Imaging High-Energy Electrons Propagating in a Crystal

It has recently become possible to focus a beam of high-energy electrons to a spot smaller than an atom, with vast potential for the study of condensed matter. We devise an experiment that can image, with subangstrom resolution, the distribution of such an electron beam as it scatters within an atomic lattice. Our experiments reveal the acute sensitivity of the scattered electron distribution to 0.1 Å shifts of the impact point. Scattering due to plasmon excitations is also examined. Implications for the study of the atomic and electronic structure of condensed matter are discussed.

Figure 1

Schematic of the experimental configuration. An electron beam, smaller than an atom, is focused onto or between atoms in gold. The resulting distribution of scattered electrons inside the gold crystal is imaged in the image plane revealing features at subangstrom resolution. (The image is recorded with the charge-coupled device). An annular RSTEM image can be formed by scanning this beam and recording the intensity reaching the annular detector at each scan position.

Figure 2

Imaging the intensity distribution in real space of an electron beam after scattering from gold (140 Å thick, $⟨111⟩$ orientation). [Circles mark atomic positions and correspond to 1 Å diameter. a)–(c) are scaled equivalently.] (a) Annular RSTEM image used to “map” atomic positions. Arrow marks the path along which the incident beam was scanned, as labeled in (b). (c) Intensity distribution in real space of the electron beam after scattering from gold, corresponding to the incident beam positions (1)–(10) in (b). (d) Number of electrons counted by the annular detector in real space at each incident beam position.

Figure 3

Computed electron intensity distribution in real space of an electron beam after scattering from gold in the $⟨111⟩$ orientation, calculated using parameters consistent with the experimental conditions in Fig. 2. Panels (a)–(c) correspond to different incident electron beam positions, as marked by the red spot, being the sixfold, threefold, and twofold symmetry sites, respectively. Circles indicate atomic positions and are 1 Å in diameter.

Figure 4

Intensity distribution in real space of the electron beam after scattering from the 29 eV plasmon in $⟨100⟩$ ${\mathrm{LaB}}_6$. Panels (a)–(c) correspond to the incident beam positions indicated in the schematic (d) which shows the ${\mathrm{LaB}}_6$ structure in the $⟨100⟩$ projection. Dark gray (red) circles indicate lanthanum atoms, light gray (yellow) circles indicate boron atoms. The arrow in each figure marks the $⟨100⟩$ direction.