碳纳米管场致发射中的空间电荷效应

采用微波等离子体化学气相沉积(MWPCVD)方法成功制备以碳纳米管束为单元的场致发射阵列,获得很好的场致发射电流发射特性,在电流密度较大时,发现I-V特性偏离由Fowler-Nordheim公式计算出的结果。采用Electron Beam Simulation(EBS)软件进行模拟分析发现:在电流密度较低时,I-V特性能很好与F-N公式吻合。但碳纳米管尖端电流密度大于106A/cm2时,碳纳米管尖端处的有效电场强度受空间电荷的影响比较明显,进而对碳纳米管的场致发射特性显现出不可忽略的影响,此时碳纳米管的发射电流密度开始受到空间电荷的限制。     

Use of the BFCPIC and BFCRAY codes to describe space charge limited emission in electron guns for gyrotrons

Numerical modelling of an electron gun in the space charge limited regime requires determining the current density distribution as well as the electric fields and electron trajectories. This is a rather complicated self-consistent problem, since the space charge influences the electric field, which in turn influences the electron trajectories. Previous simulations of magnetron electron guns using the BFCPIC and BFCRAY codes used a simple emission model (constant current density) that is approximately valid for thermionic emission. The code has been modified to include space charge limited emission. Several different ways of doing this are considered. One of the models considered uses Gauss’s law to force the electric field on the emitter to vanish; it was used in the original version of BFCPIC for the simulation of ion diodes. A second is based on the use of Child’s law (locally), which may be more appropriate for extension to fully electromagnetic particle-in-cell (PIC) codes. Calculations were performed with both models, and the results compared with each other and with experiments performed at FZK.     

On the mechanism of liquid metal electron and ion sources

The mechanisms of electron and ion generation from Taylor cones of liquid metals are discussed. In the case of electron emission the vacuum arcing mechanism of Swanson and Schwind, which accounts for the observed high current repetitive pulsing is briefly reviewed. For ion emission mechanisms from onset to the high current regime are proposed. It is concluded that at onset ions are generated exclusively by field desorption. A theory to account for the observed emitter heating is advanced, and it is concluded that high currents result from field ionization of thermally evaporated atoms. It is shown that space charge becomes important even at very low ion currents and'is instrumental in providing stabilization in all regimes of ion emission.     

空间电荷效应对热场致发射中诺廷汉效应的影响

热场致发射阴极所产生的强流电子束具有很强的空间电荷效应,为研究该效应对热场致发射过程中诺廷汉（Nottingham）效应的影响机理,在理论分析的基础上,用数值方法研究了不同逸出功和多个外加电场条件下考虑空间电荷效应对诺廷汉效应结果的影响,并与不考虑空间电荷效应时的情形进行了对比. 结果表明：空间电荷效应的强弱会显著影响到阴极表面的稳态电场,进而对诺廷汉效应产生不可忽略的影响;当逸出功在3.0–4.52 eV、外加电场在3×10⁹–9×10⁹ V/m范围内时,考虑空间电荷效应的影响后,热场致发射电子所带走的平均能量较不考虑空间电荷效应时增加0–2.5 eV,且温度越高或外加电场越大时,该增加值越大;考虑空间电荷效应对诺廷汉效应的影响后,热场致发射电子从阴极带走的平均能量随外加电场的增加呈非线性下降规律;当阴极表面温度较高时,诺廷汉效应中的冷却效应随二极管间隙距离的变大而增强. 关键词： 热场致发射 诺廷汉效应 空间电荷效应 阴极表面电场     

轴对称真空二极管空间电荷限制流

基于ArcPIC代码采用PIC-MCC方法,模拟研究了轴对称真空二极管放电时电子密度和阴极表面场强分布情况,同时给出了二维空间电荷限制流的一阶和二阶拟合公式。研究发现,真空二极管放电时阴极表面电场会随阴极注入电流密度的增加而增加,而后出现振荡并趋于一个稳定状态;二维空间电荷限制流密度值随阴极发射半径的增大而减小,且阴极发射半径越大越接近一维空间电荷限制流值。     

