Strongly anisotropic field emission from highly aligned carbon nanotube films

Carbon nanotube (CNT) films offer tremendous potential for use in multiple applications ranging from electromagnetic interference (EMI) shielding in cables and electronics, to thermal interface materials, to heating elements or conductive materials in clothing or e-textiles such as wearable antennas, and in photonic applications such as photo-cathodes.^1–3 CNT films have been widely investigated for their potential use as field emission (FE) cathodes. The majority of FE experiments reported in the literature to date have been performed on CNT films consisting of dense forests or mattes of CNTs grown on flat substrates. The anode is arranged above the film so that the current is extracted directly from the planar film surface.^4–9 Alternatively, some of us have investigated using the thin edge of a free standing CNT film as the emission surface.^10–11 The primary objective of these “edge emission” investigations has been to demonstrate that FE performance can be improved by cutting triangular patterns into the film edge and, thus, increasing the field enhancement. This has proven to be a very effective approach for improving the performance of FE cathodes made from CNT films that are comprised of unaligned CNTs.¹⁰ In the past, Hsu et al. have used an electron cyclotron resonance chemical vapor deposition technique to grow both vertically and horizontally aligned CNT arrays by manipulating the applied electric field on the substrate and the flow direction of the gases during deposition. They have shown that horizontally aligned CNT arrays show better field emission properties than vertically aligned CNT arrays.¹² 

Motivated by the results described above, this paper describes a thorough investigation of extruded, fully densified, and highly aligned CNT films as FE cathodes. These highly aligned CNT films were produced by a continuous film casting process. Commercially available CNTs were dispersed in superacid to form a liquid crystalline solution that was extruded and the acids were removed via coagulation.^13–14 Shear and elongational forces created during the extrusion process along with winding the films under tension resulted in a high degree of CNT alignment lengthwise through the film. The microstructure of the films consists of highly densified and well aligned fibrils of CNTs that are 10–100 nm in diameter with a length >50 μm. CNT films were cast in two different widths, 5 mm with a thickness of 50 μm and 10 mm with a thickness of 30 μm. The CNT films were produced in long lengths up to tens of meters and wound on a spool. Figure 1(a) shows a small cut section of the 5 mm wide film and Fig. 1(b) shows an SEM image revealing the high degree of CNT alignment.

The anisotropic nature of the films was investigated by characterizing the electrical conductivity in orthogonal directions. We extracted the specific conductivity of the CNT films by measuring linear density and resistance per unit length and applying the dimensional formula for specific conductivity = [(mg mm⁻¹) × (Ω mm⁻¹)]⁻¹. Specific conductivity is a more useful technique than standard conductivity because it accounts for the significant variance in density of CNT materials and does not require measuring the conductor cross section, which can also be highly variable in CNT materials.^15–17 Linear density (given in mg mm^─1) was measured using a Sartorius microbalance; the resistance per millimeter (given in Ω mm^─1) was measured in the direction of microstructure alignment using a four-probe Keithley multimeter with carefully painted and cured silver paint leads. To evaluate anisotropy, we used the same technique on other samples and measured the specific conductivity against the microstructure alignment. The specific conductivity in the direction of the microstructure alignment divided by the specific conductivity against the microstructure alignment is called the “anisotropy ratio” and is a critical parameter in advanced carbon-based conductors with confined transport.^18–21 

