Ab Initio Modeling of the Interaction of Electron Beams and Single-Walled Carbon Nanotubes

Single-walled carbon nanotubes are readily observable in a scanning electron microscope, which traditional models fail to explain. We present an ab initio model to explain how the electron beam can interact with these structures despite the very small, nanoscale, interaction volume. In particular, we show how the electron beam can generate very strong secondary electron emission from the tip of a nanotube under external electric field. The approach may also be used in modeling the interaction of charged particles with nanostructures in other applications such as electron detection.

Figure 1

(a) Schematic of the device cross section. (b) Cathode (left electrode) held at $-140\mathrm{V}$. Extractor (right electrode—not visible) held at ground. Note that the negative electrode is bright due to voltage contrast. Stimulated electron emission from the tip of the nanotube has started.

Figure 2

(a) Energy levels around the Fermi level and potential barrier at the tip of the nanotube with no external field ($\mathrm{HOMO}=-5.11\mathrm{eV}$). Solid lines represent occupied orbitals, and dashed lines represent unoccupied orbitals. (b) Spatial distribution of HOMO at no external field. (c) Energy levels in the presence of an extraction field of $\sim 0.5\mathrm{V}/\AA$ along the nanotube axis. (d) Difference in charge distribution between cases with and without a $\sim 1\mathrm{V}/\AA$ external field. Darker regions correspond to a higher concentration of negative charge. Note the localization at the tip due to the field.

Figure 3

Top view of the position of the incoming electron relative to the nanotube: (a) outside the tube on the side, (b) inside the tube about $6\AA$ away from the tip, and (c) inside the tube at the center of the tip.

Figure 4

Energy levels with an external field of $\sim 0.5\mathrm{V}/\AA$ for different locations of the incoming electron: (a) outside the tube on the side, (b) inside the tube about $6\AA$ away from the tip, and (c) inside the tube at the tube tip. (d) Difference in the nanotube charge distribution between the cases where there is an incoming electron in the nanotube $\sim 6\AA$ from the tip [as in Fig. 3b] and where the incoming electron is at the center of the tip. Darker regions correspond to more negative charge.