Picosecond phase-velocity dispersion of hypersonic phonons imaged with ultrafast electron microscopy

Here, we describe the direct imaging - with four-dimensional ultrafast electron microscopy - of the emergence, evolution, dispersion, and decay of photoexcited, hypersonic coherent acoustic phonons in nanoscale germanium wedges. Coherent strain waves generated via ultrafast in situ photoexcitation were imaged propagating with initial phase velocities of up to 35 km/s across discrete micrometer-scale crystal regions. We observe that, while each wave front travels at a constant velocity, the entire wave train evolves with a time-varying phase-velocity dispersion, displaying a single-exponential decay to the longitudinal speed of sound (5 km/s) and with a mean lifetime of 280 ps. We also find that the wave trains propagate along a single in-plane direction oriented parallel to striations introduced during specimen preparation, independent of crystallographic direction. Elastic-plate modeling indicates the dynamics arise from excitation of a single, symmetric (dilatational) guided acoustic mode. Further, by precisely determining the experiment time-zero position with a plasma-lensing method, we find that wave-front emergence occurs approximately 100 ps after femtosecond photoexcitation, which matches well with Auger recombination times in germanium. We conclude by discussing the similarities between the imaged hypersonic strain-wave dynamics and electron/hole plasma-wave dynamics in strongly photoexcited semiconductors.