Determination of the Sn $4\mathit{d}$ Line Shape of the Sn/Ge(111) $\sqrt{3}\times \sqrt{3}$ and $3\times 3$ Surfaces

The Sn $4d$ line shapes of the $\mathrm{Sn}/\mathrm{Ge}\left(111\right)$ $\sqrt{3}\times \sqrt{3}$ and $3\times 3$ surfaces are currently under debate. By employing LEED, core-level, and valence band spectroscopy we have been able to determine the correct Sn $4d$ line shapes for these surfaces. Contrary to a recent study we conclude that the majority of the earlier reports present line shapes close to the correct ones. At 70 K we identify three $4d$ components in the $3\times 3$ spectrum, two of which are identified with the two types of Sn atoms in the $3\times 3$ cell. The third component is attributed to Sn atoms surrounding Ge substitutional defects.