NOVEL METHOD FOR THE EXPERIMENTAL DETERMINATION OF STEP ENERGIES

The free energy of steps of monatomic height is one of the most important energetic parameters in the physics of crystalline solids. It controls the size of facets in the equilibrium shape of crystals and the curvature of rough surfaces [1]. It is likewise an important parameter in the stability of vicinal surfaces against step bunching transitions [2,3] and transitions involving a reconstruction of the surface [4,5]. Furthermore, the minimization of the step energy is the driving force for coarsening processes on surfaces, e.g., for the growth of larger islands at the expense of smaller ones, the decay of mounds during and after epitaxial growth [6–13], and for the decay of nanostructures in general. Last but not least, the equilibrium shape and the shape fluctuations of monatomic high islands (2D islands) on surfaces, and thereby also the migration of entire islands on surfaces, depend on the step-free energy [14–16]. The ubiquity of the step-free energy as the controlling parameter in many phenomena should provide ample means to determine its magnitude. This is, however, not so. The traditional way to determine the step energy from the equilibrium shape of crystals is barred with many nontrivial experimental difficulties and additionally requires as an input the free energy of the flat surfaces [17,18], which in turn is not known very accurately. The step-free energy derived from the chemical potential of islands as observed in Ostwald ripening of islands appears to be unrealistically high for reasons hitherto not understood [12]. An average step energy was recently calculated from the size dependence of the Brownian motion of islands using a continuum model [15] for the step fluctuations [19]. Possible systematic errors of the method are not known presently. Relying entirely on first principles theoretical calculation is likewise not a remedy to the situation as it seems that different respectable approaches [20,21] yield rather different results [0.38 and 0.26 eV atom for B steps on Cu(111), respectively]. While the determination of the absolute value of the step-free energy is a problem, the variation of the step energy as a function of the orientation can be measured straightforwardly from the equilibrium shape of 2D islands. Michely et al., e.g., have determined the ratio of the energies of A and B steps on Pt(111) from island equilibrium shapes [22]. Since 2D islands have no facets at finite temperature the complete orientational dependence of the step-free energy is obtained from the equilibrium shape using an “inverse” Wulff plot [1].