Efficient focusing of 8 keV X-rays with multilayer Fresnel zone plates fabricated by atomic layer deposition and focused ion beam milling

The fabrication and performance of multilayer Al2O3/Ta2O5 Fresnel zone plates in the hard X-ray range and a discussion of possible future developments considering available materials are reported.


Introduction
X-ray microscopy is an invaluable tool for many scientific and technological fields such as, for instance, material (Zschech et al., 2011), environmental (Brown & Sturchio, 2002) and life sciences (Lewis, 1997;Fouras et al., 2009). The utilization of focused X-rays has spread continuously over recent decades and includes applications such as imaging, chemical analysis (Sakdinawat & Attwood, 2010) and time-resolved investigation by exploiting pulses of synchrotron radiation (Kammerer et al., 2011;Van Waeyenberge et al., 2006;Saes et al., 2003). In contrast to electron microscopy, X-ray microscopy provides high penetration depth and enables three-dimensional imaging of complete cells (Vogt et al., 2000), large alive biological samples (Olendrowitz et al., 2012) and in situ investigation under extreme conditions (Fife et al., 2012). As the theoretical resolution is determined by the wavelength, hard X-ray microscopy is a very promising technique for highresolution imaging with chemical sensitivity (Schroer et al., 2004). Unfortunately, the focusing optics for hard X-rays are limited in terms of resolution and/or diffraction efficiency (DE). Conventionally, Kirkpatrick-Baez mirrors (KBMs) are used for focusing hard X-rays despite difficulties in manufacturing and high costs, and routinely achieve two-dimen-sional resolutions in the range of a few hundreds of nanometers (Ruhlandt et al., 2012;Riekel et al., 2009). Higher resolutions were also reported with advanced wavefrontcorrection techniques . Yet another example of advanced KBMs is based on a set of four mirrors, two elliptical and two hyperbolic, which achieved approximately 50 nm resolution (Matsuyama et al., 2012). Other approaches for two-dimensional focusing of X-rays include using, for instance, crossed nanofocusing lenses [below 50 nm foreseen (Schroer et al., 2010), 80 nm reported (Schropp et al., 2012)], crossed multilayer Laue lenses (MLLs) (Yan et al., 2011) or compound refractive lenses (Lengeler et al., 2005) with potential for high energies up to 100 keV (Vaughan et al., 2011). In one dimension X-rays could be focused down to 50 nm  with onedimensional Wolter optics and to 16 nm (Kang et al., 2008) and 7.5 nm (Ruhlandt et al., 2012) using single MLLs. The lack of high-performance optics for hard X-rays led to lensless microscopy (Falcone et al., 2011) which requires high coherence. Lensless techniques can benefit from a high flux via focusing optics, enabling an increased coherent flux density, improving the resolution (Schropp et al., 2012).
Fresnel zone plates (FZPs) (Falcone et al., 2011) provided the highest two-dimensional resolutions for soft X-rays (Chao et al., 2005(Chao et al., , 2009Vila-Comamala et al., 2009). Their resolution at the first-order focus is determined by the width of the outermost zone, Ár n , via the relation r Rayleigh = 1.22 Ár n , where r Rayleigh is the Rayleigh resolution (Attwood, 2000). It follows from this relation that decreasing Ár n increases the resolution. Electron beam lithography (EBL), the conventional method for FZP fabrication, enabled fabrication of ever smaller values of Ár n . Although FZPs fabricated via EBLbased methods are presently employed for focusing hard X-rays, the limitation in achievable aspect ratios (A r = t/Ár n , where t is the thickness) of current FZPs limits their diffraction efficiencies (Chen et al., 2008;Chu et al., 2008;Vila-Comamala et al., 2012).
