Sum rules in surface reflectivity: the case of Ge(111)-(2×1) and Si(111)-(2×1)

This paper presents experimental results of surface differential reflectivity for Ge(111)-(2×1) in the energy range 0.3–3.5 eV, obtained with light polarized with the electric vector parallel and perpendicular to the chains of the Pandey model. The process of oxidation of the clean surface is followed in the range 0–3×104 Langmuir (L). Two distinct oxidation regimes are observed: one in connection with the spectrum below 2.5 eV and a second for energies above 2.5 eV. The former shows a saturation at about 1000 L, the same exposure where the (2×1) LEED pattern disappears. The latter does not show a saturation even at 3×104 L. This different behavior demonstrates that two distinct groups of electrons are involved. Sum rules for anisotropic surfaces applied to experimental results show that the dangling-bond electrons have not exhausted their oscillator strength at 1 eV and that they contribute in a significant way to the spectrum above the bulk gap. The comparison with Si(111)-(2×1) is also discussed. The effective numbers of electrons associated with the transitions below 2.5 eV in germanium and 3.5 eV in silicon show that approximately 1.5 and 1 electron per surface atom contribute to the spectra in germanium and silicon, respectively.