New scaling of child-langmuir law in the quantum regime

Instability of modified Zakharov-Kuznetsov solitons in an inhomogeneous partially degenerate electron-ion magnetoplasma

Linear and nonlinear propagation characteristics of multidimensional drift ion-acoustic (IA) solitons are studied in an inhomogeneous partially degenerate electron-ion magnetoplasma. A modified Zakharov-Kuznetsov (mZK) equation is deduced, accounting for the longitudinal as well as the transverse dispersions. It is shown that the mZK equation admits a distinct solution, revealing excitation of a pulse-shaped soliton when the phase speed exceeds by the wave dispersion. For the instability condition of the waves, a novel growth rate (γ) is derived by modifying the standard small-k expansion scheme. The instability criterion, given for long-wavelength IA waves, has not been described elsewhere. Numerical analysis show that solitary pulses gain energy from the ion drift, involving into instability: it saturates with amplification of the unstable potentials. Similarly trapped electrons lead to unstable growth of the solitary waves by enhancing γ. This study is relevant to compact stars and to high-density facilities where density inhomogeneity ensues the unstable drift modes. The instability analysis is important in understanding anomalous diffusion, which reduces the lifespan (τ=γ^{-1}) of magnetically confined plasma.

Space-charge-limited current density for nonplanar diodes with monoenergetic emission using Lie-point symmetries

Understanding space-charge-limited current density (SCLCD) is fundamentally and practically important for characterizing many high-power and high-current vacuum devices. Despite this, no analytic equations for SCLCD with nonzero monoenergetic initial velocity have been derived for nonplanar diodes from first principles. Obtaining analytic equations for SCLCD for nonplanar geometries is often complicated by the nonlinearity of the problem and over constrained boundary conditions. In this Letter, we use the canonical coordinates obtained by identifying Lie-point symmetries to linearize the governing differential equations to derive SCLCD for any orthogonal diode. Using this method, we derive exact analytic equations for SCLCD with a monoenergetic injection velocity for one-dimensional cylindrical, spherical, tip-to-tip (t-t), and tip-to-plate (t-p) diodes. We specifically demonstrate that the correction factor from zero initial velocity to monoenergetic emission depends only on the initial kinetic and electric potential energies and not on the diode geometry and that SCLCD is universal when plotted as a function of the canonical gap size. We also show that SCLCD for a t-p diode is a factor of four larger than a t-t diode independent of injection velocity. The results reduce to previously derived results for zero initial velocity using variational calculus and conformal mapping.

Nano-gap planar metal electrodes: fabrication and I-V characteristics

The nanowires/bars and nano-gap electrodes are vital components for emerging electronics and have wide ranging applications in flat-panel displays, sensors, sub-100 nm transistor circuits, and miniaturized computers/devices. Focused ion beam (FIB) has emerged as a powerful and unique tool for nanofabrication. The research work described here is concerned with (a) the FIB fabrication of planar metallic (copper and gold) nanostructures, (b) their current-voltage (I–V) measurements in situ, and (c) a viable method for extracting the realistic values of emission parameters. The planar electrodes with gap of 80-100 nm are realized by FIB milling of thin metal films. The difficulties faced in objective interpretation of their I-V data (based on known mechanisms) are highlighted. For determining the parameters (namely, effective emission area α eff, apparent work function ф, and the field enhancement factor β), Fowler-Nordheim [ln(I/V2) versus 1/V] plots showing a minimum with straight line of negative slope can be used. The striking findings demonstrated are (i) occurrence of emission from a tiny region (<1 nm2) vis-à-vis physical area (400 μm × 200 nm), (ii) significant lowering of barrier height, and (iii) enhancement of local field due to protrusions present. Typical values of α eff, ϕ, and β deduced are 52.3 Å2, 1.62 eV, and 39.3, respectively for copper planar electrodes (gap ∼100 nm); the corresponding data for the case of gold (gap ∼80 nm) are 29.1 Å2, 1.97 eV, and 12.1, respectively. Moreover, β lowering observed with bias is accompanied by increase in the emission area due to progressive smoothening of protrusions at the cathode surface. The electrodes are found rough/rocky at the nanoscale with protrusions and varying separations at places. These features make the electron emissive region small and pointed with an enhanced local electric field and effectively of a lower barrier height. The current discrepancy in the Child-Langmuir’s space charge regime is attributed to the emission occurring from a restricted area only. These findings are important for futuristic nano-devices like thermo-tunnelling refrigerator, energy harvester, etc.

