A study of selected slope values in growth fronts of Au thin films

In this work, we compare the experimental slope values measured at the border of the surface protrusions that appear in growth fronts of evaporated Au films with the slope values predicted by the selected slope theories, showing a good agreement between them. For this purpose, a theoretical expression for the histogram of terrace widths at the borders of surface protrusions is developed for surfaces composed of paraboloidal-shaped elements whose shape parameters have a low statistical correlation and a high statistical dispersion between each other. The theoretical histogram was compared with those experimentally measured in Au(111) films grown on single-crystal and polycrystalline substrates. Experimental minimum values of terrace widths at the protrusion borders (that correspond to maximum slopes) obtained from the single-crystal-growth agree with those provided by the selected slope theory. An extension of the selected slope theory has been performed to interpret the additional maximum slope value observed in the polycrystalline films.