Two-dimensional atomic correlations of epitaxial layers

We have evaluated the two-dimensional atomic pair correlation function for surfaces containing finite layers of adsorbed atoms and having a random distribution of steps. The step probabilities for the two lateral directions are mutually dependent. We employ a third-rank tensor formalism to describe the two-dimensional array of occupation probability vectors from which we derive the pair correlation function. The two-dimensional electron diffraction angular profile is obtained from this pair correlation function. We have made detailed calculations with the two-layer system as an example and found that the diffraction characteristics describe qualitatively a recent molecular beam epitaxy experiment of Si on Si(111) surface.