Electron-Beam Mapping of Vibrational Modes with Nanometer Spatial Resolution C. Dwyer, 1,* T. Aoki, 2 P. Rez, 1 S. L. Y. Chang, 2 T. C. Lovejoy, 3 and O. L. Krivanek 3,1 1 Department of Physics, Arizona State University, Tempe, Arizona 85287, USA 2 LeRoy Eyring Center for Solid State Science, Arizona State University, Tempe, Arizona 85287, USA 3 Nion Company, 11511 NE 118th Street, Kirkland, Washington 98034, USA (Received 1 June 2016; published 15 December 2016) We demonstrate that a focused beam of high-energy electrons can be used to map the vibrational modes of a material with a spatial resolution of the order of one nanometer. Our demonstration is performed on boron nitride, a polar dielectric which gives rise to both localized and delocalized electron-vibrational scattering, either of which can be selected in our off-axial experimental geometry. Our experimental results are well supported by our calculations, and should reconcile current controversy regarding the spatial resolution achievable in vibrational mapping with focused electron beams. DOI: 10.1103/PhysRevLett.117.256101 Introduction.—It has recently become possible to use high-energy electrons in a scanning transmission electron microscope (STEM) to perform vibrational spectroscopy of materials [1–3]. While more-established vibrational- spectroscopic techniques, such as Raman scattering and infrared absorption, are applicable primarily to samples having at least micrometer dimensions, a highly focused electron beam should allow mapping of the vibrational spectra of materials at nanometer, or even subnanometer, spatial resolution. Such spatial resolutions have been demonstrated for substrate sample geometries using tip-enhanced Raman scattering in scanning tunnelling microscopy [4,5]. Vibrational spectroscopy in the STEM, on the other hand, would enable nanometer-scale mapping of vibrational modes, e.g., due to interfaces or defects, in a broad class of freestanding materials, free of thick substrates. However, recent analyses of the scattering physics of electron-induced vibrational excitations [6–12] have reached contradictory conclusions about the attainable spatial resolution. Some of them have claimed that sub- nm, and even atomic, spatial resolution should be achiev- able [6,8], while others have stressed that, in practice, the spatial resolution will remain limited by the long-ranged electron-dipole interactions [7]. Thus far, the STEM experi- ments have supported the latter view, achieving spatial resolutions of only several tens of nm at best, a far cry from the sub-nm resolution routinely achieved in other forms of high-energy electron-beam imaging and spectroscopy. Here, we demonstrate better than 2 nm spatial resolution in vibrational spectroscopy using a focused electron beam, advancing current state-of-the-art STEM results [1–3] by at least 1 order of magnitude, and several orders of magnitude better than that permitted with the more-established vibra- tional spectroscopies. We achieve this using an off-axial beam geometry that isolates the localized vibrational scattering from the delocalized dipole scattering, hence vastly improving the spatial resolution, extending it into the one-nanometer regime. Good quantitative agreement between our experimental results and our electron scatter- ing calculations strongly supports our conclusions. Our results open the door to nanometer-scale electron-beam mapping of vibrational modes as a powerful tool for nanomaterials analysis. Dipole vs localized vibrational scattering.—For our demonstration, we use hexagonal boron nitride, a polar dielectric exhibiting mixed covalent-ionic bonding. The vibrational properties of h-BN make it very well suited to the present study of spatial resolution. A first-principles calculation [13] of the material’s vibrational (phonon) mode energies is shown in Fig. 1. These calculations agree with recent experimental data [18] and other calculations in the literature [19,20]. The four highest-energy optical modes are of particular interest here. These are modes in FIG. 1. Density-functional-theory calculation of h-BN’s vibrational (phonon) energies for major symmetry paths in the Brillioun zone basal plane. Long-wavelength (cyan) and shorter-wavelength vibrations (magenta) are indicated. PRL 117, 256101 (2016) PHYSICAL REVIEW LETTERS week ending 16 DECEMBER 2016 0031-9007=16=117(25)=256101(5) 256101-1 © 2016 American Physical Society