Oblique collision of ion acoustic solitons in a relativistic degenerate plasma

The interaction (oblique collision) of two ion acoustic solitons (IASs) in a magnetized relativistic degenerate plasma with relativistic degenerate electrons and non-degenerate cold ions is studied. The extended Poincaré–Lighthill–Kuo (PLK) method is used to obtain two Korteweg deVries (KdV) wave equations that describe the interacting IASs, then the phase shifts due to interaction are calculated. We studied influence of the fluid number density on the interaction process, interacting solitons phase shifts and also phase velocities. The introduced model is valid for astrophysical objects with high density matter such as white dwarfs, neutron stars, degenerate electrons gas in metals and laboratory degenerate plasma. An inverse proportionality between the phase shifts, phase velocity and the equilibrium electron fluid number density \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n_{eo}$$\end{document}neo was established in the range \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^{35}\,{\text {m}}^{-3}>n_{eo}>10^{38}\,{\text {m}}^{-3}$$\end{document}1035m-3>neo>1038m-3. We found that the soliton waves get sharper (narrower) and higher with increasing the electrons fluid number density \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n_{eo}$$\end{document}neo, and hence less spacial occupying. The phase shifts and the phase velocity remain approximately unchanged in the range of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^{35}\,{\text {m}}^{-3}<n_{eo}<10^{38}\,{\text {m}}^{-3}$$\end{document}1035m-3<neo<1038m-3. The impact of the obliqueness angle \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta $$\end{document}θ on the soliton interaction process is also studied.

Functional Charge Transfer Plasmon Metadevices

Reducing the capacitive opening between subwavelength metallic objects down to atomic scales or bridging the gap by a conductive path reveals new plasmonic spectral features, known as charge transfer plasmon (CTP). We review the origin, properties, and trending applications of this modes and show how they can be well-understood by classical electrodynamics and quantum mechanics principles. Particularly important is the excitation mechanisms and practical approaches of such a unique resonance in tailoring high-response and efficient extreme-subwavelength hybrid nanophotonic devices. While the quantum tunneling-induced CTP mode possesses the ability to turn on and off the charge transition by varying the intensity of an external light source, the excited CTP in conductively bridged plasmonic systems suffers from the lack of tunability. To address this, the integration of bulk plasmonic nanostructures with optothermally and optoelectronically controllable components has been introduced as promising techniques for developing multifunctional and high-performance CTP-resonant tools. Ultimate tunable plasmonic devices such as metamodulators and metafilters are thus in prospect.

Electrical transport and persistent photoconductivity in monolayer MoS2 phototransistors

We study electrical transport properties in exfoliated molybdenum disulfide (MoS₂) back-gated field effect transistors at low drain bias and under different illumination intensities. It is found that photoconductive and photogating effect as well as space charge limited conduction can simultaneously occur. We point out that the photoconductivity increases logarithmically with the light intensity and can persist with a decay time longer than 10⁴ s, due to photo-charge trapping at the MoS₂/SiO₂ interface and in MoS₂ defects. The transfer characteristics present hysteresis that is enhanced by illumination. At low drain bias, the devices feature low contact resistance of [Formula: see text] ON current as high as [Formula: see text] 10⁵ ON-OFF ratio, mobility of ∼1 cm² V^-1 s^-1 and photoresponsivity [Formula: see text].

Highly efficient tunable and localized on-chip electrical plasmon source using protruded metal-insulator-metal structure

