Determination of surface step distributions on Ge using RHEED

The overwhelming feature of reflection high-energy electron diffraction (RHEED) is its extreme sensitivity to atomic steps at a surface. These steps dominate the characteristic shape of the diffracted beams and in epitaxy contribute to the time dependence of the diffracted intensity. We distinguish between two types of stepped surfaces: low-index surfaces and vicinal surfaces. A low-index surface consists of islands and islands on top of islands on top of an otherwise featureless plane. The distribution of islands on each level can be different. A vicinal surface is a surface which has been cut slightly off a low-index plane and consists of a staircase of terraces. It is easiest to treat the case where the distribution of islands on each level is identical. The diffraction from a low-index surface characteristically has a central spike due to the long-range order and a broad component due to the step disorder. The relative magnitude of these two components depends primarily on the glancing angle of incidence. A vicinal surface gives split diffracted beams, which depend more on azimuthal angle of incidence. Vicinal surfaces provide and operational measure of the coherence length of the diffractometer corresponding to the smallest observable misorientation. For our instrument, this is about 8000 Å. Once these characteristic shapes are understood one can determine the distribution of steps on a surface if certain stochastic assumptions are made.