The surface roughening transition was introduced by Burton and Cabrera [1] more than fifty years ago in the framework of their classic theory of crystal growth. Below the roughening temperature, TR, the surface of the crystal (in equilibrium with its own vapor) is atomically flat, while above TR it is rough because the free energy to create a step vanishes. The roughening temperature is proportional to the surface energy per atom, and, thus, any physical factor contributing to the surface energy will influence TR.
Recently, the layer-dependent electronic energy contributed by Quantum Well States (QWS) to the total energy of ultrathin metallic films with confined electrons has been shown to influence the thermal stability of ultrathin metallic films deposited on semiconducting or metal substrates, and the appearance of magic heights in the equilibrium distribution of metallic islands [2].
We report here on a real space, direct determination of the layer dependence of TR in the QWS-controlled system of Pb/Cu(111). The temperature dependence of the population of each layer is determined by in-situ variable temperature STM from 98K to 300K. Simultaneously the energy of the QWS and their spatial distribution are measured by means of STS, which allows an unequivocal identification of the layer thickness. By repeating this experiment for different initial Pb thicknesses we were able to determine their TR [3]. The layer-dependent TR shows three periods of an oscillatory behavior with bilayer periodicity plus a first beating period. By choosing Pb thicknesses (8 or 10 ML) with the last occupied QWS far below the Fermi level (-0.9 eV), the layer-dependence of TR has been exploited to stabilize at 300K films of Pb on Cu(111) that are atomically flat over lateral length scales of microns. It is worth to mention that at room temperature Pb on Cu(111) grows in the Stranski-Krastanov mode of growth.
[1] W.K. Burton and N. Cabrera, Disc. Faraday Soc. 5, 33 (1949).
[2] R. Otero, A.L. Vázquez de Parga and R. Miranda, Phys. Rev. B 55,10791 (2002).
[3] F. Calleja et al., Phys. Rev. Lett. 97, 186104 (2006)
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