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

F. Murphy‐Armando, Éamonn Murray+4 more|arXiv (Cornell University)|Nov 27, 2019

Advanced Electron Microscopy Techniques and Applications4 citations

TL;DR

This study combines first-principles calculations and time-resolved x-ray diffuse scattering experiments at the LCLS to model non-thermal phonon and electron dynamics in photo-excited germanium on picosecond timescales. It identifies intervalley electron-phonon scattering between Δ and L conduction band valleys as the dominant source of non-thermal phonons near the L-point of the Brillouin zone, with simulations matching experimental data without adjustable parameters.

ABSTRACT

We investigate from first-principles theory and experiment the generation of phonons on picosecond timescales and the relaxation of carriers in multiple conduction band valleys of photo-excited Ge by inter-valley electron-phonon scattering. We provide a full description of the phonon and electron relaxation dynamics without adjustable parameters. 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 time-resolved x-ray diffuse scattering experiments, performed at the LCLS x-ray free-electron laser facility, which measures the diffuse scattering intensity following photo-excitation by a 50 fs near-infrared optical pulse. Comparing calculations and measurements show that the intensity of the 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 $Δ$ and L valleys. Non-thermal phonon populations throughout the Brillouin zone are observed and simulated from first principles without adjustable parameters for times up to 10 ps. 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.

Motivation & Objective

• To understand the microscopic origin of non-thermal phonon populations in photo-excited germanium observed via time-resolved x-ray diffuse scattering.
• To resolve the dynamics of electron and phonon relaxation across multiple conduction band valleys (Γ, Δ, L) on picosecond timescales.
• To develop a first-principles simulation framework that captures energy and momentum conservation in electron-phonon and phonon-phonon scattering without adjustable parameters.
• To explain the experimentally observed gradual increase in diffuse scattering intensity near the L-point of the Brillouin zone over 3–5 ps.

Proposed method

• Employed first-principles band structure and electron-phonon coupling matrix elements derived from density functional theory.
• Used adaptive k-point grids to resolve scattering processes in small, localized regions of the Brillouin zone, particularly around Δ and L valleys.
• Formulated coupled rate equations for electron and phonon populations, incorporating inter- and intra-valley electron-phonon scattering and 3-phonon anharmonic decay.
• Implemented a tetrahedron-based integration scheme with energy-conserving weights to compute scattering kernels and phonon populations across momentum space.
• Calculated the time-dependent x-ray diffuse scattering structure factor using simulated phonon populations for direct comparison with LCLS experimental data.
• Enforced energy conservation in scattering processes by assigning weighted contributions to tetrahedral vertices based on proximity to the energy-conserving surface.

Experimental results

Research questions

• RQ1 What is the microscopic origin of the non-thermal phonon population observed near the L-point of the Brillouin zone in photo-excited Ge?
• RQ2 Why does the diffuse x-ray scattering intensity near the L-point grow gradually over 3–5 ps instead of immediately after photo-excitation?
• RQ3 How do intervalley electron-phonon scattering processes between Δ and L conduction band valleys contribute to phonon generation and relaxation?
• RQ4 To what extent can first-principles simulations reproduce the full time evolution of non-equilibrium phonon and electron populations without adjustable parameters?
• RQ5 What role do 3-phonon anharmonic processes play in shaping the observed non-thermal features in the x-ray diffuse scattering intensity?

Key findings

• The non-thermal phonon population near the L-point is primarily generated by intervalley electron-phonon scattering between the Δ and L conduction band valleys.
• The growth of the diffuse scattering intensity near the L-point occurs over 3–5 ps due to a slow scattering process with a weak matrix element and delayed onset, as electron populations first accumulate in the Δ and L valleys.
• Simulations based on first-principles parameters reproduce the experimental x-ray diffuse scattering intensity with excellent agreement, without any adjustable parameters.
• Phonon-phonon scattering via 3-phonon processes accounts for additional non-thermal features in the x-ray signal, such as broadening and asymmetries in the scattering intensity.
• The use of adaptive k-point grids and tetrahedron-based energy-conserving integration enables accurate modeling of localized scattering processes critical to non-equilibrium dynamics.
• Energy conservation in scattering is rigorously maintained through a weighted averaging scheme over tetrahedral vertices, ensuring physical consistency in the simulation.