Two-Dimensional Fin-Shaped Carbon Nanotube Field Emission Structure with High Current Density Capability

Abstract

A vacuum electron device requires a high-performance electron source that provides high current and current density. A carbon nanotube (CNT) field emission cold cathode is the optimal choice. To achieve its higher emission current capacity, its macroscale and microscale structures should be combined. Here, a two-dimensional fin-shaped CNT field emission structure is proposed, integrating a macroscale CNT fin with billions of nanoscale nanotubes. The fin contributes two-dimensional heat dissipation paths, and the nanotubes provide a high field enhancement factor, both of which enhance the high-current field emission characteristics. A model combining macro- and microstructures was simulated to optimize the structure and fin-shaped array parameters. The calculation of the field enhancement factor of the compound structure is proposed. It was also determined that the fin-shaped array configuration can be densely arranged without field screen effects, thereby enhancing the emission area efficiency. The fin-shaped CNT emitter and array emitters with different parameters were fabricated by laser ablation, which demonstrated superior field emission characteristics. A 16.55 mA pulsing emission current, 1103.33 A/cm² current density, and 6.13% current fluctuation were achieved in a single fin-shaped CNT emitter. An 87.29 mA pulsing emission current, 0.349 A/cm² current density, and 1.9% current fluctuation were achieved in a fin-shaped CNT array. The results demonstrate that the high-current field emission electron source can be realized in a well-designed emission structure that bridges the nanoscale emitter and macroscale structure.

1. Introduction

Carbon nanotubes (CNTs) have been proven to be excellent field emission materials, and CNT cold cathodes have been applied in several kinds of vacuum electronic device (VED) prototypes such as X-ray tubes [1,2], gyrotrons [3], and back-wave oscillators [4,5], etc., demonstrating significant advantages, including room temperature operation, fast turn-on time, small size, and narrow energy distribution [6]. Such types of VEDs all require high current and high current density to boost their power performance based on the power law P = IV. At a fixed voltage, the current and current density are proportional to power. Regarding device application, the primary target is to increase the emission current and current density of the CNT cathode.

As a one-dimensional nano-emitter, the CNT cathode predominantly fails due to Joule heating-induced vacuum breakdown in high current density working situations [7,8,9,10]. The heat generated from its emission tip and body has to be transported along the axis of the tube to the substrate, which is not sufficient and causes a temperature ramping that burns out the CNT. As a thin-film emitter, densely arranged CNTs experience a serious electric field screening effect, which reduces the field enhancement at their tips [11,12]. To avoid this, the CNT pattern array has been regularly designed to separate the CNTs one by one [13,14,15]. The best ratio of CNT length to spacing was deemed to be 1:2 to avoid the screening effect [16,17]. In addition, the emitters are designed with a large height-to-diameter ratio (>10) to achieve a high field enhancement factor [18,19]. The combination of these two strategies raises another problem: the large spacing occupies a large area that does not contribute to field emission. Although CNT arrays can emit a uniform field emission current at low electric fields, their relatively small effective emission area limits their ability to achieve higher current and current density.

In macroscale device applications, the cathode has a large area on the order of mm² or cm². Meanwhile, the one-dimensional emitter has a nanoscale structure and morphology. To take advantage of the nanotip field enhancement factor and fully utilize the whole surface area, it is necessary to design a field emission structure that combines macroscale and nanoscale features, thereby maximizing the advantages of each and avoiding their drawbacks.

Here, a two-dimensional fin-shaped CNT field emission structure is proposed. The vertically aligned CNTs are densely arranged in a straight line to form a fin shape. The whole fin-shaped CNT acts as a two-dimensional emitter that combines a macrostructure fin and nanostructure CNTs. The first advantage is that the top of the CNT fin forms a two-dimensional continuous line shape that arranges more emission sites without gaps, fully using the line area. At the same time, the screening effect is minimal because the sharp fin inherently possesses a field enhancement factor. The second advantage is that the sidewall of the CNT fin is a two-dimensional surface, which provides a large area for heat dissipation. The heat generated at the top of the fin can dissipate through two-dimensional pathways, reducing the temperature rise in the CNT body. Therefore, the fin can effectively prevent the destruction of the CNT and maintain a large emission current capacity. In addition, the fin shape is also an ideal cathode structure for specified device applications [20,21]. For example, the sheet electron beam is popular for the terahertz traveling wave tube and back-wave tube [22,23,24].

