Secondary Emission Model Research Articles

Secondary Emission From Glass Grains: Comparison of the Model and Experiment

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The surface potential of dust grains immersed in surrounding plasma results from the balance of many charging processes such as photoemission, electron/ion attachments, and secondary and field emissions. Since hot electrons are often present in space as well as laboratory plasmas, the understanding of the secondary electron (SE) emission process for small dust grains is of great interest because their size effects modify well-known characteristics of large samples. This paper compares the measured surface potential of <formula formulatype="inline"><tex>$ \hbox{SiO}_{2}$</tex></formula> spherical dust grains with the results of the Monte Carlo model of secondary emission developed for metallic samples. It was found that 1) the model can be used for description of the secondary emission process from cosmic dust, 2) the backscattering of primary beam electrons is the most important factor for the charging of small grains, and 3) the actual value of the surface grain potential is given by the energy spectrum of SEs. </para>

The influence of ion-enhanced field emission on the high-frequency breakdown in microgaps

This paper contains the results of the detailed simulation study of the role of ion-enhanced field emission on the breakdown voltage in argon, xenon and krypton at high frequencies. Calculations were performed by using a one-dimensional particle-in-cell/Monte Carlo collisions (PIC/MCC) code with the secondary emission model adjusted to include field emission effects in microgaps. The obtained simulation results clearly show that electrical breakdown across micron-size gaps may occur at voltages far below the minimum predicted by the conventional Paschen curve. The observed breakdown voltage reduction may be attributed to the onset of ion-enhanced field emission.

Model of secondary emission and its application on the charging of gold dust grains

Dust grains of various shapes and materials can be found anywhere in the space where the temperature decreases under a melting point. Many plasma processes are driven by the grain charge but, on the other hand, dust grain charging can be influenced by several different processes, too. Among others, secondary emission can play a dominant role wherever the plasma is hot. In the present paper, a further development of our previous simple numerical secondary emission model, now using techniques for a beam interaction modelling applied in electron microscopies, is sketched and its application onto charging of spherical dust grains by a narrow electron beam is discussed. The model fits experimental data rather well and, thus, our conclusion suggests that the model is a very useful tool for considerations on the dust charging under different conditions in the space.

Start‐Up Transient in a Hall Thruster

AbstractFor the first time a two dimensional axisymmetric fully kinetic Particle‐in‐Cell/Monte Carlo Collision (PICMCC) model is used to describe the start‐up transient of the acceleration channel in a Hall thruster. The Poisson equation and a secondary electron emission model are invoked for the description of the plasma dynamic phase. Numerical results have been used to see the formation and evolution of the discharge inside the channel. (© 2006 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Modelling of low-pressure gas breakdown in uniform DC electric field by PIC technique with realistic secondary electron emission

This paper compares the basic phenomenological model based on the Townsend’s theory and the detailed simulation of the gas breakdown in argon in uniform DC electric field. Calculations were carried out by using a one-dimensional particle-in-cell/Monte Carlo (PIC/MCC) code with three velocity components with a new secondary emission model. The simulation results clearly show how different models of the secondary electron emission affect the breakdown voltage. The fact that results of simulation are in a good agreement with the available experimental data merely means that phenomenological secondary electron yields were developed to fit the experiment. However, oversimplified models cannot predict all features of Townsend discharges and cannot be reconciled with binary collision data. One such example is the need to predict the DC volt-ampere characteristics in order to reveal the predominant physical processes by studying the j/p 2 scaling.

On the Computation of Secondary Electron Emission Models

Secondary electron emission is a critical contributor to the charge particle current balance in spacecraft charging. Spacecraft charging simulation codes use a parameterized expression for the secondary electron (SE) yield delta(E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> ) as a function of the incident electron energy E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> . Simple three-step physics models of the electron penetration, transport, and emission from a solid are typically expressed in terms of the incident electron penetration depth at normal incidence R(E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> ) and the mean free path of the SE lambda. In this paper, the authors recall classical models for the range R(E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> ): a power law expression of the form b <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n1</sup> and a more general empirical double power law R(E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> )=b <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n1</sup> +b <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n2</sup> . In most models, the yield is the result of an integral along the path length of incident electrons. An improved fourth-order numerical method to compute this integral is presented and compared to the standard second-order method. A critical step in accurately characterizing a particular spacecraft material is the determination of the model parameters in terms of the measured electron yield data. The fitting procedures and range models are applied to several measured data sets to compare their effectiveness in modeling the function delta(E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> ) over the full range of energy of incident particles