Specific conductivity measurements were performed on both 5 mm wide and 10 mm wide CNT films. For the 5 mm wide CNT films, the measurements performed along the aligned microstructure direction resulted in a value of 3357 Sm²kg⁻¹. This value is above single crystal graphite at 1100 Sm²kg⁻¹ and in the range of similar materials produced by this superacid extrusion technique (2000–3600 Sm²kg⁻¹.^22–24 The films were then baked overnight at 500 °C in a vacuum. Subsequent measurements resulted in a specific conductivity value of 1690 Sm²kg⁻¹. When measured in the orthogonal direction, the specific conductivity was considerably less, resulting in an anisotropy ratio of 70. For comparison, CNT textiles composed of aligned few-wall CNTs can have anisotropy ratios spanning from 8²⁵ to 24²⁶; in the case of an extremely aligned and densified single-wall CNT buckypaper, the anisotropy ratio was found to be 60.²⁷ Thus, the value of 70 is very high. It is known that residual acid trapped within CNT fibers dopes the CNTs and enhances their conductivity²⁸ and can be outgassed when heated. For the 10 mm wide films, the measured specific conductivity was 2550 Sm²kg⁻¹ and the anisotropy value was lower, only 24. After the overnight vacuum bake, the specific conductivity similarly dropped 40% to 1480 Sm²kg⁻¹, although again the anisotropy ratio remained the same. The bake-out conductivities measured here are representative of the CNT film conductivity during steady-state FE experiments. This is due to the fact that initial FE experiments were performed to allow the CNT films to heat up under vacuum and outgas trapped acids.

FE measurements were performed in a diode configuration in a custom designed UHV chamber built by McAllister Technical Services.^{12–13,29–34} Measurements were made in a background pressure of 5.0 × 10⁻⁹Torr. The anode probe tip is made from stainless steel and is conical with a 1.5 mm diameter flat tip. Additional FE measurements were performed with a larger 20 mm diameter flat plate anode. The anode is driven with a stepper motor with a 2.5 μm step size for precise control of the anode–cathode (A–K) gap distance. The anode was centered over the mounted CNT film cathodes by using an x–y translation stage with the aid of two optical cameras directed through viewports positioned at 90° from each other in the same plane. An Infinity SK Long Distance Microscope was used for imaging the CNT film cathode and measuring the anode–cathode gap distance. A Keithley 2650 source meter was used for providing voltages up to 3 kV and measuring the current. During FE measurements, the A–K gap was set at either 1 or 2 mm and the voltage was ramped up at a rate of 10 V/s. A minimum of three voltage ramp ups were performed prior to taking data. This conditioning process allows for outgassing to occur prior to taking data.³² Examples of the FE characteristics observed during conditioning of some of the films reported hereafter are shown in the supplementary material. They are representative of all the FE characteristics measured during conditioning of all films in which the loop-type behavior due to the difference between the up and down sweeps of the applied voltage gradually disappears after conditioning.

The goal of the FE experiments was to determine how electron emission from the cathode surface is affected by the orientation of the CNT alignment direction relative to the applied electric field (E field). For the “planar sample”, the CNT film cathode was mounted flat relative to the anode so that the electron emission direction was directly out of the flat film surface [Fig. 2(a)]. The planar sample was mounted by laying it flat on a copper substrate and bonding it to the substrate by placing conductive silver paint at the film edges. For the vertically mounted films, we adopt the nomenclature of “parallel sample,” meaning the alignment direction of the CNT microstructure in the film was oriented parallel to the applied E field, and “perpendicular sample” for the sample with the CNT microstructure oriented perpendicular to the applied E field [Fig. 3(a)]. The samples were prepared by razor cutting the CNT films into 5 mm squares. Vertical film mounting was accomplished by using silver paint on the film edge and sandwiching it between two copper plates to produce a free standing film with a horizontal emission edge facing the anode. The parallel sample was rotated 90° with respect to the perpendicular sample. The initial anode diameter (1.5 mm) was chosen so that it was smaller than the width of the film. Additional FE experiments were performed with the larger diameter (20 mm) anode that covered the entire edge of the vertically mounted films.

Initial experiments were performed with an anode–cathode (A–K) gap of 2 mm and a voltage ramp up to 2 kV for a maximum applied E-field strength of 1 V/μm. FE experiments on the planar sample resulted in unstable, erratic emission and arcing, which made conditioning the films difficult. Eventually, a stable measurement was made that reached a maximum emission current of 0.02 mA. SEM imaging after FE revealed damage to the planar film surface caused by the CNT fibrils pulling up and out of the film plane in a disordered manner to align with the E field as shown in Fig. 2(b).

