Abstract

Experiments at the bending magnet beamline at BESSY II (EDR beamline) profit from the excellent coherence properties of third generation synchrotron sources. Considering the exponentially decaying incident spectrum, and because no optical elements are installed except slits and vacuum windows, coherence experiments can be performed between 5 keV< E<15 keV. First, the energy dependence of spatial coherence properties were determined measuring diffraction at single and double pinholes. Next, the coherent white radiation was used to probe the morphology of thin films in reflection geometry. The recorded intensity maps (reflectivity versus sample position) provide speckle patterns which reveal the locally varying sample morphology. Setting the incident angle, α_i, smaller or larger than the critical angle of total external reflection, α_c, one should be able to separate the surface height profile from the subsurface density modulation of a sample. The validity of this approach is verified at the example of reciprocal space maps taken from a polymer surface where we could reconstruct the lateral height profile from speckle data.

Keywords:Synchrotron radiation; Coherence; X-ray reflectivity; Polymer surface morphology

PACS: 07.85.Qe; 42.25.Kb; 61.10.Kw; 68.35. Md; 82.35.Gh

Article Outline

1. Introduction

2. Experiment

3. Characterization of the incident beam by pinhole experiments

4. Coherent reflectivity from polymer surfaces

5. Reconstruction of the sample profiles

6. Conclusion

Acknowledgements

References

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Fig. 1. Experimental set-up for pinhole experiments (position A) and reflectivity measurements with coherent radiation (position B) at the EDR beamline of BESSY II.

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Fig. 2. Fraunhofer diffraction pattern obtained after scattering at a 10, 15, 25 and 35 μm pinhole. From the visibility of fringes one can already see by eye that the transversal coherence length has a value between 25 and 35 μm.

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Fig. 3. Energy dependence of the visibility as a function of energy. The black lines show the functional behaviour expected for 10 μm (a), 15 μm (b) and 25 μm (c) using the real geometric parameters s, and R of the beamline. The dotted lines are fits through the data taken from Fig. 2.

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Fig. 4. Double pinhole interference pattern measured in forward direction after scattering at two 2 μm pinhole separated by —Young's slit experiment (a) and after reflection under α_i=0.05° from two 0.5 mm width mirrors separated —bi-mirror experiment (b). The respective experimental set-up used is shown as an inset.

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Fig. 5. Sample scans pattern of a thin polymer film recorded at three different α_i. The spatial resolution is 10 μm. The number of visible thickness fringes increases with increasing α_i (a). For α_i=0.282° (b) we show a single spectrum I(α_i,y) taken at a certain sample position y (left) and the sum spectrum (right).

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Fig. 6. Line scans extracted for particular q_z-values, but recorded at different α_i. Whereas the features for α_i=0.239° (b) and 0.289° (c) are similar; they differ from those recorded at α_i=0.152° (a).

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Fig. 7. Reciprocal space map of a polymer sample at a particular sample position. The left figure (a) represents the raw data I(E,Δα), obtained by taking several off-set scans with different off-set angle Δα. The right figure (b) is obtained after transformation into reciprocal space coordinates using Eq. (1).

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Fig. 8. Results of the fitting procedure of selected line scans taken from Fig. 7b (left graph) and the reconstructed spatial profile (right graph). The lines are vertically displaced. It is seen again, that the pattern for a q_z value smaller than the critical momentum transfer differs significantly from those reconstructed for larger q_z.

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