Effects of hole scattering on two-photon photoemission from metal surfaces

Abstract

By the nonequilibrium Green function method, we investigate the effects of the inelastic scattering of photoexcited holes at metal surfaces on the two-photon photoemission (2PPE) spectra. The 2PPE spectra of a metal surface we study show two peaks attributed to an occupied localized state $(2\ensuremath{\omega}$ peak) and an unoccupied localized state $(1\ensuremath{\omega}$ peak). Energy transfer between the surface and the bulk due to the hole scattering accounts for the occurrence of the $1\ensuremath{\omega}$ peak, while it is usually considered that this peak occurs due to dephasing in macroscopic theories. As well as the $1\ensuremath{\omega}$ peak, the peak height and width of the $2\ensuremath{\omega}$ peak, which is usually considered to occur due to a direct two-photon excitation process, are affected by the hole scattering. By comparing with a macroscopic theory based on the density matrix method, we discuss the relation of the macroscopic energy relaxation time and the dephasing time with intrinsic lifetimes of the electrons and holes in detail.