Theory Of Electron Emission Research Articles

Generalized Electron Emission Theory for One-Dimensional Conducting Materials

This research focuses on exploring generalized electron emissions in one-dimensional conducting materials, specifically examining field emission and thermionic emission. Additionally, this study investigates one-dimensional thermal radiation. The current density is derived for both one-dimensional thermionic emission and one-dimensional field emission. A generalized current density in one dimension is devised, taking into account arbitrary accelerating fields and temperature conditions. The formula for the one-dimensional current density is depicted with accelerating field and temperature across various work function materials. The emission current is represented as a function of temperature for various electric fields. The emission current is also represented as a function of the electric field for various temperatures.

Physical Modeling of Metal Insulator-SiC Hydrogen-Sensitive Sensors and Simulation of Superconducting Temperature and High-Precision Characteristics

The response mechanism of a metal insulator-SiC (MISiC) Schottky barrier diode (SBD) gas sensor is analyzed. By combining the SBD hot electron emission theory with the hydrogen adsorption and desorption theory, a physical model of the MISiC SBD gas sensor is developed by considering the barrier height modulation effect and the variation of the ideal factor with the external conditions. Using this model, the relationship between device characteristics and insulation layer thickness is analyzed, and the optimal design is carried out between sensitivity, reliability and operating current/current resolution factors.

Study on the electron emission characteristics of a thermal emission cathode with grid for micro-electric thruster

The Thermal Emission Cathode with Grid (TECG) is a type of cathode that operates without a working medium based on electric field modulation, which can be effectively adapted with micro-electric thrusters to perform high-precision space science missions. This research first analyzes the thermal electron emission theory, and the key dimensional and electrical parameters of the TECG, such as the grid width, the grid-emitter distance, the grid orifice diameter, the grid voltage, and the anode voltage, are simulated using the electromagnetic simulation software OPERA to obtain the optimal combination. Subsequently, the TECG was designed and machined using the parameters above for experimental testing and verification against the simulation results. The relative error between the experimental and simulation results was less than 20%. Under specific working conditions, the TECG’s total emission capability can be increased by approximately 8 times, and the maximum emission current can reach up to 27.525 mA. Afterward, the research also discusses the electric field distribution in the entire space of the TECG, along with the electron distribution behavior caused by the electric field. Finally, after pointing out its shortcomings, the research provides guidance and prospects for future related work.

Near-infrared tunable Tamm plasmons high-performance hot electron photodetector based on Ag/Ge2Sb2Te5 low Schottky barrier

Hot electron photodetector is a typical hot electron optoelectronic device, which can realize the narrow band photoelectric detection with high tunability and sensitivity. The Tamm plasmons (TPs) based on the planar metal film/distributed Bragg reflector (DBR) has the advantages of simple structure, low manufacturing cost, and high absorption efficiency. A multilayer thin film device structure for high-performance near-infrared hot electron metal-semiconductor-metal photodetectors is proposed. The structure is based on Ag/Ge2Sb2Te5 (GST) Schottky barrier and TPs formed by SiO2/MoS2 DBR. The simulation results of hot electron emission theory show that DBR can effectively extend the absorption spectrum of Ag film and the response spectrum of the device, and enhance the absorption rate of Ag film and the response of the device. The responsivity which is up to 53 mA/W can be obtained by adjusting the structure parameters of the DBR, the thickness of the Ag film, and the GST layer. At the same time, we also propose a digital display system based on the arrangement of crystalline GST and amorphous GST. It provides a new way for the realization of high-performance near-infrared hot electronic devices and is conducive to expanding the application field of hot electronic photodetectors.

Wave packet theory for non-resonant x-ray emission and non-resonant Auger electron emission in molecules.

