Advances in Momentum Resolved EELS

Abstract

Vibrational modes affect conduction of heat and sound in solids, and are altered by local structure such as defects and interfaces. Angle Resolved Electron Energy Loss Spectroscopy (AR-EELS) within the Scanning Transmission Electron Microscope (STEM) provides a way to probe the four dimensional phonon band dispersion relation, S(qx, qy, qz, ω), with nanometer spatial resolution [1]. The technique has benefited from significant advances in recent years, including increased efficiency by parallel acquisition using slot-shaped spectrometer entrance apertures and the introduction of low-noise high dynamic range direct detectors for EELS [2]. Together with high-brightness electron sources, brightness-preserving monochromators, and next-generation spectrometers, these improvements have reduced the acquisition time for phonon band dispersion diagrams from hours [3] to minutes [2]. Even with these advances, phonon band structure measurement in the STEM has been limited to ideal systems containing light elements with Z=5-7 (e.g. boron nitride, or carbon), where the phonon structure spans roughly 0-200 meV energy loss. Phonon band structures in materials with heavier atoms, where the energy range can be significantly smaller, have been elusive until now. Figure 1 shows a phonon band dispersion diagram acquired from silicon with probe size ~5 nm, the diffraction limit with 1 mrad illumination half-angle at 30kV. The full width of the pattern is about 65 meV. The transverse acoustic (TA) phonon branch, which rises from the energy origin at the Γ point to about 14 meV at the L point, is clearly resolved. The dispersion of the longitudinal acoustic (LA) phonon branch from 0 to ~54 meV is visible. At the L point, the splitting of the longitudinal optical (LO, ~62meV) and transverse optical (TO, ~54 meV) appears as a wide band at this energy resolution. A less intense reflection of the pattern is just visible on the gain side, showing that room temperature (kT ~25meV) thermal excitation of energy gain is significant on this energy scale. Similar to previous reports [2], the projector lenses were used to rotate and scale the diffraction pattern from the ~70nm thick Si[110] oriented sample such that a rectangular spectrometer entrance aperture , 2mm x 125um, spanned the [000] and [-111] diffraction spots (i.e the Γ-L direction in the silicon Brillouin zone). The total acquisition time was ~13 min. The energy resolution in these conditions was about 8meV full-width-at-half-maximum for the zero loss peak (ZLP), and the current was ~2pA. High angular resolution at high current introduces significant and competing demands on the instrumentation, which tend to degrade the energy resolution. Under typical operating conditions with the Nion UHERMES system used here, 5 meV energy resolution at 30kV is routine. Resolving the phonon band dispersion diagram in a variety of materials in the STEM is the first step toward a larger goal of resolving the effect of local structure on vibrational modes [4]. Adding spatial dimensions to the acquisition places additional demands on the system, especially increasing the current so that the signal can be collected in a reasonable time without compromising the energy resolution too https://doi.org/10.1017