X-ray diffraction from amorphous Ge/Si Cantor superlattices

X-ray measurements on Cantor superlattices are reported. Indexing and scaling laws are derived for the distribution of peaks in the diffraction spectra of perfect superlattices. The peaks are indexed by three indices and the largest scaling exponents of the intensities are proportional to the fractal dimensions of the Cantor sets. The theoretical indexing scheme of the peaks is confirmed by experiment. The influence of the absorption and sample imperfections on the scaling of the peaks is investigated by means of numerical simulations. A discussion of the nature of the diffraction spectra in the thermodynamic limit is also included.