The use of the lattice-space Weyl-Wigner formalism quantum dynamics particles in solids, coupled with nonequilibrium Green's-function techniques, provides a rigorous and straightforward derivation an exact integral form equation for distribution function many-body quantum-transport theory. We show that present more realistic calculations, both numerical (particularly, highly transient simulations) analytical (fully gauge-invariant calculations), which include full effects effects, can be...

In this article, we examine the Fowler–Nordheim (FN) equation for field emission using pedagogical models to introduce and illuminate its origins, limitations, extensions, application multidimensional structures. The analyses of modern electron sources generally invoke either FN or Richardson–Laue–Dushman (thermionic emission) interpret experimental data. These equations have ranges validity that are increasingly challenged by operating conditions. present article shall therefore several...

Intrinsic high-frequency oscillations (\ensuremath{\approxeq}2.5 THz) in current and corresponding quantum-well density have been simulated for the first time a fixed-bias voltage negative differential resistance (NDR) region of current-voltage (I-V) characteristics resonant tunneling diode. Scattering self-consistency are included. Hysteresis ``plateaulike'' behavior time-averaged I-V curve NDR region. bistability is manifested by phenomenon unstable electron charge buildup ejection from...

The canonical equations of electron emission are the Richardson-Laue-Dushman equation for thermionic emission, Fowler-Nordheim field and Fowler-Dubridge photoemission. They widely used experimentally well vetted determination current density from sources. While all three may be obtained a general underlying formulation, they treated as distinct their domains applicability do not overlap. Here, tractable analytical model is given that only devolves to equations, but also more importantly...

Field emitter arrays (FEAs) stand to strongly impact device performance when physical size, weight, power consumption, beam current, and/or high pulse repetition frequencies are an issue. FEAs capable of instant ON/OFF performance, brightness, current density, large transconductance capacitance ratio, and low voltage operation characteristics. Advanced microwave tubes, in particular, inductive output amplifiers, by far the most technically challenging use date. Other important uses include,...

The emittance of high brightness electron sources, particularly field emitters and photocathodes but also thermionic is increased by surface roughness on the emitter. Such structure causes local enhancement complicates both prediction underlying emission models which such predictions depend. In present work, a method to find trajectories near regions given applied for field, photo, thermal an analytically tractable hemispherical model. dependence current density, spatial variation,...

Classical field emission theory relates the material work function and applied electric at emitter surface to tunneling current density, based upon one-dimensional, planar Fowler–Nordheim equation. The extension of this nonplanar, tip-anode geometries is complicated by spatial variation resultant density along microtip surface. To relate spatially dependent voltage in tip-to-plane geometry, experimenters have adopted empirically determined enhancement factors (i.e., F=βV) area terms explain...

We have demonstrated a general framework for realizing and modulating perpendicular magnetic anisotropy in rare-earth-element heavy-metal-free material system. Using GaAs(001)/Fe(001) template, we developed synthesis scheme to produce epitaxial body center tetragonal Fe-N with (001) texture. By varying the N doping concentration, crystal tetragonality ($c$/$a$) can be tuned relatively wide range. It is found that layer strong crystalline (MCA) as it approaches iron nitride interstitial...

Analytically tractable models of thermal-field emission, field enhancement, and heating mechanisms (Nottingham resistive) are developed combined to make estimates the fields temperatures that accompany development growth asperities. The relation asperity dimensions dark current is discussed in two experimentally motivated examples. hypothetical microscopic sources breakdown context Nottingham resistive heating. latter estimated using a general methodology. A point-charge model used find...

Cathodes consisting of arrays high aspect ratio field emitters are great interest as sources electron beams for vacuum electronic devices. The desire currents and current densities drives the cathode designer towards a denser array, but ungated emitters, also lead to increased shielding, in which enhancement factor β each emitter is reduced due presence other array. To facilitate study these arrays, we have developed method modeling using tapered dipole line charges. This can be used...

A compact introduction to the history and canonical equations of electron emission is given for thermal (Richardson), field (Fowler-Nordheim), photoemission (Fowler-DuBridge), secondary (Baroody), as well space-charge-limited flow (Child-Langmuir law). general equation derived related equations. Processes that affect emission, such coatings, shielding, excitation transport, space charge, emittance, material properties, are considered. Requirements imposed by beam evolution discussed.

Theoretical models of thermal, field, and thermal-field emission electrons generally require the evaluation Gamow, or tunneling, factor. A rapid means to do so is developed using shape factor methods for general potentials, but, in particular, image charge (or Schottky-Nordheim) barrier from which Fowler-Nordheim (field emission) Richardson-Laue-Dushman (thermal equations are derived. The method provides greater accuracy than elliptical integral functions that electron conventionally rely on...

