Theory of phonon effects on photoemission spectra

Some important phonon effects observed in core and valence level photoemission spectra are discussed on the basis of nonequilibrium Green’s function theory. This theoretical framework allows us to incorporate phonon effects, such as Debye–Waller (DW) factors, Franck–Condon (FC) factors and electron–phonon interactions in a natural way. For the description of the electron–phonon interaction the phonon part of the screened Coulomb propagator plays a crucial role. We separately discuss those effects on photoemission spectra from localized core and extended valence levels. In case of core level excitation, taking into account the core-hole effects on phonon spectra, we can relate the Franck–Condon factors to the electron–phonon interaction, which are interpreted as the intrinsic phonon losses. Phonon losses during propagation in solids can be described by loss Keldysh diagrams similar to those for the plasmon losses, which are closely related to extrinsic losses. In case of extended valence excitation we show that the phonon effects destroy the interference between photoelectron waves in high-energy region, which enhances specific features in the X-ray photoelectron diffraction as observed before. In contrast the DW factors play a very minor role in low energy (UPS) region, and we can obtain detailed information on band structures by the use of angle-resolved measurements.