Finite size effects in crystalline/amorphous multilayers

Extended x-ray diffraction experiments have been used to investigate the structure of Pb/Ge multilayers with asmall (<15) number of bilayers. The detailed finite size structure in the x-ray diffraction profiles indicates that the multilayers are of very high quality. We present a one-dimensional kinematical calculation for these diffraction profiles, including continuous and discrete random fluctuations in layer thickness. The introduction of both continuous and discrete fluctuations causes a decrease in the number of secondary single- layer 'finite size' maximain the high angle region, in agreement with the experimental results. No quantitative agreement is reached for the low angle region, which shows more finite size structure than predicted by the fluctuations deduced from the high angle region.