Theory for the dynamics of excited electrons in noble and transition metals

Using the Boltzmann equation in the random-k approximation we study in detail the dynamics of excited electrons in noble and transition metals. We present results showing the role of secondary electrons, transport and electron-phonon collisions in the hot-electron distribution, the two-photon photoemission (2PPE) current and the relaxation time and compare them to experimental data for noble and transition metals. The calculated relaxation times in Cu and Au show an unusual peak at the threshold for photoexcitation from the d band in agreement with results from 2PPE experiments. The height of the peak depends linearly on the d-hole lifetime, which can be explained by tracing the origin of the peak to Auger electrons. At zero temperature, ballistic transport of electrons strongly reduces the relaxation time of low-energy electrons in the noble metals. Taking into account elastic electron-phonon scattering, the relaxation time increases significantly with rising temperature due to the randomization of electron momenta by electron-phonon collisions. This result may explain the surprising temperature dependence of the relaxation time observed in Cu. The calculations for thin films show that the confinement of excited electrons in the film reduces the transport effect and increases the relaxation time as compared to a bulk sample. For the ferromagnetic transition metals Fe, Co and Ni, the relaxation time is strongly spin dependent and the spin-averaged relaxation time is much shorter than in the noble metals. Comparison with experimental results reveals that the magnitude and spin dependence of the relaxation time are determined by the density of states as well as the, Coulomb matrix elements. It is of interest that our results shed light on the validity of the random-k approximation. This is important for extending our theory to allow for k-dependent relaxation.