We present a time-dependent theory for non-resonant x-ray emission spectrum (XES) and normal Auger spectrum (NAS) calculation, based on a fully quantum description of nuclear dynamics using the vibrational wave packet concept. We compare two formulations of the time-dependent theory, either employing a two-time propagation scheme or using spectral integration over the electron energy continuum. We find that the latter formulation is more efficient for numerical simulations, providing a reasonable accuracy when the integration step is shorter than the lifetime broadening of the core-ionized state. We demonstrate our approach using the example of non-resonant x-ray emission from a water molecule, considering the lowest core-ionized K-1 and first core-ionized shake-up K-1V-1V1 intermediate states. These channels exemplify the developed theory on bound-bound, bound-continuum, continuum-bound, and continuum-continuum transitions. Our results suggest that the time-dependent approach is efficient for simulating XES involving dissociative states, whereas the time-independent approach, based on Franck-Condon factors, is more efficient for bound-bound transitions expressed as discrete frequency dependence in the energy domain. The methods and discussion have general applicability, including both NAS and more complex systems, such as liquid water.

Exploring the absolute yield curve of secondary electrons using machine learning methods.

Knowledge of absolute secondary electron yield (δ) is important for various applications of electron emission materials. Besides, it is also crucial to know the dependence of δ on primary electron energy Ep and material properties like atomic number Z. The available experimental database of δ reveals a large discrepancy among the measurement data, while the oversimplified semi-empirical theories of secondary electron emission can only present the general shape of the yield curve but not the absolute yield value. This limits not only the validation of a Monte Carlo model for theoretical simulations but also presents large uncertainties in the applications of different materials for various purposes. In applications, it is highly desirable to have the knowledge of the absolute yield of a material. Therefore, it is highly desirable to establish the relationship of the absolute yield with material and electron energy based on the available experimental data. Recently, machine learning (ML) methods have been increasingly used for the prediction of material properties mainly based on the atomistic calculations with the first-principles theory. We propose here the application of ML models to a material property study, starting with experimental observations and unfolding the relationship of δ with basic material properties and primary electron energy. Our ML models are able to predict δ(Ep)-curve covering a wide energy range of 10 eV-30 keV for unknown elements within the uncertainty range of the experimental data and can suggest more reliable data among the scattered experimental data.

Field emission: calculations supporting a new methodology of comparing theory with experiment.

This paper provides a demonstration-of-concept of a new methodology for comparing field electron emission (FE) theory and experiment. It uses the parameter κ in the mathematical equation I m = CV m κ exp[-B/V m] (where B and C are weakly varying or constants) that is taken to describe how measured current I m depends on measured voltage V m for electronically ideal FE systems (i.e. systems that (i) have constant configuration during voltage application and (ii) have I m(V m) given by the emission physics alone). Experimental parameter values (κ m) are used to compare two alternative FE theories, for which allowable (but different) κ ranges have been established. At present, contributions to the 'total theoretical κ' made by voltage dependence of notional emission area are not well known: simulations reported here provide data about four commonly investigated emitter shapes. The methodology is then applied to compare 1928/1929 Fowler-Nordheim (FN) FE theory and 1956 Murphy-Good (MG) FE theory. It is theoretically certain that the 1956 theory is 'better physics' than the 1928/1929 theory. As in previous attempts to reach known correct theoretical conclusions by experimentally based argument, the new methodology tends to favour MG FE theory, but is formally indecisive at this stage. Further progress needs better methods of establishing error limits and of measuring κ m.

Interpretation of field emission current–voltage data: Background theory and detailed simulation testing of a user-friendly webtool

