Integral representation of the diffracted intensity from one-dimensional stepped surfaces and epitaxial layers

An integral representation of the diffracted intensity from one-dimensional stepped surfaces and overlayers is obtained based on the single-scattering (kinematic) theory. We find exact solutions for an arbitrary terrace or island size distribution on stepped surfaces or epitaxial layers in an extremely simple manner. This theory greatly expands the utility of the kinematic analysis of electron, atom, or grazing x-ray diffraction data. A particularly useful area of application is the quantitative study of the nucleation kinetics during the epitaxial growth of thin films. Several surface ordering models are discussed in terms of this simplified approach.