In this work we report the preparation and testing of highaspect-ratio FZPs with high efficiency in the hard X-ray range. The new fabrication method employed delivers multilayer FZPs (ML-FZPs) and implicates the use of atomic layer deposition (ALD) and focused ion beam (FIB) milling (Mayer et al., 2011). ML-FZPs (also called 'sputtered-sliced' FZPs) were introduced in the 1980s as an alternative approach to fabricate FZPs with high A r (Rudolph & Schmahl, 1980;Rudolph et al., 1981). Unfortunately, three decades after its introduction, and despite the fact that the approach has been pursued by various groups (Bionta & Skulina, 1993;Golant et al., 2007;Koyama et al., 2011;Liese et al., 2011;Tamura, 2011), ML-FZPs failed to achieve the anticipated high resolution and DE for hard X-rays, as fabrication techniques failed to meet the required high precision. Recently, our group fabricated a high-quality ML-FZP by combining ALD and FIB and demonstrated the resolution of sub-39 nm structures at 1.2 keV (Mayer et al., 2011), the highest resolution achieved by a ML-FZP to the best of our knowledge. The method consists of coating a wire with alternating layers of two materials of proper refractive indices. Subsequent slicing/ polishing delivers the ML-FZP of desired thickness t. As there is no limitation to the thickness t of a ML-FZP, the method is especially suited for fabricating high-A r FZPs. While ALD gives atomic control over Ár n , i.e. resolution, via highly conformal layers around the substrate with very high quality interfaces, FIB slicing of the multilayer ensures local control, a precise cut and preserves the integrity of the layers. Focusing properties of the ML-FZPs with Ár n = 35 and 10 nm were tested at 8 keV, from which experimental DEs were estimated. Estimates were compared with the results of the thin-grating (TG) approximation (Kirz, 1974;Yun et al., 1992) within the framework of scalar diffraction theory and considering the volume effects described by coupled wave theory (CWT) (Schneider et al., 2008) using published data for complex refractive indices [CXRO, LBNL, USA (Henke et al., 1993)]. Scanning transmission X-ray microscopy (STXM) with one of the FZPs with Ár n = 35 nm was also performed at 1.5 keV. Following theoretical calculations and fabrication prospects, issues concerning the choice of material for ML-FZPs at 8 and 17 keV for future developments are discussed.

Experimental method
Commercial glass optical fibers (A2 by SCHOTT AG, Germany; D = 30 mm) were coated with alternating layers of Al 2 O 3 and Ta 2 O 5 via ALD following the zone-plate law. The total layer thickness was 4 mm, composed of 103 to 360 zones, resulting in ML-FZPs with 38 mm diameter and an active focusing region that is 37.7% of the total area. ML-FZPs with Ár n = 35 and 10 nm were prepared; their parameters and names are given in Table 1. The resulting multilayer structures were sliced and polished using FIB (Nova NanoLab, FEI, The Netherlands) to deliver the ML-FZPs which were mounted on molybdenum TEM grids for easy handling. According to CWT calculations the required thickness for the best efficiency, t Optimum , of ZP10 is 2.45 mm whereas it is 8.85 mm for a ML-FZP with Ár n = 35 nm. The realised thickness, t Real , of the ZP10, ZP35t and ZP35opt ML-FZPs were $ 1.9, $ 5.9 and $ 8.5 mm, respectively. A r values of ML-FZPs here are extremely high (169 for ZP35t, 243 for ZP35opt and 190 for ZP10) when compared with zone plates used for soft or hard X-ray microscopy prepared by e-beam lithography, the maximum of  Table 1 Summary of properties of the ML-FZPs.
ZP35t: ML-FZP with 35 nm outermost zone width and less than optimum thickness. ZP35opt: ML-FZP with 35 nm outermost zone width and thickness close to optimum thickness. ZP10: ML-FZP with 10 nm outermost zone width. r T /r Act : total radius of the FZP/width of the active area. A f Active : area fraction of active zones. Ár n : outermost zone width. N: number of zones in the active area. f 8 keV : focal distance at 8 keV. t Optimum /t Real : optimum thickness according to CWT/realised thickness. A r : realised aspect ratio, t Real /Ár n .