The effect of magnetic field on the electrical breakdown characteristics

This paper presents a simple phenomenological model and detailed simulation studies of the breakdown of a gas under the simultaneous action of electric and magnetic fields. In deriving expressions for the breakdown voltage variations of both the ionization coefficient and the secondary electron yield in a magnetic field are taken into account. Calculations were carried out by using the XOOPIC code with the old and the improved secondary emission models adjusted to involve the influence of the magnetic field on the secondary electron production. It was shown that the incorporation of the variation of the secondary electron yield with magnetic field leads to the better agreement with existing experimental results.

Modelling of a low-pressure argon breakdown in combined fields

This paper reports the results of the detailed theoretical and simulation study of the dependence of the breakdown voltage on the product of the gas pressure and the electrode separation (pd) under the simultaneous application of radio-frequency (rf) and dc fields. Calculations were performed by using a one-dimensional particle-in-cell/Monte Carlo collision code with three velocity components with a new secondary emission model. Our simulation results show that in combined discharges during breakdown an ambiguity region of the left-hand branch of the breakdown curve appears not only by increasing the rf voltage but also by decreasing it. In other words, with lowering of the pressure, the rf voltage first decreases and passes through an inflection point and a minimum on the breakdown curve and then it grows and approaches the turning point on the breakdown curve. In addition, simulation results are also compared with the theoretical predictions based on the phenomenological method. Analytical expressions for the rf breakdown voltage with a superimposed weak dc electric field corresponding to the minimum, to the inflection point and to the turning point on the breakdown curve have been derived.

Modeling of breakdown behavior in radio-frequency argon discharges with improved secondary emission model

This work represents the investigation of the dependence of the breakdown voltage on the gas pressure and on the frequency in radio-frequency argon discharges. Calculations were performed by using a one-dimensional particle-in-cell/Monte Carlo code with three velocity components with a new secondary emission model. The obtained results show that the multivalued nature of the left-hand branch of the breakdown curve can be achieved only by taking into account energy dependence of the yield per ion. The multivalued nature of the left-hand branch of the breakdown curve is attributed to the influence of the secondary emission characteristics of the electrodes on the breakdown voltage. Simulation results show a good agreement with the available experimental data. Disagreements between simulation results and theoretical predictions based on the phenomenological method indicate that a more accurate determination of molecular constants is needed. As a result of the satisfactory agreement between simulation and experimental data for dependence of the breakdown voltage on the frequency, a frequency scaling law is proposed.

Recent Developments to the MICHELLE 2-D/3-D Electron Gun and Collector Modeling Code

Recent developments to the MICHELLE electron gun and collector design tool are reported in this paper. The MICHELLE code is a new finite-element (FE) two-dimensional and three-dimensional electrostatic particle-in-cell code that has been designed to address the recent beam optics modeling and simulation requirements for vacuum electron devices, ion sources, and charged-particle transport. Problem classes specifically targeted include depressed collectors, gridded-guns, multibeam guns, sheet-beam guns, and ion thrusters. The focus of the development program is to combine modern FE techniques with improved physics models. The code employs a conformal mesh, including both structured and unstructured mesh architectures for meshing flexibility, along with a new method for accurate, efficient particle tracking. New particle emission models for thermionic beam representation are included that support primary emission, with an advanced secondary emission model. This paper reports on three significant advances to MICHELLE over the past year; hybrid structured/unstructured mesh support, a time-domain electrostatic algorithm, and an ion plasma model with charge exchange.

