Modeling and simulation for the field emission of carbon nanotubes array

To optimize the field emission of the infinite carbon nanotubes (CNTs) array on a planar cathode surface, the numerical simulation for the behavior of field emission with finite difference method was proposed. By solving the Laplace equation with computer, the influence of the intertube distance, the anode–cathode distance and the opened/capped CNT on the field emission of CNTs array were taken into account, and the results could accord well with the experiments. The simulated results proved that the field enhancement factor of individual CNT is largest, but the emission current density is little. Due to the enhanced screening of the electric field, the enhancement factor of CNTs array decreases with decreasing the intertube distance. From the simulation the field emission can be optimized when the intertube distance is close to the tube height. The anode–cathode distance hardly influences the field enhancement factor of CNTs array, but can low the threshold voltage by decreasing the anode–cathode distance. Finally, the distribution of potential of the capped CNTs array and the opened CNTs array was simulated, which the results showed that the distribution of potential can be influenced to some extent by the anode–cathode distance, especially at the apex of the capped CNTs array and the brim of the opened CNTs array. The opened CNTs array has larger field enhancement factor and can emit more current than the capped one.     

Field emission of carbon nanotube array with normal-gate cold cathode

A hexagon pitch carbon nanotube (CNT) array vertical to the normal gate of cold cathode field emission displayer (FED) is simulated by solving the Laplace equation. The calculated results show that the normal gate causes the electric field around the CNT tops to be concentrated and emission electron beam become a column. The field enhancement factor and the emission current intensity step up greatly compared with those of diode structure. Emission current density increases rapidly with the decrease of normal-gate aperture. The gate voltage exerts a critical influence on the emission current.     

纳米碳管阵列场增强因子的计算

采用悬浮球模型，结合对称的镜像电荷层方法，对静电场中纳米碳管阵列的场增强因子进行了计算，并在考虑极板间距的情况下，对其计算结果做了修正.结果表明：纳米碳管阵列的间距对纳米碳管阵列的场发射性能影响很大.当纳米碳管阵列中碳管间距小于碳管高度时，场增强因子随间距的减小而急剧减小；而当碳管间距显著大于碳管高度时，场增强因子几乎不变.但当考虑阴阳极之间单位面积通过的场发射电流时，可论证当管间距与管高度相若时，能使场发射电流密度最佳(最大).另外，极板间距对场增强因子的影响很小，但是可以通过减小极板间距，来降低纳米碳管作为场发射体的场发射的开启电压，优化纳米碳管的场发射性能. 关键词： 纳米碳管阵列 场增强因子 开启电压     

一种平行栅碳纳米管阵列阴极的场发射特性研究

建立一种平行栅碳纳米管阵列阴极,利用悬浮球模型和镜像电荷法进行计算,给出碳纳米管顶端表面电场与电场增强因子的解析式. 在此基础上,进一步分析器件各类参数以及接触电阻对阴极电子发射性能的影响. 分析表明,碳纳米管间距大约为2倍碳纳米管高度时阵列阴极的分布密度最佳,靠边缘部位的碳纳米管发射电子能力比其中心部位的大;除碳纳米管的长径比之外,栅极宽度和栅极间距也对电场增强因子有一定作用;接触电阻的存在大幅度降低碳纳米管顶端表面电场与发射电流,而接触电阻高于800 kΩ时,器件对阳极驱动电压的要求更高. 关键词： 平行栅碳纳米管阵列 悬浮球 场增强因子 接触电阻     

纳米碳管阵列场发射电流密度的理论数值优化

以纳米碳管阵列为研究对象,利用镜像悬浮球模型及Fowler-Nordheim电流密度公式,对纳米碳管阵列的场发射电流密度进行计算,进而综合考虑场发射增强因子及场发射电流密度对纳米碳管阵列场发射性能进行定量优化.参考碳管阵列场发射电流密度最大值及场发射增强因子,表明当纳米碳管阵列间距为碳管高度十分之一时,纳米碳管阵列的场发射性能得到优化.与以前的理论估算结果相比,优化的阵列间距进一步减小.当纳米碳管间距过大,场发射增强因子增加,而场发射电流密度会在更大程度上减小;当纳米碳管密度较大时,场发射增强因子受到静电 关键词： 纳米碳管 场发射 增强因子 电流密度     