Type  (Mayer et al., 2011). Focusing tests at 8 keV were carried out at beamline ID06 of ESRF (Grenoble, France). In these tests the ML-FZPs were mounted on precision translation and rotation stages (HUBER Diffraktionstechnik GmbH, Germany) downstream of the X-rays. A CCD camera with 1376 Â 1040 pixels and 6.45 mm pixel size (Sensicam QE, PCO AG, Germany) equipped with a scintillator, which converts X-rays into visible light, and an objective lens (Olympus, UPLAPO) with 10Â magnification were utilized as the detector. Hence, the resolution is 1.3 mm (2 pixels) and the field of view is 887 mm Â 670 mm. First, the camera and ML-FZP were centred on the optical axis. Then, the sample stage and camera were moved towards each other until a section of or a complete bright ring appears in the projection image of the zone plate on the CCD camera. The bright ring consists of light which is diffracted from the active zones of the ML-FZP. At the same time as the bright ring appears, the area on the zone plate from which the light is diffracted away appears dark in the image. If only a section of a ring appears, the inclination between zone plate and beam has to be corrected via rotation about the pitch and yaw axes (Fig. 2) until the ML-FZP surface is perfectly perpendicular to the beam. When aligned to the optical axis, the active zones of the ML-FZP form a hollow cone of diffracted light which narrows towards the focal length (projection distance p < f ; see Fig. 2), reaches a spot with minimum diameter at the focal length (p = f ) and then diverges again ( p > f). In the case of ZP35t and ZP35opt (Ár n = 35 nm), the first-and second-order focus could be reached ( p = f and p = f /2, respectively) whereas in the case of ZP10 (Ár n = 10 nm) it was not possible to approach the camera close enough to be able to reach the first-order focal spot as the camera body prevented it coming closer to the ML-FZP ( p > f ). The evaluation of DE from the focusing experiments was performed according to the following procedure: the amount of incident light on the FZP (I i ) was determined by multiplying the count density from an unobstructed area in the vicinity of the FZP by the active area of the FZP. Then, a background-subtraction algorithm was employed (Sternberg, 1983;Bleiner et al., 2011) to subtract the effect of radiation transmitted through the glass core prior to determination of the total light intensity in the diffraction pattern (I f ). The ratio I f /I i gives the estimated DE. It should be noted that the method employed here is not exact but should be taken only as an estimate owing to difficulties in separating the background intensity from that of the first-order focus. In the case of ZP35opt, which was tested on three occasions in two synchrotron experiments, the DE was estimated by taking all experiments into account.
In order to further evaluate the performance of the ML-FZPs as focusing optics for X-ray microscopy, ZP35t was also tested in a dedicated X-ray scanning transmission microscope at 1.5 keV (MAXYMUS, BESSYII, Berlin, Germany) by imaging a standardized Siemens star as a test object (X30-2-2, Xradia, USA). The MAXYMUS is a highly stable microscope which allows for very high resolution imaging (Follath et al., 2010).

Experimental results and discussion
After alignment of the ML-FZPs perpendicular to the X-ray beam by tuning pitch and yaw axes the initial far-field projection of the ML-FZPs on the CCD [Figs. 3(a) and 3(e)] transformed into circularly symmetric diffraction rings [Figs. 3(b) and 3(f ), p > f ]. The symmetry of the diffraction pattern is a result of the high overall quality of the ML-FZPs and shows that all portions of the optical device function properly. When the distance p was decreased, the radii of the diffraction rings became proportionally smaller until a focal spot was observed on the camera at the focal distance. In the cases of ZP35t and ZP35opt, it was possible to find the focal plane (within the precision of the set-up) as shown in Fig. 3(c), p = f. The diffraction pattern at position p = f (first-order focal spot) is spread over several pixels owing to pixel cross-talk and the grained structure of the scintillator. As p was reduced further, the diameter of the first-order focal ring increased again and, as it approached f /2, it was possible to observe the secondorder focus and underfocused first-order diffraction ring ( p = f /2) on the same CCD image (Fig. 3d). The activation of the second diffraction order, which should not exist for a perfect Scanning electron micrographs of ML-FZPs with Ár n = 35 nm (ZP35) (a) and 10 nm (ZP10) (b). Note the high quality of the zones.

