Thermal Field Emission Electron Research Articles

A unified thermal-field emission theory for metallic nanotips

The role of curvature effects, in the thermal-field (TF) emission of electrons from nanotips, has been investigated. It is found that for field emitter tips having tip radius of curvature Ra<50 nm, the error on using the planar tunneling potential to evaluate the current density is significant compared to the curvature-corrected potential. Furthermore, the error is found to be strongly temperature dependent at low apex fields, whereas at high fields, it is only moderate. For emitter tips having tip radius Ra≥5 nm, a unified expression for current density applicable for field, thermal-field, and thermionic emission is obtained. In the analysis, a single linearization point corresponding to the peak of the normal energy distribution of electrons is chosen, about which the Gamow exponent is expanded. The temperature-dependent curvature-corrected current density equation is numerically validated against a benchmark that performs the current density integral with the Kemble form of the Wentzel–Kramers–Brillouin transmission coefficient up to the peak of the tunneling potential, while above the barrier, the Morse transmission coefficient is used. The agreement is found to be good. It is inferred that the curvature plays a significant role in field and thermal-field emission, whereas in thermionic emission, it is not as important. In the limit where the apex radius of curvature Ra→∞, it is able to retrieve the Murphy–Good equation as well as the Richardson–Laue–Dushman equation in their respective limits.

Modeling of the Influence of Thermal-Field Electron Emission from the Cathode with a Thin Insulating Film on its Heating in Glow Discharge

Modeling of the Influence of Thermal-Field Electron Emission from the Cathode with a Thin Insulating Film on its Heating in Glow Discharge

Thermal-field electron emission from three-dimensional Dirac and Weyl semimetals

A model is constructed to describe the thermal-field emission of electrons from a three-dimensional (3D) Dirac and Weyl semimetal hosting Dirac/Weyl node(s). The traditional thermal-field electron emission model is generalized to accommodate the 3D nonparabolic energy band structures in the Dirac/Weyl semimetals, such as cadmium arsenide $({\mathrm{Cd}}_{3}{\mathrm{As}}_{2})$, sodium bismuthide $({\mathrm{Na}}_{3}\mathrm{Bi})$, tantalum arsenide (TaAs), and tantalum phosphide (TaP). Due to the nontrivial energy decomposition of the energy dispersion and the vanishing transverse density of states, an unusual dual-peak feature is observed in the total energy distribution spectrum. This nontrivial dual-peak feature, absent from traditional materials, plays a critical role in manipulating the magnitude of the emission current through the variation of an applied field, temperature, and Fermi level. This feature suggests that a higher Fermi level will achieve a larger current density (apart from low work function). At zero temperature limit, a ${F}^{3}$ scaling law for pure field emission is derived and it is different from the well-known Fowler-Nordheim ${F}^{2}$ scaling law. Furthermore, these new behaviors have shown to exist beyond the Dirac cone approximated model. This model expands the recent understandings of electron emission studied for the Dirac two-dimensional (2D) materials into the 3D regime, and thus offers a theoretical foundation for the exploration in using Dirac semimetallic materials as novel electrodes.

EFFECT OF ELECTRON EMISSION PROCESSES ON MACROPARTICLE CHARGING IN PLASMA SYSTEMS WITH ELECTRON BEAM

The effect of different electron emission processes on macropraticle (MP) charging in a plasma at the presence of electron beam is investigated. A complete model of the MP charging in the beam-plasma systems, which includes possible electron emission processes from the MP surface, such as secondary electron emission, the thermionic electron emission, the field electron emission and thermal-field electron emission, is presented.

On vibration characteristics of thermal field emission electron gun filament

Thermal field emission electron gun is used as electron source in scanning electron microscope. Its filament made by tungsten wire is bended like a hairpin and is prone to vibration disturbance, therefore deteriorating outcome images. To model filament’s mechanical performance under vibrating conditions, finite element modal analysis was carried out, and frequency response was calculated. It was shown that the filament was more sensitive to lateral excitation, and due to its unique structure, vibration characteristics were different in two lateral directions. Stiffness of the two lateral directions was compared through static calculation to verify the calculated mode order. Besides, characteristics between room temperature and working temperature were compared. If allowed, electron gun should be mounted in the way that its sensitive direction be kept away from the most intensive excitation’s direction.

