Grazing incidence X-ray fluorescence of periodic structures – a comparison between X-ray standing waves and geometrical optics calculations

Falk Reinhardt,Max Schoengen,Burkhard Beckhoff,Jean-Claude Dousse,Stanisław H Nowak

doi:10.1039/c4ja00164h

Abstract

Geometrical optics calculations are able to reproduce experimentally found modulations in GIXRF which are beyond the potential of the XSW model.

Highlights

Analytical methods which allow for reliable characterization of nanostructured surfaces are in demand in a variety of elds that range from environmental analysis to industrial process control
For periodic surface structures some features of the measured angular pro les cannot be reproduced by the present X-ray standing wave (XSW) approach. For such types of structured surfaces the geometrical optic-based ray tracing method is more suitable the Geometrical Optics (GO) calculations can be signi cantly more time-consuming
The two features were found to be reliably described by XSW and GO simulations

Summary

Introduction

Analytical methods which allow for reliable characterization of nanostructured surfaces are in demand in a variety of elds that range from environmental analysis to industrial process control. To investigate the differences between the two theoretical approaches and to check the reliability of XSW calculations for quantitative GIXRF measurements on highly structured surfaces, a periodic arrangement of chromium stripes on a silicon substrate was produced (see Fig. 1). The uorescence intensity measured at each incident angle was compared to calculated XSW excitation intensities and to the intensities obtained from GO calculations

Samples and experiment

X-ray standing wave eld calculations

Geometrical optics calculations

Results

Conclusions

Outlook