Figure 3(a) shows the measurement configurations for the parallel and perpendicular samples. Figure 3(b) shows the I–V curves for the planar, parallel, and perpendicular samples. The parallel sample emitted 0.78 mA, while the perpendicular sample emitted 0.17 mA. SEM imaging of the perpendicular and parallel samples after the FE experiments showed a dramatic difference in the amount of surface damage. Figure 4(a) reveals that the emission edge of the perpendicular sample was completely covered in long loose, dangling fibrils that pulled out from the film to align with the E field, creating a highly irregular surface. This is similar to the result shown for the planar sample in Fig. 2(b). In contrast, the surface of the parallel sample shown in Fig. 4(b) shows little damage. Since the fibrils are already aligned with the E field, they do not pull out from the surface. There appears to be a light layer of nanoprotrusions on the surface due to exposure of the cut fibril tips to the E field. However, the edge boundary reveals torn, jagged, pieces of CNT film that resulted from the cutting process that appear to have pulled up to align with the electric field. If they are higher than the film edge, they will create unwanted emission “hot spots” due to their high local field enhancement.

SEM imaging of additional samples taken before FE experiments highlighted additional problems. Figure 5(a) shows the emission edge of a perpendicular sample and reveals loose dangling fibrils that occur at the natural edge of the film which will pull up to align with the E field and produce unwanted emission sites. Figure 5(b) shows the parallel sample revealing surface features such as sharp features that occur due to the razor cutting process. These surface features and dangling fibrils will cause unwanted field enhancement. To eliminate these problems, we folded the films to create a ridge for the emission surface. This approach eliminated the stray fibrils and torn edges that can impact the FE experiment. Folding the films also created a sturdier structure when vertically mounted, which made it easier to control the sample height and uniformity. Additionally, a folded cathode offers the benefit of improved thermal management due to doubling the attachment points at the substrate.³⁴ 

Figure 6 shows SEM imaging of the ridge of the folded CNT films. The ridge width was ∼120 μm wide, which was used to calculate the emission area. For the small diameter anode, the macroscopic or “footprint” area was calculated as the ridge width times the anode diameter (120 μm × 1.5 mm). The larger 20 mm diameter anode covered the entire width of the film, so the emission area was dependent on the film width. Therefore, the macroscopic area was 120 μm × 5 mm (120 μm × 10 mm) for 5 mm (10 mm) film widths.

Figures 7(a) and 7(b) show the conditioning curves for both parallel and perpendicular samples made from the 5 mm wide CNT film. The FE experiments were performed with the 1.5 mm anode. The voltage was ramped up to 2 kV and allowed to dwell for 100 s before being ramped down. The initial emission current from the perpendicular sample was unstable and erratic, making it more difficult to condition than the parallel sample. The voltage up and down sweeps for both samples are shown in Figs. 7(c) and 7(d). The parallel sample reached a maximum emission current of 0.582 mA, while the perpendicular sample reached a current value of 0.0026 mA.

FE experiments were performed using the larger 20 mm diameter anode for the purpose of obtaining larger currents. The increased mass of the larger anode prevents anode expansion due to heating when measuring multiple milliamperes of current. Experiments were performed on different samples cut from the same spool of CNT films to demonstrate the repeatability of the FE performance. The A–K gap was 2 mm and the maximum voltage was 3 kV. Figure 8 shows the I–V curves for two different conditioned samples in both the parallel and the perpendicular configurations. The parallel samples reached maximum current values of 6.39 and 6.27 mA. The perpendicular samples reached maximum current values of 2.55 and 2.49 mA.