Secondary electron images obtained with a standard photoelectron emission microscopeset-up

The first results of secondary electron images excited by 3–4.3 keV electrons are presented. Theimages are obtained with a standard FOCUS-PEEM set-up equipped with an imaging energyfilter (IEF). The electron gun was mounted on a standard PEEM entrance flange at an angle of25° with respect to the sample surface. A low extraction voltage of 500 V was used to minimizethe deflection of the electron beam by the PEEM extraction electrode. The secondaryelectron images are compared to photoelectron images excited by a standard 4.9 eV UVlamp. In the case of a Cu pattern on a Si substrate it is found that the lateral resolutionwithout the IEF is about the same for electron and photon excitation but thatthe relative electron emission intensities are very different. The use of the IEFreduces the lateral resolution. Images for secondary electron energies betweeneV1 andeV2 were obtained bysetting the IEF to −V1 and −V2≈−(V1+5V) potentials and taking the difference of both images. Images up to 100 eV electron energieswere recorded. The material contrast obtained in these difference images is discussed interms of a secondary electron and photoelectron emission model and secondary electronenergy spectra measured with a LEED-Auger spectrometer.

Secondary emission from dust grains with a surface layer: comparison between experimental and model results

The motion, coalescence, and other processes in dust clouds are determined by the dust charge. Since dust grains in the space are bombarded by energetic electrons, the secondary emission is an important process contributing to their charge. It is generally expected that the secondary emission yield is related to surface properties of the bombarded body. However, it is well known that secondary emission from small bodies is determined not only by their composition but an effect of dimension can be very important when the penetration depth of primary electrons is comparable with the grain size. It implies that the secondary emission yield can be influenced by the substrate material if the surface layer is thin enough. We have developed a simple Monte Carlo model of secondary emission that was successfully applied on the dust stimulants from glass and melamine formaldehyde (MF) resin and matched very well experimental results. In order to check the influence of surface layers, we have modified the model for spheres covered by a layer with different material properties. The results of model simulations are compared with measurements on MF spheres covered by a nickel layer.

A Model of Secondary Emission From Dust Grains and Its Comparison With an Experiment

Secondary emission from metal surfaces is well described by the theory of Sternglass. His theory and resulting "universal" curve can be applied for planar uncharged surfaces in an energy range from tens of electronvolts to several kiloelectronvolts. However, space dust is composed of silicates, ice, and graphite, i.e., nonconducting materials. Their surfaces are highly curved, and they are usually charged to nonnegligible potentials. Since previous attempts to describe the size effect on emission properties of the dust succeeded only partly, we have used the original Sternglass approach and developed a computer model of secondary emission from small bodies. The model follows individual trajectories of primary electrons inside the grain and, based on simple assumptions consistent with the Sternglass theory, calculates a probability of escaping of the excited electrons. The model provides measurable quantities (the yield of secondary emission, the charge accumulated in the grain, or the surface potential) but it can illustrate processes which are not accessible by direct measurements. Free parameters of the model depend on the grain material and can be determined by a fit of model results to the experimental data. The paper presents model assumptions and results of calculations for spheres of different diameters and two insulating materials. The theoretical results are compared with the laboratory experiment when the grains with approximately 1, 2, 5, and 10 /spl mu/m of diameter were charged by an electron beam in a range 300 eV-10 keV. The comparison shows a good agreement of the experiment and theory. Moreover, the reversal of the sign of the grain charge in a certain range of beam energies and grain diameters predicted by the model was confirmed by the experiment.

The michelle three-dimensional electron gun and collector modeling tool: theory and design

The development of a new three-dimensional electron gun and collector design tool is reported. This new simulation code has been designed to address the shortcomings of current beam optics simulation and modeling tools used for vacuum electron devices, ion sources, and charged-particle transport. The design tool specifically targets problem classes including gridded-guns, sheet-beam guns, multibeam devices, and anisotropic collectors, with a focus on improved physics models. The code includes both structured and unstructured grid systems for meshing flexibility. A new method for accurate particle tracking through the mesh is discussed. In the area of particle emission, new models for thermionic beam representation are included that support primary emission and secondary emission. Also discussed are new methods for temperature-limited and space-charge-limited (Child's law) emission, including the Longo-Vaughn formulation. A new secondary emission model is presented that captures true secondaries and the full range rediffused electrons. A description of the MICHELLE code is presented.

