Efficient and Versatile Model for Vibrational STEM-EELS

We introduce a novel method for the simulation of the impact scattering in vibrational scanning transmission electron microscopy electron energy loss spectroscopy simulations. The phonon-loss process is modeled by a combination of molecular dynamics and elastic multislice calculations within a modified frozen phonon approximation. The key idea is thereby to use a so-called $\delta$ thermostat in the classical molecular dynamics simulation to generate frequency dependent configurations of the vibrating specimen’s atomic structure. The method includes correlated motion of atoms and provides vibrational spectrum images at a cost comparable to standard frozen phonon calculations. We demonstrate good agreement of our method with simulations and experiments for a 15 nm flake of hexagonal boron nitride.

Figure 1

Schematic overview of our simulation method. The idea is to generate sets of snapshots for each energy bin, which is excited by the $\delta$ thermostat. The snapshots are subsequently used to simulate the propagation of an elastic electron wave function through the crystal using the multislice method. Thereafter the difference $⟨|\mathrm{\Psi }{|}^2⟩-|⟨\mathrm{\Psi }⟩{|}^2$ of incoherent and coherent snapshot averages of the exit wave function $\mathrm{\Psi }$ gives access to the vibrationally scattered intensity $I_{\mathrm{vib}}$. Integration over detector collection angles yields spectra, which can be integrated over energy to form images of the specimen. We distinguish in this Letter between a dark field (DF) and bright field (BF) detector positions as indicated in the central image in the lowest row. Refer to the main text for more details on the calculation process and used parameters.

Figure 2

Dark field results: in the center, the broadened vibrational electron energy loss spectra at on- and off-column beam positions indicated in the top image are plotted. These spectra display the largest difference in integrated intensity for any pair of spectra in the data set. The top image is formed by integrating the corresponding spectrum over the energy range 50–225 meV at every pixel. The two lower images are formed by integrating over 50–100 and 180–220 meV. Refer to the main text for more details on the simulated conditions. The scale bars correspond to a distance of 2 Å.

Figure 3

Same as Fig. 2, for the case of a bright field detector.