Figure 2
Schematic representation of the experimental set-up that was used at beamline ID06 of the ESRF for focusing and DE measurements (not to scale). rectangular standard FZP, is a result of deviations from the ideal FZP. Controlling this effect can be used for higher-order imaging for increased resolution (Baciocchi et al., 1994;Yi et al., 2011). Here, this activation could be a result of the nonideal zone profile, a line-to-space ratio that is different from 1 : 1 and a non-ideal zone placement or a combination thereof. In the same way after alignment the diffraction pattern of ZP10 appears as a ring on the screen of the camera [Figs. 3( f ) and 3(g)] and is again a sign of the good quality of and symmetry of the zone plate. In these experiments all three ML-FZPs were shown to behave like a lens and focus 8 keV hard X-rays as expected.
The experimental DE of the ZP35t was estimated to be 15.58% versus 20.14% as predicted by the CWT which means that more than 77% of the theoretical DE was reached at 8 keV photon energy. ZP35opt was found to be 11.93% efficient with a standard deviation of 2.82% in three different measurements exhibiting reasonable repeatability. This corresponds to 48% of the theoretical DE which is lower than the ZP35t sample and will be discussed below. The measured DE of ZP10 was 1.87% which corresponds to about 81% of the theoretically predicted DE of 2.31%, according to CWT (see Fig. 4). High performances of the ML-FZPs were enabled by the outstanding quality of the layers as a result of the ALD process. From Fig. 4, it can be seen that the theoretical DEs of a ML-FZP with Ár n = 35 nm according to the CWT and TG approximation are very close even at very large aspect ratios. CWT and TG approximations give especially close estimations of efficiencies when the difference in photon wavelength and Ár n is large and the thickness of the structure is lower than the optimum thickness (see Fig. 4).
The reason for the difference in the abilities of ZP10, ZP35t and ZP15opt to approach their respective theoretical DE may be speculated to be the different thicknesses of the ML-FZPs.
The thicker ML-FZPs ZP35t and ZP35opt are more sensitive to perfect alignment of the FZP and the structural irregularities that may be present in the propagation direction of the X-rays. The accumulated impact of these errors may be reflected by a reduced performance as the thickness increases. Although in-depth investigations should be carried out to find the exact reason for these differences, the effect of thickness should be taken into account when selecting a proper material pair for the design of a ML-FZP as t Optimum for any candidate material should be as thin as possible in order to reduce the impact of imperfection on performance.
Taking advantage of its relatively low thickness, ZP35t was also tested at a lower photon energy (1.5 keV) in order to gain an insight into the focusing properties of the ML-FZP at the Theoretical efficiencies of ML-FZPs made out of Al 2 O 3 and Ta 2 O 5 with different Ár n as a function of thickness. CWT parameters were: zones parallel to optical axis, magnification of 10000Â, line-to-space ratio 1:1.

Figure 3
Diffraction experiments at 8 keV. Top row: far-field image of ZP35t on camera: (a) misaligned and defocused, (b) aligned and defocused, p > f, (c) camera in first-order focus, p = f (contrast enhanced for visibility), and (d) camera in second-order focus, p = f /2. Bottom row: far-field projection of ZP10 on camera: (e) misaligned and far from focus, ( f ) aligned and overfocused, p >> f, and (g) camera as close to the focus as the set-up permits, p > f. scanning X-ray microscope MAXYMUS. The STXM images of a Siemens star test object were recorded using ZP35t as the objective lens (Fig. 5). The spikes in the second ring from the center have smallest local periods of 120 nm which were clearly resolved. Theoretically, the resolution of this ML-FZP should have been $ 43 nm full period according to the Rayleigh criterion. Interestingly, in spite of attempts to resolve the innermost ring with 60 nm smallest local period, the achieved resolution was about 120 nm period, i.e. 60 nm feature size. This was presumably due to the low signal-tonoise ratio which was in turn caused by the very low DE of ZP35t at 1.5 keV (0.56%, theoretically) and the absence of a beamstop. The core of the ML-FZP which consists of silica glass of 5.9 mm thickness has a transmission of more than 20% at 1.5 keV which causes strong background radiation. Combined effects of a low DE and the absence of a beamstop resulted in the pronounced noise in the image shown in Fig. 5. It is believed that this increased noise caused the smallest structures to remain unresolved. When the STXM images in Fig. 5 are closely inspected, an apparent astigmatism is observed that is a variation in resolution in different directions. This could be due to several reasons, one of which is the misalignment of ZP35t from the optical axis as there were no possibilities to correct any misalignment at the MAXYMUS set-up. Owing to the very high aspect ratio of the ML-FZP, any misalignment from the optical axis may also cause a reduction in the numerical aperture due to a reduction of the effective active zone area leading to deterioration of the resolution in certain directions. A tilt stage which can be fit into the MAXYMUS to correct for possible misalignments is currently under development and will be available in the next months. Astigmatism may also originate from the variation of deposition thickness along and around the fiber which is very challenging to characterize in three-dimensions and must be investigated in more depth. The circularity of the core fiber as a possible source of astigmatism is excluded since it was already shown in a previous study that the fiber is cylindrical enough to be used as a substrate for a ML-FZP (Mayer et al., 2011).