Electron transmission studies of diamond films

Diamond is an attractive cold emitter candidate because of specific negative-electron-affinity (NEA) surfaces and good electron transport properties. In this study, transmission electron spectroscopy is used to examine the low-energy electron transport and emission properties of thin CVD diamond films. After injecting electrons into diamond films using an external electron gun, the transmission of low-energy secondary electrons is examined. In particular, the intensity and energy distribution of the transmitted electrons are measured as a function of the film properties (thickness, doping concentration) and incident beam properties (energy, intensity). Electron transmission through a heavily-doped, 5μm thick film exhibits a larger energy spread and lower intensity than electron transmission through a medium-doped, 2μm thick film. However, the transmission yields are relatively low for both films compared to the reflected yield measurements. Furthermore, the incident beam parameters influence the transmitted electron distribution in ways that cannot be explained by our secondary emission model. On the other hand, the results of the study concerning the transmission of high-energy electrons confirm the theoretical predictions of electron penetration depths in diamond. These initial electron transmission measurements from thin diamond films indicate that the transport process is quite complex, and the study reveals several issues that need to be examined further before the cold emission capabilities of diamond can be assessed.

Multipactor electron discharge physics using an improved secondary emission model

This study details particle-in-cell simulations of the multipactor effect and discharges created using this effect. A detailed secondary emission model which accounts for the energy and impact angle dependence of yield is developed to simulate accurately the phenomenon. It is shown that a steady state multipactor can be built up from a very low density initial electron distribution and an oscillatory steady state can be achieved. Steady state is reached when the cavity detuning and space charge of the built-up beam balance the phase focusing. The results for a more accurate secondary electron distribution are compared with simpler analytic models and extended. It is shown that, while the energy spread of secondary electrons differs from the monoenergetic analytical model, the weighted average energy is the same. Resistive loading of the circuit due to multipacting electrons is presented. The behavior of the system with Q values of between 20 and 200 is discussed.

Reduction of crossed-field diode transmitted current due to anode secondary emission

The limiting current theory for planar crossed-field diodes has long been studied extensively for various emission energies and temperatures. However, experimental measurements of transmitted current have shown significant departure from theory. This paper attempts to explain the reduction in transmitted current from that expected in theory in terms of secondary electron emission created by electrons hitting the anode. It is proposed that the presence of the secondary electrons increases the charge density in the gap, thereby reducing the amount of current transmitted. A detailed secondary emission model is implemented in a particle-in-cell code to study current reduction. The effect of secondary electrons on charge density, and on the resultant electric field and potential is also presented.

Secondary electron emission from beryllium irradiated by plasmas in a magnetic field

A Monte-Carlo simulation model of secondary electron emission from beryllium is combined with the kinetic equation analysis for the Lorentz force perpendicular to an oblique magnetic field and the acceleration due to the sheath electric field normal to the surface. The emphasis is put on the energy distribution of secondary electrons entering into an edge plasma after their transport in the sheath, as well as the effective secondary electron yield. Some of the secondary electrons emitted from the surface return to the surface within their first gyration, resulting in low effective secondary electron yield. The higher the energies of the secondary electrons or the lower the temperature of the edge plasma electrons, the more the secondary electrons return to the surface. Lowering of the yield is accompanied by a low-energy shift of the energy distribution.

Simulation of Kinetic Electron Emission from Beryllium by keV Ion Impacts

A Monte Carlo simulation model of ion-induced kinetic secondary electron emission from beryllium, a candidate material for plasma-facing components in thermonuclear fusion devices, is developed. In the model, the conduction electron excitation by a projectile ion and the cascade multiplication process of the excited electrons are involved in production of secondary electrons in the solid. Due to increase in the excitation probability, the secondary electron yield increases with increasing impact energy and initial charge state of the projectile, and decreasing mass of the projectile. Nevertheless, the majority of secondary electrons are produced through the cascade process, so that the peak of the energy distribution of secondary electrons depends little on the impact energy and the species of the projectile. Due to increase in the energy transferred from the projectile to the electrons, however, the distribution progressively broadens towards the high-energy side as the impact energy is increased or as the mass of the projectile is reduced.

Secondary electron emission from oxides: Part I. Model concepts and methodology

Abstract The model of secondary electron emission from oxides with various electron structure is developed. The theory is shown to be a basis for new methods in studies of semiconductors, ferroelectrics, HT superconductors (determination of electron structure parameters, detection of phase transitions, analysis of phase composition, oxygen deficiency measurements, etc.).