LINE-SHAPE ANALYSIS OF HIGH-RESOLUTION X-RAY-DIFFRACTION SPECTRA OF FINITE-SIZE THUE-MORSE GAAS-ALAS MULTILAYER HETEROSTRUCTURES

We present a detailed and thorough theoretical and numerical line shape analysis of high resolution X-ray diffraction spectra of Thue-Morse GaAs-AlAs superlattice heterostructures having finite size (2(n) layers), which fully confirms the essentials of the preliminary analysis of previous work [1]: Most of the peaks are labeled by the irreducible rationals k/(3.2(m)), k and m integers, in convenient units, the dependence of their intensity on sample size is governed by exponents alpha(n)(q), 0 < alpha(n)(q) < 2 and the diffraction spectrum retains the essential properties of a singular continuous measure. The effects of instrumental parameters is taken into account, in particular detector resolution effects. Furthermore we investigate the effects on the diffraction spectrum of MBE deposited layer roughness, represented by a random fluctuation of layer thickness.