A 30 mm-wide beamstop as a central obstruction corresponds to 62% of the surface area of the lens, which leads to a significant apodization effect and resultant transfer of energy to the side-lobes of the Airy pattern (Simpson & Michette, 1984) with an accompanied shift of first zero-crossing radius of the Airy pattern, which is the definition of Rayleigh resolution (Attwood, 2000), to approximately 32.7 nm instead of 42.7 nm. Any negative or positive impact of this effect on the presented ML-FZPs remains to be confirmed.
Up to this point it has been shown that the ML-FZPs investigated in this work function properly at 8 keV with remarkable diffraction efficiency performances. In spite of low theoretical DEs and low signal-to-noise ratios owing to the absence of a beamstop, it was possible to perform scanning X-ray microscopy even at 1.5 keV thanks to the precision of the fabrication methods through which the ML-FZPs were fabricated. Furthermore, it was shown by this experiment that a FZP with A r = 169 can perform very well with hard and soft X-rays, and can resolve at least 60 nm-sized features. As a future work the ultimate resolution of the present ML-FZPs with hard X-rays needs to be determined through rigorous testing in an optimized set-up for higher signal-to-noise ratio. For future work and development of ML-FZPs an important point to be considered is the appropriate choice of material. At this point it has to be noted that the selection of the pair Al 2 O 3 /Ta 2 O 5 in this work was not made for optimized DE at a specific wavelength but was a compromise between availability and ease of deposition via ALD and reasonable DE. Future possibilities for materials choices and resulting achievable resolutions at reasonably high efficiencies will be discussed in the next section in the light of theoretical calculations.

Materials selection and performance expectations for future ML-FZPs
In addition to the rather reasonable DE of Al 2 O 3 /Ta 2 O 5 both with soft (Mayer et al., 2011) and hard X-rays, these materials were essentially selected for their established deposition routes via ALD. Nevertheless, the choice of material can be optimized. In this section the optimization of material selection for the hard X-ray range from 8 to 17 keV based on theoretical considerations and current advances in ALD deposition and the availability of materials will be discussed.
