1. 1 BROOKHAVEN SCIENCE ASSOCIATES Can the optics get to 1-nm? Hanfei Yan NSLS-II, Brookhaven National Laboratory

2. 2 BROOKHAVEN SCIENCE ASSOCIATES 2 Multilayer-Laue-Lens (MLL) deposition Al Macrander 1 Chian Liu 1 Ray Conley 1 MLL characterization and focusing measurement Brian Stephenson 2,3 Hyon Chol Kang 2,3 Theoretical Modeling Jörg Maser 1,2 Stefan Vogt 1 Collaborators 1.Advanced Photon Source, Argonne National Laboratory 2.Center for Nanoscale Materials, Argonne National Laboratory 3.Materials Science Division, Argonne National Laboratory

3. 3 BROOKHAVEN SCIENCE ASSOCIATES Outline What x-ray optics are capable of nanofocusing? What is multilayer Laue lens (MLL)? Why MLL? Can we really get to 1-nm focus by MLL? What are the properties of MLL? What are the fabrication challenges?

4. 4 BROOKHAVEN SCIENCE ASSOCIATES Overview of x-ray focusing optics Reflective optics  Waveguide, capillary, K-B mirror w/o multilayer  Achieved: ~25 nm  Hard limit: ~ 10 nm Refractive optics  Compound refractive lenses (CRLs): ~ 10 nm  Adiabatically focusing lenses (AFLs): no hard limit, but has practical limit for nanofocusing  Achieved: ~50 nm Diffractive optics  Fresnel zone plates (FZPs): fabrication limit  Multilayer Laue Lenses (MLL’s): no hard limit, suitable for hard x-ray focusing –Achieved line focus: ~16 nm –Promising for true nanometer focus –Chosen as candidate 1-nm optics for NSLS-II Kinoform lenses (Kenneth Evans-Lutterodt), multilayer mirrors

5. 5 BROOKHAVEN SCIENCE ASSOCIATES 1-D structure allows fabrication via thin film deposition techniques Almost limitless aspect ratio very small zone width (1nm) MLL’s are capable of achieving nanometer focus with high efficiency Multilayer-Laue-Lens (MLL) Lithography method: >15 nm zone width <30 aspect ratio (w/  r n ) Limited resolution and efficiency for hard x-ray focusing: Au, w=300 nm, efficiency=15% @ 1 keV; 0.3% @ 30 keV H. C. Kang et al., Phys. Rev. Lett. 96, 127401 (2006). http://www.xradia.com/Products/zoneplates.html Fresnel Zone Plate w rnrn Introduction to Multilayer Laue Lenses

6. 6 BROOKHAVEN SCIENCE ASSOCIATES 6 Full Wave Dynamical Diffraction Theory is Needed ! Zone plate law: Zone width: Resolution limit: For the geometrical-optical theory be valid, the zone plate has to be “thin” so that the multiwave scattering (dynamical) effect can be ignored. Geometrical-Optical theory: Optimum thickness: (phase zone plate) w rn/frn/f At optimum section depth, dynamical diffraction properties begin to dominate when the outmost zone width becomes smaller than ~ 10 nm! http://www.xradia.com/Products/zoneplates.html

7. 7 BROOKHAVEN SCIENCE ASSOCIATES A Takagi-Taupin Description of Dynamical Diffraction for Volume Diffractive Optics Diffraction from MLL’s is akin to that from strained single crystals. Takagi-Taupin-similar equations can be derived for MLL’s. x’x Fresnel Zone Plate1:1 Binary Bars nth 1st T A B z Central equations: Pseudo Fourier series: H. Yan, J. Maser, A. T. Macrander, Q. Shen, S. Vogt, B. Stephenson and H. C. Kang, Phys. Rev. B 76, 115438(2007)

8. 8 BROOKHAVEN SCIENCE ASSOCIATES Focusing Properties of MLL hh k0k0 khkh 11 22 33 -1-1 -2-2 -3-3 Ewald sphere Physical NA ≠ Effective NA!  =0  =1.1 mrad  =2.1 mrad  =3.2 mrad

9. 9 BROOKHAVEN SCIENCE ASSOCIATES Focus profile as a function of tilting angle WSi 2 /Si, 19.5 keV, outermost zone width of 5 nm, half structure.