In this paper, the fabrication of the fin-shaped CNT structure is introduced. The field emission characteristics were measured to achieve high current and current density. The fin-shaped CNT array was also designed. The relationships among the structural parameters, field enhancement factors, electrostatic field distribution, and thermal transport ability were simulated. An optimal structure parameter for the fin-shaped CNT array, including fin height and spacing between fins, was achieved. It was found that the spacing of the macro-emitter could be reduced to match that of the nanostructures, which means that macro-emitters with a high height–diameter ratio could be distributed as densely as the tiny emitters. In addition, a simulation method combining macrostructure and nanostructure was introduced to improve simulation accuracy over multiple scales.

2. Materials and Methods

The fabrication methods for a fin-shaped CNT emitter can vary. In this work, a laser ablation method was introduced. Firstly, a macroscale 5 mm × 5 mm in area, 500 μm in height, vertically aligned multi-walled CNT thick film was synthesized on a planar quartz substrate by thermal chemical vapor deposition, as shown in Figure 1a. Secondly, the CNT thick film was transferred to a conductive stainless-steel substrate using conductive silver paste. Then, a power pulsing laser illuminated the interface of the CNT and quartz substrate to detach the CNT film from the quartz. Thirdly, a focused laser with focal spots of approximately 160 μm was employed to ablate the CNT films along a predetermined motion trajectory, as shown in Figure 1b. Consequently, the designed pattern on the CNT film can be obtained. In this work, a fin-shaped CNT was ablated. By modifying the laser motion path, the fin-shaped CNT with widths of 0.3 μm, 50 μm, and 150 μm, and fin-shaped CNT arrays with spacings of 160 μm, 360 μm, and 600 μm were fabricated.

The morphologies of the fin-shaped CNT emitters and fin-shaped CNT array emitters were observed using scanning electron microscopy (SEM, ZEISS Supra 55, Oberkochen, Germany). Field emission characteristics were measured in an ultra-high vacuum chamber at a pressure of 9 × 10⁻⁶ Pa. A diode test structure was adopted with a gap of 200 μm between the cathode and anode. Both the DC and pulsing field emission characteristics were measured to determine the maximum current and current density. To avoid heat-induced outgassing of the silver paste due to electron bombardment at the anode, a water-cooling heatsink was installed at the back of the anode plate to facilitate heat dissipation. The three-dimensional electrostatic field distributions of various parameters and heat transfer capacities were calculated using COMSOL Multiphysics software(Version 5.4).

3. Results

A fin-shaped CNT was ablated by a laser, and its morphology is shown in Figure 2a. The fin has a length of 5000 μm, a height of 280 μm, and a width of 300 nm. At the top of the fin, many nanotube tips protrude upwards, with a typical height of several micrometers and a diameter of 10 nm, as shown in Figure 2b. It is a compound structure with macro fins and nanotubes, spanning five orders of magnitude in dimensions. The fin acts as a base for heat dissipation and electron transport, while the nanotubes act as emission tips with a high field enhancement factor. Based on its morphological characteristics, a model was built to simulate the intensity and distribution of the electrostatic field at the top of the structure.