A reformulated general thermal-field emission equation

Theoretical models of thermal, field, and thermal-field emission of electrons generally require the evaluation of the Gamow, or tunneling, factor. A rapid means to do so is developed using shape factor methods for general potentials, but, in particular, for the image charge (or Schottky-Nordheim) barrier from which the Fowler-Nordheim (field emission) and Richardson-Laue-Dushman (thermal emission) equations are derived. The shape factor method provides greater accuracy than the elliptical integral functions that the electron emission equations conventionally rely on and eliminates the need to use them. The mild overprediction of the field emission current by the Fowler-Nordheim equation at very high fields is corrected. Undesired behaviors associated with prior versions of the general Thermal-Field equation in the thermal-field regime are eliminated by properly identifying the maximum of the current density integrand and accounting for its shape. The methodology to rapidly identify the current density maximum in general is demonstrated for various combinations of field, temperature, and work function, and the improvements demonstrated. The utility of the reformulated methodology for the simulation of electron beams and the ability to characterize cathode configurations of technological interest are discussed.

The model of thermal field emission from tungsten fuzz

Tungsten fuzz is a material formatted due to interaction of helium plasma with tungsten surface. This material consists of large number of thin nanostructures “growing” on the tungsten surface and having enhanced field emission properties. However, the calculation of field amplification factor from emission current-voltage characteristic gives large value which is not correlated with geometrical parameters of the nanostructures. Thermal field electron emission model that takes into account the Joule heating by emission current is presented in this work. This model predicts qualitatively similar current values corresponding to experiment and explains enhanced field amplification factor from the current-voltage characteristic.

A laboratory X-ray microscopy setup using a field emission electron source and micro-structured reflection targets

We present a computed tomography (CT) setup for materials characterization with significantly improved resolution as compared to state of the art mirco- or subμ-CT systems. The system presented here is composed of a customized JEOL JSM7100-F scanning electron microscope with a thermal field-emission electron source allowing to focus an intense electron beam onto specially designed micro-structured reflection target thereby further reducing the size of the X-ray source spot by reducing the electron interaction zone and thus reducing image blur at high magnifications.With the proposed setup geometric magnifications up to M=1000 and spatial resolutions down to 100nm can be achieved. We also demonstrate the phase contrast capabilities of the setup.

Heat effect of thermal-field emission of electrons from metal

A method for determining the heat effect that accompanies the thermal-field emission of electrons from metal into vacuum is proposed in the context of a standard model of free-electrons in the metal. Particular attention is given to a quantitative investigation of the cooling regime of a metal surface due to the electron emission. It is demonstrated that for cathodes with low work function on the order of 1 eV, cathode cooling intensity on the order of 10 kW/cm2 can be reached at temperature of 300 K.

Phenomenological model of an abnormal thermal field electron emission from the 2D nanoheterostructured surfaces

Phenomenological model of an abnormal thermal field electron emission from the 2D nanoheterostructures of a kind: a conductor – a thin dielectric film, is offered and developed.

Low temperature refrigeration by using thermal-field electron emission in a coaxial cylindrical diode

This paper explores possibility of refrigeration by using thermal-field emission of electrons in a coaxial cylindrical diode with a nanometer scale inner electrode (or cathode). Our calculation shows that it is possible to provide cooling at temperatures down to 200 K if the work function of the cathode is about 1 eV. The limitation on using a low work function cathode can be improved by applying an external axial magnetic field to create an additional potential barrier near the anode, more efficiently restricting the emission of low energy electrons (below the Fermi energy level). Because of this extra filtering process, emitters of arbitrary work functions can be used to provide an improved cooling capability from 300 to 10 K. The optimal conditions to maximize cooling power density are determined both numerically and analytically. The space charge effects of the emitted electrons in the gap are included self-consistently.

Anomalous thermal field emission

The field emissivity of ZrO2/W(100) nanoheterostructures made by applying a thin (≈10 nm) ZrO2 layer on the surface of a needle-like W(100) microcrystal is studied. At a nanoheterostructure temperature of ≈2000 K, electron emission is found to start at a low extracting (Laplace) field (below 50 V/μm). Under the conditions of steady electron emission, the emission current density from the surface of the heterostructure may reach anomalously high values (∼108 A/cm2). A phenomenological model of anomalous thermal field emission of electrons from the surface of the conductor (metal)-thin insulator heterostructure is suggested.

