Microfabricated silicon gratings as neutron-optical components
Introduction
Ultra-small-angle scattering using perfect silicon crystals was developed decades ago for X-rays [1] and adapted for thermal neutrons [2]. This technique provides a resolution of the order of in reciprocal space. The typical structure size probed with the technique ranges from a few tenths of a micrometer up to a few tens of micrometers making this destruction-free method an interesting option for various branches in condensed matter science and technology, e.g. Ref. [3]. Artificial periodic structures have already become a topic of interest for fundamental quantization aspects in neutron optics [4], [5], [6]. For the studies presented here a series of silicon gratings with periods ranging from 12 to was fabricated using an anisotropic dry etching process (reactive ion etching, RIE) [7], [8]. This technique allows for high aspect ratios of the etched features with good profile control. To match the neutron beam cross-section available at the instrument S18 the patterned area of these gratings was chosen exceptionally large at . After optimization of the etching process a nearly ideally rectangular profile of the trenches was achieved [9], Fig. 1.
Section snippets
Experimental
Experiments were performed with the USANS option of the instrument S18 at the ILL, Grenoble. The set-up is a double perfect crystal diffractometer in Bonse–Hart configuration with two triple-bounce channel-cut perfect silicon crystals serving as monochromator and analyser, which are mounted on a common optical bench, Fig. 2. The crystals are optimized for Bragg reflections under from the [2 2 0] crystal plane, yielding a neutron wavelength of 1.9 Å after the monochromator. USANS patterns are
Scattering curves
The density distribution of line gratings does not depend on the coordinate y parallel to the trenches. For small scattering angles the problem can be treated in the plane parallel to the grating surface. This corresponds to the so called projection approximation [10]. The three dimensional scattering length density distribution of the line gratings is replaced by its projection along the incoming beam.where z is the coordinate along the incident neutron beam
Correlation functions
The scattered intensity can be interpreted as the Fourier transform of the Patterson- or autocorrelation function where is the scattering length density distribution. Scattering intensity and correlation function form a Fourier pair like scattering amplitude and scattering length density distribution . For the case of discrete diffraction orders from gratings with period a the Fourier transform can be replaced by a
Comparison with results from SESANS
The new spin echo SANS technique (SESANS) developed at the Delft University of Technology during recent years measures a signal closely related to the correlation function of the scattering length density distribution [11], [12]. The method is based on the Larmor precession of polarized neutrons passing through magnetic fields with inclined faces, Fig. 5. The trajectory of the neutron scattered by the sample is encoded by the precession angle. The measured quantity is the degree of polarization
Summary
We have presented scattering experiments performed on artificial silicon lattices. The model samples developed for these measurements allow a calibration and stability check of neutron small-angle scattering instruments over a wide Q-range. Testing devices and methods with model structures of well-known geometries will further pave the way of ultra-small-angle neutron scattering towards a standard method. The complementarity of USANS and the new SESANS method could be demonstrated by comparison
Acknowledgments
We acknowledge K. Unterrainer, G. Strasser and W. Schrenk, Center for Micro- and Nanostructures, Vienna University of Technology, for their support in the development and fabrication of the silicon gratings. We thank M.T. Rekveldt and W.G. Bouwman, Delft University of Technology, for the SESANS data. This work was financially supported by the Austrian Science Fund (FWF), Project FWF-SFB15 No. F1514.
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