Evaluations of carbon nanotube field emitters for electron microscopy

Brightness of carbon nanotube (CNT) emitters was already reported elsewhere. However, brightness of electron emitter is affected by a virtual source size of the emitter, which strongly depends on electron optical configuration around the emitter. In this work, I-V characteristics and brightness of a CNT emitter are measured under a practical field emission electron gun (e-gun) configuration to investigate availability of CNT for electron microscopy. As a result, it is obtained that an emission area of MWNT is smaller than its tip surface area, and the emission area corresponds to a five-membered-ring with 2nd nearest six-membered-rings on the MWNT cap surface. Reduced brightness of MWNT is measured as at least 2.6×10⁹ A/m² sr V. It is concluded that even a thick MWNT has enough brightness under a practical e-gun electrode configuration and suitable for electron microscopy.     

Space charge effects on radiative ultrashort laser-plasma interactions: Relativistic fluid model

Ultrashort laser-gas interaction is a promising candidate for the intense broad band far-infrared radiation in which the gas ionization and the resultant plasma formation occur consequently. The electron current produced in the process is the most important influential parameter which affects the far-infrared radiation generation. Although the interacting forces of the process are the space charge electric and the laser electromagnetic forces, the effect of the former one, has not been investigated on the gas-plasma THz generation. It is noteworthy that the space charge electric force, due to its effect on the electron distribution, has potential influence on the produced electron current and its consequent emission. Here, a 2D relativistic fluid model is presented in which the ions and the resultant space charge field are incorporated. The model investigates the air ionization, electron-ion plasma formation, and the system's evolution, spatiotemporally. Moreover, as the model is based on the transient electron current, as the source for the electromagnetic pulse radiation, it gives the temporal profile of the radiated field in which the space charge effects are observable. Our results show that the space charge field affects the electron velocity and its resultant current. Therefore, the temporal profiles and amplitudes of the radiated field components are affected and their resemblance to the experimental data is enhanced. The results indicate that the amplitude of the radiated field increases in the presence of the space charge field. In addition, it is shown that the space charge effects become more pronounced with the laser intensity.     

空间电荷效应对阴极微凸起热不稳定性的影响

 由于金属微凸起爆炸电子发射的预发射电流密度一般都超过108 A/cm2,因此必须考虑其空间电荷效应的影响。基于金属微凸起爆炸电子发射起始过程模型,通过理论分析和数值模拟,给出了考虑预发射电流空间电荷效应的微凸起爆炸发射延迟时间随二极管平均电场的变化关系。与不考虑预发射电流空间电荷效应的结果进行对比表明,预发射电流的空间电荷效应可以显著增加金属微凸起的爆炸发射延迟时间。     

Surface reconstruction of a field electron emitter

The surface and emission images of a metal field’s electron cathode in the form of a tip are simulated. The surface structure is calculated in the thin-shell and broken-bond (local-environment) models for the perfect crystal lattice. The cathode shape and macroscopic electric field are represented by the sphere-on-cone model. The amplification of a local electric field is the adjustable parameter of the model. The method of determination of the emitter tip’s crystal faces based on the analysis of the surface atoms’ environment geometry is proposed. It is shown that it is enough to restrict the consideration of geometric environment by the fifth order of the nearest neighbors for the emitter radius of 100–1000 lattice parameters (31.6–316 nm for the tungsten). The crystallographic model of work function anisotropy in the broken-bond approach is used: the local work function’s value is set in accordance with Miller indices of the face containing this area. The model adequacy is corroborated by the comparison of current-voltage characteristics and emission images with the data of the natural experiment.     

Computer simulation of liquid metal ion source optics

A numerical calculation of the electric field and current density distribution for a liquid metal ion (LMI) source has been carried out. If a field evaporation mechanism for ion formation is assumed an elongated Taylor cone shape emitter is required to account for the observed total currents. Trajectory calculations including the effect of uniform space charge have been carried out as a function of total current and particle mass. The predicted emission characteristics compare favorably with experimental results for Ga, however the homogeneous space charge model is unable to account for all of the experimentally observed increase in beam divergence with increasing mass and current.     

