6 eV for MWCNTs (Ago et al. ; Su et al. )), A and B are constants with values of 1.56 × 10−6 (A·eV/V2) and 6.83 × 109 (V·eV−3/2 m−1), respectively, and β is the field enhancement factor that characterizes the ratio between the applied macroscopic
field and the local microscopic field felt by the apex of the emitter (Bonard et al. ). By fitting the data of Figure 2 to the FN expression, Figure 3 clearly shows that regardless of the AR value Thiazovivin clinical trial of the cathodes, two different domains can be distinguished in the FN plots, namely, high-field (HF) and low-field (LF) regimes. Accordingly, separate β HF and β LF enhancement factors were extracted from the slopes of the linear fits (Figure 3) and tabulated in the table at the bottom of Figure 3. First of all, in both HF and LF regimes, the enhancement factors are seen check details to increase significantly (by a factor of 2.2 and 1.7 for β HF and β LF, respectively) as the AR is increased from 0 to 0.6. Respective β HF and β LF values as high as 6,980 and 2,315 were obtained for the h-MWCNTS cathodes with an AR value of 0.6. This confirms that the hierarchical texturing developed here is effective in enhancing further the local microscopic fields felt by the apex of the MWCNTs. On the other hand, the occurrence of distinct HF and LF regimes in the FN plots of MWCNT
emitters has been reported by other groups (Chen et al. ; Bai & Kirkici ). This indicates that the conventional FN model that describes the FEE of our h-MWCNT cathodes in the LF region cannot be extended to the HF region. Indeed, the CHIR98014 evident kink in the FN plots, which is found to occur at the same field value for all the pyramidally texturized cathodes, denotes a clear regime change in the
FEE of the MWCNTs. Although there is no consensus about the origin of this regime change (Chen et al. ), the enhanced FEE observed in the HF regime is often attributed to space charge effects surrounding the emission MYO10 sites (Xu et al. ; Barbour et al. ). Such vacuum space charge buildup is expected to occur more easily on textured substrate with high density of Si pyramids (where higher electric fields are felt by the emitting tips) than on a flat Si cathode (from which some individual nanotubes protrude). This would explain the breakpoint (Figure 3) occurring at rather low-field values in the pyramidally textured cathodes than in the flat Si ones (approximately 2.1 V/μm versus approximately 3.8 V/μm, respectively). Figure 2 Field electron emission properties of the developed hierarchal MWCNT cathodes versus their AR. (a) Typical J-E curves of the field electron emitting hierarchal MWCNT cathodes with various pyramid AR values along with that of flat Si reference substrate. The inset shows a zoomed-in part of the J-E curves to compare their threshold field (TF).