I-V characteristics of the CNT emitters
The vertically aligned CNT emitters are atomically sharp tips that enhance the field emission properties43. The I-V characteristics play an important role to explain the uniform filed emission performance which is influenced by the types of materials, arrangements, and surface morphology of the emitters, respectively37. The properties of vertically aligned CNT emitters, namely a work function (ϕ), high aspect ratio, and excellent electrical properties are the important key which is optimized in our previous experiment30,42. Figure 3 exhibits the I-V characteristics of the one-island cone-shaped CNT with 14 × 14 emitters as the function of the applied voltage. In Fig. 3, when the applied voltage is increasing the emission current is also exponentially increasing after the threshold voltage of 810 V. In 900 V, the emission current is measured at 0.34 µA, and 0.30 µA without focusing and with a focusing electrode (-200 V), respectively. After 900 V, the emission current is increasing dramatically with the applied voltage because of the high electric field effect between the gate electrode and the focusing electrode. The current density of the electron beam spot is increasing 8 times from 5.89 µA/cm2 to 47.15 µA/cm2 in the anode with the optimized condition of focusing electrode. This optimized focusing electrode is playing an important role to push the electrons toward the central axis and increasing the current density and brightness of the beam spot without loss of current.
Field emission microscopy image with the focusing electrode
FEM image provides quantitative information about the microscopic properties of the CNT emitters. A focusing electrode is used to evaluate the electron beam spot in the MCP. The FEM image is captured in the center of the MCP, which provides the real electron beam trajectory. The incident electron beam passes towards the MCP-in electrode with its beam axis. When electrons depart towards the phosphor screen of MCP, it is converted into photons and green light emits. Figure 4 exhibits the FEM image of the 14 × 14 CNT emitters in the center of the MCP in which the applied voltage and the brightness shutter time were fixed at 900 V, and 1/3 second, respectively during the whole experiment, according to our previous experiment42. In our previous experiment, the FEM image-capturing process was optimized by reducing the signal-noise ratio without focusing electrode with its real beam spot size of 2.71 mm. The potential difference between the CNT emitter and the gate mesh is fixed at 900 V. The applied voltage in MCP-out electrode and the phosphor electrode is fixed at 375 V and 1,600 V, respectively in this experiment. The electron beam spot size of the 14 × 14 CNT emitters can be analyzed with the help of the FEM image. The symmetrically distributed beam electron beam spot is well described by the Gaussian distribution7,44, \(G(x)=G(0)+A.\exp \left\{ {\left. { - 0.5{{\left( {\frac{{x - {x_0}}}{\sigma }} \right)}^2}} \right\}} \right.\), Where \(A,{x_0}\), and\(\sigma\) represents the peak intensity, mean (maximum peak intensity), and standard deviation of the distribution respectively. In the electron beam spot profile, the width of the intermediate of the maximum intensity value represents the FWHM which is expressed as \(2\sqrt {2\ln } \sigma\). In Fig. 4(a)-(e), the focusing electrode voltage is -30 V, -50 V, -100 V, -150 V, and − 200 V in which the FWHM of FEM electron beam spot is calculated to be 2.23 mm, 2.00 mm, 1.78 mm, 1.61mm, 0.90 mm, respectively. The size of high-dense bright spot is continuously reducing and the brightness is increasing with increasing the current density at the maximum collimation due to the reduction of the opening angle of the electron beams28,29,45.
Figure 5 represents the comparison of the high-dense bright spot of the field emission electron beam with different focusing electrode holes such as 1 mm, 2 mm, 4 mm, and without focusing electrode, respectively. The cathode voltage is fixed at -900 V and the focusing electrode voltage is continuously changing from − 30 V to -200 V in which the electron beam spot is reducing. The electron beam spot without the focusing electrode is calculated to be 2.71 mm which is shown in Fig. 5. Under the focusing electrode voltage of -200 V, the FWHM of high-dense bright spot is calculated to be 0.89 mm and 0.90 mm in the focusing electrode hole of 1 mm, and 2 mm, respectively. Experimentally, it is found that the electron beam spot is similar at -200 V between the focusing electrode hole of 1 mm and 2 mm. Figure 6(a)-(d) represents the electron beam spot without focusing electrode, with focusing electrode hole size of 4 mm, 2 mm, and 1 mm at -200 V, respectively. The intensity of the electron beam spot is continuously increasing and the beam spot is continuously decreasing with the focusing bias, as shown in Fig. 6(e). The beam spot and intensity of the electron beam spot are found similar to each other at the 1 mm and 2 mm of the focusing electrode hole. Experimentally, it is confirmed that the focusing electrode hole size of 2 mm is optimized for the vertically aligned CNT emitters to reduce the high-dense bright spot with high current charge density and brightness. The fabrication of 2 mm hole focusing electrode is easier and cheaper as compared to the 1 mm hole size of the focusing electrode.
Figure 4 and 6 confirm that the high-dense bright spot of the electron beam is symmetrically distributed in the phosphor screen with the uniform field emission performance from the cone-shaped vertically aligned 14 × 14 CNT emitters. The diameter of the high-dense electron beam spot is reduced 3 times from the original position under the focusing electrode voltage of – 200 V. In this experiment, the experimental result is compared with the simulation result in detail which confirm the electron beam trajectory of the CNT emitters.