Figure 9(a) shows the emission surface of the parallel sample after FE. As compared to the pre-FE image [Fig. 6(a)] the surface shows some areas of damage but is still largely intact. Figure 9(b) shows a higher magnification image revealing a fairly uniform pattern of minimal damage across the surface. Figure 9(c) shows the perpendicular sample surface revealing severe damage over the entire film ridge. Figure 9(d) shows a higher magnification image revealing the surface to be split open, creating porous regions and protruding film fragments. These images show that the parallel sample configuration is optimal due to its ability to produce higher emission currents that induce significantly less surface damage.

Additional FE experiments were performed on the 10 mm wide folded films. The A–K gap was lowered 1 mm due to the difficulty in obtaining stable emission from the perpendicular sample at a gap distance of 2 mm. The I–V curves for two different parallel samples are shown in Fig. 10(a). The maximum voltage used for conditioning was lowered to 1.5 kV due to the high currents that were obtained, which can result in anode heating and expansion. Robustness tests were performed on both the parallel and the perpendicular samples at higher voltage values and dwelling for 100 s when the maximum voltage value was reached. I–T curves for both parallel and perpendicular samples are shown in Fig. 10(b). For the perpendicular sample, the voltage was ramped up to 3 kV and the sample failed at 2.9 mA during the dwell. For the parallel sample, the compliance setting on the sourcemeter was set to 20 mA, which was reached at 2.1 kV, and the current stabilized during the 100 s dwell.

The experimental FE data were analyzed using the orthodox Fowler–Nordheim (FN) theory.³⁵ The I–V data were plotted in FN coordinates as shown in Figs. 11–14. The characteristic parameters (i.e., the effective field enhancement factor and effective formal emission area) were extracted from the FN curves and subjected to the orthodoxy test developed by Forbes.³⁶ FN data are defined as orthodox if the current–voltage characteristics are determined by the following: (i) the total system geometry is unchanging with respect to the biasing conditions, (ii) the emission process is due to tunneling that takes place through a Schottky–Nordheim (SN) barrier, and (iii) there is no significant voltage dependence of the emission area and the local work function. If the FN data are not orthodox, then the characteristic parameters determined by FN analysis may be spurious.³⁷ For all of these data sets that were analyzed, the FN data generated by the parallel samples easily satisfied the orthodoxy test, while the parallel samples mostly did not. This is due to the instability of the perpendicular sample emission surface, as shown in Figs. 4(a), 8(c), and 8(d).

A complete development of the orthodox FN theory is contained in the supplementary material; here we present only a brief summary. A large area field electron emitter (LAFE) contains very many individual emitters or emission sites, each with its own characteristics. In particular, each site will have its own local conversion length, $ζC$⁠, defined as

where $FC$ is the localized field at emission site “C”, $γC$ is the characteristic local field enhancement factor, and $Vm$ and $FM$ are the measured voltage and E field, respectively. The measured emission current, $im$⁠, can be expressed as

A_M is the total macroscopic emission area and α_n and α_f are the notional and formal area efficiencies, respectively. A_f ≡ α_fA_M is the formal emission area parameter that can be extracted from experiments in “orthodox” emission situations, and $ν$ is the exponential correction factor for a SN barrier.³⁸ We have not considered the effect of leakage current in the paper and assumed it is negligible. In this case, the measured current $im$ will be equal to the emission current $ie$⁠.

We define the characteristic scaled barrier parameter, f_C, as

where ϕ  = 4.65 eV is the local CNT work function.³⁹ We define $fextr$ as the value of $fc$ that is extracted from an experimental FN plot. This value of $fextr$ has upper and lower bounds that are determined by the degree of the linearity of the straight line fit to the FN data within a range of upper and lower $Vm$ values. If the upper and lower bounds of $fextr$ are considered to be in the reasonable range (⁠$0.14≲fextr≲0.44$ for the local work function considered in this work³⁶, then the calculated values of$ζC$⁠, $Af$⁠, $γC$ are legitimate. Otherwise, they are considered to be spurious and unreliable.

