Numerical and experimental study of disordered multilayers for broadband x-ray reflection

The effect of layer thickness disorder in periodic multilayers on x-ray reflectivity is investigated numerically and experimentally. We present ensemble calculations, taking into account absorption and interfacial roughness. It is demonstrated that layer thickness disorder yields band broadening and increased integrated reflectivity. For applications we concentrate on extrema of the ensembles, giving the highest integrated reflectivity. We develop global optimization methods that can also be used to generate specified reflection band structures. In a few examples, applications of the optimization methods are discussed. To illustrate the practical applicability of the methods, we compare experimental realizations to the calculation. In one case we achieve a 42% increase in integrated reflectivity in the 130 Å < l < 190 Å spectral range with respect to a periodic multilayer with its first-order Bragg peak in the center of that range. Accurate control of layer thicknesses is our main experimental obstacle.