Tabletop Nanometer Extreme Ultraviolet Imaging in an Extended Reflection Mode using Coherent Fresnel Ptychography
Matthew D. Seaberg, Bosheng Zhang, Dennis F. Gardner, Elisabeth R. Shanblatt, Margaret M. Murnane, Henry C. Kapteyn, Daniel E. Adams
TTabletop Nanometer Extreme Ultraviolet Imaging in an Extended Reflection Modeusing Coherent Fresnel Ptychography
Matthew D. Seaberg*, Bosheng Zhang, Dennis F. Gardner, Elisabeth R. Shanblatt,Margaret M. Murnane, Henry C. Kapteyn, and Daniel E. Adams
JILA, University of Colorado at Boulder, Boulder, CO 80309, USA*[email protected]
We demonstrate high resolution extreme ultraviolet (EUV) coherent diffractive imaging in themost general reflection geometry by combining ptychography with tilted plane correction. Thismethod makes it possible to image extended surfaces at any angle of incidence. Refocused lightfrom a tabletop coherent high harmonic light source at 29 nm illuminates a nanopatterned surfaceat 45 ◦ angle of incidence. The reconstructed image contains quantitative amplitude and phase (inthis case pattern height) information, comparing favorably with both scanning electron microscopeand atomic force microscopy images. In the future, this approach will enable imaging of complexsurfaces and nanostructures with sub-10 nm-spatial resolution and fs-temporal resolution, which willimpact a broad range of nanoscience and nanotechnology including for direct application in actinicinspection in support of EUV lithography. Dramatic advances in coherent diffractive imaging (CDI) using light in the extreme ultraviolet (EUV) and X rayregions of the spectrum over the past 15 years have resulted in near diffraction-limited imaging capabilities usingboth large and small scale light sources [1, 2]. In CDI, also called “lensless imaging,” coherent light illuminates asample, and the scattered light is directly captured by a detector without any intervening imaging optic. Phaseretrieval algorithms are then applied to the data set to recover an image. CDI has already been used to study avariety of biological and materials systems [3–7]. However, the potential for harnessing the power of CDI for imagingcomplex nano-structured surfaces, which requires the use of a reflection geometry for imaging, has been much lessstudied. Surfaces are critical in nanoscience and nanotechnology, for example in catalysis, energy harvesting systemsor nanoelectronics. A few successful demonstrations have applied CDI to reflection-mode imaging. However, work todate has either been limited to highly reflective EUV lithography masks in a normal incidence geometry [8], restrictedto low numerical aperture through the use of a transmissive mask [9], or restricted to isolated objects [10, 11].Here we demonstrate the most general reflection-mode coherent diffractive imaging to date using any light source,by combining the extended ptychographical iterative engine (ePIE) [12] with curved wavefront illumination [13].This allows extended (non-isolated) objects to be imaged at any angle, which will enable tomographic imaging ofsurfaces. This work also represents the first non-isolated-object, high fidelity, tabletop coherent reflection imaging,which expands the scope of applications for CDI significantly. This work demonstrates a powerful new capability thatcan impact a very broad range of science and technology. First, our approach removes restrictions on the numericalaperture, sample, or angle, so that general extended objects can be imaged in reflection mode at any angle of incidence.Second, illumination of the sample with a strongly curved wavefront removes the need for a zero-order beam-stopby reducing the dynamic range of the diffraction patterns. The curved illumination also allows the size of the beamto vary according to the sample size, alleviating the need for a large number of scan positions. This also results infewer necessary scan positions when imaging a large field of view. Third, reflection ptychography produces surfaceimages containing quantitative amplitude and phase information about the sample that are in excellent agreementwith atomic force microscopy (AFM) and scanning electron microscopy (SEM) images, and also removes all negativeeffects of non-uniform illumination of the sample or imperfect knowledge of the sample position as it is scanned. Theresult is a general and extensible