In field electron emission (FE) studies, interpretation of measured current–voltage characteristics and extraction of emitter characterization parameters are usually carried out within the framework of “smooth planar metal-like emitter (SPME) methodology”, using a data-analysis plot. This methodology was originally introduced in the 1920s. Three main data-plot types now exist: Millikan–Lauritsen (ML) plots, Fowler–Nordheim (FN) plots, and Murphy–Good (MG) plots. ML plots were commonly used in early FE studies, but most modern analysis uses FN plots. MG plots are a recent introduction.Theoretically, it is now known that ML and FN plots are predicted to be slightly curved in SPME methodology, but a Murphy–Good plot will be very nearly straight. Hence (because 1956 Murphy–Good emission theory is “better physics” than 1928 Fowler–Nordheim emission theory as corrected in 1929), expectation is that parameter extraction using a MG plot will be more precise than extraction using either ML plots or FN plots.In technological FE studies, current–voltage characteristics are often converted into other forms. Thus, measured voltage may be converted to (apparent) macroscopic field, and/or current values may be converted to macroscopic current densities. Thus, four data-input forms can be found in the context of analysing FE current–voltage results.It is also the case that over-simplified models of measurement-system behaviour are very widely assumed, and the question of whether simple use of a data-analysis plot is a valid data-interpretation procedure for the particular system under investigation has often been neglected. Past published studies on field emitter materials development appear to contain a high incidence of spurious values for the emitter characterization parameter “characteristic field enhancement factor”. A procedure (the so-called “Orthodoxy Test”) was described in 2013 that allows a validity check on measurement-system behaviour, and found that around 40% of a small sample of results tested were spuriously high, but has had limited uptake so far.To assist with FE current–voltage data interpretation and validity checks, a simple user-friendly webtool has been under design by the lead author. The webtool needs as user input some system specification data and some “range-limits” data from any of the three forms of data-analysis plot, using any of the four data-input variations. The webtool then applies the Orthodoxy Test, and—if the Test is passed—calculates values of relevant emitter characterization parameters.The present study reports the following: (1) systematic tests of the webtool functionality, using simulated input data prepared using Extended Murphy–Good field electron emission theory; and (2) systematic comparisons of the three different data-plot types, again using simulated input data, in respect of the accuracy with which extracted characterization parameter values match the simulation input values. The paper is introduced by a thorough summary review of the theory on which modern SPME-based current–voltage data-analysis procedures are based. The need in principle to move on (in due course) to data-analysis procedures based on curved-emitter emission theory is noted.An important result is to confirm (by simulations) that, particularly in respect of the extraction of formal emission areas, the performance of the Murphy–Good plot is noticeably better than the performances of Fowler–Nordheim and Millikan–Lauritsen plots. This result is important for field electron emission science because it is now known that differences as between different theories of field electron emission often affect the formal emission area.

Research on the influence of cathode surface topography on spark discharge

To obtain the relation between spark discharges and the topography of electrode surfaces, some models, such as a micro-initial model of cone and spherical head cylinder, generated from the scanning of a scanning electron microscope are introduced. Based on the principles of energy conservation and thermal equilibrium, the second-order non-homogeneous differential equation is established. The relationships between the temperature of the cathode surface and the distance from the top of micro-protrusions, the cone angle, and the radius of the ball head are derived from a set of second-order non-homogeneous differential equations. When introduced electron emission theory, the main emission type at the initial stage of the discharge is electron field emission. As the discharge progresses, the Joule heat generated by the emission current will cause thermionic emission. During this progress, the emission current density gradually increases. When the temperature of the cathode surface reaches the melting point of the cathode metal, the current density will increase sharply. Observed from the discharge, the temperature of the cathode surface is inversely proportional to the cone angle and the radius of the ball head maintains a gradually decreasing slope. It is proportional to micro-protrusions maintaining a gradually increasing slope. When the cone angle is less than 12° and the radius of the ball head is less than 0.04 µm, the temperature of the cathode surface changes more dramatically. Through this study, a further understanding of factors that affect the density of cathode current emission can be obtained, which is of great significance to improve the capacity of cathode emission.

