Tip radius quantification using feature-size mapping of field ion microscopy images

We are presenting a rapid and straightforward approach to determine the tip radius of sharp tungsten tips characterized by field ion microscopy. The utilization of certain features with well-known dimensions on the surface of these tips around the crystallographic [111] direction allows us to increase the accuracy of the radius measurement by almost one order of magnitude in comparison to standard methods. By employing a few reasonable approximations, it is possible to derive an analytical expression for the tip radius as a function of the observed feature size on the microchannel plate and some geometric parameters of the setup. Finally, we show that field ion microscopy images can be reconstructed on the atomic level by using a perfect hemisphere with the determined radius as a starting value and a low number of modifications in the topmost surface layers. In particular, this is useful for quantifying tip-sample interactions and characterizing material properties in atomic force microscopy.

Figure 1

(a)–(c) FIM images showing three possible (111) terminations of W tips. (d)–(f) Corresponding ball models of (111) surface layers of the bcc crystal structure. The topmost, second, and third surface layers are shown in green, light gray, and dark gray, respectively. The blue lines highlight the boundaries of characteristic (111) features. In each case, the [111] direction is located in the center of the features and pointing out of the image plane. The [110] direction (not shown) is located on the left side of the shown features (indicated by white arrow) [compare to Fig. 2].

Figure 2

(a) Schematic illustration of the point-projection model. Black line: true ion trajectory; red line: radial line for crystallographic direction $\left[h^{\prime }{k}^{\prime }{l}^{\prime }\right]$; blue line: approximated straight line from projection point $P$ to spot on the screen $\left[h^{\prime }{k}^{\prime }{l}^{\prime }\right]$. (b) Field ion micrograph with indexed crystallographic directions. Red dashed box shows field of view used for the tip reconstruction in Fig. 3. Red circle displays boundary of active MCP area (diameter $d_{\mathrm{MCP}}=45\mathrm{mm}$). Note that since the position of the [111] and $\left[11\overline{1}\right]$ directions can be determined much more precisely than the [110] direction, we place this direction in the center between the other two directions. (c) Schematic illustration of the projection of a surface feature onto the imaging plane.

Figure 3

(a) FIM image ($U_{\mathrm{FIM}}=7.3\mathrm{kV}$, $p_{\mathrm{He}}=3\times {10}^{-5}\mathrm{mbar}$). Software-detected high-intensity spots highlighted with gray spheres. High-intensity spots around the $\left[111\right]$/$\left[11\overline{1}\right]$ termination are shown with green spheres. Blue line displays the boundary of observed $\left(111\right)/\left(11\overline{1}\right)$ features. Observed feature size $s_{\mathrm{feat}}$ for $\left(111\right)$ termination and MCP scale shown with white bar. (b) Superposition of reconstructed point-projection image and FIM image. Only kink site atoms with seven or more missing (nearest/second-nearest) bonds were considered for the projection [48]. Projected atoms with a high-intensity spot at a distance smaller than the spot radius of (a) are shown in dark green. (c) Ball model showing deviation between reconstruction and perfect sphere with removed/added atoms shown in white/green color and atoms part of perfect sphere shown in gray color, respectively. For the ball model, a radius of 5.25 nm was used, which is the closest value to the fitted radius from the feature-size mapping method that results in the daisylike (111) surface feature.

Figure 4

(a),(b) Relative deviation between observed and calculated feature size as a function of tip radius $r$ and tip-MCP distance $L$. (b) Zoom into smaller radius window. (c) “Best-fitting radius” as a function of tip-MCP distance $L$ and MCP size $d_{\mathrm{MCP}}$. Values for the $\left[111\right]$/$\left[11\overline{1}\right]$ directions are shown as empty/filled symbols, respectively. Gray dashed lines mark the expected radius window for $L=50\pm 2\mathrm{mm}$ and $d_{\mathrm{MCP}}=45\pm 4.5\mathrm{mm}$.