imaging technique that can provide a comprehensive and definitive characterizationof how light at any wavelength scatters from an object, with no fundamental limitation on resolution. This completeamplitude and phase characterization thus is fully capable of pushing full field optical imaging to its fundamentallimit. Finally, because we use a tabletop high harmonic generation (HHG) 30 nm source [14], in the future it will bepossible to image energy, charge and spin transport with nm spatial and fs temporal resolution on nanostructuredsurfaces or buried interfaces, which is a grand challenge in nanoscience and nanotechnology [15, 16].The experimental geometry for reflection mode Fresnel ptychography is shown in Fig. 1. A Ti:sapphire laser beamwith wavelength ≈
785 nm (1.5 mJ pulse energy, 22 fs pulse duration, 5 kHz repetition rate) is coupled into a 5cm-long, 200 µ m inner diameter, hollow waveguide filled with 60 torr of argon. Bright harmonics of the fundamentallaser are produced near a center wavelength of 29 nm (27th harmonic) since the high harmonic generation process iswell phase-matched [17], ensuring strong coherent signal growth and high spatial coherence. The residual fundamentallaser light, which is collinear with the high harmonic beam, is filtered out using a combination of two silicon mirrors(placed near Brewsters angle for 785 nm light) and two 200 nm-thick aluminum filters. The EUV beam is then sent a r X i v : . [ phy s i c s . op ti c s ] D ec through an adjustable ≈ ≈ ◦ . The actual focus is 300 µ m behind the sample, so that theHHG beam wavefront has significant curvature. The angle of incidence on the curved mirror is approximately 2 ◦ ,which introduces small amounts of astigmatism and coma onto the HHG beam. FIG. 1: Experimental setup for reflection mode Fresnel ptychography.
The EUV beam propagatesthrough an adjustable ≈ ≈
30 nm-thick titanium patterned on a silicon substrate using e-beam lithography (seemethods section for details). A scanning electron microscope (SEM) image of this object is shown in Fig. 2b. Thescattered light from the object is measured using an EUV-sensitive CCD detector (Andor iKon, 2048 × µ msquare pixels), placed 67 mm from the object, and oriented so that the detector surface was normal to the specularreflection of the beam. The sample was positioned 300 µ m before the circle of least confusion along the beam axis,so that the beam diameter incident on the sample was approximately 10 µ m. Diffraction patterns were measured ateach position of 10 adjacent 3 × µ m step size between positions. The positions were randomized byup to 1 µ m in order to prevent periodic artifacts from occurring in the ptychographic reconstruction[18].Due to the non-normal angle-of-incidence on the sample, the patterns must be remapped onto a grid that is linear FIG. 2: Diffraction data and ptychographic reconstruction. (a) Representative diffraction pattern, scaled tothe power, taken from the 90-scan dataset. (b) SEM image of the Ti patterned Si sample. Note that the largedefect circled in the SEM image resulted from contamination after the ptychography measurement. (c)Reconstructed amplitude (thresholded at 5%) of the HHG beam. The inset shows the reconstructed phase(displayed modulo-2 π ). (d) Ptychographic reconstruction of the object shown in (b). The reconstruction is plottedas the complex amplitude, where brightness represents reflected amplitude and hue represents the phase of thereconstruction. Note that the majority of defects seen in the SEM image of the Ti nanostructures are reproduced inthe ptychographic reconstruction. The scale bar in (b) is shared among (b)-(d).in spatial frequencies of the sample plane, in order to use fast Fourier transforms (FFTs) in the data analysis. We usedtilted plane correction to accomplish this[19]. An example of a corrected diffraction pattern is shown in Fig. 2a. Thediffraction patterns were cropped such that the effective numerical aperture was 0.1, enabling a half-pitch resolutionof 150 nm. The image was reconstructed using the ePIE, along with the sub-pixel position determination method[20, 21]. A starting guess for the probe was calculated based on the estimated distance of the sample from the focus.The reconstructed complex amplitude of the object is shown in Fig. 2d. During the course of the reconstruction, thealgorithm