Discrete and continuous disorder in superlattices

We have derived a general diffraction relation for crystalline-crystallinesuperlattices including discrete fluctuations on the number of atoms in a layerand continuous fluctuations on the interface distance, both of a Gaussian type.We show that discrete fluctuations can markedly increase the linewidth ofhigh-angle (large-/ital q/) diffraction peaks in lattice-mismatched systems.Moreover, we show that this line broadening increases strongly with increasinglattice mismatch and prove that these fluctuations on lattice-matched systemssuch as semiconductor superlattices are difficult to detect by high-anglediffraction techniques. These results have serious implications for theclassical interpretation of x-ray diffraction from superlattices regarding thedetermination of elastic strains and the reconstruction of compositionprofiles.