Ab initio Simulation of Helium-Ion Microscopy Images: The Case of Suspended Graphene

Helium ion microscopy (HIM), which was released in 2006 by Ward et al., provides nondestructive imaging of nanoscale objects with higher contrast than scanning electron microscopy. HIM measurement of suspended graphene under typical conditions is simulated by first-principles time-dependent density functional theory and the 30 keV ${\mathrm{He}}^{+}$ collision is found to induce the emission of electrons dependent on the impact point. This finding suggests the possibility of obtaining a highly accurate image of the honeycomb pattern of suspended graphene by HIM. Comparison with a simulation of ${\mathrm{He}}^0$ under the same kinetic energy shows that electron emission is governed by the impact ionization instead of Auger process initiated by neutralization of ${\mathrm{He}}^{+}$.

Figure 1

(a) Impact points $A\mathrm{\text{−}}F$ of the ${\mathrm{He}}^{+}$ ion. The numbers are the corresponding valence charge (electrons per Å), at a height of 8 Å from the graphene sheet. (b) The distribution of the valence charge density (lateral axis) plotted along the axis normal to the graphene sheet (vertical axis) for impact points $A\mathrm{\text{−}}F$. The plots shown in the panels are averaged parallel to the graphene sheet for snapshots at $t=2.9\mathrm{fs}$ when the He atom has already crossed the graphene layer and reached a distance of 14 Å, far from it. The dotted line denotes the graphene sheet, and the dashed-dotted line denotes where the charge density of the emitted electron shows a peak. (c) Contour map of the intensity profile of the secondary emitted electron as a function of the impact points of the helium ion, which produces a HIM image. The maximum and minimum values of the contour lines are shown in electrons per angstrom. The values of the contour lines are on a linear scale.

Figure 2

(a) Time evolution of the height distribution of the valence charge for the ${\mathrm{He}}^{+}$ ion colliding with site $E$ in Fig. 1a. The height of the graphene was the zero level. The change in the He atom position is indicated by arrows. The He ion lost about 88 eV in kinetic energy; however, this energy-loss introduces a very small change in the He trajectory displayed in this figure. (b) The same simulation starting with a neutral He atom.

Figure 3

(a) Comparison between valence charge density and simulated HIM image, Fig. 1a. (b) Valence charge density at graphene edge with spatial broadening factor ranging from 0.01 to 0.5 Å, the last one corresponds to the beam diameter of 2 Å. The inset is an experimentally reported HIM image at an edge of highly oriented pyrolytic graphene [34]. (c) Charge redistribution on the graphene sheet for the ${\mathrm{He}}^{+}$ ion impact point $E$ at $t=2.9\mathrm{fs}$. The impact point is denoted by the arrow. The red (thick) and blue (thin) lines are contour maps for electrons and holes, respectively. The maximum quantity of the contour lines for holes is 0.0067 $e/(\mathrm{Bohr}\mathrm{rad}{)}^3$, whereas that of the contour lines for electrons is 0.024 $e/(\mathrm{Bohr}\mathrm{rad}{)}^3$, with a linear interval of 0.000 67$e/(\mathrm{Bohr}\mathrm{rad}{)}^3$.