was used to further solve for the complex amplitude of the probe as well, resulting in the illumination shownin Fig. 2c. As discussed in the supplementary information (SI), the reconstructed probe is completely consistent witha measurement of the unscattered beam at the detector. The high fidelity of the CDI reconstruction is evident by the FIG. 3: Height profile comparison between CDI and AFM. (a) 3D profile of the object based onptychographic reconstruction. (b) 3D profile of the object based on an AFM measurement. Any features taller than40 nm were thresholded to 40 nm for the 3D rendering. The histograms plotted under (a) and (b) were used tocalculate the average feature thicknesses of 35 nm and 32.7 nm based on the CDI and AFM measurements,respectively. The scale axis shown in (a) is shared by both (a) and (b). Note that the large debris spot on the rightof the AFM image was introduced after the CDI image was taken.fact that the majority of small defects visible in the SEM image of the Ti patterns (Fig. 2b) are also clearly visiblein the CDI reconstruction (Fig. 2d). Note that the large defect circled in the SEM image in Fig. 2b was the resultof sample contamination after the ptychography measurement. The SI contains a more detailed comparison betweenthe defects seen in the CDI reconstruction, and those seen in the SEM and AFM images (Fig. S3).Ptychography solves for the complex amplitudes of both the object and the probe (or incident beam) simultaneously[12, 18]. As a result, reliable quantitative information about the object can be obtained from the reconstruction, sincethe effect of the probe on the diffraction patterns is essentially divided out. The reflectivities of titanium and siliconat 29 nm for 45 ◦ angle of incidence are 9% and 0.5%, respectively [22]. The object reconstruction shows a ratio of ≈ − h cos θ , where h is the height above a reference (such as the substrate) and θ is the angle of incidence. At 45 ◦ angleof incidence for a feature thickness of 30 nm, the round trip path length difference between the silicon substrate andthe patterned titanium features is 42.4 nm. At 29.5 nm wavelength, this corresponds to between 1 and 2 wavelengthspath length difference. Thus, some prior knowledge is required in order to retrieve the absolute height of the features.A flattening method was applied to the reconstructed phase of the silicon substrate, similar to that used in atomicforce microscopy, due to some residual phase curvature reconstructed on the flat substrate. The peak-to-valleyheight variation of the subtracted surface fit was < × µ m field of view. After flattening,the reconstruction shows an average of 4.26 radians of phase difference between the titanium and silicon surfaces,corresponding to a 49.5 nm path length difference (when 2 π is added). This corresponds to a 35 nm average thicknessof the titanium patterns. A height map of the sample could then be produced by assuming that 2 π should be addedto any part of the reconstruction that exhibited an amplitude above 25% of the maximum (based on the relativereflectivities of titanium and silicon, as discussed above). The result of this analysis is displayed in Fig. 3a, andrepresents a significant improvement in image quality compared with all tabletop coherent reflective imaging to date.After the ptychography measurements were taken, an independent height map of the sample was obtained using aDigital Instruments Dimension 3100 AFM. The resulting AFM height map is shown in Fig. 3b, after applying thesame flattening method as that used for the CDI reconstruction. The AFM measurement shows an average height forthe titanium features of 32.7 nm, which agrees with the ptychography result within < ◦ ) and not on the absolute height difference. While the debris locations are still evident inthe CDI reconstruction (Fig. 2d), the modulo 2 π ambiguity of the phase information combined with the very shortwavelength prevents us from extracting the absolute height information of all features. However, a tomographic ormulti-wavelength approach would enable full 3D reconstructions of all features on a surface.Finally, we note that previously it was believed that full knowledge of the probe was necessary when using Fresnel(curved wavefront) ptychography for phase retrieval [13]. However, we find that for ptychographic grids of 3 × µ m