Prospects of spatial resolution in vibrational electron energy loss spectroscopy: Implications of dipolar scattering

We use scattering theory to study the spatial resolution achievable in vibrational energy loss spectroscopy using a focused beam of high-energy (∼100 keV) electrons. We first outline a theory for calculating vibrational-spectroscopic images of crystalline or noncrystalline materials at nanometer spatial resolution or better (up to atomic resolution). The electron scattering and the atomic vibrations are treated quantum mechanically. Dipolar scattering from long-wavelength optical vibrations is included. We present calculated atomically resolved vibrational-spectroscopic images of a polar crystalline material (hexagonal boron nitride). For such materials, dipole scattering from long optical vibrations can give rise to a strong background in the images, which has implications for the attainable spatial resolution. We show that an annular collection geometry can significantly reduce the dipole background, thereby reducing the electron dose required to observe atomic-scale contrast.