In ungated field emitter arrays, the enhancement factor β of each tip is reduced below value it would have in isolation due to presence adjacent emitters, an effect known as shielding or screening. Reducing distance b between emitters increases density emission sites, but also reduces per site, leading existence optimal spacing that maximizes array current. Most researchers identified this comparable height h, although there disagreement about exact optimization. Here, we develop a procedure...

Field emitter arrays are high-brightness electron sources with important current and future applications in vacuum electronics, particle accelerators, directed energy. The produced by individual emitters these is controlled the total electric field on their surfaces, which depends background field, space charge from previously-emitted electrons, enhancements due to geometric features at macro-, meso-, micro-scales. To facilitate study of shielding effects arrays, we have developed a...

Electron emission and transport through over potential barriers is an essential process requiring modeling simulation to meet the design needs characterization of exceedingly broad range technologically important devices processes. The description thermal, field, photoemission, related concerns space–charge affected electron flow, often make use specialized formulations developed in early days quantum mechanics. Advancements utilization sources particularly applications using advanced...

A general electron emission equation is developed to account for both tunneling and thermal potentials, particularly when processes are non-negligible. It then applied the image charge potential that basis Fowler-Nordheim (FN) [Proc. R. Soc. London A119, 173 (1928)] Richardson-Laue-Dushman (RLD) equations of A107, 377 (1925)]. The leading order terms in a series expansion used derive “refined” FN-RLD extends range validity FN RLD parameters where traditional forms either fail or perform poorly.

A model of photoemission from coated surfaces is significantly modified by first providing a better account the electron scattering relaxation time that used throughout theory, and second implementing distribution function based approach (“Moments”) to emission probability. The latter allows for evaluation emittance brightness beam at photocathode surface. Differences with Fowler-Dubridge are discussed. impact Moments on estimation quantum efficiency metal surfaces, either bare or partially...

An analytical formula of the emittance a field emitter is given. In contrast to thermal and photoemission, such contains complexity due multidimensional nature source. A formulation given for one- three-dimensional (3D) emitters. The 3D makes use point charge model unit cell coupled with trajectory analysis follow electrons an evaluation plane where determined. single tip theory extended array resulting predicts Spindt-type square emitters 0.2cm on side producing 2000A∕cm2 23mmmrad. Theory...

Field emitters rely on high gradients microfabricated structures to enable substantial levels of emitted current, which can in turn act reduce the field at emission site a single emitter. An account that effect is obtained following steps: model emitter geometry based point charge allows for determination apex radius and enhancement factor arbitrarily sharp given, followed by an analytical formula calculation total current from such structure then suppressing site. Predictions impact space...

The current associated with field emission is greatly dependent on the electric at emitting electrode. This a combination of in vacuum and space charge created by current. latter becomes more important as currentdensity increases. Here, study performed using modified classical 1D Child-Langmuir description that allows for exact solutions order to characterize contributions due charge. Methods connect approach an array periodic 3D structures are considered.

Models of space-charge affected thermal-field emission from protrusions, able to incorporate the effects both surface roughness and elongated field emitter structures in beam optics codes, are desirable but difficult. The models proposed here treat meso-scale diode region separate micro-scale regions characteristic sites. consequences discrete events given for one-dimensional (sheets charge) three dimensional (rings models: former, results converge steady state conditions found by theory...

Design methodologies for high-performance photocathodes become increasingly important, driven by the needs of advanced x-ray light sources and ultrafast electron diffraction microscopy. Cathode design has been hampered interdependent performance metrics, where improving one compromises another. Rapid developments in modeling nanomaterial fabrication allow tailoring electronic structure ways that influence fundamental mechanisms photoemission: absorption, transport, emission. This survey...

Quantum transport through one-dimensional potential barriers is usually analyzed using either the transmission coefficient (TC) or Wigner distribution function (WDF) approach. Fast, accurate, and efficient numerical algorithms are developed for each compared (a) calculating current-field relationships field-emission potentials with silicon parameters (and current-voltage resonant tunneling diodes), (b) their ability to accommodate scattering, self-consistency, time dependence, (c) behavior...

The authors introduce a trajectory methodology to describe elementary space- and time-dependent events in tunneling process the resonant diode (RTD). A for constructing quantum particle trajectories is presented. RTD are presented their behavior, as function of scattering self-consistency, shown be consistent with steady-state current-voltage/quantum well electron density characteristics RTD, response sudden bias switch. also exhibit conservation-of-energy-like behavior. formulation thus...