A compact and highly efficient tunable and localized source of propagating surface plasmon-polaritons is proposed based on a protruded metal-insulator-metal (pMIM) structure. The protrusion along a segment of the pMIM forms a nanometer gap and allows a low voltage bias to generate a localized tunneling current. The tunneling current excited plasmons can be fully coupled to the metal-insulator-metal (MIM) waveguiding segment of the pMIM without leakage and propagate a long distance as the gap in the MIM waveguiding segment is much larger than the gap in the protruded segment of the pMIM. Eigenmode and numerical analyses show that by using MIM structures as a benchmark, the pMIM structure enhances the total amount of average power that is transferred from the tunneling current into the excitation of intrinsic eigenmodes of the MIM waveguiding segment. Depending on the magnitude of the applied voltage bias, the pMIM structure supports single, dual and multi modes for a typical Au-SiO₂-Au design with a 500 nm-thick SiO₂. Among all excited modes, the single mode operation allows highly efficient excitation of long travelling surface plasmon-polaritons (SPPs) of up to 30 µm. The electrical excitation of SPPs using pMIM structures opens up the possibility of integrating plasmon sources into nanoscale optoelectronic circuits to facilitate on-chip data communications.

Weakly nonlinear ion-acoustic excitations in a relativistic model for dense quantum plasma

The dynamics of linear and nonlinear ionic-scale electrostatic excitations propagating in a magnetized relativistic quantum plasma is studied. A quantum-hydrodynamic model is adopted and degenerate statistics for the electrons is taken into account. The dispersion properties of linear ion acoustic waves are examined in detail. A modified characteristic charge screening length and "sound speed" are introduced, for relativistic quantum plasmas. By employing the reductive perturbation technique, a Zakharov-Kuznetzov-type equation is derived. Using the small-k expansion method, the stability profile of weakly nonlinear slightly supersonic electrostatic pulses is also discussed. The effect of electron degeneracy on the basic characteristics of electrostatic excitations is investigated. The entire analysis is valid in a three-dimensional as well as in two-dimensional geometry. A brief discussion of possible applications in laboratory and space plasmas is included.

Ultrafast strong-field photoelectron emission from biased metal surfaces: exact solution to time-dependent Schrödinger Equation

Laser-driven ultrafast electron emission offers the possibility of manipulation and control of coherent electron motion in ultrashort spatiotemporal scales. Here, an analytical solution is constructed for the highly nonlinear electron emission from a dc biased metal surface illuminated by a single frequency laser, by solving the time-dependent Schrödinger equation exactly. The solution is valid for arbitrary combinations of dc electric field, laser electric field, laser frequency, metal work function and Fermi level. Various emission mechanisms, such as multiphoton absorption or emission, optical or dc field emission, are all included in this single formulation. The transition between different emission processes is analyzed in detail. The time-dependent emission current reveals that intense current modulation may be possible even with a low intensity laser, by merely increasing the applied dc bias. The results provide insights into the electron pulse generation and manipulation for many novel applications based on ultrafast laser-induced electron emission.

Charge transfer plasmon resonances across silver–molecule–silver junctions: estimating the terahertz conductance of molecules at near-infrared frequencies

Quantum plasmon resonances have been recently observed across molecular tunnel junctions. The present work extends these studies theoretically using a generalized space-charge corrected electromagnetic model for a wider range of molecules.

Scaling for quantum tunneling current in nano- and subnano-scale plasmonic junctions

When two conductors are separated by a sufficiently thin insulator, electrical current can flow between them by quantum tunneling. This paper presents a self-consistent model of tunneling current in a nano- and subnano-meter metal-insulator-metal plasmonic junction, by including the effects of space charge and exchange correlation potential. It is found that the J-V curve of the junction may be divided into three regimes: direct tunneling, field emission, and space-charge-limited regime. In general, the space charge inside the insulator reduces current transfer across the junction, whereas the exchange-correlation potential promotes current transfer. It is shown that these effects may modify the current density by orders of magnitude from the widely used Simmons’ formula, which is only accurate for a limited parameter space (insulator thickness > 1 nm and barrier height > 3 eV) in the direct tunneling regime. The proposed self-consistent model may provide a more accurate evaluation of the tunneling current in the other regimes. The effects of anode emission and material properties (i.e. work function of the electrodes, electron affinity and permittivity of the insulator) are examined in detail in various regimes. Our simple model and the general scaling for tunneling current may provide insights to new regimes of quantum plasmonics.

