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

Daniel X. Du,David J. Flannigan

doi:10.1063/1.5144682

Abstract

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.

Highlights

Compared to a ratio of 2.4 for the kinematic approximation, the ratio of maximum to minimum normalized counts for the dynamical model is increased to 11.8 [Fig. 3(a)]. This is in better agreement with experimentally observed contrast strengths, suggesting that the model is a better quantitative descriptor of the contrast dynamics arising from propagating acoustic phonons observed with ultrafast electron microscope (UEM) bright-field imaging.[52,58]
We have conducted both kinematical and dynamical simulations of UEM bright-field images of coherent Lamb-mode guided waves propagating through a pristine single-crystal Ge wedge specimen
Static-imaging approaches to strain fields calculated from a continuum mechanics model, we find that strain states on the order of 1% and less are readily observable as coherent contrast bands in the UEM bright-field images

Summary

INTRODUCTION

Photoexcitation of materials below the ablation threshold with ultrashort laser pulses leads to the generation of coherent acoustic phonons composed of a propagating elastic lattice distortion.[1,2,3,4] The precise nature and the behavior of these transient elastic deformations depend upon a number of factors, including the structure, composition, and morphology, as well as specimen geometry, defect density and type, and photoexcitation conditions.[5,6,7,8,9,10] As such, the observed responses can be varied and complex, with the spatiotemporal dynamics evolving over times ranging from femtoseconds to microseconds or longer. While the simulations do capture the fixed velocity and single-propagation direction of each wavefront (indicated by the dashed line), an apparent dispersion behavior emerges, as indicated by the differing slopes of the neighboring wavefronts Though this matches experimental observations,[58] it arises from an obfuscation of the peak position of the contrast, rather than an actual physical response, owing to the use of a single, nondispersive Lamb mode (see Table I). This is in better agreement with experimentally observed contrast strengths, suggesting that the model is a better quantitative descriptor of the contrast dynamics arising from propagating acoustic phonons observed with UEM bright-field imaging.[52,58] While this result is expected, the model and approach described here will be useful for quantifying the basic properties of the propagating phonon modes giving rise to the imaged lattice distortions, including energies, strain states, and symmetries. Strong photoexcitation leading to the generation of significant chargecarrier densities and associated plasma waves can produce an associated acoustoelectric effect, where lattice strain waves can effectively sweep carriers along the phonon wavefronts.[17,85–91] Owing to the dependence of the Howie-Whelan formalism on the Fourier coefficients of the electrostatic potentials in the lattice,[64] it would be interesting to consider the effect fs photoexcitation of large carrier densities in semiconductors has on the transient responses imaged with UEM

A NOTE ON THE INFLUENCE OF CHANGES IN SPECIMEN ORIENTATION

SUMMARY AND OUTLOOK