Imaging phonon dynamics with ultrafast electron microscopy: Kinematical and dynamical simulations

Ultrafast x-ray and electron scattering techniques have proven to be useful for probing the transient elastic lattice deformations associated with photoexcited coherent acoustic phonons. Indeed, femtosecond electron imaging using an ultrafast electron microscope (UEM) has been used to directly image the influence of nanoscale structural and morphological discontinuities on the emergence, propagation, dispersion, and decay behaviors in a variety of materials. Here, we describe our progress toward the development of methods ultimately aimed at quantifying acoustic-phonon properties from real-space UEM images via conventional image simulation methods extended to the associated strain-wave lattice deformation symmetries and extents. Using a model system consisting of pristine single-crystal Ge and a single, symmetric Lamb-type guided-wave mode, we calculate the transient strain profiles excited in a wedge specimen and then apply both kinematical- and dynamical-scattering methods to simulate the resulting UEM bright-field images. While measurable contrast strengths arising from the phonon wavetrains are found for optimally oriented specimens using both approaches, incorporation of dynamical scattering effects via a multi-slice method returns better qualitative agreement with experimental observations. Contrast strengths arising solely from phonon-induced local lattice deformations are increased by nearly an order of magnitude when incorporating multiple electron scattering effects. We also explicitly demonstrate the effects of changes in global specimen orientation on the observed contrast strength, and we discuss the implications for increasing the sophistication of the model with respect to quantification of phonon properties from UEM images.