Optimization for field emission from carbon nanotubes array by Fowler–Nordheim equation

In order to optimize the field emission from carbon nanotubes (CNTs) array by the emission current density, the calculation of the field emission was extended with the floating sphere model and the Fowler–Nordheim equation, and the trend of the emission current density versus the intertube distance (the distance between the nearest CNTs) was mainly discussed in this paper. Only considering the field enhancement factor in the previous works, the field emission from CNTs array was optimized only by possibly decreasing the intertube distance with the maximal field enhancement factor. Herein, both the field enhancement factor and the emission current density were taken into account, the field emission from CNTs array could be optimized analytically with the intertube distance of 10th of the tube height, which was much smaller than the estimated value and the experiment result.     

An improved planar-gate triode with CNTs field emitters by electrophoretic deposition

An improved planar-gate triode with carbon nanotubes (CNTs) field emitters has been successfully fabricated by conventional photolithography, screen printing and electrophoretic deposition (EPD). In this structure, cathode electrodes and ITO arrays linked with gate electrodes were interdigitated and paralleled on the same plane although the gate electrodes and cathode electrodes were isolated by dielectric layer, a so-called improved planar-gate triode structure. An electrophoretic process was developed to selectively deposit CNTs field emitters onto cathode electrodes in the CNTs suspension by an applied voltage between the gate electrodes and cathode electrodes. The optical microscopy and FESEM image showed that the CNTs emitters with the uniform packing density were selectively defined onto the cathode electrodes. In addition, field emission characteristics of an improved planar-gate triode with CNTs field emitters were investigated. The experiment results indicated that the turn-on voltage of this triode structure at current density of 1 μA/cm² was approximately 55 V. The anode current and gate current came to 396 μA and 325 μA, at gate voltage and anode voltage of 100 V and 4000 V, respectively and at the anode-cathode spacing of 2000 μm. The emission image became brighter and the luminous image with dot matrix on the anode plate obviously increased with the increase of the gate voltage. Moreover, the emission current fluctuation was smaller than 5% for 11 h, which indicated that the improved planar-gate triode has a good field emission performance and long lifetime.     

太赫兹源场致发射电子源

通过粒子模拟(PIC)软件模拟计算了在ps级别下二极与三极结构碳纳米管场致发射的电流密度与电子注聚焦性能。阳极电压在2 kV时,二极结构下电流密度达到1.85 A/cm2;三极结构下,栅压700 V时发射电流密度达到2.3 A/cm2,且在一定的三极结构参数与电极电压下,可以获得较好的电子注聚束效果。通过碳纳米管二极管发射实验,获得了6.6 A/cm2的发射电流密度,总发射电流达到52.1 mA,可以为太赫兹器件提供连续发射的电子注。     

碳纳米管冷阴极场致发射中栅网特性

利用三维粒子模拟软件对大面积生长无序碳纳米管冷阴级三级结构发射特性进行仿真,对六边形、三角形和正方形3种不同网孔结构栅网下的碳纳米管冷阴极场致发射特性进行研究。通过计算冷阴极表面电场分布及场致发射电子注的通过率,得到不同图形发射效率随网孔尺寸变化的规律。进一步横向对比,得出栅网最佳图形为六边形的结论,其最大电子注通过率为75%。     

Micro-gated-field emission arrays with single carbon nanotubes grown on Mo tips

Using our approach previously reported, we have fabricated relatively large area micro-gated-field emission arrays with carbon nanotube (CNT) grown on Mo tips. By redesigning the device and fabrication processes, the percentage of single CNTs increased to about 50-70% with a substantial improvement in leakage current between gate and cathode and gate interceptive current. The I-V measurement of a 11000 cell array at a gate to cathode voltage of 92 V showed an anode current of 1.2 mA, corresponding to a current density of 0.57 A/cm², with a gate current only 3.3% of the anode current.     

