Comment on “A note on surface stress and surface tension and their interrelation via Shuttleworth’s equation and the Lippmann equation” by D. Kramer and J. Weissmüller [Surf. Sci. 601 (2007) 3042]

We present the first study revealing the electronic structure and electron dynamics of the excited adatom state at the Ge ( 1 1 1 ) :Sn ( 3 × 3 ) R 30 ° surface. By the use of time- and angle-resolved photoemission spectroscopy, the normally unoccupied electronic structure of the partly empty Sn adatom can be probed. From the angle-resolved data we conclude that the adatom electrons at the Ge:Sn surface are more delocalized than at the clean Ge ( 1 1 1 ) c ( 2 × 8 ) surface. A unique pump-and-probe technique, based on a pulsed femtosecond laser-system, has also allowed us to study the recombination process of the excited state. We connect the recombination process of the excited electrons to the coherent fluctuations of the Sn adatoms. As a result we present an estimate for the time between each collective and coherent adatom flip Δ t = 9 ps , i.e. an adatom switching frequency ν sw ≈ 0.1 THz . We find that our results, contrary to scanning tunneling microscopy measurements [F. Ronci, S. Colonna, S.D. Thorpe, A. Cricenti, G. Le Lay, Phys. Rev. Lett. 95 (2005) 156101], agree very well with values extracted from molecular dynamics simulations found in the literature [J. Avila, A. Mascaraque, E.G. Michel, M.C. Asensio, G. Le Lay, J. Ortega, R. Pérez, F. Flores, Phys. Rev. Lett. 82 (1999) 442; D. Farias, W. Kaminski, J. Lobo, J. Ortega, E. Hulpke, R. Perez, F. Flores, E.G. Michel, Phys. Rev. Lett. 91 (2003) 16103].