Dynamics of Excited Electrons in Copper: Role of Auger Electrons

Abstract

Within a theoretical model based on the Boltzmann equation, we analyze in detail the structure of the unusual peak recently observed in the relaxation time in Cu. In particular, we discuss the role of Auger electrons in the electron dynamics and its dependence on the d-hole lifetime, the optical transition matrix elements and the laser pulse duration. We find that the Auger contribution to the distribution is very sensitive to both the d-hole lifetime tau_h and the laser pulse duration tau_l and can be expressed as a monotonic function of tau_l/tau_h. We have found that for a given tau_h, the Auger contribution is significantly smaller for a short pulse duration than for a longer one. We show that the relaxation time at the peak depends linearly on the d-hole lifetime, but interestingly not on the amount of Auger electrons generated. We provide a simple expression for the relaxation time of excited electrons which shows that its shape can be understood by a phase space argument and its amplitude is governed by the d-hole lifetime. We also find that the height of the peak depends on both the ratio of the optical transition matrix elements R=|M_{d \to sp}|^2/|M_{sp \to sp}|^2 and the laser pulse duration. Assuming a reasonable value for the ratio, namely R = 2, and a d-hole lifetime of tau_h=35 fs, we obtain for the calculated height of the peak Delta tau_{th}=14 fs, in fair agreement with Delta tau_{exp} \approx 17 fs measured for polycrystalline Cu.