The simulation model consists of two parts, as shown in Figure 2c–e. One is a macro fin (the blue part in Figure 2c,d) with a length of 400 μm, a height of 280 μm, and a width that varies. The second component is a nanocylinder (the red part in Figure 2c,d) with a height of 20 μm and a diameter of 10 nm, representing the nanotube. Along the top of the fin, the nanotubes are densely arranged with 2 μm spacing in the width direction and 40 μm spacing in the length direction. The gap between the cathode and anode in the model was 200 μm. In simulations, the three-dimensional finite element method faces significant challenges in establishing grids when the size of macrostructures exceeds three orders of magnitude compared to microstructures. Considering the accuracy of the calculated results, the grids in the nanostructures are designed to be quite small, and the grids at the interface of macro- and nanostructures are similarly small to maintain the grids’ continuity. The large inner grids in the macrostructure are difficult to be compatible with these grids at the interface. To solve this problem, the methodology employed involved the construction of several dense one-dimensional segments at the interface. Then these segments were isometrically mapped to the nanostructure and continuously mapped to the macroscopic structure with proportional increases to create two-dimensional grids on a fin, nanocylinders, and computational domains. Ultimately, the two-dimensional grids were scanned to three dimensions at a specific size. It is noted that the cross-sectional shape of the fin was set as a rectangle in the simulation, while its actual shape was a triangular prism. The reason was that the bottom shape of the fin had less effect on its field enhancement factor. This simplification does not change the simulation results.

The number of nanocylinders in the width direction increased with the width of the fin. To explore the influence of the two structures on the field enhancement factor, they were calculated separately as a fin and as a long nanotube and then as a whole. The field enhancement factor β is defined as the ratio of the simulated electric field at the top of the nanotube to the macro electric field at the cathode–anode gap, which is equal to the voltage divided by the cathode–anode distance. The results are shown in Figure 2d. By comparing the products of the field enhancement factors of two independent structures with the field enhancement factor of their compound, the field enhancement factor of the compound β_c can be expressed as follows:

$${\beta }_c\approx \alpha {\beta }_a{\beta }_i,$$

(1)

where α is an effective coefficient ranging from 0.85 to 0.95, β_a is the field enhancement factor of the macrostructure, and β_i is the field enhancement factor of nanostructures. The dominant influence of β_c on the compound structure originates from the nanotips. All three β values exhibit a rapid decline as the width of the fin increases from 1 μm to 50 μm, after which they stabilize near a constant value as the width increases from 50 μm to 500 μm. The decline in β_a is attributed to the fin becoming a cube as its width increases. The decline in β_i is attributed to the enhancement of electric field screening produced between the nanostructures with an increase in their numbers.

Heat transport in the CNT cathode is mainly caused by heat conduction because heat radiation in the vacuum is negligible. In a fin-type CNT film, the two-dimensional heat transport path possesses more efficient heat transport properties than the one-dimensional path in a single CNT. A heat transport simulation of a fin-shaped CNT emitter was also carried out using a compound fin model, as shown in Figure 3a. The fin had a length of 400 μm, a height of 298 μm and a width of 200 nm, which simulated the fin-shaped CNT film, while inside the fin, the nanostructures had a height of 300 μm, a radius of 10 nm, and spacings of 4 μm and 8 μm, simulating the CNT emitting tip in a vertical CNT film. For comparison, a one-dimensional model (Figure 3b) was established. The one-dimensional model had a macro cylinder with a height of 298 μm, a radius of 100 nm, and the same nanostructure as that in the fin. The heat conductivity coefficients of the nanostructure and the fin were set to different values because the heat conductivity along the CNT and between the CNTs is different. The heat conductivity coefficient in the nanostructure was set to 3000 W/(m·K) as the ideal CNT due to its ballistic heat transport along the tube [25]. In the fin, it was set to 3 (W/m·K) because the heat transport from tube to tube was weak due to the effect of phonon scattering caused by defects and carbon pollution [26]. The top surface of the nanostructure was set as the heat source to simulate the Joule heat generated during field emission from protruding CNTs. The heating power was calculated using the equation P = I²R. The current I was set to 100 μA, and the resistance R was set to 200 Ω for each CNT to simulate the temperature runaway under high-current conditions. The specific heat capacity was set to 710 J/(Kg·K). The nanostructure density was set to 1500 Kg/m³, which equals the density of a single CNT, and the fin density was set to 400 Kg/m³, reflecting the lower density of a CNT film due to the presence of gaps between CNTs. All parameters were based on reported studies [25,26,27,28,29].