Novel scaling laws for the Langmuir-Blodgett solutions in cylindrical and spherical diodes

It is found that the Langmuir-Blodgett solutions for the space charge limited current density, for both cylindrical and spherical diodes, may be approximated by Japp=(4/9)ε0sqrt[(2e/m)](Ec3/2/sqrt[D]) over a wide range of parameters, where Ec is the surface electric field on the cathode of the vacuum diode and D is the anode-cathode spacing. This dependence is valid whether Ra/Rc is greater than or less than unity, where Ra and Rc are, respectively, the anode and cathode radius. Minor empirical corrections to the above scaling yield fitting formulas that are accurate to within 5% for 3×10(-5)<Rc/Ra<500. An explanation of this scaling is given. An accurate transit time model yields the Langmuir-Blodgett solutions even in the Coulomb blockade regime for a nanogap, where the electron number may be in the single digits, and the transit time frequency is in the THz range.

Fowler-Nordheim tunneling induced charge transfer plasmons between nearly touching nanoparticles

Reducing the gap between two metal nanoparticles down to atomic dimensions uncovers novel plasmon resonant modes. Of particular interest is a mode known as the charge transfer plasmon (CTP). This mode has been experimentally observed in touching nanoparticles, where charges can shuttle between the nanoparticles via a conductive path. However, the CTP mode for nearly touching nanoparticles has only been predicted theoretically to occur via direct tunneling when the gap is reduced to ~0.4 nm. Because of challenges in fabricating and characterizing gaps at these dimensions, experiments have been unable to provide evidence for this plasmon mode that is supported by tunneling. In this work, we consider an alternative tunneling process, that is, the well-known Fowler-Nordheim (FN) tunneling that occurs at high electric fields, and apply it for the first time in the theoretical investigation of plasmon resonances between nearly touching nanoparticles. This new approach relaxes the requirements on gap dimensions, and intuitively suggests that with a sufficiently high-intensity irradiation, the CTP can be excited via FN tunneling for a range of subnanometer gaps. The unique feature of FN tunneling induced CTP is the ability to turn on and off the charge transfer by varying the intensity of an external light source, and this could inspire the development of novel quantum devices.

Theory for large-amplitude electrostatic ion shocks in quantum plasmas

We present a generalized nonlinear theory for large-amplitude electrostatic (ES) ion shocks in collisional quantum plasmas composed of mildly coupled degenerate electron fluid of arbitrary degeneracy and nondegenerate strongly correlated ion fluid with arbitrary atomic number. For our purposes, we use the inertialess electron momentum equation including the electrostatic force, pressure gradient, and relevant quantum forces, as well as a generalized viscoelastic ion momentum (GVIM) equation for strongly correlated nondegenerate ions. The ion continuity equation, in the quasineutral approximation, then closes our nonlinear system of equations. When the electric field force is eliminated from the GVIM equation by using the inertialess electron momentum equation, we then obtain a GVIM and ion continuity equations, which exhibit nonlinear couplings between the ion number density and the ion fluid velocity. The pair of nonlinear equations is numerically solved to study the dynamics of arbitrarily-large-amplitude planar and nonplanar ES shocks arising from a balance between harmonic generation nonlinearities and the ion fluid viscosity for a wide range of plasma mass densities and ion atomic numbers that are relevant for the cores of giant planets (viz., Jupiter) and compact stars (viz., white dwarfs). Our numerical results reveal that the ES shock density profiles strongly depend on the plasma number density and composition (the atomic-number) parameters. Furthermore, ion density perturbations propagate with Mach numbers which significantly depend on the studied plasma fractional parameters. It is concluded that the dynamics of the ES shocks in the superdense degenerate plasma is quite different in the core of a white dwarf star from that in the lower density crust region.

SIMULATION OF HIGH CURRENT FIELD EMISSION FROM VERTICALLY WELL-ALIGNED METALLIC CARBON NANOTUBES

We have studied the intense electron beams emitted from multiple metallic, vertical and well-aligned Carbon Nanotube (CNT) field emitters. A two-dimensional (2D) particle-in-cell simulation code MAGIC2D is used to obtain the I–V characteristics near to the apex of the emitters' surface for a given applied electric field and field enhancement factor over a wide range of parameters. The effects of electron space charge and electric field shielding from neighboring emitters are compared in low current and high current regimes. It is found that the electron space charge is dominant in high current regime, where the Fowler–Nordheim (FN) law becomes the 2D Child–Langmuir (CL) law. The emitter spacing, number of emitters, and emitter's uniformity are also particularly studied, and they are more critical in low current regime. Smooth transition from the FN law to CL law is demonstrated.

