Scale-bridging Simulations of Electronic Relaxation from Master Equation with first-principles-derived Rates

The lifetime of excited electrons in metals is limited by both electron-electron and electron-phonon scattering. Quantum well states (QWS) in thin metals films offer an ideal probing ground for exploring the competition between both relaxation mechanisms. We performed first-principles density-functional (DFT) calculations adressing the electronic band structure of few-atomic-layer Pb films on Si(111). In addition, phonon spectra and matrix elements for electron-phonon coupling within deformation potential theory were obtained from DFT calculations. This enables us to calculate state-specific rate constants for the electron-phonon scattering in particular QWS. The contribution of impact ionization processes to the lifetime can be estimated from the imaginary part of the electronic self-energy calculated in the GW approximation. By combining both channels and numerically solving rate equations for the electronic occupations coupled to a phononic heat bath, we are able to follow the dissipation of the electronic excitation energy to the Pb lattice vibrations over long time. The time scales extracted from the simulations are compared to experimental data from time-resolved pump-probe experiments.