Three-dimensional calculation physical model for corona onset characteristics of AC grading rings

Corona discharge on the surface of power transmission and transformation fittings becomes increasingly serious with increasing voltage levels, especially for many grading rings in transformer substations. With the enhancement of people’s environmental awareness, the environmental protection administration requires noise and electromagnetic environment at transformer substations shall meet relevant standards. In order to suppress corona discharge on the surface of a grading ring, it is necessary to study its corona onset characteristics. Considering the basic physical process of the corona discharge, in this study, the electric field intensity is first calculated at any point in the space around the grading ring through ring charge simulation. Then, based on the theory of secondary electron emission, criteria for calculating the onset voltage of negative corona of the grading ring are derived, leading to an area factor of a photon absorption function suitable for the grading ring. In this way, a three-dimensional (3D) calculation physical model of the corona onset suitable for the grading ring is developed. This study calculates the corona onset voltage and field intensity of the grading ring under the typical working conditions by using the proposed 3D calculation physical model of the corona onset. The calculation results are compared with test results of the corona onset voltage and field intensity of grading rings in an outdoor 750 kV transformer substation in an ultrahigh voltage (UHV) alternating current (AC) test base. Furthermore, the simulation results of the area factor of the photon absorption function, electron collision coefficient, electron adsorption coefficient, and effective ionization coefficient in the 3D calculation physical model are obtained. In this way, the accuracy of the 3D calculation physical model of the corona onset proposed in this paper is verified. The research results can provide a theoretical basis for the corona prevention design of grading rings in extra high voltage/UHV AC power transmission and transformation projects.

Comment on "Design and circuit simulation of nanoscale vacuum channel transistors" by J. Xu, Y. Qin, Y. Shi, Y. Yang and X. Zhang, Nanoscale Adv., 2020, 2, 3582.

These comments aim to correct some apparent weaknesses in the theory of field electron emission given in a recent paper about nanoscale vacuum channel transistors, and to improve the presentation of this theory. In particular, it is argued that a “simplified” formula stated in the paper should not be used, because this formula is known to under-predict emission current densities by a large factor (typically around 300 for an emitting surface with local work function 4.5 eV). Thus, the “simplified” formula may significantly under-predict the practical performance of a nanoscale vacuum channel transistor.

A Quantum Theory of Electron Emission from a Metal–Dielectric Structure in High Electric Fields

A generalized formula for electron emission current as a function of temperature, field, and electron work function in a metal–dielectric system has been derived with regard to the quantum nature of image forces. For free electrons, the Fermi–Dirac distribution and a quantum image potential obtained in terms of the electron polaron theory have been used. The well-known Richardson–Schottky formula (for thermionic emission) and Fowler–Nordheim formula (for field emission) have been derived in the limit of the image force classical potential. It has been shown that at high temperatures and electric fields E ≥ 10 MV/cm, the polaron contribution grows with field and declines with rising temperature. The decrease in emission current is associated with the increase in effective work function of electrons, which is due to the electron polaron effect. Extrapolation formulas suitable for theoretical estimation of thermionic and cold emission currents have been obtained.

Об электронной эмиссии из фокальной области симметрично сходящейся поверхностной плазмонной волны на свободной поверхности металлической пленки

Based on the theory of reflection of a plane electromagnetic wave from a plane-layered structure, the excitation and focusing of a radially converging surface plasmon wave on the free surface of a gold film in the Kretschmann scheme are considered. The distribution of the electric field in the vicinity of the focus on the free surface of the film is quantitatively studied. Based on this distribution and the theory of thermofield electron emission from a metal, the time averaged current of electron emission is estimated depending on the amplitude of the normal component of the electric field of the wave at the center of the focal distribution. It was shown that the main part of the emission current comes from a region around the focus center with a diameter of the order of a tenth of the working wavelength in vacuum, and a negligible part of the emission current comes from surrounding the central maximum of the diffraction rings.

