Final-state correlation effects in Auger line shapes: Application to SiO2

Final-state correlation effects in Auger line shapes are considered within the cluster linear combination of atomic orbitals-molecular orbitals-configuration interaction theory with a parametrized Hamiltonian. A model problem is solved analytically to elucidate the role of final-state hole-hole correlation and to understand the localization of the holes on rather small subclusters of the system. The relationship of the correlation effects to the relative magnitudes of the one-center hole-hole repulsion $u$ and the bandwidth $\Gamma$ has been previously reported; however, this previous work has been limited to metallic single element conductors. This work extends the theory to covalently bonded insulators (and possibly semiconductors) consisting of more than one element. Application of the theory is made to the O $\mathrm{KVV}$ and Si $L_{23}\mathrm{VV}$ Auger line shapes from Si${\mathrm{O}}_2$. A high-energy shoulder at 511 eV in the O $\mathrm{KVV}$ line shape is interpreted as arising directly from correlation effects. A peak at 50 eV in the Si $L_{23}\mathrm{VV}$ line shape, its intensity significantly underestimated by the previous theory, is now accounted for; a peak at 70 eV previously suggested to be a shake satellite is now indicated also to arise from correlation effects. Both line shapes reveal a density of states primarily localized on an ${\mathrm{Si}}_2$O subcluster. The magnitude of the hole-hole repulsion on the subcluster and between neighboring ${\mathrm{Si}}_2$O subclusters is empirically determined from the Auger line shapes to be ∼ 11 and 4 eV, respectively. The oxygen $2p$ nonbonding bandwidth is estimated to be ∼ 6 eV, but in light of other theoretical and experimental results, our result is believed to be 1-2 eV too large. Reasons for our overestimate are discussed.