10. 10 BROOKHAVEN SCIENCE ASSOCIATES Trade-off between efficiency and effective NA Geometrical theory becomes valid when the lens is thin enough and does not diffract “dynamically”. In geometrical theory, physical NA = effective NA Example: MLL with flat zones and outmost zone width of 1 nm Focal size Total Efficiency E=19.5 keV

11. 11 BROOKHAVEN SCIENCE ASSOCIATES Can we achieve high efficiency and large effective NA simultaneously? Bragg condition needs to be satisfied. Each zone is tilted progressively to satisfy the local Bragg condition, resulting in a wedged shape. First order, m=1, all zones shrink homogeneously by a factor,

12. 12 BROOKHAVEN SCIENCE ASSOCIATES Wedged MLL Wedged MLL, 0.75 nm outmost zone width, WSi 2 /Si, energy at 19.5 keV, FWHM=0.7 nm, total efficiency=50%. The wedged structure is an approximation to the ideal structure, but it is enough for 1-nm focusing.

13. 13 BROOKHAVEN SCIENCE ASSOCIATES Properties of 1-nm MLL optics Narrow energy bandwidth: Short work distance: 2~3 mm, limited by the deposition techniques (accuracy and growth time) More suitable for hard x-rays focusing (easier to fabricate) For wedged MLL’s, only within a small range around an optimum energy, which is determined from the tiling angle of the wedged structure, can its full physical NA be utilized.

14. 14 BROOKHAVEN SCIENCE ASSOCIATES For a MLL with flat zones, as long as f=const. the zone plate law is satisfied. However for a wedged MLL its focal length is determined by the shrinkage factor in order to satisfy the Bragg condition, As a result, only at a specific energy the performance of a wedged MLL is optimized. Optimum Operating Energy for Wedged MLL’s

15. 15 BROOKHAVEN SCIENCE ASSOCIATES Initial wedged structure R. Conley/APS f=2.64 mm, =0.151 Å Optimum energy: 82.1 keV. Within ±10% of the optimum energy the focal spot is not broadened.

16. 16 BROOKHAVEN SCIENCE ASSOCIATES Challenges Build-up stress High quality thin films (defects, roughness, interface diffusion and uniformity) Fast growth rate (~100 µm) Long-term machine stability to ensure nanometer accuracy during deposition (~days) Deposition techniques for wedged structures Slicing and polishing techniques Engineering challenges of assembling two MLL’s for point focusing

17. 17 BROOKHAVEN SCIENCE ASSOCIATES Growth Error Actual zone profile Calculated intensity isophote pattern Comparison H. Yan, H. C. kang, J. Maser et al., Nuclear Inst. and Methods in Physics Research, A 582, 126-128(2007) Optical axis Diffraction Limit: 30 nm Measured size: 50 nm

18. 18 BROOKHAVEN SCIENCE ASSOCIATES Current state-of-the-art MLL 40% of full structure, 5 nm outermost zone width 5 nm thick, 5  m wide Pt nano-layer Pt L , ,  MLL Fluorescence detector X-rays Far-field detector Line focus measurement H. C. Kang, H. Yan, J. Maser et al., to appear in Appl. Phys. Letts FWHM =16 nm

19. 19 BROOKHAVEN SCIENCE ASSOCIATES Conclusions No hard theoretical limit prevents hard x-rays from being focused to 1-nm by MLL method. To achieve 1-nm focus with high efficiency, wedged MLL’s are required. There are significant technical challenges on 1- nm MLL fabrication. With the R&D effort, we believe that 1-nm spatial resolution is achievable.