Abstract
Specially designed instrumentation for electron energy loss spectroscopy (EELS) in a scanning transmission electron microscope makes it possible to probe very low-loss excitations in matter with a focused electron beam. Here we study the nanoscale interaction of fast electrons with optical phonon modes in silica. In particular, we analyze the spatial dependence of EEL spectra in two geometrical arrangements: a free-standing truncated slab of silica and a slab with a junction between silica and silicon. In both cases, we identify different loss channels, involving polaritonic and nonpolaritonic contributions to the total electron energy loss, and we obtain the corresponding energy-filtered maps. Furthermore, we present a comparison of the theoretical simulations for a silica-silicon junction with experimental results, and we discuss the spatial resolution attainable from the energy-filtered map considering optical phonon excitations in a conventional experimental arrangement.
Highlights
Recent instrumentation advances in electron energy loss spectroscopy (EELS) in the scanning transmission electron microscope (STEM)[1] have made it possible to record energy losses in the infrared (IR) energy range.[2]
Despite the high spatial resolution that is routinely achieved in STEM imaging[11] as well as in core-loss EELS,[12] the information in low-loss EEL spectra is usually collected from an area significantly beyond the beam focus, i.e. the beam interacts via the electromagnetic (EM) field with sample areas that are far away from the actual beam position.[13,14]
The long-range interaction contributing to the EEL signal can be even more pronounced, when the beam interacts with samples supporting collective polaritonic excitations, such as plasmons or optical phonons strongly coupled with electromagnetic waves
Summary
EELS of low-loss valence and vibrational excitations can be modeled using classical electrodynamics where the sample geometry and the local dielectric properties ε(r, ω) determine the response of the system. The electron energy loss ∆E can be calculated as the work W of the induced electromagnetic field Eind coming from the beam-sample interaction against the fast moving electron:[13,26]. To calculate the EEL probability, one needs to know the z component of the induced electric field along the electron trajectory. Maxwell’s equations can be solved analytically for several simple geometrical arrangements, including an electron moving in an infinite medium,[13] along infinite interfaces[30,39] or penetrating through infinite slabs.[26,40,41,42] in more complex geometries the solution has to be obtained numerically, it is often possible to understand EEL spectral features by considering limiting geometrical cases that are solved analytically.
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