FE experiments were performed on the unfolded 5 mm wide CNT films using the 1.5 mm diameter anode. Figure 11(a) shows the I–V curves for both the parallel and the perpendicular samples and Fig. 11(b) shows the corresponding FN plots. These data correspond to the films discussed in Figs. 3–5. The linear fit to the parallel sample FN data is highlighted by the dashed line. The range of V_m for a least square fitting was 8.772 × 10⁻⁴ V⁻¹ ≤ 1/V_m ≤ 1.111 × 10⁻³V⁻¹, which corresponds to the measured emission current, $ie$⁠, in the range of 4.959 × 10⁻⁵ mA ≤ i_e ≤ 6.962 × 10⁻³ mA. The extracted mid-value read, (1/V_m)^(expt), from the horizontal axis of a nearly linear FN plot was (1/V_m)^(expt) = 9.940 × 10⁻⁴ V⁻¹.

For the perpendicular sample, we observed both low and high voltage regimes. For the low voltage regime, the range of V_m for the linear fit to the FN data was 9.524 × 10⁻⁴ V⁻¹ ≤ 1/V_m ≤ 1.265 × 10⁻³ V⁻¹ corresponding to the range for $ie$ of 2.211 × 10⁻⁵mA ≤ $ie$ ≤ 1.718 × 10⁻⁴ mA. The extracted mid-value read, (1/V_m)^(expt), from the horizontal axis of a nearly linear FN plot was (1/V_m)^(expt) = 1.109 × 10⁻⁴ V⁻¹. For the high voltage regime, the range of V_m was 5.780 × 10⁻⁴ V⁻¹ ≤ 1/V_m ≤ 7.093 × 10⁻⁴ V⁻¹ corresponding to the range for $ie$ of 3.525 × 10⁻³ mA ≤ $ie$ ≤ 6.560 × 10⁻² mA. The extracted mid-value read, (1/V_m)^(expt), from the horizontal axis of a nearly linear FN plot was (1/V_m)^(expt) = 6.436 × 10⁻⁴ V⁻¹.

Table I shows the characterization parameters extracted from the FN plots for the unfolded parallel and perpendicular samples. For the parallel sample, the $fextr$-values are clearly in a reasonable range for an orthodox FE for the local work function considered. The emission area A_f was calculated to be 0.37(2) μm², and the γ_C was found to be 6.655(9). For the perpendicular sample in the low voltage regime, the $fextr$-values are in a “clearly unreasonable” range for an orthodox FE for the local work function considered. In this case, $ζC$⁠, A_f, and γ_C are not reliable quantities, and the symbol [*] means unorthodox emission. For the perpendicular sample in the high measured voltage regime, the $fextr$-values are clearly in a reasonable range for an orthodox FE. Furthermore, it is interesting to see that the formal area extracted in this case is approximately 500 times lower than that found for the parallel sample.

FE experiments were performed on the folded 5 mm wide CNT films using the 1.5 mm diameter anode. Figure 12(a) shows the I–V characteristics for both the parallel and the perpendicular samples and Fig. 12(b) shows the corresponding FN plots. These data correspond to the samples discussed in Fig. 6. For the parallel sample, the region used for the linear fit to the FN data is highlighted by the dashed line. The range of V_m for a least square fitting was 8.850 × 10⁻⁴V⁻¹ ≤ 1/V_m ≤ 1.111 × 10⁻³ V⁻¹, which corresponds to the range for $ie$ of 5.460 × 10⁻⁶ mA ≤ $ie$ ≤ 4.420 × 10⁻⁴ mA. The extracted mid-value read, (1/V_m)^(expt), from the horizontal axis of a nearly linear FN plot was (1/V_m)^(expt)= 9.980 × 10⁻⁴ V⁻¹.