57Fe Mössbauer, FT-IR and FE SEM investigation of the formation of hematite and goethite at high pH values

The ferrihydrite suspensions were precipitated at high pH values, and crystallizations of α-Fe 2O 3 and α-FeOOH were monitored by Mössbauer and FT-IR spectroscopies and thermal field emission electron microscopy. α-Fe 2O 3 crystallization in dense ferrihydrite suspension at 160 °C was a fast process governed by the dissolution/reprecipitation mechanism. Between 40 and 60 min of crystallization traces/small amounts of α-FeOOH precipitated and dissolved, so that between 6 and 24 h only platelet-like α-Fe 2O 3 particles were present. On the other hand, the kinetics of crystallization in a dense ferrihydrite suspension at RT was slow and upon 90 days of ageing α-FeOOH as an end-product was detected. These α-FeOOH particles were strongly elongated along the crystallographic c-axis. α-FeOOH particles were also obtained as a single phase at 160 °C, but with decreased Fe 3+ concentrations (0.1 or 0.05 M FeCl 3). These particles also showed a strong lateral aggregation and the formation of a dendritic microstructure. The crystallization process in a dense ferrihydrite suspension was strongly influenced by ultrasound energy. The application of ultrasound energy of 141 W cm −2 for 2 h induced a coalescence-like effect in the ferrihydrite suspension, as observed by FE SEM. With ultrasound energy increased up to 424 W cm −2 the crystallization of α-Fe 2O 3 particles was observed. The geometrical shape of these α-Fe 2O 3 particles was poor compared with those crystallized in the absence of ultrasound.

Low temperature refrigeration by electron emission in a crossed-field gap

A method of refrigeration using thermal-field electron emission from nanoscale emitters of arbitrary work function in a vacuum crossed-field gap is proposed. With an external crossed magnetic field, an additional potential barrier near the anode is created to restrict the tunneling of low-energy electrons (below the Fermi energy) and thus provids a versatile cooling capability from 300 down to 10K. Optimal conditions are determined numerically and analytically, which give local cooling power densities (per emitter) of about 600kW∕cm2 (at 300K), 2.7kW∕cm2 (at 50K), and 20W∕cm2 (at 10K).

Preparation and characterization of transparent ZnO thin films obtained by spray pyrolysis

Structural, optical, chemical and electrical properties of thin films of ZnO obtained by spray pyrolysis over Pt or silica substrates are determined at temperature ranges between 223 and 373 K. The thin films are pure ZnO with a preferred crystalline orientation of (0 0 2). Grain-boundary barriers are created by the band bending and the mobility of charge carriers is limited by the thermal field emission of electrons at the grain-boundary barriers. The density of ionized acceptor atoms and the width of the space charge, both obtained from the capacitance–voltage ( C– V) method, are consistent with the theory of the depletion layer in the Schottky barrier device. The density of states of defect, obtained from admittance spectroscopy, only presents a maximum at approximately 0.44 eV, whose position in the band gap does not change under bias.

Nanotube electronic states observed with thermal field emission electron spectroscopy

We observe nonmetallic electronic states above the Fermi level in single-walled carbon nanotubes by measuring the energy distribution of thermal-field-emitted electrons. This measurement method examines electronic states associated with the nanotube cap or end termination, and with it, we resolve electronic states greater than 3 eV above the Fermi level. The observed emitting states are broad at high temperatures (0.7–1.5 eV full width at half maximum), and the peak positions shift linearly with applied voltage. We present possible mechanisms responsible for these states.

