Microfabrication of hard x-ray lenses

Frederik Stöhr

Research output: Book/ReportPh.D. thesisResearch

1220 Downloads (Pure)


This thesis deals with the development of silicon compound refractive lenses (Si-CRLs) for shaping hard x-ray beams. The CRLs are to be fabricated using state of the art microfabrication techniques. The primary goal of the thesis work is to produce Si-CRLs with considerably increased structure heights and improved uniformity compared to what is currently available. To this end, established fabrication procedures are improved and the toolbox used for lens development is enriched.
The central theme of this thesis is x-ray microscopy (XRM). As a spearhead of today’s materials research it provides characterization details that cannot be obtained by other means. The respective x-ray techniques largely benefit from continuously improved x-ray sources, x-ray detectors and x-ray optics. For instance, some techniques aiming for structural investigation of poly-crystalline materials directly benefit from more intense and wider line beams with narrower waists.
The thesis starts with a review of alternative x-ray lenses. Si-CRLs are identified as valuable optical components that allow shaping hard x-rays efficiently and creating beam waists that are clearly in the nanometer range. They stand out by their potential for compact integration, which makes them cost-effective, easy to handle and stable on-axis optics.
A Si-CRL comprises multiple bi-parabolic cylindrical cavities. The bi-parabolic patterns are defined lithographically and vertically transferred into the Si substrate using deep reactive ion etching (DRIE). Based on a theoretical framework for CRLs, stringent requirements on the pattern transfer are found. Most crucially, the sidewalls of the cavities must be strictly parallel. Already slight deviations from the ideal parabolic shapes result in non-uniform and broadened waists of focused x-ray beams.
Two strategies are demonstrated, which guarantee shape fidelity, while the heights of etched lenses can be increased. Both are based on defining the bi-parabolic cavities at their perimeter by trenches of uniform width, where one trench wall is comprised of sacrificial material. The two strategies differ in the way the unwanted sacrificial material inside the cavities is removed subsequent to DRIE. While the first strategy utilizes etching of the trenches through the entire thickness of the wafer for releasing the sacrificial portions, the second strategy relies on thin sacrificial structures that can be completely oxidized and removed by selective etching. Both strategies have proven to be equally successful in achieving a substantial increase of the heights of Si-CRLs and to facilitate accurate sidewall profile control necessary for uniform x-ray focusing.
A precise manufacture in turn asks for highly precise metrology. Therefore, a mix of techniques including optical profilometry and atomic force microscopy (AFM) has been used to obtain reliable information about the detailed three-dimensional shapes of the lenses. Adequate sample preparation and measuring procedures have been developed. Inverse replica molding in PDMS of the CRLs was established as an effective way to circumvent the limitations AFM probes have when concave surfaces need to be characterized, e.g. due to the finite lengths of AFM probes.
Four different x-ray optical components have been designed, manufactured and characterized with respect to their shape. Their optical performances were tested at the European Synchrotron Radiation Facility (ESRF). Two 1D-focusing Si-CRLs suitable as condensers in hard-XRM were developed utilizing the aforementioned two different strategies. The first Si-condenser showed focusing of a 56 keV x-ray beam into a 310 μm wide line and a waist of 980 nm (FWHM, full width at half maximum) at a focal length of 1.3 m. The second Si-condenser allowed the focusing of 17 keV x-rays into a 180 μm-wide line with a waist of 430 nm (FWHM) at a focal length of 0.215 m. Both systems leave plenty of space for sample surroundings and ensure low-divergent and wide x-ray beams with narrow waists. Both results are substantial improvements to what was available at the start of this thesis work.
The challenge of making x-ray objectives in silicon by interdigitation of lenslets alternately focusing in the vertical and horizontal directions was addressed. A functioning prototype of a 2D silicon objective for use in a bright-field hard-XRM was demonstrated. The results are promising; showing acceptably low aberration and performance close to theoretical expectations. A resolution of 300 nm with 17 keV x-rays and a focal length of 300 mm was achieved. By harnessing the potential for making more compact objectives and avoiding shape defects, one could significantly improve the focusing power, transmission and numerical aperture.
Polymer injection molding was explored as a novel route for x-ray lens manufacture. A Si-CRL template was used as a master for obtaining nickel mold inserts. CRLs made of polyethylene have proven to be promising highly efficient x-ray optics. A 55 μm long line focus with a minimal waist of 770 nm (FWHM) at a focal length of 350 mm was obtained with 17 keV x-rays. A final production rate larger than 10 pieces per hour indicates the economic value of injection molded x-ray lenses, which may have applications in more readily available small laboratory x-ray instruments or medical devices.
In each case, observed non-uniformities of the shaped x-ray beams were investigated and found to be in agreement with the lens shape measurements. In iterative steps the lenses have been improved and the most recent results allow yet another whole range of improvements to be made. The fundamentals for an advanced fabrication of silicon CRLs are laid out, which will contribute to their future use in novel applications.
Original languageEnglish
PublisherTechnical University of Denmark
Number of pages191
Publication statusPublished - 2015


Cite this

Stöhr, F. (2015). Microfabrication of hard x-ray lenses. Technical University of Denmark.