For the perpendicular sample, the region used for the linear fit is also highlighted by the dashed line. The range of V_m for the least square fitting was 5.291 × 10⁻⁴ V⁻¹ ≤ 1/V_m ≤ 6.135 × 10⁻⁴ V⁻¹, which corresponds to the range for $ie$ of 1.464 × 10⁻³ mA ≤ $ie$ ≤ 2.206 × 10⁻³ mA. The extracted mid-value read, (1/V_m)^(expt), from the horizontal axis of a nearly linear FN plot was (1/V_m)^(expt)= 5.713 × 10⁻⁴ V⁻¹.

Table II shows the characterization parameters extracted from the FN plots. For the parallel sample, the $fextr$-values are clearly in a reasonable range for an orthodox FE for the local work function considered. For the perpendicular sample, $ζC$⁠, A_f, and γ_C are not reliable quantities, since $fextr$-values are in a “clearly unreasonable” range for the local work function considered.

Additional FE experiments were performed on the folded 5 mm wide CNT films using the larger 20 mm diameter anode that covered the entire length of the folded film ridge. Figure 13(a) shows the I–V characteristics for both the parallel and the perpendicular samples and Fig. 13(b) shows the corresponding FN plots. These data correspond to the films shown in Fig. 9. For the parallel sample, the range of V_M for the least square fit to the FN data was 5.406 × 10⁻⁴ V⁻¹ ≤ 1/V_m ≤ 7.093 × 10⁻⁴ V⁻¹, which corresponds to the range for $ie$ of 1.361 × 10⁻³ mA ≤ $ie$ ≤ 1.380 × 10⁻¹ mA. The extracted mid-value read, (1/V_m)^(expt), from the horizontal axis of a nearly linear FN plot was (1/V_m)^(expt) = 6.249 × 10⁻⁴ V⁻¹.

For the perpendicular sample, the range of V_m for the least square fitting was 4.739 × 10⁻⁴ V⁻¹ ≤ 1/V_m ≤ 6.411 × 10⁻⁴ V⁻¹, which corresponds to the range for $ie$ of 1.773 × 10⁻³ mA ≤ $ie$ ≤ 1.55 × 10⁻¹ mA. The extracted mid-value read, (1/V_m)^(expt), from the horizontal axis of a nearly linear FN plot was (1/V_m)^(expt) = 5.575 × 10⁻⁴ V⁻¹. Table III shows the characterization parameters extracted from the FN plots. Both data pass the orthodoxy test for the local work function considered.

FE experiments were performed on folded 10 mm wide CNT films using the larger 20 mm diameter anode that covered the entire length of the folded film ridge. Figure 14(a) shows the I–V characteristics for both the parallel and the perpendicular samples and Fig. 14(b) shows the corresponding FN plots. For the parallel configuration, the region where linear fit has been considered is highlighted by the dashed line. The range of V_m for a least square fitting was 8.197 × 10⁻⁴ V⁻¹ ≤ 1/V_m ≤ 1.042 × 10⁻³ V⁻¹, which corresponds to the range for $ie$ of 1.451 × 10⁻³ mA ≤ $ie$ ≤ 1.800 × 10⁻¹ mA. The extracted mid-value read, (1/V_m)^(expt), from the horizontal axis of a nearly linear FN plot was (1/V_m)^(expt) = 9.307 × 10⁻⁴ V⁻¹. The data shown in parallel configuration respect the orthodox emission. In fact, the effective formal area found was the largest [2.70(2) μm²] compared with all previous results.