diameter pinhole across the beamnear the focus. The probe that is retrieved using this method can be propagated to the sample plane for comparisonto the probe found in the course of the sample reconstruction. We found very good agreement between the two probereconstructions, independent of the accuracy of the starting guess for the probe. More details of this comparison canbe found in the SI.We have demonstrated the first general, tabletop, full field reflection mode CDI microscope, capable of imagingextended nanosurfaces at arbitrary angles in a non-contact, non-destructive manner. This technique is directly scal-able to shorter wavelengths and higher spatial and temporal resolution, as well as tomographic imaging of surfaces.By combining reflection-mode CDI with HHG sources in the keV photon energy region, it will be possible to capturenanoscale surface dynamics with femtosecond temporal and nanometer spatial resolution. Moreover, full characteri-zation of the curved wavefront of the illuminating HHG beam at the sample plane through ptychography opens up thepossibility for reflection keyhole CDI [23, 24]. This is significant for dynamic studies, since in contrast to ptychographyCDI which requires overlapping diffraction patterns, keyhole CDI needs only one diffraction pattern, and thereforerequires no scanning of the sample. METHODS
The process for obtaining the reconstruction shown in Fig. 2d was as follows:1. Tilted plane correction was applied to each of the 90 diffraction patterns in the full dataset.2. The standard ePIE algorithm [12] was applied to the corrected data, with subpixel scan position precisionhandled as in Maiden et al. [21]. A starting guess for the probe was calculated using knowledge of the sample-to-focus distance (300 µ m). The object starting guess was set to unity and the probe guess was normalizedto contain the same energy as the average diffraction pattern in the dataset. The algorithm was allowed toupdate the probe guess in parallel with the object guess at each sub-iteration. The algorithm was run in thisway for 20 full ptychographic iterations, at which point the probe guess had made much more progress towardsconvergence than the object guess. The object guess was reinitialized to unity, and the algorithm was restartedusing the new probe guess, and allowed to run for 100 iterations, long enough for both the object and probe toconverge to stable solutions.3. The object guess was re-initialized as described in step 2, and the probe guess was set to that found at the endof step 2. The subpixel position correction method [20] was applied to the ePIE, and the overlap constraint wasapplied with subpixel shifts of the probe[21]. The position correction feedback parameter β was started at avalue of 50, and automated as in Zhang et al. [20]. The probe guess was not allowed to update during this step.Again, the algorithm was run for 100 iterations, until the position corrections converged to < ◦ C. It was then spin-coated withMicrochem 2% PMMA in anisole, molecular weight 950 at 4000 r.p.m. for 45 seconds. Afterwards it was baked at180 ◦ C for 90 seconds. Electron beam lithography was performed using a FEI Nova NanoSEM 640, using NanometerPattern Generation System (NPGS) software and patterns. The resist was then developed by immersion in a 1:3solution of methyl-isobutyl-ketone:isopropanol for 30 seconds. Approximately 30 nm of titanium was evaporated ontothe surface using a CVC SC3000 3-boat thermal evaporator. The lift-off step was accomplished in acetone using asonicator.
AUTHOR CONTRIBUTIONS
M. S., B. Z., and D. A. designed the experiment. L. S. fabricated the sample. M. S., B. Z., D. A., and D. G.performed the experiments. M. S., B. Z., and D. A. analyzed the data. M.M and H.K. designed the HHG source andplanned the experiments. All authors contributed to the manuscript.
ACKNOWLEDGMENTS
We gratefully acknowledge support from the Semiconductor Research Corporation grant 2013-OJ-2443, the DARPAPULSE program through a grant from AMRDEC, a National Security Science and Engineering Faculty Fellowship, andfacilities provided by the National Science Foundation Engineering Research Center in EUV Science and Technology.D. G. and E. S. acknowledge support from an NSF IGERT program. [1] Miao, J., Charalambous, P. & Kirz, J. Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens.
