Phonon Spectroscopy at Atomic Resolution

Advances in source monochromation in transmission electron microscopy have opened up new possibilities for investigations of condensed matter using the phonon-loss sector of the energy-loss spectrum. Here, we explore the spatial variations of the spectrum as an atomic-sized probe is scanned across a thin flake of hexagonal boron nitride. We demonstrate that phonon spectral mapping of atomic structure is possible. These results are consistent with a model for the quantum excitation of phonons and confirm that $Z$-contrast imaging is based on inelastic scattering associated with phonon excitation.

Figure 1

(a) Schematic showing four detector positions labeled BF, $A$, $B$, and $C$ relative to a simulated convergent-beam electron diffraction pattern for hexagonal BN in [0001] orientation and of 15 nm thickness, as used in the experiments. The solid black circle shows the extent of the bright-field disk (31.5 mrad semiangle), while the inner angle of a typical HAADF detector is indicated by a solid white line at 70 mrad semiangle. For practical reasons, the optical conditions used for these experiments resulted in a slightly wider (100 mrad) HAADF inner angle, indicated by a dotted white circle. The detector positions are achieved by deflecting the beam post specimen. (b) Energy-loss spectra averaged over the detector at three of the positions indicated in (a), using otherwise identical acquisition parameters, normalized by total acquisition time and scaled as indicated.

Figure 2

(a) Low-loss spectra for the detector in position $C$ averaged over probe positions on the atomic columns, labeled “columns” (blue squares on the inset on left) and in the holes between the columns (red squares), labeled “holes.” The whole zero-loss peak is shown in the inset on the right. (b) The same as (a) except that the detector is now in the BF position. Energy-loss ranges used for mapping are indicated in both (a) and (b) by shaded areas.

Figure 3

(a) EELS intensity maps formed by signal integration over the energy windows indicated in Fig. 2 (detector at position $C$) and (b) for the energy windows indicated in Fig. 2 (detector in BF position). Scale bars: 2 Å.

Figure 4

(a) Simulations of the CBED pattern tilted to effectively put the detector, in the forward direction, in position $C$; of the spectrum map into the 22 mrad detector; and of the image into the ADF detector. (b) The same as (a) but the detector is in the BF position. The contrast is defined in terms of the maximum and minimum intensity by $(I_{\max }-I_{\min })/(I_{\max }+I_{\min })$. Scale bars: 2 Å.