For the perpendicular configuration, we observed two regimes. For the low measured voltage regime, the range of V_m for a least square fitting was 1.149 × 10⁻³ V⁻¹ ≤ 1/V_m ≤ 1.351 × 10⁻³ V⁻¹, corresponding to the range for $ie$ of 5.045 × 10⁻³ mA ≤ $ie$ ≤ 1.622 × 10⁻² mA. The extracted mid-value read, (1/V_m)^(expt), from the horizontal axis of a nearly linear FN plot was (1/V_m)^(expt) = 1.250 × 10⁻³ V⁻¹. For the high voltage regime, the range of V_m was 3.484 × 10⁻⁴ V⁻¹ ≤ 1/V_m ≤ 5.319 × 10⁻⁴ V⁻¹, which corresponds to the range for $ie$ of 3.780 × 10⁻¹ mA ≤ $ie$ ≤ 2.320 mA. The extracted mid-value read, (1/V_m)^(expt), from the horizontal axis of a nearly linear FN plot was (1/V_m)^(expt) = 4.402 × 10⁻⁴ V⁻¹. For a perpendicular configuration, $fextr$-values extracted in the low and high voltage regimes are in “clearly unreasonable” limits of orthodox emission. Then, the parameters extracted [*] are not reliable in this case, and, therefore, a comparison with orthodox findings is not recommended. These results are shown in Table IV.

These results demonstrate that all of the parallel samples were able to satisfy the orthodoxy test, resulting in the ability to determine realistic values for $Af$ and γ_C. Most of the perpendicular samples did not satisfy the orthodoxy test. In the two cases where they did, $Af$ was significantly smaller and γ_C was larger than that for the same sample in the parallel configuration. The 10 mm wide parallel sample had the highest $Af$ and lowest γ_C.

The experiments performed above and their analysis using orthodox classical FN theory provide a qualitative picture to account for the difference in FE performance between the parallel and the perpendicular samples. We suggest that this can be explained by field-induced morphology changes in the emission surface leading to differences in emission area and field enhancement factor. Note that, because the folding region spans a range over $50μm$⁠, the modulation of band structure due to straining or stretching of the lattice is expected to be only minimal. This immediately rules out the possibility of having strain-induced band structure features^40–42 that enhance FE, such as the generation of additional sub-bands or Van Hove singularities that could significantly increase the electron supply for FE.

The extracted values of $Af⊥<Af∥$ and $γc⊥>γc∥$ between the orthogonal configurations can be further explained by the fibrils pulling out and extruding from the emission layer. This affect is significantly more pronounced for the perpendicular sample where the fibrils undergo significant reorientation to align with the electric field. As charge builds up on the fibrils at the emission surface, repulsive electro-static forces increase between adjacent fibrils forcing them to separate. This leads to the creation of loose dangling fibrils that pull up and align with the electric field, as shown in Figs. 4(a), 9(c), and 9(d). A few of these longer fibrils can dominate the emission process, resulting in large field enhancement and small emission area. The overall FE characteristic of a macroscopic CNT field emitter sample can be strongly dominated by the electron emission from just a few protruding CNT fibrils, as was recently demonstrated with CNT looped fibers.⁴³ Thus, a few fibrils that extend the furthest from the surface will strongly boost the local electric fields, while maintaining a relatively small area of emission sites leading to the observed behaviors of $Af⊥<Af∥$ and $γc⊥>γc∥$⁠.

Figure 4(b) clearly reveals that fibril separation on the emission surface of the parallel samples does not occur to the same significant degree as with the perpendicular samples. The fibrils appear to pull up to align with the applied E field in a gradual and uniform manner. Having the fibrils aligned in the direction of the most efficient conduction pathways reduces electron scattering during transport to the emission layer, resulting in an increased electron supply at the emission surface. This leads to a more efficient emission process and less buildup of electro-static repulsive forces between adjacent fibrils. The reduced buildup of electro-thermal stress on the emission surface results in less damage. Figure 4(b) reveals that other than for the jagged torn edge resulting from the film cutting process, the surface morphology appears to consist of a layer of small nanoprotrusions which are the emission sites resulting from the uneven morphology of the mechanically cut film edge. By contrast, Fig. 4(a) reveals that the fibrils on the perpendicular surface must pull up through a 90° angle to align with the applied E field, resulting in a highly disordered surface morphology. This instability of the surface morphology during FE results in an unstable emission area, which explains the difficulty in getting the perpendicular samples to conform to the orthodox classical FN theory. In contrast, the $fextr$-values for the parallel samples were always within reasonable limits of orthodox emission than those for the perpendicular samples.

