Modeling Multilayer X-Ray Reflectivity Using Genetic Algorithms

M. Sánchez del Río 1) , G. Pareschi 2) , and C. Michetschläger 1)

1) European Synchrotron Radiation Facility, BP 220, 38043 Grenoble-Cedex, France
2) Osservatorio Astronomico di Brera, Via E. Bianchi 46, I-23807 Merate (Lc), Italy

Abstract. 

The x-ray reflectivity of a multilayer is a non-linear function of many parameters
(materials, layer thickness, density, roughness). Non-linear fitting of experimental data with
simulations requires the use of initial values sufficiently close to the optimum value. This is a
difficult task when the topology of the space of the variables is highly structured. We apply
global optimization methods to fit multilayer reflectivity. Genetic algorithms are stochastic
methods based on the model of natural evolution: the improvement of a population along
successive generations. A complete set of initial parameters constitutes an individual. The
population is a collection of individuals. Each generation is built from the parent generation by
applying some operators (selection, crossover, mutation, etc.) on the members of the parent
generation. The pressure of selection drives the population to include "good" individuals. For
large number of generations, the best individuals will approximate the optimum parameters.
Some results on fitting experimental hard x-ray reflectivity data for Ni/C and W/Si multilayers
using genetic algorithms are presented. This method can also be applied to design multilayers
optimized for a target application.