The electron emission characteristics of GaAs photocathode with vacuum-channel structure

The photocathode was an ideal electronic source with fast response, centralized distribution of electronic capabilities, and many other advantages. But for its low emission current density and short lifetime at ion bombardment environment, it will not be used in power devices and large scientific devices. Although the emission current of the photocathode can be increased with the aid of electric filed, it was not reach the milliamperelevel. In the field emission cathode, the strong electric field can effectively reduce the surface barrier of the emitter, so that the cathode produces electron emission. Based on the photoelectric conversion mechanism of photocathode and the electron emission theory of field emission cathode, a vacuum channel structure photocathode module is designed. The cathode modules with GaAs substrate were fabricated by the peritoneal and etching process. The parameters of vacuum channel were 3 μm × 700 μm, and its array structure was 1 × 100. The deep of the vacuum channels were 400 nm. It can be seen from the test result, the emission current of the photocathode was 26.12 mA with the laser beam power 5 W, and its emission current density was 5.33 A/cm<sup>2</sup>. During cathode operation, the laser beam and emission will cause the temperature of the photocathode material to rise, and this could icreasing the conductivity of the GaAs, the efficiency of electron supplement from negative electrode to electron emission area of the GaAs will also be improving. Its emission current could reach 89.69 mA at 400 ℃. Because there is no active atom on the photocathode surface, its lifetime was longer than the traditional photocathode that astivated by Cs/O. The life test of the photocathode modules was carried out, its emission current was 4.5 mA ± 0.3 mA within the 144 h, and its performance was not attenuate significantly. The vacuum channel was the main area of the photocatode electron emission, and the shape of electron beam can be easily obtained by adjusting the structure of the vacuum channel parameters. This advantage can improve the applicability of high current density photocathode in vacuum electronic devices and equipment.

The investigation of temperature dependent electrical characteristics of Au/Ni/β-(InGa)2O3 Schottky diode

We have grown β-(In0.04Ga0.96)2O3 thin film by pulsed laser deposition(PLD) on Sn doped β-Ga2O3(-201) substrates and fabricated the Au/Ni/β-(InGa)2O3 Schottky diodes on it. The electrical characteristics of the diodes were investigated within the temperature range from 300K to 400K. Based on the theory of thermal electron emission (TE), the extracted barrier height ϕb and ideality factor n are strongly temperature dependent. ϕb increasing from 0.83 eV to 0.93 eV while n decreasing from 2.82 to 1.83, respectively. By taking the Gaussian distribution of the Schottky barrier height into account, the average barrier height was calculated to be 1.18 eV with a standard deviation of 0.135 V and the effective Richardson constant A* was also determined to be 42.34 Acm−2K−2.

Thermionic emission laws for general electron dispersion relations and band structure data

In this article, a thermionic electron emission theory for general electron dispersion relations E(k) is presented, relating electron energy E to wave-vector magnitude k = |k|. This theory does not require the construction of a model Hamiltonian for the electrode's materials, like Dirac or Weyl Hamiltonians. Instead, use is made of the material's band structure data, e.g., the parabolic E(k) approximation for the Richardson–Dushman equation and linear E(k), as used for graphene and 3D Dirac semimetals. This new theory confirms previous findings on parabolic E(k), e.g., that the emission current is independent of effective electron mass in the material as long as it is larger than real electron mass m0. For effective mass lower than m0, the emission is reduced and tends to zero for vanishing effective mass. For materials with negative electron affinity, additional terms arise in the emission current equation. It turns out that the linear E(k) dispersion, e.g., for Dirac semimetals, does not have the potential to surpass the Richardson emission in materials with the same work function. In addition, a more rigorous electron emission theory is established by utilizing real anisotropic band structure data En(k) for electrode materials. For collimated electron emission normal to the surface, the transverse electron velocities tend to zero, i.e., the transverse derivatives of En(k) have to be comparatively small. If stable electrode materials of this kind can be realized, a considerable increase of electron emission by a factor 100 or more can be achieved, compared to the Richardson–Dushman theory, especially for small lattice constants perpendicular to the emission direction.