Effect of dipole structures on field emission of wide-gap semiconductor emitters

It is shown that dipole structures placed in a thin (less than 1 nm) near-surface layer of a high-resistivity field emitter produce small domains on the emitting surface in which the electric field may exceed 10⁸ V/cm. In these domains, the emitter surface potential is positive, providing effective electron transport from inside the emitter to the emission boundary. Optimal dipole orientations ensuring maximal electric fields at the surface are found. When the surface density of dipoles localized in the near-surface layer is on the order of 10⁶ cm⁻², one can expect an emitter-averaged emission current density of higher than 1 A/cm². The dipole structures in the near-surface layer may persist owing to incorporated impurity molecules having a dipole moment or result from a random combination of positively charged ionized impurities and electrons captured by deep traps. Trap charging/discharging asymmetry accounts for the hysteresis of the emission I–V characteristics.     

The effect of the crystal structure of the field emitter on field ion energy distributions

The field ionization probability of an atom as a function of distance from the field emitter is discussed in terms of the atomic arrangement and the electron scattering properties of the ion cores of the emitter in the immediate neighborhood of the atom to be ionized, and the electron transmission properties of the potential barrier between the emitter and that atom. This approach to field ionization calculations is somewhat similar to field ionization calculations based on low energy electron diffraction (LEED) procedure in that it takes into account electron scattering from the first few atomic layers of the emitter. It differs from LEED type calculations, because it considers the highly localized nature of the ionization near a surface atom. This localization makes the ionization probability relatively insensitive to the two-dimensional periodicity of the emitter surface. A one-dimensional calculation, in which only the potential barrier and three ion core scatterers in line with the field are considered, shows secondary structure in the predicted field ion energy distributions near the critical energy deficit, as well as the well known, primary field induced resonance peaks. The surface orientation dependence of these distributions arises naturally from this model because the secondary structure depends strongly upon the crystal parameter along a line parallel to the field. This one-dimensional calculation can be no more than an approximation to a complete calculation. It is interesting, however, that such a simple physical model, in which scattering from the image potential and only two or three ion cores is considered, rather than scattering from a complete crystal, can give prodicted field ion onergy distributions which are similar to those experimentally observed.     

爆炸电子发射初期阴极表面电场的研究

为了研究二极管爆炸电子发射初始阶段阴极表面复杂的物理现象及规律, 建立了由场致电子发射阴极构成的一维平板真空二极管物理模型,通过自行编程数值求解泊松方程, 考虑了发射出的电子对阴极表面电场的非线性影响,自洽模拟得到了阴极表面电场随时间的变化情况. 模拟结果表明,爆炸电子发射初期,阴极表面电场随时间的增加而呈现出不断振荡的规律, 且振荡幅度越来越小,最终到达一个稳态的值,二极管两极板之间的外加电场越大, 阴极表面稳态电场的绝对值越大;电场增强系数越大,阴极表面稳态电场的绝对值越大. 在整个时间演变过程中,阴极表面的实际电场强度决定着阴极发射的电流密度大小, 反过来阴极发射的电流密度又会影响到阴极表面的电场.     

TWO-DIMENSIONAL NUMERICAL SIMULATION OF LOW FREQUENCY OSCILLATIONS OF SPACE CHARGE AND POTENTIAL IN THE GYROTRON ADIABATIC TRAP

The development of oscillations of the space charge and potential in the adiabatic trap of a gyrotron between the cathode and the cavity is studied numerically. The PIC method is applied, with the real two-dimensional distributions of the electric and magnetic fields taken into account. Secondary emission is included into the numerical model, as well as such factors as the electron beam space charge, thermal velocities of electrons, and emitter roughness. The value of the trapped space charge as a function of time is calculated. Time dependences of the potential in various cross-sections of the formation system are traced. The amplitudes of its variable component have been found and then the corresponding frequency spectra have been calculated. The process of cathode bombardment is investigated. The energy distribution and time dependence of the current in the electron beam coming to the operating space are found. Some ways to reduce the oscillations of the potential and the space charge are discussed.     

