THE ROLE OF STEP COLLISIONS ON DIFFRACTION FROM VICINAL SURFACES

To assist efforts to extract information about the energetics of step structure from measured diffraction profiles, we have used Monte Carlo simulations to compute correlation functions and diffraction profiles of the terrace-step-kink model of vicinal surfaces. We compare the results to the predictions of simple scaling arguments. We concentrate on the temperature dependence of correlations along the average step-edge direction. These correlations are well-known to reflect the (sometimes strong) temperature dependence of the mean distance between step-step collisions, y(coll). Our calculations show explicitly how y(coll) governs the behavior of correlations parallel to the step edge. For example, only at length scales larger than y(coll) can one observe the well-known logarithmic divergence in surface height correlations, and the consequent power-law lineshape of the structure factor. (For large momentum transfer (short length scales), we find a Lorentzian component in the structure factor with a width proportional to the mean collision distance.) We discuss the feasibility of estimating kink energies from the temperature dependence of diffraction profiles. By scaling the profiles at different temperatures and/or misorientations, one can extract variations in y(coll) and thence the step-edge stiffness. Finally, we discuss how energetic interactions between steps influence diffraction features such as line shapes, spot anisotropies, and scaling properties. Comparison is made with recent experiments on Si(111).