This surface phenomenon effect also explains the large 223× difference in the emission currents between the parallel and the perpendicular samples observed in Fig. 7. These data were obtained with the smaller anode, which resulted in significantly lower emission currents. In this lower emission current regime, the perpendicular surface was still evolving and most likely not fully conditioned as evidenced by Table III, which shows that orthodoxy conditions were not satisfied. Using the larger anode at higher field strengths allowed for larger emission currents and more efficient conditioning of the perpendicular sample surface, as shown in Fig. 8(b). For this case, the difference between the maximum emission current for the parallel and the perpendicular samples was reduced to a factor of 2.5. However, even though the emission curves indicated a fully conditioned surface, Figs. 9(c) and 9(d) showed that it was severely damaged when compared with the parallel sample surface in Figs. 9(a) and 9(b). Initial emissions from the perpendicular samples were erratic, unstable, and prone to arcing, making them difficult to condition. Current spikes would occur during the conditioning process that were higher than the final conditioned current value.

We attribute the reduction in surface damage in the parallel sample to the more efficient transport in the direction of the aligned CNT microstructure, which leads to a reduced contact resistance at the CNT film to substrate interface. The contact resistance is dependent on the resistance of the CNT film and our measurements showed an anisotropy ratio of 70 for the difference in specific conductivity between the parallel and the perpendicular samples for the 5 mm wide CNT films. The contact resistance has a direct impact on FE performance,⁴⁴ so the reduced contact resistance for the parallel sample contributes to the higher emission current when compared with the perpendicular sample. Reducing the contact resistance even further for the parallel sample should decrease the amount of bending in the FN curve in the high field regime, as shown in Figs. 12(b), 13(b), and 14(b). This would also allow for the parallel sample to conform to the orthodox classical FN theory in the higher current regime. Of course, this regime should also be consistent with the applied fields producing local fields at CNT film surfaces sufficiently below the field strength required to lower the tunneling barrier height by an amount equal to the local work function. This is an area of ongoing investigation.

Experiments performed on FE cathodes made from highly aligned and densified CNT films revealed that cathode performance is dependent on the cathode mounting configuration. With the cathode arranged in a planar configuration with the anode placed above the flat film surface, the emission current was the lowest and the surface damage to the film observed after FE measurements was significant due to fibrils pulling up to align with the applied E field. Edge emission from a vertically mounted cathode is a much more efficient way to generate FE current; however, the cathode performance was shown to be dependent on the orientation of the CNT microstructure relative to the direction of the applied E field. With the CNT microstructure aligned parallel to the applied E field, the emission current was higher, the field enhancement was lower, and damage to the cathode surface was minimal. Parallel samples conform to the orthodox classical FN theory allowing for an accurate calculation of the emission area. With the CNT microstructure aligned perpendicular to the applied E field, the emission current was lower, the field enhancement was higher (considering orthodox emission results), and the surface damage was significant. For the cases where the perpendicular samples did conform to the orthodox classical FN theory, the emission area was found to be 10–500 times less than that for the same sample mounted in the parallel configuration. These results demonstrate that these CNT films can be used as efficient and robust cathodes when mounted with their highly aligned microstructure aligned parallel to the applied E field.

See the supplementary material for the complete development of the orthodox Fowler–Nordheim theory. Examples of the FE characteristics observed during conditioning of some of the films are also shown. The orthodoxy test is applied to the conditioning runs of the 10 mm wide CNT films to demonstrate reproducibility of the characteristic parameter calculations.

This material is based on work supported by the Air Force Office of Scientific Research. Y. S. Ang and L. K. Ang would like to acknowledge the support of AFOAR-AOARD Grant No. FA2386-17-1-4020. T. A. de Assis is grateful for the financial support of the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) under Grant No. 308343/2017-4.

The data that support the findings of this study are available from the corresponding author upon reasonable request.