PERTURBATION-THEORY OF DIFFUSE RHEED APPLIED TO ROUGH SURFACES - COMPARISON WITH SUPERCELL CALCULATIONS

We present a thorough investigation of the conditions under which the perturbation theory of diffuse RHEED [Phys. Rev. B 48, 8345 (1993)] (d iffuse scattering treated as the transition between states in thr peri odic part of the potential) can be used for the evaluation of experime ntal diffuse scattering data from occupational disorder (e.g., steps). Such an investigation is desirable because this method solves the con figuration problem, i.e., the presence of many statistically varying d isorder configurations, within the scope of a dynamical theory. We hav e carried out comparisons with rigorous supercell calculations for str eak profiles due to bilayer steps upon a Si(100) surface. The general trend of the results obtained is supported by some simple analytical c onsiderations. An analytical expression is derived that predicts the a pproximate error made in the perturbation approach compared to an exac t treatment. Besides general features, such as defect concentration an d the strength of the atomic potential, the important structural quant ity that determines the quality of the perturbation approach is the co rrelation length of the disorder along the incident beam azimuth. If t his length is sufficiently small, perturbation theory works well and i s independent of the diffraction condition. Otherwise, the applicabili ty of perturbation theory depends on the diffraction condition. The ph ysics behind conditions suitable for perturbation theory to work, as w ell as their experimental realization, is discussed.