Thermalization dynamics of primary and secondary electrons in metals

Abstract

Collisional relaxation of high-energy primary electrons (PEs) and generation of secondary electrons (SEs) in a metal are simulated self-consistently by the quantum Boltzmann equation taking into account dynamic screening. An efficient scheme to evaluate the multi-dimensional integral in the collision term is introduced, which enables one to compute time evolutions of nonequilibrium energy distribution functions over an energy range up to a few keV until the whole system reaches thermal equilibrium. Numerical results reveal that rapid energy loss of PEs by plasmon excitation occurs in an early stage, followed by a cascade excitation of SEs near the Fermi level. The overall energy distribution eventually converges to the equilibrium Fermi distribution of partially degenerate electron gas, corroborating the quantum-mechanical H-theorem; time evolutions of the corresponding nonequilibrium entropies are also simulated. The electron temperature and total number of SEs in the final state are consistent with thermodynamic values predicted from the initial energy density of PEs. The number of SEs excited during an early stage (initial 10 fs) turns out smaller for higher PE energies; this feature would bear relevance to an estimation of transient radiation damage in a metallic sample irradiated by an intense femtosecond x-ray laser pulse.