X-RAY-DIFFRACTION SPECTRA OF DETERMINISTIC NONPERIODIC STRUCTURES - DYNAMIC VERSUS KINEMATICAL THEORY

Layered systems (e.g., semiconductor superlattices) with a deterministic nonperiodic structure exhibit characteristic lengths at all scales, therefore their properties are especially interesting in the infinite limit. X-ray-diffraction spectra of such systems are usually analyzed in terms of their Fourier transforms, i.e., within the kinematical theory of scattering. The diffraction pattern of an infinite lattice, though, is rigorously described only by the dynamical theory of scattering which, in particular, takes multiple reflections and extinction into account. As an example, the diffraction pattern of the Thue-Morse lattice is studied theoretically in the infinite limit. The results of high-resolution x-ray diffraction measurements on a GaAs-AlAs Thue-Morse superlattice are presented and analyzed. Photoluminescence and photoluminescence excitation spectra of the same structure are also discussed.