平面二极管爆炸发射阴极特性实验研究

 在电压0.6~1.0 MV,脉冲重复频率为100 Hz条件下,实验研究了爆炸发射阴极的有效发射面积、平均发射电流密度、二极管阻抗、电子束能量损耗机制等特性。结果表明：阴极有效发射面积随时间呈方波变化,在脉冲开始后5 ns内有效发射面积基本达到稳定。在碳纤维、天鹅绒、石墨、不锈钢4种阴极材料中,碳纤维阴极有效发射面积最大且变化相对稳定,并且碳纤维阴极具有最大的平均发射电流密度。二极管阻抗随着阴阳极间隙的增加并非呈平方关系增加,而是呈线性增长,阻抗失配是降低电子束能量传输效率的主要机制。     

Electric field enhancement in field-emission cathodes based on carbon nanotubes

The problem of determining the field enhancement factor in field-emission cathodes based on carbon nanotubes (CNTs) is considered. The electrostatic problem of finding the field enhancement factor for nanotubes with different shapes of the tip as a function of the angle the nanotube makes with the cathode surface and of the interelectrode spacing is solved. The dependence of the electric field enhancement factor on the spacing between vertically oriented nanotubes constituting an array is derived. Making allowance for this dependence gives an optimal value of the surface density of nanotubes in the array at which the emission current density is maximal. The I—V characteristic of CNT-based cathodes is studied with regard to the statistical straggling of their orientation angles. This I—V characteristic is compared with the characteristic obtained with regard to the statistical straggling of the CNT geometrical parameters.     

Optimization of the parameters of a carbon nanotube-based field-emission cathode

A procedure for optimizing a field-emission cathode based on carbon nanotubes (CNTs) is developed. An array of identical equidistant vertical CNTs is considered. The optimization procedure takes into account the effect of screening of an electric field by neighboring nanotubes by solving a Laplace equation and the thermal instability of nanotubes, which limits the emission current density of a nanotube, by solving a heat conduction equation. The relation between the emission current and the applied voltage is described by the Fowler-Nordheim relationship containing the CNT tip temperature as a parameter. Upon optimization, the optimum distance between CNTs that ensures the maximum emission current density is calculated. The calculation results demonstrate that this parameter depends substantially on both the applied voltage and the nanotube geometry. These dependences are weakly sensitive to the choice of the transport coefficients (thermal conductivity, electrical conductivity) of nanotubes.     

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.     

激光烧蚀对碳纳米管薄膜场发射性能的影响

采用丝网印刷工艺制作了碳纳米管(CNTs)薄膜阴极.经适当能量激光烧蚀后,相互粘连的CNTs随表面粘附有机物的蒸发而分散开,管间隙增加、屏蔽效应减小,使得场发射性能大幅度提高,开启场强降低、场倍增因子β增大.Raman光谱分析表明,随激光能量增加,CNTs表面缺陷增多,成为新的场发射点,对其β增大的贡献加强.相对于两电极结构,三电极中平栅极结构场发射性能经激光烧蚀有更显著的改善.这说明激光烧蚀是提高CNTs场发射性能的有效方法. 关键词： 碳纳米管薄膜 场发射 激光烧蚀 Raman光谱     

Characteristics of polymer velvet as field emitters under high-current pulsed discharge

In this paper we investigated the surface morphology and emission property of polymer velvet in a cathode test system powered by a ∼400 ns, ∼400 kV pulsed generator. After a series of pulse shots, the velvet surface exhibited an obvious decrease in the amount of emitters, namely, the smoothing of microprotrusions, indicating a lower field enhancement factor or a higher turn-on electric field than that for no shots. As the velvet cathode lifetime proceeded, the beam degradation was observed in terms of the voltage pulse length, maximum emission current, and rise time of diode current. Further, the average current density significantly decreased during a 100 pulse shot test, from 280 to 160 A/cm². The surface discharge caused many plasma spots on the velvet surface. The cathode plasma expands towards the anode, directly leading to the diode gap closure. The degradation in the velvet performance after high-current emission may be related to this behavior of cathode plasma. Finally, the electron emission mechanisms, how to affect the surface morphology of velvet, are presented.     

