Structure and phase transitions of the Sn/Ge(1 1 1) surface

The low-temperature phase of Sn/Ge(1 1 1) 3 × 3 is studied by means of first-principle calculations at the DFT level and in the GW approximation. Experimental STM images taken at 80 K are presented and compared with theoretical predictions. This analysis allows to give support to a geometry in which one Sn adatom is higher than the other two in the surface unit cell and excludes the complementary geometry in which two Sn adatoms are higher than the third. Concerning the very low temperature phase (T < 30 K), we show that from a purely energetic point of view a 3 × 3 geometry cannot be excluded, being almost degenerate with the 3 × 3 phase.