Quantitative characterization of the surface morphology using a height difference correlation function

A height difference correlation function was defined for the analysis of experimentally obtained real space images of a surface morphology. Using scanning tunneling microscope images of two different surfaces, the Si(111)-7×7 reconstruction and hyperthermally deposited thin Co films on Si(111), we demonstrate the advantages of this characterization procedure. Parameters such as the grain size and the roughness at short length scale, which are difficult to determine, especially for surfaces exhibiting randomly distributed closely packed grains, can be easily obtained from an appropriate fit of the height difference correlation function. This fit, based on the theory of kinetic roughening, simultaneously provides quantitative information on the roughness at short (Hurst parameter) and large length scales and surface in-plane correlation length of the film. The results for the overall surface roughness are consistent with the values which can be directly obtained from scanning tunneling microscope measuremen...