Numerical study on the field emission properties of aligned carbon nanotubes using the hybrid field enhancement scheme

The magnitude of the local electric field and the electron emission current density for an array of aligned carbon nanotubes is estimated. For describing in detail the properties of the local electric field in the vicinity of the nanotube tips, a hybrid method allowing for the local determination of the field enhancement factor is introduced. The field factor consists of two parts: an internal factor which describes the structure of the carbon nanotubes and an external factor which represents the field screening effect due to neighboring nanotubes. The current density is obtained using the Fowler–Nordheim equation with the hybrid field enhancement scheme. As a result, the emission properties for an array of nanotubes with a given length are described satisfactorily, and an optimum value for the nanotube spacing is determined. PACS 85.45.Fd; 85.45.Db     

Effect of screening on the emissivity of field electron emitters based on carbon nanotubes

The effect of screening on the emissivity of a field cathode built around a carbon nanotube array is analyzed. A numerical method of solving the Laplace equation for intricate-shape cathodes is developed that makes it possible to relate the amplification factor to the nanotube spacing in arrays containing as many as 225 emitters. Mutual screening of the tubes, which shows up in the dependence of the field amplification factor on the average emitter spacing, is studied numerically. The optimal spacing between the tubes that provides an emission current maximum density at a given applied voltage is determined. The role of edge effects in carbon nanotube screening is established.     

铌镁酸铅-钛酸铅铁电阴极电子发射特性

研究了铌镁酸铅-钛酸铅铁电材料的铁电、介电性能对阴极发射阈值电压的影响, 以及铁电阴极发射电流与激励脉冲电压和抽取电压之间的关系, 并分析了其发射机理. 结果表明, 室温介电常数高、极化强度变化量大的弛豫铁电体0.9Pb(Mg_1/3Nb_2/3)O₃-0.1PbTiO₃具有较小的发射阈值电压; 铁电阴极电子发射与快极化反转和等离子体的形成有关; 由极化反转所致电子发射的自发射电流随激励脉冲电压的增大呈幂律增长关系, 其发射电流开始于激励脉冲电压的下降沿; 在抽取电压较大时, 发射电流随抽取电压的增大呈线性增长关系, 说明大电流主要取决于抽取电压; 其发射电流开始于激励脉冲电压的上升沿, 与“三介点”处的场增强效应和等离子体的形成有关; 当抽取电压为2500 V 时, 得到的发射电流幅值为210 A, 相应的电流密度为447 A/cm².     

Influence of charge deposition in a field-emission display panel

Field-emission displays (FEDs) have been studied intensively in recent years as a candidate for flat-display panels in the future. In a FED, electrons emit from field emitters. Some electrons may impinge on the insulator surface between cathode and gate electrodes and cause charging of that surface because the yield of secondary electron emission is usually not equal to one. The charging of the insulator walls between cathode and gate electrodes is one of the important factors influencing the performance of a FED. In this paper, a simulation program is used to calculate this charge deposition, electric field distribution and electron trajectories. From the change of the electric field upon charge deposition in the triode region, it is shown that the insulator surface is negatively charged at a low gate voltage, e.g. 20 V. However, positive charge is deposited when the gate voltage is high, e.g. 100 V. The simulations also show that the emission current will increase even further after coating the dielectric with a thin film of a material with a high-secondary emission coefficient such as MgO. If a cone-shaped dielectric aperture is used in a triode, the emission current will decrease after charge deposition. However, the focus performance of the electron beam is improving in this case.