2D Helium Atom Diffraction from a Microscopic Spot

A method for measuring helium atom diffraction with micron-scale spatial resolution is demonstrated in a scanning helium microscope (SHeM) and applied to study a micron-scale spot on the (100) plane of a lithium fluoride (LiF) crystal. The positions of the observed diffraction peaks provide an accurate measurement of the local lattice spacing, while a combination of close-coupled scattering calculations and Monte Carlo ray-tracing simulations reproduce the main variations in diffracted intensity. Subsequently, the diffraction results are used to enhance image contrast by measuring at different points in reciprocal space. The results open up the possibility for using helium microdiffraction to characterize the morphology of delicate or electron-sensitive materials on small scales. These include many fundamentally and technologically important samples which cannot be studied in conventional atom scattering instruments, such as small grain size exfoliated 2D materials, polycrystalline samples, and other surfaces that do not exhibit long-range order.

Figure 1

Schematic of the SHeM scattering geometry, illustrating the presented measurement mode, where the detection angle $\theta$ to the sample surface normal (dashed red lines), is varied by changing the distance $z$ from the pinhole. To keep the same spot on the sample illuminated during the variation of $\theta$, it is also translated in the $x$ direction. The sample azimuthal angle $\alpha$ is varied to obtain a complete 2D reciprocal space measurement.

Figure 2

(a) Helium micrograph of the cleaved LiF (100) surface, taken with the reciprocal-space detection condition far from any diffraction peak. A suitable measurement point was then chosen in the image, indicated by the yellow dot. A series of detection angle scans were taken on the spot at different azimuthal orientations; two examples are shown in (b), where diffraction peaks are clearly evident. By taking detection angle scans across the full 360° azimuthal range, the in-plane diffraction pattern shown in (c) was built up. All azimuthal directions were measured independently and are not repeated using knowledge of the lattice symmetry. The pattern was translated by $(5.5,3.0){\mathrm{nm}}^{-1}$ so that $\mathrm{\Delta }K=0$ corresponds to where the principle axes meet. The 2D diffraction pattern (c) obtained from the measurements clearly indicates the cubic arrangement of the LiF crystal, where the diffraction peaks observed along $⟨110⟩$ have a lower intensity than those along $⟨100⟩$. The first order peaks in these directions consistently have the highest respective intensities. (d) An image taken at the reciprocal-space detection condition corresponding to the strong $(\overline{1}\overline{1})$ diffraction peak, as indicated by the white point in panel (c). Because of the strongly varying scattering distribution at the new detection condition, contrast is significantly enhanced in (d) compared to (a), revealing variations in the cleaved surface.

Figure 3

(a) Contour plot along [100] showing equipotential lines of the He-LiF potential from [19]. (b) 2D diffraction plot generated with the same method as Fig. 2, but using data calculated using a set of close-coupled equations predicting scattering probabilities, which were subsequently used in a ray-tracing framework to simulate scattered intensities from angular scans of He-LiF. The lower intensities of the diffraction peaks along $⟨100⟩$ as compared to $⟨110⟩$, are in agreement with the experimental data presented in Fig. 2.

Figure 4

Positions marked in green of the LiF sample’s tracked corner as it was rotated, with the fitted circle plotted in red and its center of rotation marked in blue. The maximum distance between the real positions of the corner and the fitted circle is $27\mathrm{\mu }\mathrm{m}$, with the inset demonstrating one of these deviations from the expected trajectory in more detail.