Evolution of non-thermal phonon and electron populations in photo-excited germanium on picosecond timescales

Abstract

We investigate the generation of phonons on picosecond timescales and the relaxation of carriers in multiple conduction band valleys of photo-excited Ge by intervalley electron-phonon scattering. Simulations of the time-evolution of phonon populations, based on first-principles band structure and electron-phonon and phonon-phonon matrix elements, are compared with data from timeresolved x-ray diffuse scattering experiments, performed at the LCLS free-electron laser facility, which measures the diffuse scattering intensity following photo-excitation by a 50 fs near-infrared optical pulse. Non-thermal phonon populations throughout the Brillouin zone are observed and simulated for times up to 10 ps. Comparing calculations and measurements show that the intensity of non-thermal x-ray diffuse scattering signal, that is observed to grow substantially near the L-point of the Brillouin zone over 3-5 ps, is due to phonons generated by scattering of carriers between the ∆ and L valleys. With inclusion of phonon decay through 3-phonon processes, the simulations also account for other non-thermal features observed in the x-ray diffuse scattering intensity, which are due to anharmonic phonon-phonon scattering of the phonons initially generated by electron-phonon scattering.

Temperature-dependent photoluminescence in Ge: Experiment and theory

“…) and ( ), respectively. The electron-phonon interaction is written as (17) where is the so-called deformation potential, and ( ) are the creation/annihilation operators for a phonon of wave vector q in branch j. Prefactors have been chosen to match the standard Conwell definitions of intervalley deformation potentials [41,56]. Theorists [57] are more likely to use the matrix element (18) where M is the mass of a Ge atom.…”

“…theoretical methods have been used to model such experiments [39,41,64,65], and in the case of Tandon et al…”

“…Thus, we find that a single transition channel per phonon is sufficient for this purpose, leading in fact to excellent agreement with experiment. For the selection of the relevant "forbidden" processes we are guided by ab initio calculations of the electron-phonon interaction in Ge [39][40][41]. In particular, the work of Tandon et al is very useful for this purpose because it presents electron-phonon matrix elements over the entire BZ [40].…”

Four-Dimensional Imaging of Lattice Dynamics using Inelastic Scattering

“…Note that we do not explicitly include the phonon scattering channels in our approach. When included, these scattering channels will increase the phonon population with time at other k points that satisfy the momentum and energy conservation 17,36,37 .…”

“…In particular, as we illustrate, our approach is well-suited to image the first-order states (i.e., emission or absorption of a single phonon at q 0 from inelastically scattering photons or disorderactivated continuum 34 ) and second-order 'squeezed' states 17 in the k-t domain (squeezed states are generated in the entire reciprocal lattice immediately after pumping the sample with a visible or near-infrared pump pulse) 17,35 . The temporal evolution and decay of the measured intensity from the change in phonon occupation at a given k point due to electronelectron, electron-phonon, and phonon-phonon scattering channels 17,36,37 are not explicitly included within the current framework. However, we consider the finite lifetime of first-or second-order states by including the phonon linewidths.…”