Spatial Resolution in Aloof EELS

An important question in electron microscopy is: where does our information come from? The simple answer “where the recorded electrons penetrate the sample” is not even approximately true in aloof-beam EELS, where a focused probe of electrons is placed a distance b (the impact parameter) beyond the edge of a specimen. Aloof measurements are useful for investigating plasmonic modes in small particles and for extracting information from beam-sensitive specimens with minimal radiation damage [1–3]. Dipole-mode inelastic scattering can be simulated using finite-element methods, e.g. COMSOL. Calculated spectra for vibrational energy losses in a 100nm-thick SiO2 slab are shown in Fig. 1. The spectra contain a peak at about 155 meV, representing a bulk polariton mode, a peak around 140 meV representing excitation at the (coupled) top and bottom surfaces, and a peak between 135 and 140 meV arising from a mode localized at the edge of the sample [4]. Figure 2 shows the calculated polarization P(r), which is seen to have approximately cylindrical symmetry about the probe axis (r = 0). As seen in Figure 3, the depth-integrated polarization is roughly proportional to 1/r for both aloof and transmission geometry. This is consistent with a transmission-mode 1/r2 point-spread function for Coulomb delocalization [3] if contributions to the EELS signal are proportional to polarization/r [5]. Integrating P/r over distance x (= r − b) from the edge of the sample, the width x50 containing 50% of the signal is found to be approximately b (see Fig. 4), indicating that the aloof spatial resolution is (within a factor of 2) equal to the impact parameter of the probe. The y-axis resolution is about a factor of two worse and the edge-surface mode is slightly more delocalized (see Fig. 4), consistent with a smaller angular width of the scattering [5]. These ideas suggest that (for a given probe current) the radiolysis sensitivity in aloof mode might be proportional to 1/b2, which would be consistent with the observation that fading of the C=O vibrational-mode signal from guanine was measurable at b = 10 nm but not at b = 30 nm [4]. However, this b-dependence needs to be verified experimentally. Although the examples given here relate to vibrational-mode energy losses, similar principles apply to dipole-mode electronic excitation (including plasmon losses), but with length scales typically a factor of ten smaller. For inner-shell energy losses or vibrational-mode impact scattering, the delocalization distance approaches atomic dimensions, making aloof-beam EELS impractical. In the case of small particles, all of the excitations become standing waves and the EELS signal comes predominantly from within a single particle. COMSOL calculations of the energy-loss spectra for small aloof probes at different distances b from the edge of a 100nm-thick SiO2 slab. The uppermost spectrum is for the transmission geometry, with an electron probe far from the edge of the specimen. Polarization P within a 100nm slab of SiO2, due to an aloof beam (vertical arrow) of 60keV electrons located at a distance b = 100 nm from the edge, which in this example has been rounded into a hemisphere to make the geometry more realistic. Depth-integrated polarization ∫ P(r) dz as a function of distance r from the electron probe, for b = 10 nm (yellow or red line), b = 100 nm (gray), and transmission mode (blue). Median distance x50 into the sample, containing 50% of the energy-loss signal at y = 0, as a function of impact parameter, for several values of (SiO2 vibrational-mode) energy loss.

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