Phase-space structures in quantum-plasma wave turbulence

The quasilinear theory of the Wigner-Poisson system in one spatial dimension is examined. Conservation laws and properties of the stationary solutions are determined. Quantum effects are shown to manifest themselves in transient periodic oscillations of the averaged Wigner function in velocity space. The quantum quasilinear theory is checked against numerical simulations of the bump-on-tail and two-stream instabilities. The predicted wavelength of the oscillations in velocity space agrees well with the numerical results.

Quantum model of space-charge-limited field emission in a nanogap

This paper presents a modified Thomas-Fermi-approximated quantum model for space-charge-limited field emission in a nanogap with metal electrodes, where the image-charge potential (including anode screening), direct tunnelling, space-charge effects and exchange-correlation effects of the tunnelling current are treated in a one-dimensional quantum model. It is found that the traditional Fowler-Nordheim (FN) law (even with the classical model of anode screening) is no longer valid in a nanogap of less than 10 nm. The smooth transition of our proposed model to the traditional FN law extended to large gap spacing is demonstrated. Application of the model to estimate the emission area of an experimental I-V curve in a nanogap is discussed.

Nonlinear theory for a quantum diode in a dense Fermi magnetoplasma

We present a simple analytical nonlinear theory for quantum diodes in a dense Fermi magnetoplasma. By using the steady-state quantum hydrodynamical equations for a dense Fermi magnetoplasma, we derive coupled nonlinear Schrödinger and Poisson equations. The latter are numerically solved to show the effects of the quantum statistical pressure, the quantum tunneling (or the quantum diffraction), and the external magnetic field strength on the potential and electron density profiles in a quantum diode at nanometer scales. It is found that the quantum statistical pressure introduces a lower bound on the steady electron flow in the quantum diode, while the quantum diffraction effect allows the electron tunneling at low flow speeds. The magnetic field acts as a barrier, and larger potentials are needed to drive currents through the quantum diode.

Fluid turbulence in quantum plasmas

Nonlinear fluid simulations are developed by us to investigate the properties of fully developed two-dimensional (2D) electron fluid turbulence in a very dense Fermi (quantum) plasma. We find that a 2D quantum electron plasma exhibits dual cascades, in which the electron number density cascades towards smaller turbulent scales, while the electrostatic potential forms larger scale eddies. The characteristic turbulent spectrum associated with the nonlinear electron plasma oscillations (EPO) is determined critically by a ratio of the energy density of the EPOs and the electron kinetic energy density of quantum plasmas. The turbulent transport corresponding to the large-scale potential distribution is predominant in comparison with the small-scale electron number density variation, a result that is consistent with the classical diffusion theory.

Nonlinear interactions between electromagnetic waves and electron plasma oscillations in quantum plasmas

We consider nonlinear interactions between intense circularly polarized electromagnetic (CPEM) waves and electron plasma oscillations (EPOs) in a dense quantum plasma, taking into account the electron density response in the presence of the relativistic ponderomotive force and mass increase in the CPEM wave fields. The dynamics of the CPEM waves and EPOs is governed by the two coupled nonlinear Schrödinger equations and Poisson's equation. The nonlinear equations admit the modulational instability of an intense CPEM pump wave against EPOs, leading to the formation and trapping of localized CPEM wave pipes in the electron density hole that is associated with a positive potential distribution in our dense plasma. The relevance of our investigation to the next generation intense laser-solid density plasma interaction experiments is discussed.

Ultrashort-pulse child-langmuir law in the quantum and relativistic regimes

This Letter presents a consistent quantum and relativistic model of short-pulse Child-Langmuir (CL) law, of which the pulse length tau is less than the electron transit time in a gap of spacing D and voltage V. The classical value of the short-pulse CL law is enhanced by a large factor due to quantum effects when the pulse length and the size of the beam are, respectively, in femtosecond duration and nanometer scale. At high voltage larger than the electron rest mass, relativistic effects will suppress the enhancement of short-pulse CL law, which is confirmed by particle-in-cell simulation. When the pulse length is much shorter than the gap transit time, the current density is proportional to V, and to the inverse power of D and tau.