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Core-level photoemission spectra of the buckled Ge͑001͒-2ϫ1 surface taken at various energies and emission angles are analyzed, using the inelastic mean free path ͑IMFP͒ to constrain the intensities of the contributions to the 3d signal of the first two surface layers and the bulk. This ansatz successfully represents data from the clean Ge͑100͒ surface at all emission angles and photon energies. The surface core-level shifts of the up-dimer atom, down-dimer atom, and subsurface atom are then found at Ϫ442, Ϫ183, and ϩ93 meV, respectively. They are in good agreement with the final-state theoretical calculations by Pehlke and Scheffler ͓Phys. Rev. Lett. 71, 2338 ͑1993͔͒. The IMFP is 3.5Ϯ0.2 Å at 26 eV kinetic energy. Furthermore, we found that bulk and surface atoms have distinct spin-orbit splittings of 594 and 561 meV, respectively.Photoemission data from the Ge͑100͒ surface with buckled-dimer reconstruction have led to a number of divergent interpretations and conclusions. 1-4 We reexamine this subject, using data taken over a wide range of photon energies and emission angles. We develop an interpretation in which layerwise contributions are constrained by the inelastic mean free path ͑IMFP͒, and obtain the kinetic-energy dependence of the IMFP in the range from 11 to 40 eV.Resolved photoemission signals from the individual surface layers of a solid make it possible to determine the IMFP of the energetic photoelectrons, provided that the individual line intensities are not distorted by diffraction or elastic scattering. This method has been successfully applied to the alkali metals 5 and the Si͑001͒-2ϫ1 surface, 6 yielding a welldefined minimum IMFP of 4.0 and 3.25 Å, respectively, near a kinetic energy of 20 eV. Germanium is another good candidate for such a determination, because resolved photoemission signals have been obtained from the surface layer of atoms for a number of different surface orientations. We develop an interpretation of such data in which the layerwise intensities are constrained by the IMFP and emission angle.Photoemission experiments were performed at the Synchrotron Radiation Research Center in Hsinchu, Taiwan, Republic of China. Monochromatic radiation was provided by a low-energy spherical-grating monochromator. Photoelectrons were collected with a 125-mm hemispherical analyzer OMICRON Vakuumphysik GmbH in an UHV chamber with base pressure better than 3ϫ10 Ϫ11 Torr. The combined photon plus electron energy resolution for the spectra shown is about 65 meV. A clean Ge͑100͒-2ϫ1 surface was preoxidized according to the Ishizaki and Shiraki method, and annealed at a constant temperature of 550°C in the photoemission chamber. Figure 1 shows Ge 3d core-level photoemission spectra taken at various photon energies ͑left panel͒ and various emission angles at 60 eV photon energy ͑right panel͒. On cursory inspection, these spectra clearly exhibit a shoulderlike component at the smallest binding energy, which has been commonly assigned to emission from the up-dimer atoms S͑0͒u, which make up one-hal...
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