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Fitting of X-ray reflectivity from periodic thin film structures: Improved convergence properties in genetic algorithm by rotation of coordinates

Jouni Tiilikainen 1Teppo Hakkarainen Harri Lipsanen 

1. Helsinki University of Technology, Micro and Nanosciences Laboratory, Micronova, Espoo 02015, Finland

Abstract

Novel genetic algorithm (GA) is developed for precise X-ray reflectivity (XRR) curve fitting. The algorithm does the mating procedure in rotated coordinate frame to reduce effect of
interparameter dependencies, called genetic linkage. The convergence properties of the novel GA using a few different rotation techniques are compared to real-valued conventional (CGA). Realistic XRR curve fitting problem is used as a test case where the curves are computed based on a periodic nanolaminate model. The importance of the used model arises from the wide tunability of the properties of these artificial materials. The desired nanolaminate properties such as conductivity depend heavily on structural properties of repetitive individual layers but cannot be determined from XRR measurements with currently existing fitting algorithms. The determination of unknown structural properties can be carried out most precisely by using Parratt's recursive formalism combined with Nevot-Croce interfacial roughness approximation in a curve calculation. In this formalism, one recursion cycle contains the calculation of reflectivity coefficient based on the previous coefficient and the three parameters, thickness, mass density and roughness. The calculation begins from the bottom substrate and continues until the surface is met. When applied to nanolaminates, the formalism includes tens of tightly linkaged parameters but interparameter dependencies can be reduced by the rotation of coordinates. In this work, the rotation of coordinates to reduce genetic linkage is found to improve significantly the convergence properties of the genetic algorithm. The present algorithm allows more efficient determination of parameters from complex periodic layer structures.

 

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Related papers

Presentation: Poster at E-MRS Fall Meeting 2007, Symposium G, by Jouni Tiilikainen
See On-line Journal of E-MRS Fall Meeting 2007

Submitted: 2007-05-03 09:08
Revised:   2009-06-07 00:44