Theory of Auger electron and appearance-potential spectroscopy from solids with partially filled valence bands: Effects of valence-band–core interaction

CVV Auger electron and appearance-potential spectra of solids are well known to exhibit strong satellite features depending on the ratio of on-site Coulomb interaction among the valence-band electrons U and the width of the free Bloch band W. We present a theory that additionally includes the effects of the Coulomb interaction between the valence-band electrons and the core electrons ${\mathit{U}}_{\mathit{c}}$. The spectra are influenced by the screening of the core hole in the initial state for Auger electron spectroscopy (AES), the sudden response of the valence-band electrons after the destruction of the core hole and, for appearance-potential spectroscopy (APS), by the scattering at the core hole in the final state. These effects become important especially for systems with partially filled energy bands. For APS, however, the ${\mathit{U}}_{\mathit{c}}$ interaction already yields nontrivial effects for the limiting case of a completely empty valence band. The localized core hole implies a breakdown of translational symmetry in the distribution of the valence-band electrons, which renders the calculation more difficult. But, extending the theory to finite temperatures, we will show that the translational symmetry may be reestablished in a formal way. Both the AES and APS intensities are directly related to a proper three-particle spectral density that exactly reflects the crystal periodicity. Within the framework of the single-band Hubbard model, which is extended to include the ${\mathit{U}}_{\mathit{c}}$ interaction, we calculate the three-particle spectral density in a generalized ladder approximation. The ${\mathit{U}}_{\mathit{c}}$ interaction is treated by means of perturbation theory. We develop the theory for the zeroth- and first-order contributions and look at the interesting limiting cases of a completely filled and empty valence band.