First-principles dynamic simulations of field emission from carbon nanotubes on gold substrate

In order to investigate the usability of carbon nanotubes as electron-beam sources, we carry out dynamic simulations of the field emission of open-tip armchair single-wall carbon nanotubes in a fully first-principles manner. By including a metallic substrate in the structure, the charge transfer from the substrate to the carbon nanotubes under external electric fields is self-consistently taken into account and the description of the potential becomes more realistic. It is found that $s$-like $\pi$ states near the Fermi level make a major contribution to the emission current. The emission patterns of the $s$-like $\pi$ states take the shape of a small spot at the center and a ring around it.

Figure 1

(Color online) Atomic model and potential profile of the (10,10) hydrogen-passivated open-tip single-wall CNT standing on a gold (111) monolayer. External voltage is $0.4\mathrm{V}∕\mathrm{\AA }$ and the contour spacing is $0.5\mathrm{V}$.

Figure 2

(a) Snapshots of isodensity surface images of a state in time evolution steps. Vertical lines divide the CNT region and the vacuum region. (b) The amount of the electronic charge inside the CNT region. When the charge decreases linearly, the current is the slope in the time-charge plot. $1\mathrm{a.u.}=0.0242\mathrm{fs}$.

Figure 3

(Color online) Isosurfaces of typical wave functions of (a) an $s$-like $\pi$ state, (b) an $s$-like ${\pi }^{*}$ state, and (c) a $p$-like state. Red and blue mean positive and negative signs of the wave function. (d) Band structure of the (10,10) CNT without a metal substrate. “$s\text{−}\pi$”, “$s\text{−}{\pi }^{*}$”, and “$p$” indicate the bands related to the wave functions in (a), (b), and (c), respectively. Vertical lines indicate $\mathbf{k}=n\pi ∕\left(1.05L\right)$, where $L$ is the physical length of the tube.

Figure 4

Projected density of states on the CNT when the external field is (a) $0.0\mathrm{V}∕\mathrm{\AA }$ and (b) $0.4\mathrm{V}∕\mathrm{\AA }$. “$s$” indicates $s$-like $\pi$ and ${\pi }^{*}$ (doubly degenerate) levels. “$p$” indicates $p$-like doubly degenerate levels. The dashed vertical lines indicate the original Fermi level of the pristine CNT.

Figure 5

(a) Number of transfered electrons from the substrate to the CNT as a function of external electric fields pointing from the CNT to the substrate. (b) Difference between the charge density under the electric field of zero and $0.4\mathrm{V}∕\mathrm{\AA }$ along the tube axis. A positive value means the electrons gather at that position when the finite $(0.4\mathrm{V}∕\mathrm{\AA })$ electric fields are applied.

Figure 6

Snapshots of isodensity surfaces of an electronic state as time evolves in the dynamic simulations of the field emission. The state is a typical $s$-like $\pi$ state. The value of the isodensity surface is ${10}^{-8}e∕a_B^3$ and $1\mathrm{a.u.}=0.0242\mathrm{fs}$ in the time evolution.

Figure 7

Emission currents of the states under the external field of $0.4\mathrm{V}∕\mathrm{\AA }$. The points indicated by “$s\text{−}\pi$”, “$s\text{−}{\pi }^{*}$”, and “$p$” correspond to the states in Fig. 3.

Figure 8

(Color online) Field emission shape of the $s$-like $\pi$ state contributing to the most of the current under the external field of $0.4\mathrm{V}∕\mathrm{\AA }$. The image shows the projection of the charge density on the plane $10\mathrm{\AA }$ away from the tube edge at $50\mathrm{a.u.}$ in elapsed time. Red color means the maximum in the relative color-bar scale. Horizontal and vertical axes are the positions in angstroms.