# Field Emission from Carbon Nanostructures
## 2 Field Emission from Carbon Nanostructures
### Emission from Individual Nanotubes
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**CNT Length** & **CNT Radius** & **CNT Apex-Anode** & **Setup** & \(\beta\) & **Turn-on Voltage (V)** & **Ref.** \\ (\(\upmu\)m) & **(nm)** & **Distance (\(\upmu\)m)** & & & **or Field (V/\(\upmu\)m)** & **Ref.** \\ \hline
3.2 & 17 & 0.06–5 & TIP & 230–460 & 47–185 V & [115] \\
5.83 & 24 & 10 & TIP & 208 & 270 V & [116] \\
0.5 & 15–20 & 10–50 & TIP & 500–750 & 60–260 V & [117] \\
1.5 & 20 & 20 & P-P & 200–500 & 150–400 V & [118] \\
3.9 & 15.8 & 0.40 & P-P & 300 & 100 V & [109] \\
8 & 40 & 1–60 & TIP & 100–800 & 40–5 V /\(\upmu\)m & [108] \\
1.3 & 50 & 0.29 & P-P & 140 & 90 V & [119] \\
2.1 & 30 & 1.4–13.5 & P-P & 100–700 & 50–70 V & [120] \\
5 & 30 & 0.8 & TIP & 110 & 30 V/\(\upmu\)m & [13] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Field emission characterization of individual multi-walled CNTs for (CNT apex-anode) distances below 100 \(\upmu\)m. Geometrical parameters of the CNT (length and radius), setup configuration being parallel-plate (P-P) or tip-shaped (TIP), field enhancement factor \(\beta\) and turn-on voltage or field are also listed. [PERSON] et al. [117] developed a selective growth method to realize individual CNTs (using a hot-filament CVD technique with a mixture of C\({}_{2}\)H\({}_{2}\) and H\({}_{2}\) gases under a negative substrate biasing) on silicon micro-fabricated tips of about 20 nm diameter. A micro-controlled probe (curvature radius of about 10 \(\upmu\)m) was used to perform the FE characterization in a vacuum chamber at a base pressure of 1.7 \(\times\) 10\({}^{-4}\) Pa. The poor vacuum level was recognized as the responsible of current instability. I-V characteristics were measured for a cathode-anode separation from 10 to 50 \(\upmu\)m, reporting a turn-on voltage in the range 60-260 V.  
[PERSON] et al. [118] studied the FE properties of individual CNTs grown on silicon tips. The experimental setup, in a SEM chamber with a tungsten probe-tip as anode, allowed precise measurements of CNT morphology as well as geometry of the FE device before and after the events of vacuum breakdown. They recorded un upper limit in emission current density of 10\({}^{3}\) A/m\({}^{2}\). From the comparison of two CNTs of similar length (\(\sim\)1.5 \(\upmu\)m) and different diameter (3 nm and 40 nm) they also demonstrated that the vacuum breakdown of the CNTs results in melting of the Si tip. Interestingly, a study of the field emission properties for individual multi-walled CNTs has been performed inside a transmission electron microscope [119], analyzing the effect of different vacuum levels as well as of contamination conditions. The experimental set up allowed three different geometries for the CNT cathode: a side emission geometry (reporting no emission current); a circular CNT for which only small current (below 5 \(\upmu\)A) was recorded; and end-emission geometry (i.e., standard emission from the CNT apex) that resulted in the most favorable configuration for FE. From I-V measurements at a cathode-anode distance of 0.29 \(\upmu\)m a field enhancement factor of 140 and a turn-on voltage of about 90 V were reported. [PERSON] et al. [120] focused on the characterization of field emission from individual CNTs, for cathode-anode separation distances below 15 \(\upmu\)m. A wide ranging, systematic study was performed by measuring current-voltage characteristics for several distances in the range 1.4-13.5 \(\upmu\)m. From the analysis of experimental data in the framework of F-N theory, it was shown that turn-on voltage as a function of the separation distance d followed an empirical power relation \(\sim\)_ad\({}^{b}\)_(with \(a\) and \(b\) constants), while the field amplification factor followed the relation \(\sim\)_d\(/(d+h)\)_, where \(h\) is the CNT height.