The calculated results are shown in Figure 3. When the temperature at the top of the nanotube increases to 502 K, the fin-shaped CNT emitter with dense nanotips needs 948 μs, while the one-dimensional emitter needs 94.8 μs. Prolonging the time to 948 μs increases the temperature of the one-dimensional emitter to 903.79 K. Obviously, the two-dimensional fin structure helps dissipate heat in an efficient way, allowing the CNTs in the fin to achieve a higher emission current. The temperature difference between the two-dimensional fin emitter with dense nanotips (4 μm spacing, purple line in Figure 3c) and sparse nanotips (8 μm spacing, green line in Figure 3c) is due to the heat generation capacity. In the dense tips, the heat generation rate exceeds the heat dissipation rate; thus, the temperature increases faster. In the sparse tips, the heat generation rate is slightly higher than the heat dissipation rate; thus, the temperature varies mildly. Therefore, maintaining the heat transport balance is key to achieving high current and current density. In the two-dimensional fin-type CNT emitter, the macro fin offers additional heat transport pathways to enhance Joule heat dissipation and maintain the balance at higher current levels, while the nanotube structure has a high field enhancement factor to emit a large current and generate significant heat. By managing heat dissipation, a stable field emission stage can be achieved under high-current conditions.

To form a multiple-fin array, the relationship between the spacing of two fin-shaped structures (s) and the height of the fin compound structure (h) on field emission performance was also investigated through simulation. The model consists of five individual fin-shaped CNT structures, as shown in Figure 4a. The parameters are the same as those mentioned above. The electric field intensity at the center fin (indicated by the green circle) and the edge fin (indicated by the red circle), along with the variation in the spacing-to-height ratio (s/h), were calculated, as shown in Figure 4b. The electric fields of the edge and the center emitters show significant differences when s/h is less than 0.6, while they become similar when s/h is greater than 0.6. This means the screening effect is weak and can be ignored when s/h > 0.6. Thus, the fin-shaped CNT array can be arranged more closely to each other to obtain a more effective emission area and achieve a higher current and current density. The conclusion differs from the traditional view that the maximum emission current is reached when the spacing between neighboring emitters is at least twice their height. The reason for this is that the previous simulation models considered only the construction of microstructures. Therefore, their conclusions are not suitable for direct extension to macrostructures. An accurate model should be a combination of microscale and macroscale elements. The emitted electrons come mainly from the nanotips. For CNTs involved in the emission, the screening effect generated by the neighboring macrostructure may be overestimated because its field enhancement factor is much smaller than that of the nanotips. The main screening effect on the CNT tip is generated by the neighboring nanotubes in the local macrostructure.

To verify the point of view, the field emission measurement of the fin-shaped CNT emitter and its array emitter were carried out. Firstly, a single fin-shaped CNT emitter structure with a fixed height of 300 μm, a fixed length of 5000 μm, and different widths of 0.3 μm, 50 μm, and 150 μm was fabricated by laser ablation, as shown in Figure 5a–c. The inset figures show magnified top–down views of the fin widths. Its DC and pulsing field emission current vs. voltage characteristics are shown in Figure 5d,e. The inset Fowler–Nordheim (FN) plots show a linear downward slope, which confirms typical field emission behavior in accordance with the F–N equations, as shown in Formulas (2) and (3). The field enhancement factor β can be estimated from the F–N plot using Formula (4) derived from Formula (2) as follows:

$$\mathrm{I}=\mathrm{A}{\displaystyle \frac{{\beta }^2{E}^{2}S}{\varphi }}\exp \left(-{\displaystyle \frac{B{\varphi }^{\frac{3}{2}}}{\beta E}}\right),$$

(2)

$$\ln \left({\displaystyle \frac{I}{E^2}}\right)=-{\displaystyle \frac{B{\varphi }^{\frac{3}{2}}}{\beta }}{\displaystyle \frac{1}{E}}+\ln \left(\mathrm{A}{\displaystyle \frac{{\beta }^{2}S}{\varphi }}\right),$$

(3)

$$\mathsf{\beta }=-{\displaystyle \frac{B{\varphi }^{\frac{3}{2}}}{k_s}}$$

(4)

where I is the emission current, E is the applied electric field, S is the area, and Φ is the work function of CNT, here assumed to be 5 eV. A is equal to 1.54 × 10⁻⁶ (A·eV)/V², B is equal to 6.83 × 10³ V/(μm·eV^3/2), and k_s is the slope of the F-N curve.

