Kinoform hard X-ray optics for sub-10nm beams, Lecture notes of Optics

Download Kinoform hard X-ray optics for sub-10nm beams and more Lecture notes Optics in PDF only on Docsity! nsis Can Kinoform hard X-ray optics produce IR Uv ix sub-10nm beams? K.Evans-Lutterodt A.Stein ¢ Brief review of Refractive optics ¢ Motivation for kinoforms ¢ Are there fundamental limits of these optics U.S. DEPARTMENT OF ENERGY HAWEN OFFICE OF Basic ENERGY SCIENCES iio tee rarer ay Main points of this talk 1. We do not need to fabricate lenses with feature sizes comparable to the optics resolution. (Why?) 2. Numerical Aperture not limited by absorption 3. Wecan exceed the critical angle limit with , compound lenses. —We can get down to below 10nm (no new physics or technology, just improve what we are doing now) Status 1a: Local NSLS results Submicron performance with 100micron Aperture *Knife edge consists of Cu metal grating with 2 micron period. *Figure on left shows a knife edge scan with and without a lens in the path. *Efficiency is greater than 60% Intensity (Arbitrary) Total incident flux s| Oo z Tos Knife Edge Position (millimeters) 8 g 7 ; & 8 Detailed knife edge scan showing submicron performance. Distance between experimental points is 0.5 micron -0.945, -0.94 -0,935 -0.93 Knife Edge Position (millimeters) What is a kinoform A kinoform is a phase optic Assymetric computer generated profile Efficiency and resolution are metrics to consider Phase profile accuracy is important; => Elliptical shape for point to parallel refractive optic. For far field optics, resolution is A/(Numerical Aperture) Limiting value of N.A. is 1 “State of the Art* ” of the different microscopies Method Optical 200nm 200nm 1 Electrons 0.05nm 0.1nm 2 Soft X-rays | 10nm 30nm 3 Hard X-rays |0.1nm 50nm 500 (We need better optics) *Very crude What is a lens anyway? *A lens takes the diffracted beams from the sample and recombine them in the image plane, while maintaining the relative phases. *Lens resolution is ~ A/(numerical aperture) ; limiting value is 2. *Fither shorten the focal length or open up the aperture ( preferably both) Why a compound lens X rays F=R/28 O — X rays F=R/2N8 d NON” N R~ (0.1m * le-6) = 0.1microns; aperture too small! N lenses reduce focal length: f=f,/N So reduce the curvature by N ( open the aperture) and stack N lenses up Can’t make circles as small as you would want with drilling A. Snigirev, V. Kohn, I. Snigireva et al., “A compound refractive lens for focusing high- energy X-rays,” Nature 384, 49-51 (1996). A commercial product: Refractive parabolic Beryllium lenses B. Lengeler, C. Schroer M. Kuhlmann, B. Benner, T. F. Giinzler, O. Kurapova IL. Physikalisches Institut B, Aachen University, Germany A. Snigirev, L Snigireva ESRF Grenoble My entry point: Deep RIE etching of Bragg-Fresnel optics Since we have complete control of the profile with the electron-beam writer, why not Minimize the “dead” regions? write the curvature as small as we want, instead of using a compound lens? What is the best shape anyway? What is the best shape for the lens? From Fermats theorem for n<1 the best shape for a point to parallel converter 1s an ellipse. nx +n'/(F-x)’ +y* =n'F y +(28 —87)x? —28Fx =0 Clearly, the ellipse and parabola are Fw similar near the optical axis . Hecht Physical intuition tells you a parabola is not correct This result is physically appealing; rays on the extrema incoming lof the ellipse go through the monochromatic focal point and are deflected by Plane wave the critical angle! lens medium A way out: make compound lens N lenses reduce focal length: f=f)/N So reduce the curvature by N ( open the aperture) and stack N lenses up Ideally use varying shape for each one If there is no loss, this will work. Roadblock: If the aperture is limited by loss you do not win. For most refractive optics, absorption limits aperture, and hence resolution Focal point Absorption limits effective aperture of lens Hard X-ray; n<1 Is there a way around this? Can we beat the loss limitations? * Yes, but we have to give up something. ¢ First lets learn something about zone plates Fresnel lens (kinoform) ; main point ¢ Ifyou are willing to work at a fixed wavelength, you can reduce loss. * Remove sections such that at a fixed wavelength the phase shifts by multiples of 27. Original Fresnel lighthouse lens had large phase shifts (>> 27). ¢ Steps are = thick corresponding to 27 phase shift, or multiples (N+1)r — NA (-6é Spot size of order smallest feature Consequence of fixed phase shift choice Spot size versus Energy 0.006 0.005 0.004 e e 0.003 e Sigma (mm) e 0.002 ° 0.001 Energy (KeV) Is it diffractive or refractive? Kinoform WA AW noes Binary zone plate ‘NATURE| VOL d01|28 OCTOBER 1999] E. Di Fabrizio’, F. Romanato*, M1. Gentilit, S Cabrinit, B. Kaulich?, J, Susinit & R. Barrett: * TASC-INEM (National Institute for the Physics of Matter), Elettra Synchrotron Light Source, Lilit Beam-line SS14 kin 163.5, Area Science Park, 34012 Basovizza, Trieste, Italy ‘tIstituto di Elettronica dello Stato Solido, Via Cineto Romano 42, 00156 Rome, Ttaly + X-Ray Microscopy Beamline, European Synchrotron Radiation Facility, BP220, Not really a valid question; ce refractive limit is A~0 ¢ In the best case, the optic is designed not to absorb much heat. Should have a high heat load capability. * Complicated to calculate ¢ First pointed out by Lengeler,Snigirev. B. Néhammer**, C_ David*, H. Rothuizen”. J. Hoszowska‘, A. Simionovici* “Laboratory for Micra- and Nanotechnology, Paul Scherrer Institut, CH-5232 Villigen-PSI, Switzerland "IBM Research, Zurich Research Laboratory, CH-8003 Riischlikon, Switzerland “European Synchrotron Radiation Facility, BP. 220, F-38043 Grenoble Cedex, France Microelectronic Engineering 67-68 (2003) 453460 Etching Diamond for high heat loads! Potential road block for zone plate Zone Plate Path Length L+ 4 / t 1 Source Focal Point Path Length L Wn, width of nth zone va T, zone plate thickness ¢ The spot size is of order the smallest zone Work at harmonics, reduces efficiency ¢ As photon energy increases, the zone plate thickness T increases To get smallest spot sizes at hard x-ray energies requires => Large aspect ratios that are difficult to manufacture Calculational Approach (Up 1 a Hupieecere pre aperture distribution itself, Thus in ‘the region of Fraunhofer diffraction (or equiva- Jently, in the far feld), ct yy views) = well Ug, mex |— JZ 008 + vp | dean, 6-25) FIGURE 4.1 Az Diffraction geometry. ‘Consider first a rectangular aperture with an amplitude transmittance given by alized Normalize ) intensity ial.) = wea(56-) weai(”. wy PP Some reasons we resort to numerical simulation The function U(€) contains phase and amplitude of lens 22td For material of thickness t, the phase shift is A For the familiar, solid, lossless refractive lens U(€)=exp( i) _2mtd 27106 C4) A . 2 exp( —i 7 ) = exp( -i ims Af ) = exp( - =) Both A and 6 are energy dependent. doc pE? Transverse scan is difficult analytically Phase profile comparison between “full” lens and kinoform Series In the calculation the 2pi phase shifts make no difference (29?) Start with Fresnel Kirchhoff: A(z) [fre ne” " dédy inp? Switch to radial coordinates: 2a rieye * pdp 2 p Xr =-? ym +O) a5 MS Use t(p) which is lens i280) yn Panay a a a a . _— x _— 2af thickness, is discontinuous in T(p)=e =e M multiples of Fresnel zones iv 2x | Toye ™ 2 dv Vo Vv, = (7 1 vy vy Vy VL Finally we get a Sum Over fe* Pay = fem™av = foray + fe*™av ++ fe*™av all the M sized Fresnel % vo % 4 via zones up to the full size of the lens aaiFs| Illustrating M sized zones for M=1 and M=2 _ ant = a56 MG =I M=2 _ 4 Focal length 2f 20 Focal length f M=1 ; a FYE JE F 4)3 2 “Bragg peaks” 4) “Form factor” Ty Normalized focal length In the top panel are all the allowed foci at 1/n in normalized units. In b the middle panel the is shown the “form factor’ with zeroes at most of these allowed foci and in c we show the product, leaving a single focus. = a -_ 4.50E-10 4.00E-10 3.50E-10 | 3.00E-10 £& > 2.50E-10 a S o 2 £ 2.00E-10 1.50E-10 1.00E-10 5.00E-11 + 0.00E+00 © Transverse dependence | \ —e 1.0*lambda —s— 1.02*lambda — 1.04 —— 1.06 — 1.08 1.1 0.00E+0 5.00E-07 1.00E-06 1.50E-06 2.00E-06 0 Transverse coordinate (m) *Use Fresnel limit diffraction calculation* *AE/E ~ 10% *Now take each profile, fit to a gaussian shape* “Comparison” of experimental data with simulation 7.00E-03 6.00E-03 \ —e— Simulation data 5.00E-03 |S —s- Experimental Data 4.00E-03 3.00E-03 2.00E-03 1.00E-03 0.00E+00 1 1 1 9.50 10.50 11.50 12.50 13.50 How compound kinoform lenses can improve resolution Incident beam 8 NA~0, =< \ —_ (= V28 1 lens ™ » N.A~ 20, ——_——_—_> — 2 lenses 1 silicon lens ~ 40nm ° N.A= MO, enses Since resolution is A/(N.A.), M lenses will have A/(M*(N.A.)) Remember that each lens introduces some loss. ——> 98+ A dummy lens calculation for NSLS2 ¢We consider a compound lens fabricated out of a stack of Fresnel lenses. For Beryllium at 10keV 5x3.1x10°, and B~7.5x10-!°, and so the transmission T of a single Beryllium Fresnel lens T~0.9985. For 200 lenses, corresponding to 100 lenses for each axis, the total transmission is 75% of the incident light. ¢ For the paraxial limit we make the standard approximation that the focal length of the stack is (f)/N) where f, is the focal length of an individual lens and N is the number of lenses. If we conservatively stay within the paraxial limit, we estimate a focal length of fy~2.2y/ V8 where y is the required aperture and 8 is the refractive index. ¢The aperture y is of order 5x10-4 m, (® 3 x (distance from source) x oy’ =3 x 40m x 4x10 ). The estimated f, is 0.64 m. The net focal length for 100 lenses is 6.5mm, and the resulting resolution is 4/(Numerical Aperture) is 1.6nm. Consider breakdown of linear approximation Incident un-focused light a \Z- Line Focus? U(P,)=— = Jue ee exp(iki, ) cos ds Ae 7) Tor = x YM 2 2 2 = z[(1+— — hy =Ve +(x—-6) +(y-77) I cS Y +3 2)! showing the replacement of the spherical wave by a pair of orthogonal parabolic terms. [x-€% +0y-"?? ook 4A For 100micron aperture, focal length lcm, we can use crossed lenses down to at least 10nm, but how far can we go?