Tunneling energy barriers of emitted electrons in single-walled carbon nanotubes

By use of the first-principles calculations, we systematically investigate and demonstrate the localized characteristics of electronic wave functions, corresponding to quantized energy levels in the vicinity of the Fermi level, in one individual finite-length single-walled carbon nanotube. Within the framework of the energy levels emission model, quantized energy levels relevant to electron emission are considered, and the corresponding tunneling energy barriers and integrated emitting energy levels widths are calculated with respect to the spatial emission locations. The emission trend and contributions to the emission current from $\pi$ electrons at the tip are sensitively dependent on the locations of $\pi$ electrons and the orientations of corresponding localized electronic states under the external electric field. This would give rise to the nonhomogeneous electron emission energy distribution.

Figure 1

Geometrical structure of finite-length capped armchair $\mathrm{C}(5,5)$ nanotube. $\mathrm{L}1$, $\mathrm{L}2$, $\mathrm{L}3$, and $\mathrm{L}4$, respectively, correspond to the different atomic locations of the tip.

Figure 2

(a) The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), (b) the Fermi level, and (c) the energy difference between the HOMO and LUMO of the $\mathrm{C}(5,5)$ capped nanotube as functions of the tube length. Dashed line with symbol $▵$, solid line with symbol $▾$, dotted line with symbol $°$, and dash dotted line with symbol $•$ represent the HOMO, LUMO, Fermi level, and energy difference, respectively.

Figure 3

Distribution of energy levels in the vicinity of the Fermi level. The arrow represents the Fermi level. The dashed and solid lines, respectively, correspond to unoccupied and occupied energy levels.

Figure 4

Integrated emitting energy levels width $E_{iw}$ of the different atomic locations of the tip.