The emitter with a 0.3 μm width had the lowest turn-on field of 1.49 V/μm (turn-on field is defined as the electric field required to generate a 10 μA emission current) due to the sharper fin having a larger field enhancement factor of 13,858, calculated from a small k_s of −5.51. The maximum achieved current was 4.21 mA at an electric field of 2.9 V/µm, with a corresponding current density of 280.67 A/cm². The other two emitters had a much larger turn-on field while having a similar maximum current. The F-N curve slopes of the fins with 50 µm and 150 µm widths were found to be nearly identical. This means that the field enhancement factor of the protruding CNT on the fin structure with a width of 150 µm is not significantly different from that on the fin structure with a width of 50 µm. The emitter with a width of 150 µm possesses a larger edge and provides a larger emission area, which offers a slight enhancement in field emission current performance. The results aligned well with the simulation findings. The narrow width of the fin makes a notable contribution to the field enhancement factor, which cannot be ignored. In contrast, when the width is as large as several tens of micrometers, its field enhancement effect can be neglected. The achieved maximum currents of all three emitters were similar, which means that a large emission area at the top of the fin cannot guarantee a high current. An effective emission area is key to achieving the emission current. Pulse mode can reduce Joule heat damage to the CNTs and help achieve a higher maximum emission current. The pulse parameters were set to a 10 µs pulse width, 0.2% duty ratio, and 200 Hz frequency. A maximum pulse current of 16.55 mA was recorded at 4.18 V/μm, with a corresponding current density of 1103.33 A/cm² for the 0.3 μm wide fin-shaped CNT sample. The current stability measurements of these samples were conducted for 1 h, starting with a direct current of 2.2 mA. The current fluctuations for the 0.3 μm, 50 μm, and 150 μm wide fin-shaped CNT emitters were 6.13%, 8.16%, and 5.17%, respectively, as shown in Figure 5f. The fin-shaped CNT with a narrow width exhibits excellent field emission characteristics, showing the feasibility and superiority of the macro–nano compound field emission structure.

Secondly, the fin-shaped CNT arrays with different spacings of about 160 μm, 360 μm, and 600 μm were fabricated, as shown in Figure 6a–c. The three sample areas are the same at 0.25 cm², which means that the emitter density of the fin-shaped CNT array with smaller spacing is larger. All the fin-shaped CNT emitters were ablated with a length of 5000 μm, a height of 300 μm and a width of 0.3 μm. Thus, the corresponding s/h values were 0.53, 1.2, and 2, respectively. The field emission characteristics of the three array samples and a raw CNT thick film with the same area were measured in DC and pulse modes. All test conditions were the same as mentioned above. Figure 6d,e show the current vs. electric field curves in DC and pulse modes, respectively. The maximum DC emission current was 29.56 mA, measured from the array with an s/h ratio of 0.53, and its turn-on field was 0.81 V/μm. The corresponding current density was 0.118 A/cm². The maximum pulsed current reached 87.29 mA, with a corresponding current density of 0.349 A/cm². The k_s value was calculated to be −6.29, and then the β was determined to be 12,140.

