Can the optics get to 1-nm?

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

2. Collaborators • Multilayer-Laue-Lens (MLL) deposition • Al Macrander1 • ChianLiu1 • Ray Conley1 • MLL characterization and focusing measurement • Brian Stephenson2,3 • HyonCholKang2,3 • Theoretical Modeling • JörgMaser1,2 • Stefan Vogt1 Advanced Photon Source, Argonne National Laboratory Center for Nanoscale Materials, Argonne National Laboratory Materials Science Division, Argonne National Laboratory

3. 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. 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. Introduction to Multilayer Laue Lenses Fresnel Zone Plate Multilayer-Laue-Lens (MLL) rn w http://www.xradia.com/Products/zoneplates.html 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 Lithography method: • >15 nm zone width • <30 aspect ratio (w/rn) 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).

6. Full Wave Dynamical Diffraction Theory is Needed! rn/f w http://www.xradia.com/Products/zoneplates.html 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: Zone plate law: Zone width: At optimum section depth, dynamical diffraction properties begin to dominate whenthe outmost zone width becomes smaller than ~10 nm! Resolution limit: Optimum thickness: (phase zone plate)

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

8. Focusing Properties of MLL Ewald sphere 3 kh 2 1 k0 -1 -2 -3 h =1.1 mrad =0 =2.1 mrad =3.2 mrad Physical NA ≠ Effective NA!

9. Focus profile as a function of tilting angle WSi2/Si, 19.5 keV, outermost zone width of 5 nm, half structure.

10. 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 E=19.5 keV Focal size Total Efficiency

11. 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. Wedged MLL Wedged MLL, 0.75 nm outmost zone width, WSi2/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. 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. Optimum Operating Energy for Wedged MLL’s 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.

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

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

19. 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.