Theory of electron transport and emission from a semiconductor nanotip

An effective mass based model accounting for the conduction band quantization in a high aspect ratio semiconductor nanotip is developed to describe injected electron transport and subsequent electron emission from the nanotip. A transfer matrix formalism is used to treat electron scattering induced by the variation in the tip diameter and in the electron emission. Numerical analysis of the scattering and emission probabilities is performed for the diamond parametrized nanotip model. Our scattering and emission models are further combined with a Monte Carlo (MC) approach to simulate electron transport through the nanotip. The MC simulations, also accounting for the electron-phonon scattering and externally applied electric field, are performed for a minimal nanotip model and an equivalent width diamond slab. An effect of the level quantization, electron scattering due to the nanotip diameter variation, and electron-phonon scattering on the nanotip emission properties are identified and compared with the case of a bulk slab.

Electron emission by long and short wavelength lasers: Essentials for the design of plasmonic photocathodes

The theory of electron emission by metallic photocathodes under the exposure of long wavelength lasers will be studied. Photon energy in long wavelength lasers is less than the work function of the photocathode's material and can only emit electrons via tunneling through the potential barrier. The optical resonance effects (e.g., plasmonic resonances) will be studied as an improvement to the performance of photocathodes. This paper is intended to provide self-sufficient materials to design optical resonant surfaces (e.g., metasurfaces) for electron emission applications.

Fractional Fowler–Nordheim Law for Field Emission From Rough Surface With Nonparabolic Energy Dispersion

The theories of field electron emission from perfectly planar and smooth canonical surfaces are well understood, but they are not suitable for describing emission from rough, irregular surfaces arising in modern nanoscale electron sources. Moreover, the existing models rely on Sommerfeld's free-electron theory for the description of electronic distribution which is not a valid assumption for modern materials with nonparabolic energy dispersion. In this paper, we derive analytically a generalized Fowler-Nordheim (FN) type equation that takes into account the reduced space-dimensionality seen by the quantum mechanically tunneling electron at a rough, irregular emission surface. We also consider the effects of non-parabolic energy dispersion on field-emission from narrow-gap semiconductors and few-layer graphene using Kane's band model. The traditional FN equation is shown to be a limiting case of our model in the limit of a perfectly flat surface of a material with parabolic dispersion. The fractional-dimension parameter used in this model can be experimentally calculated from appropriate current-voltage data plot. By applying this model to experimental data, the standard field-emission parameters can be deduced with better accuracy than by using the conventional FN equation.

Evidence of universal inverse-third power law for the shielding-induced fractional decrease in apex field enhancement factor at large spacings: a response via accurate Laplace-type calculations

Numerical simulations are important when assessing the many characteristics of field emission related phenomena. In small simulation domains, the electrostatic effect from the boundaries is known to influence the calculated apex field enhancement factor (FEF) of the emitter, but no established dependence has been reported at present. In this work, we report the dependence of the lateral size, L, and the height, H, of the simulation domain on the apex-FEF of a single conducting ellipsoidal emitter. Firstly, we analyze the error, ε, in the calculation of the apex-FEF as a function of H and L. Importantly, our results show that the effects of H and L on ε are scale invariant, allowing one to predict ε for ratios L/h and H/h, where h is the height of the emitter. Next, we analyze the fractional change of the apex-FEF, δ, from a single emitter, , and a pair, . We show that small relative errors in (i.e. ), due to the finite domain size, are sufficient to alter the functional dependence , where c is the distance from the emitters in the pair. We show that obeys a recently proposed power law decay (Forbes 2016 J. Appl. Phys. 120 054302), at sufficiently large distances in the limit of infinite domain size (, say), which is not observed when using a long time established exponential decay (Bonard et al 2001 Adv. Mater. 13 184) or a more sophisticated fitting formula proposed recently by Harris et al (2015 AIP Adv. 5 087182). We show that the inverse-third power law functional dependence is respected for various systems like infinity arrays and small clusters of emitters with different shapes. Thus, , with m = 3, is suggested to be a universal signature of the charge-blunting effect in small clusters or arrays, at sufficient large distances between emitters with any shape. These results improve the physical understanding of the field electron emission theory to accurately characterize emitters in small clusters or arrays.