Intense femtosecond (fs) photoexcitation of semiconducting materials can lead to the generation of high densities of charge carriers, shifting the Fermi-Dirac distribution into a highly non-equilibrium state. The relaxation pathways available to this new state are numerous, and the associated mechanisms can be intermingled and highly non-linear . One particular pathway is via the excitation of highly-coherent, low-frequency acoustic phonons that propagate outward from the photoexcited zone . For initially high carrier concentrations, this behavior is attributed either to a time-varying deformation potential or a time-varying thermoelastic effect, depending upon the band structure and the nature of photoexcitation. Importantly, these two regimes can be differentiated temporally, depending upon the carrier densities generated; at relatively high concentrations, Auger recombination begins to further augment the time-varying thermoelastic effect. Indeed, a material as simple as undoped germanium (Ge) displays several intriguing transient behaviors within the context just described. For example, the excited carrier-density lifetimes can be quite long and can significantly overlap with the electron-phonon coupling times, thus heavily interweaving the various relaxation pathways [3,4]. Further, intense fs photoexcitation can lead to the generation of hypersonic electron-hole plasma waves, the nature of which may evolve into coherent acoustic-type oscillatory behaviors . This suggests such behaviors may manifest as coherent, transient lattice-strain effects, the properties of which are directly linked to the hypersonic plasma waves .
Here, we describe our efforts to link the photoexcited charge-carrier dynamics in single-crystal Ge to the lattice degrees of freedom using fs electron imaging in an ultrafast electron microscope [7,8]. By leveraging the extreme sensitivity of local diffraction contrast to changes in reciprocal-lattice orientation, we are able to directly image the generation and the evolution of highly-coherent acoustic phonons initially propagating at hypersonic velocities in the plane of the crystal . While each phonon wavefront propagates with a constant velocity, the entire wave train displays a time-varying phase-velocity dispersion, relaxing from initial velocities greater than 35 nm/ps to the Ge longitudinal speed of sound (5 nm/ps) within one nanosecond. Analysis of the dispersion curves expected for symmetric dilatational and asymmetric flexural modes indicates the dynamics match most closely to a single, low-order symmetric mode. Interestingly, this symmetric mode appears to give rise only to increased scattering for each wavefront, indicating the reciprocal-lattice shapes (approximated here as rods) are only brought further onto the Ewald sphere rather than being equally distributed during the oscillation. Further, by using a plasma lensing technique , we find that the onset of the first phonon wavefronts are delayed by tens of picoseconds or more, relative to the moment of fs photoexcitation. Combined, these anomalous behaviors provide tantalizing hints of charge-carrier-dominant dynamics, rather than lattice deformations caused by coherent phonons, as producing the observed ultrafast contrast behaviors. Those possibilities are explored here.
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