The sample with s/h ratios 1.2 and 2 has a smaller maximum current and a larger turn-on field. The results are consistent with the simulation prediction that the smaller the s/h, the larger the emitter density, resulting in a higher current and current density. The differences between the simulation and measurement can be attributed to the disorganization of the actual nanotips. Because of the limitations of the size of the laser focal spot, more densely arranged arrays cannot be fabricated for testing. The fin-shaped array with 600 μm spacing (s/h = 2) has a much smaller maximum current due to the significant loss of cathode area. Large fin structures with a height of 300 μm, based on a model combining macro- and microelements, can be arranged as densely as tiny structures with a height of 75 μm, based on the traditional model. The waste from the emission area is greatly reduced. The raw, unprocessed CNT film has the smallest maximum current due to a strong field screening effect, as expected. Figure 6f shows the current stability of these samples. The direct current fluctuation rate of fin-shaped CNT arrays with an s/h ratio of 0.53 was only 1.9% at 15 mA over one hour, which demonstrated the reliability of the fin-shaped arrays and their suitability for device applications. The direct current fluctuations of the 1.2 and 2 s/h fin-shaped CNT arrays are 1.1% and 9.91% at 10.5 mA and 6 mA, respectively. In contrast, the unprocessed CNT film recorded the worst current stability, with a fluctuation of 23.04% at 4 mA.

To comprehend the performance of CNT emitters, comparisons of current, current density, field enhancement factor, and turn-on field between this work and other 1D/2D field emission structures are shown in

Table 1. Comparison of the field emission characteristics in this work with other reported 1D/2D nanomaterials.

Cathodes	Area	Maximum Emission Current	Current Density	Field Enhancement Factor	Turn-On Field (V/μm)
Single CNT [30]	-	14.5 μA	-	1325	-
Buckypaper [31]	1 μm2	10 μA	1000 A/cm2	30	140 (0.01 nA)
Vertical graphene [32]	1 μm2	31 nA	3.1 A/cm2	32	70 (1 pA)
Single MoS2 nanosheet [33]	-	20 nA	-	17	100
Vertical CNT film [34]	0.36 mm2	2 mA	0.555 A/cm2	3000	1 V (10 μA/cm2)
Vertical CNT array [13]	1 cm2	1 mA	0.001 A/cm2	1760	4.71 (1 μA/cm2)
Vertical CNT array [35]	0.803 cm2	26.5 mA	0.033 A/cm2	4977	1.57 (1 μA/cm2)
Cone-shaped CNT array [19]	0.04 cm2	5.78 mA	0.145 A/cm2	-	1.6 (1 μA)
Single fin-shaped CNT emitter (this work)	0.0015 mm2	16.55 mA	1103.33 A/cm2	13,858	1.49 (10 μA)
Fin-shaped CNT array (this work)	0.25 cm2	87.29 mA	0.349 A/cm2	12,140	0.81 (10 μA)

. The combination of the macrostructure and the microstructure in the fin-shaped CNT array results in both a significantly high field enhancement factor and a comparatively reduced turn-on field. The uniform emission sites of the single fin-shaped CNT emitter can provide a large current within a small area. The optimized, densely arranged CNT array can maintain high current density over a large area. A slight reduction in the field enhancement factor of the fin-shaped CNT array confirms the simulation result that the macrostructure has little effect on the shielding of the nanotips. This work demonstrates that the fin-shaped CNT structure can effectively improve the performance of CNT-based electron sources.

4. Conclusions

A two-dimensional fin-shaped CNT field emission structure was proposed to improve its maximum emission current and current density performance. This compound structure, with a macroscale fin and nanoscale nanotubes, possesses both the advantages of two-dimensional heat dissipation through the fin and a high field enhancement factor provided by the nanotubes. A model combining the macro- and microstructures was simulated to optimize the structural parameters and fin-shaped array parameters. The calculation method for the field enhancement factor of the compound structure was proposed. It was also found that the fin-shaped array can be densely arranged without a field screening effect, thereby improving emission area efficiency. A fin-shaped CNT emitter and array emitter with different parameters were fabricated using laser ablation. The fin-shaped CNT emitter demonstrated superior field emission characteristics. A 16.55 mA emission current, a 1103.33 A/cm² current density, and a 6.13% current fluctuation were achieved in a single fin-shaped CNT emitter. An 87.29 mA emission current, a 0.349 A/cm² current density, and a 1.9% current fluctuation were achieved in a 0.25 cm² fin-shaped CNT array. These results demonstrated that the fin-shaped CNT structure has great potential as an electron source for VEDs requiring high current and current density.