Figure 7 explains the variation of the beam divergence without and with the focusing electrode (hole size of 2 mm) at -200 V. According to our previous experiment30,42, the electron beam trajectory follows the curve fitting parameters for the simulation with the variation of the cathode height from the phosphor screen. From Fig. 7, it is clear that the simulation result is consistent with the experimental results with the reduction of the anode distance. The divergence of the electron beam depends upon the size of the electron beams, cathode to anode distance, size of the focusing electrode, and gap distance of the focusing electrode from the cathode46,47. Figure 4, 5, and 6 confirm that the electron beam is symmetrically distributed with uniform field emission to the MCP. The reduction opening angle of the electron beam is defined as29,45, \({\raise0.7ex\hbox{$D$} \!\mathord{\left/ {\vphantom {D L}}\right.\kern-0pt}\!\lower0.7ex\hbox{$L$}}={\raise0.7ex\hbox{${2\tan \theta }$} \!\mathord{\left/ {\vphantom {{2\tan \theta } {1+\left( {\sqrt {1+{\raise0.7ex\hbox{${{V_{an}}}$} \!\mathord{\left/ {\vphantom {{{V_{an}}} {\left| {{V_{em}}} \right|{{\operatorname{Cos} }^2}\theta }}}\right.\kern-0pt}\!\lower0.7ex\hbox{${\left| {{V_{em}}} \right|{{\operatorname{Cos} }^2}\theta }$}}} } \right)}}}\right.\kern-0pt}\!\lower0.7ex\hbox{${1+\left( {\sqrt {1+{\raise0.7ex\hbox{${{V_{an}}}$} \!\mathord{\left/ {\vphantom {{{V_{an}}} {\left| {{V_{em}}} \right|{{\operatorname{Cos} }^2}\theta }}}\right.\kern-0pt}\!\lower0.7ex\hbox{${\left| {{V_{em}}} \right|{{\operatorname{Cos} }^2}\theta }$}}} } \right)}$}}\)where, D, L, Van, Vem is the half-width of the half-maximum intensity of the electron beam spot on the phosphor screen, distance from the point source to the phosphor (27.17 mm), applied voltage to the MCP-in electrode ( 0 V), and applied voltage to the CNT emitters ( 900 V), respectively. Figure 8 exhibits the reduction of the opening angle of the electron beam trajectory from 30 to 0.90 in the focusing electrode hole size of 2 mm. The opening angle of the high-dense electron beam spot reduces approximately 3 times from its initial position, which plays an important role in the low dispersion of electron beams with high current density. The minimum angle is calculated at the focusing electrode of -200 V.
Beam spot analysis with simulation
Beam simulation results have been valuable for designing the beam module48 and understanding the beam trajectory49 as well as applied voltage50. The computer simulation helps to optimize and construct the electron beam configurations in the diode and triode systems. In this study, opera 3D simulation is constructed to the accelerator design as follows: hole diameter, applied voltage, and height of the focusing electrode from the gate mesh. The 3D opera simulation is modelled with CNT dot size of 3 µm with its height of 40 µm. In 3D opera simulation, the applied voltage of gate mesh and the anode voltage is fixed at 1 kV, and 5 kV respectively, whereas the cathode is grounded. The height of gate mesh is fixed at 0.15 mm from the cathode. Figure 9(a) exhibits opera 3D simulation results of high-dense bright spot of field emission electron beam with the variation of height of focusing electrode from the gate mesh electrode. The minimum electron beam spot is found at 1mm height of focusing electrode from the gate mesh electrode. After 1 mm height, the electron beam spot is increasing. Figure 9(b) represents the high-dense electron beam spots in which focusing electrode hole size is varied from 1 mm to 4 mm as well as the applied voltage is varied from − 200 V to 200 V, respectively. The minimum electron beam spot is found in 2 mm hole size of the focusing electrode. The minimum electron beam spot of 0.84 mm is calculated in the focusing electrode hole size of 2 mm at the applied voltage of -200 V because the diverged electron beams are highly focused at the center of the beam axis. Figure 10 explain the opera 3D simulation of electron beam trajectory and effective radius with the different focusing electrode hole size. In Fig. 10(a), (b), and (c), the minimum electron beam spot is calculated to be 0.9 mm, 0.84 mm and 3 mm with different hole size of 1 mm, 2 mm, and 4 mm, respectively at -200 V. In case of focusing lens hole size of 1 mm and 4 mm, the electron beam spot is repelled from the gate mesh, and unable to focus highly so that the electron beam spot is affected.
Figure 11 explains the schematic diagram for the understanding of the electron beam trajectory of the CNT emitters (one-island source). The CNT emitter is fabricated in the specified region with its height of 40 µm. The gate mesh controls the extracted electron beams and helps to pass towards anode. The focusing electrode helps to focus the diverged electrons towards the central axis. The optimization parameters of the beam are very important to focus electrons at the central axis. Figure 11(a) shows electron beam trajectory without focusing electrode in which electron beams diverge with the distance between gate and anode. Figure 11(b) shows the small hole size of 1mm of the focusing electrode, in which electrons are diverged due to the electric field effect and passing away from the central axis. Figure 11(d) exhibits the 4 mm hole size of the of focusing electrode in which electrons are unable to focus highly at the central axis. Furthermore, Fig. 11(c) shows the 2 mm of optimized focusing electrode hole size in which electrons are passing towards the central axis with minimum beam spots. So that, the electron beam size is optimized by the opera 3D simulation and compared with the experimental results in the MCP. The minimum electron beam spot is obtained at 2 mm of focusing electrode hole by the simulation results as well as the experimental results.