device was approximately 270 GHz with a curvature coefficient peak of 14 V−1 at a low DC bias voltage of 50 mV.

Analysis of Leakage Current Mechanism for Ni/Au Schottky Contact on InAlGaN/GaN HEMT

The gate leakage mechanism for InAlGaN/GaN high electron mobility transistors (HEMTs) is systematically studied using temperature‐dependent gate current–voltage characteristics. The electric field across the barrier layer is calculated through the extracted polarization charge and dielectric constant of the InAlGaN/GaN HEMT. The gate current of the InAlGaN/GaN HEMT is analyzed by fitting the experimental data using Themionic Emission (TE), Poole–Frenkel (PF), and Fowler–Nordheim (FN) tunneling. The results show that 1) reverse leakage current in the thin InAlGaN barrier layer is dominated by FN tunneling due to triangular barrier formation; 2) for thicker barrier layer, the reverse leakage current at low electric field (&lt;2.23 MV cm−1) is dominated by PF emission; 3) at high electric field near the threshold voltage the FN tunneling dominates. Extraction of effective barrier height by fitting the experimental data with models leads to the suggestion for the improvement of the device leakage current.

Behavior of a Moveable Barrier on Revetment for Mitigation of Disaster by Wave Overtopping

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High Performance Heterostructure Low Barrier Diodes for Sub-THz Detection

Heterostructure low barrier diodes (HLBD) based on lattice-matched AlGaInAs triangular barrier have been designed, fabricated, and characterized for zero-bias millimeter-wave and submillimeter-wave detection. Detectors with different barrier height and various active areas have been measured in order to determine the best structure for low-level radiometric detection. Unmatched responsivity of 1500-2000 V/W have been measured around 100 GHz with a video resistance of 400 to 800 Ω. Thanks to these low-impedances high-matched responsivity of 6000 and 5200 V/W have been demonstrated around 90 and 180 GHz, respectively, with a bandwidth of 25 GHz. Avery low noise equivalent power of about 0.6 and 0.7 pW/,/Hz have been deduced at 90 and 180 GHz, respectively. We show also that the dynamic range of these detectors is more than six decades. This performance makes the HLBD an interesting device for low-level sub-THz detection applications.

Antireflection coating of barriers to enhance electron tunnelling: exploring the matter wave analogy of superluminal optical phase velocity

The tunnelling of electrons through barriers is important in field emission sources and in interconnects within electronic devices. Here we use the analogy between the electromagnetic wave equation and the Schrodinger equation to find potential barriers that, when added before an existing barrier, increase the transmission probability. A single pre-barrier of negative potential behaves as a dielectric “antireflection coating”, as previously reported. However, we obtain an unexpected and much greater enhancement of transmission when the pre-barrier has a positive potential of height smaller than the energy of the incident electron, an unfamiliar optical case, corresponding to media with superluminal phase velocities as in dilute free electron media and anomalous dispersion at X-ray frequencies. We use a finite difference time domain algorithm to evaluate the transmission through a triangular field emission barrier with a pre-barrier that meets the new condition. We show that the transmission is enhanced for an incident wavepacket, producing a larger field emission current than for an uncoated barrier. Examples are given of available materials to enhance transmission in practical applications. The results are significant for showing how to increase electron transmission in field emission and at interconnects between dissimilar materials in all types of electronic devices.

Exact analytical theory for inverse tunneling of free vacuum electrons into a solid

This paper presents an exact analytical theory for the inverse tunneling of free vacuum electrons through a triangular potential barrier into a metal. It is found that the inverse tunneling probability is the same as that of the field emission of electrons from metal into vacuum, for the same incident electron energy, metal properties (work function, Fermi energy), and applied electric field strength. For incident electrons with velocities not normal to the vacuum-metal interface, the three-dimensional (3D) oblique tunneling is equivalent to the one-dimensional (1D) normal tunneling, by considering only the longitudinal energy of the electrons normal to the vacuum-metal interface.