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Opt. Express , 21970(2013). SUPPLEMENTARY INFORMATIONHigh Harmonic Beam Characterization Through Ptychography
To ensure that our recovery algorithm as discussed in the main text was correctly retrieving the probe illumination,we first characterized the extreme ultraviolet (EUV), high harmonic generation (HHG) beam by scanning a 5 µ mdiameter pinhole across the beam near its focus and reconstructed the illumination using ptychography. In this case,the pinhole can be thought of as the probe, while the beam is an effective object. The scan consisted of a 6 x 6 gridwith 1 µ m step size between adjacent scan positions. The reconstructed beam is shown in Fig. S1a.The reconstructed beam was propagated to the sample position (200 µ m upstream of the pinhole probe location)and calculated on the tilted plane (at 45 ◦ ) using tilted plane correction, shown in Fig. S1b. Immediately after thisptychography scan, the pinhole probe was removed and the sample was translated such that the beam illuminated oneof the star patterns on the sample (with reconstruction shown in Fig. 2d). We performed a 3 x 3 ptychographic scanacross the star feature, with 2.5 µ m step size. In this case, a probe starting guess consisting of a Gaussian amplitudeprofile with random phase sufficed to consistently retrieve the probe amplitude shown in Fig. S1c. As can be seenby comparison of Figs. S1b and c, the two beam characterization methods show very good agreement between boththe phase and the amplitude. It should be noted that the HHG beam drifted slightly inside the adjustable apertureduring the course of the two scans, resulting in slightly different beam structure during the two measurements. FIG. S1: A comparison of separate reconstructions of the HHG illumination beam, using the beamas the object in one case and as the probe in the second case. (a) Reconstruction of the HHG beam nearthe focus using a 5 µ m diameter pinhole probe. The main image displays the amplitude and the inset displays thephase. The scale bar has width 2 µ m. (b) The result of propagating the reconstructed beam from (a) to the tiltedsample plane. Again, the main image shows the amplitude and the inset shows the phase. The scale bar has width 5 µ m. (c) The amplitude (main image) and phase (inset) of the reconstructed probe based on a 3 x 3 ptychographicscan across the one of the features on the titanium sample discussed in the text. The scale bar is shared with (b).Note that the beam amplitudes in (b) and (c) are displayed in the tilted sample coordinates, resulting in elongationin the horizontal direction.As a further consistency check, the probe reconstruction discussed in the main text (shown in Fig. 2c) was propagatedto the detector, and the tilted plane correction was undone in order to examine the result in the real coordinates ofthe detector. The result of these steps is shown in Fig. S2a. A comparison was made with a direct measurement ofthe unscattered beam by translating the sample to a featureless region of the silicon substrate, shown in Fig. S2b. Ascan be seen in Figs. S2a and b, while it is evident that, as in the above sample plane comparison, some beam drift FIG. S2: Comparison between the illumination reconstructed as a ptychographic probe andpropagated to the detector, and the unscattered illumination measured directly on the detector (rawdata). (a) The probe reconstruction from Fig. 2c in the main text, propagated to the detector plane. (b) The HHGbeam measured directly on the detector by translating the sample to a featureless region of the silicon substrate.The scale bar in (a) has width 1 mm and is shared by (a) and (b).occurred during the course of the ptychographic scan, the reconstructed probe is entirely consistent with the highharmonic beam used to illuminate the sample.
Comparison between CDI reconstruction and SEM and AFM images
As mentioned in the main text, there are a number of defects visible in the sample image reconstructed throughptychography coherent diffractive imaging (CDI) which are also visible in scanning electron microscope (SEM) andatomic force microscope (AFM) images. A visual comparison between the three techniques is shown in Fig. S3. Ofthe 7 defects pointed out in the figure, only defects 1-5 are visible in all of the images. The 6th and 7th defects areonly visible in the CDI phase image and the AFM image. This is a demonstration of the fact that CDI has bothamplitude contrast (analogous to SEM) and phase/height contrast (analogous to AFM).