Resolution limits and process latitude of x-ray mask fabrication

This article reports on the process latitude and resolution limits of x-ray mask fabrication by electron beam lithography for both additive (gold plated) and subtractive (etched tungsten) masks. The experiments were performed using a vector scan thermal field emission electron beam lithography machine with a maximum beam voltage of 100 kV and a minimum beam diameter of 27 nm. Features as small as 0.075 μm have been patterned on x-ray masks. Exposure latitude was studied as a function of beam diameter and acceleration voltage. The results indicate that forward scattering in the resist is a major cause of degradation in process latitude, and that going to a higher beam energy or thinner resist provides substantial benefits. For subtractive processes where a high-Z material (e.g., tungsten) underlies the resist, backscattered electrons are also a significant factor in limiting exposure latitude and resolution. For both substrate types, increasing the accelerating voltage from 50 to 100 kV can improve the exposure latitude by a factor of 2. At 100 kV the resolution limits are caused by the high aspect ratios found in the sub-tenth micron structures. As the aspect ratio exceeds 5:1 three major problems are encountered. First, the resist tends to fall over due to a lack of mechanical strength. Second, a noticable decrease in linewidth control occurs. Finally, the plating rate becomes dependent on the feature size, causing absorber thickness nonuniformity.

Development of an Ultrahigh Vacuum High Resolution Scanning Transmission Electron Microscope

A 100 kV ultrahigh vacuum high resolution scanning transmission electron microscope (UHV-HR-STEM) has been developed for the purpose of analyzing micro-volume element clean surfaces by means of total reflection angle X-ray spectroscopy (TRAXS). The instrument is provided with a thermal field emission electron gun (T-FEG) with a build-up W(100) emitter. Since the objective lens is designed to minimize the spherical aberration coefficient (Cs) of the objective pre-field to Cs = 0.52 mm, the highest theoretical resolution of 0.17 nm is achieved. Also, the specimen stage was incorporated into a small space in the objective polepiece. A clean UHV of 2.2 × 10 −8 Pa was achieved in the specimen environment by means of a dry pump system

Low voltage, high resolution studies of electron beam resist exposure and proximity effect

Resist exposure characteristics have been studied over a voltage range from 1 to 10 kV in order to demonstrate the feasibility of using low voltage electron beam lithography (EBL) to pattern submicron features without the proximity effect problems seen at higher voltages. The exposures were done by modifying a 25 kV thermal field emission EBL machine to run in a retarding field configuration where the sample is biased at a large negative potential, thus reducing the final beam landing energy. After analyzing the linewidths of various proximity test patterns with features as small as 0.15 μm, we conclude that at these dimensions the proximity effect on silicon substrates, compared to 10 kV, is greatly reduced at 5 kV and almost negligible at 3 kV. In order to maintain resolution at these low voltages, it is normally necessary to reduce the beam current due to increased aberrations and reduced source brightness. However, calculations and experiments show that these problems are much less severe in the retarding field configuration, where the electron beam is accelerated to a high potential through most of the optical path length and then reduced to the working voltage just before striking the workpiece. In addition, the reduced beam current is compensated by an almost corresponding increase in the resist sensitivity. Thus, low voltage is shown to be an effective means of avoiding the proximity effect, and a tool using the combination of a thermal field emission electron source and a retarding field final lens is shown to have the resolution and beam current required to expose patterns at the required voltage with reasonable throughput.

100 kV thermal field emission electron beam lithography tool for high-resolution x-ray mask patterning

High-voltage (≥50 kV) electron beam lithography (EBL) is the preferred technique for fabrication of additive-process x-ray masks, because the high-voltage minimizes scattering in the resist and membrane, resulting in better resolution, straighter sidewalls, and reduced proximity effect. We have designed and built a new 100 kV column for a vector scan EBL machine for the purpose of writing high-resolution, high-precision x-ray masks in order to explore the technological and fundamental limits of x-ray lithography. The column features a 100 kV thermal field emission gun with an electrostatic condenser lens, conjugate blanking, and a liquid-cooled magnetic final lens with high-precision double magnetic deflection. The two-lens optics provides a beam diameter of 30 nm at a current of 5 nA, sufficient to expose moderately sensitive resists at pixel rates approaching the maximum deflection speed of 10 MHz. Results obtained include proximity corrected, complex patterns in thin resist with feature sizes down to 50 nm. Comparisons of proximity effects, exposure parameters, and actual resist profiles, show that 100 kV is clearly superior to 50 kV and even 75 kV for feature sizes below 0.25 μm in thick (0.75 μm) resist. Excellent linewidth control has been obtained on plated gold x-ray masks with feature sizes as small as 75 nm. Problems of patterning nanometer features with aspect ratios as high as 10:1, which include forward scattering, development effects, and plating effects, are discussed.