块状TiO2气凝胶的溶胶-凝胶过程及结构

对块状TiO2气凝胶的溶胶-凝胶过程及结构进行了实验研究,结果发现:增加催化剂的量,凝胶化时间缩短,湿凝胶的透明度降低,强度提高;增加前驱体的量,凝胶化时间缩短,湿凝胶的透明度变化不大,强度提高;增加水量,凝胶化时间先缩短后增加,湿凝胶透明度先减小后增加,强度先增加后减小。利用扫描电镜对超临界干燥法制备的不同催化剂量和密度的块状TiO2气凝胶的结构进行了表征,并对结构与溶胶-凝胶过程之间的联系进行了分析。结果表明:增加催化剂量,由于缩聚反应进行的程度提高,气凝胶粒子粒径较小且总的孔径较大。减小前驱体量,气凝胶粒子粒径增大且结构逐渐疏松。     

Mathematical modeling of a diode system based on a field emitter

A mathematical model of a diode system based on a field emitter is considered. The field emitter is modeled in the following way: the tip is a conducting sphere; the “body” is a solid dielectric with a spindle surface of revolution. The anode is a part of the spherical surface and the substrate of the emitter is a spherical surface or a plane. The influence of a space charge is not taken into account. To find the electrostatic potential distribution, the methods of separation of variables and paired equations are used. The problem of finding unknown coefficients in the eigenfunction expansion of the potential is reduced to the solution of the system of equations, which includes linear algebraic equations and the Fredholm equation of the second kind. Thus, the computational problem of the distribution of electrostatic potential in the entire domain of the investigated system is solved.     

Relaxation of excited states of an emitter near a metal nanoparticle: An analysis based on superradiance theory

Methods of superradiance theory are employed for determining the relaxation rate of the excited state of a resonant emitter (atom, molecule, or quantum dot) near a metal nanoparticle under resonant excitation of plasmons in it, viz., modes of spatially uniform (dipole) harmonic oscillations of the electron density. Detuning from resonance and nonradiative loss suppressing radiation from the emitter near the nanoparticle surface are taken into account. The results are used to estimate the threshold conditions for generating a plasmon (“dipole”) nanolaser. It is shown that the threshold conditions of induced (laser) generation of plasmons for the emitter at a distance of 5–40 nm from an ellipsoidal nanoparticle are satisfied for relatively low emitter pumping rates (on the order of the rate of spontaneous emission of the emitter into the free space).     

Optical performance of carbon-nanotube electron sources

The figure of merit for the electron optical performance of carbon-nanotube (CNT) electron sources is presented. This figure is given by the relation between the reduced brightness and the energy spread in the region of stable emission. It is shown experimentally that a CNT electron source exhibits a highly stable emission process that follows the Fowler-Nordheim theory for field emission, fixing the relationship among the energy spread, the current, and the radius. The performance of the CNT emitter under realistic operating conditions is compared with state-of-the-art electron point sources. It is demonstrated that the reduced brightness is a function of the tunneling parameter, a measure of the energy spread at low temperatures, only, independent of the geometry of the emitter.     

Effects of Emitter Sheath Ion Reflection and Trapped Ions on Thermionic Converter Performance Using an Isothermal Electron Model

This paper couples exact collisionless sheath calculations to an isothermal electron model of a thermionic converter. The emitter sheath structure takes into account reflected ions, trapped ions, and surface emission ions. It is shown that lessening the net loss of ions at the emitter in the ignited mode by these phenomena degrades performance. In addition, it is shown that when the emitter returns too many of the ions, the arc is extinguished because there is insufficient resistive heating to maintain the necessary plasma electron temperature for ionization. These results suggest that the ignited mode cannot be improved much. However, nonignited modes in which the electron temperature remains low, such as the pulsed mode, do not suffer from this adverse behavior.     

Modification of the tungsten carbide field emitter surface to localize the electron and ion emission

Using field emission microscopy, the shape modification of the tungsten carbide emitter simultaneously exposed to high electric fields and high temperatures is studied. It is shown that in this case the emitter shape changes observed on the emitter surface are the same as those observed in the pure metal emitters. The possibility to grow a single nanoprotrusion on the emitter surface which can emit charged particles with stability similar to that for the carbon material emitters is demonstrated. The values of the emission current, current density, emission angle, and reduced brightness are comparable to those for the carbon nanotube emitters, and the advantage of this single nanoprotrusion is its complete reproducibility and capability to emit not only electrons but also ions.