The diffraction behaviour of Fresnel zone plates (and gratings in general) is classified into three regimes (Maser & Schmahl, 1992;Moharam & Gaylord, 1981;Klein & Cook, 1967); (i) the Raman-Nath (Raman & Nath, 1935)   where the zone plate behaves like a thin grating and where, for instance, the theory developed by Kirz is applicable (Kirz, 1974); (ii) the Bragg regime, in which the FZP behaves like a thick grating; and (iii) the intermediate diffraction regime. The FZPs that fall into the Raman-Nath regime are characterized by very large Ár n relative to wavelength and very low aspect ratio. On the other hand, FZPs with Ár n comparable with the wavelength (or even smaller) and high thicknesses fall into the Bragg regime. The third group of FZPs cluster in the intermediate diffraction regime. Most of the high-resolution X-ray FZPs as well as the ML-FZPs presented in this work belong to this latter category (Maser & Schmahl, 1992). In this case and in the Bragg regime, volume effects within the FZP have to be taken into consideration to account for the diffraction behaviour whereupon it was also shown (Maser & Schmahl, 1992;Schneider, 1997) that high resolutions (e.g. 10 nm) at high efficiencies can essentially only be achieved if the zones are tilted towards the optical axis to locally satisfy the Bragg condition. Here, we show that an appropriate choice of materials allows this limitation to be circumvented to some extent. Depending on the materials, a reasonable DE can be obtained at hard X-rays without tilting zones for resolutions as low as 10 nm and possibly 5 nm. As an illustration, the DEs of three different material pairs were evaluated within the framework of CWT, which takes the above-mentioned volume effects into account, and are compared in Figs. 6(a) and 6(b) for Ár n = 10 and in Figs. 6(c) and 6(d) for Ár n = 5 nm at 8 and 17 keV, respectively. The DEs of the specific pair Al 2 O 3 /Ir at 8 and 17 keV for Ár n = 35 to 5 nm are also compared in Figs. 6(e) and 6(f ). In a previous study (Mayer et al., 2011) the pair Al 2 O 3 /SiO 2 was shown to be a very promising candidate for efficient focusing of soft X-rays. At harder X-rays it appears that Al 2 O 3 /Ir performs very well and has a significantly higher theoretical DE both at 8 and 17 keV photon energies with more than 20% DE for Ár n = 10 nm [Figs. 6(a) and 6(b)]. At even smaller outermost zone widths the CWT predicts reasonable efficiencies with, for instance, >4% for Ár n = 5 nm [ Fig. 6(c) and 6(d)]. However, it has to be noted that for such thin zones the resolution of the zone plate may differ from and be effectively lower than that predicted by the Rayleigh criterion (Kang et al., 2006;Schroer, 2006). The theoretical DEs of the promising Al 2 O 3 /Ir pair for various Ár n are given in Fig. 6(e) for 8 keV and Fig. 6( f ) for 17 keV. The degradation of the DE when the outermost zone width is decreased from 35 to 10 nm in an Al 2 O 3 /Ir ML-FZP at both energies is not as significant as it is in the case of Al 2 O 3 /Ta 2 O 5 (Fig. 4) and renders this material pair very interesting. The preparation of a FZP with very thin zones such as 10 nm and/or presenting a tilt angle towards the optical axis which, as previously mentioned, may be necessary to achieve even higher resolution, are paramount challenges as current fabrication techniques can barely achieve structure sizes below 10 nm. It is believed by the authors that the ALD/FIB technique has the potential to push these boundaries in the future. From a fabrication point of view, both alumina (Niinistö et al., 2004) and iridium (Aaltonen et al., 2004) can be deposited via established ALD routes. It is also worth noting that t Optimum of all above-mentioned Al 2 O 3 /Ir ML-FZPs are of the order of only a few micrometers, which would help in reducing the impact of the previously mentioned effect of structural error accumulation in propagation direction as thickness increases.

Conclusions
Efficient focusing of 8 keV hard X-rays using ML-FZPs was successfully demonstrated using ML-FZPs with Ár n = 10 and 35 nm. Efficiencies up to >15%, representing 77% of theoretically predicted values, were achieved. This was made possible by utilizing high-precision fabrication methods with control over the nanoscale multilayer thickness via atomic layer deposition and the microscale structure thickness via focused ion beam milling. Soft X-ray scanning microscopy with the ZP35t multilayer Fresnel zone plate showed that the imaging was possible, despite the very low theoretical efficiency and the lack of a beamstop which contributed to the noise in the image, by resolving features as small as 60 nm. Further developments towards efficient and high-resolution diffractive optics considering different materials were discussed using coupled wave theory (CWT) and the thingrating (TG) approximation. It was shown that use of absorptive iridium and transparent alumina in a multilayer Fresnel zone plate could lead to a theoretical efficiency of more than 20% for an outermost zone width of 10 nm at 8 and 17 keV photon energies. As future ML-FZP materials, Al 2 O 3 / Ir promises reasonably high efficiencies even without introducing a tilt angle to the zones to satisfy the Bragg condition at least down to about 10 nm resolution in the hard X-ray range. Further experiments to test these theoretical predictions are planned for the future.