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We report a Bragg beam splitter developed for utilization of hard x-ray free-electron lasers. The splitter is based on an ultrathin silicon crystal operating in the symmetric Bragg geometry to provide high reflectivity and transmissivity simultaneously. We fabricated frame-shaped Si(511) and (110) crystals with thicknesses below 10 μm by a reactive dry etching method using atmospheric-pressure plasma. The thickness variation over an illuminated area is less than 300 nm peak-to-valley. High crystalline perfection was verified by topographic and diffractometric measurements. The crystal thickness was evaluated from the period of the Pendellösung beats measured with a highly monochromatic and collimated x-ray probe. The crystals provide two replica pulses with uniform wavefront [(<1/50)λ] and low spatial intensity variation (<5%). These Bragg beam splitters will play an important role in innovating XFEL applications.
©2013 Optical Society of America
1. Introduction
Recently, the Linac Coherent Light Source (LCLS) [1] at the SLAC National Accelerator Laboratory and SPring-8 Angstrom Compact free electron Laser (SACLA) [2] at RIKEN, SPring-8 started operation of hard x-ray free-electron lasers (XFELs) based on the self-amplified spontaneous emission (SASE) scheme, which provide brilliant, coherent, and ultrafast hard x-ray pulses. Interesting applications, including structural determination of biological molecules and viruses [3–5], creation of high-energy-density states of matter [6], and investigation of x-ray-matter interactions [7,8], have been reported. For exploiting innovative applications using XFEL, the development of new optical devices is highly important. In particular, beam splitting devices will be useful for a broad range of applications. For example, beam splitters are essential components in split-delay optics (i.e., autocorrelators) that can be used to create two replica XFEL pulses with a tunable time interval in an extremely high accuracy up to the attosecond range. Another application of beam splitters is to compose a dedicated branch for photon-beam diagnostics (e.g., spectrum distribution, coherence property, wavefront, and pulse duration) [9–12], which is essential for all experiments at XFEL sources.
In XFEL applications, beam splitters are required to preserve the wavefront and temporal structure of XFEL pulses. Tunability of efficiency, as well as high robustness, is also important. Beam splitters used in the hard x-ray regime can be classified into three types: mirror-based geometrical splitters, grating-based splitters using different diffraction orders, and crystal-based splitters. An autocorrelator for the vacuum ultraviolet (VUV) FELs and the soft XFELs consisting of mirror-based splitters has been reported [13,4]. Although this type of splitters can be extended to the hard x-ray regime, the small acceptance due to the reduced critical angle makes it hard to control and stabilize the beam splitting ratio. Grating-based splitters were realized [15,16], while the delay range is limited with the small angle between the split beams. For crystal-based splitters, the Laue geometry has been widely used. For example, an interferometer [17] and an autocorrelator [18] using the Laue beam splitters have been developed. However, the devices introduce a spatial spread of the x-ray beam, called the Bormann fan (see, for example, Ref. [19]), which could provide significant complication in the two replica pulses when the devices are used to manipulate ultrafast pulses [20]. In contrast, splitters operating in the symmetric Bragg geometry (i.e., Bragg beam splitters) generate replica pulses with simple spatial and temporal structures, which is suitable for most XFEL applications.
To date, there were only a few reports of the Bragg beam splitters because of the difficulties in fabrication processes [21]; the crystal must be sufficiently thin for decreasing absorption in the refraction branch, while lattice bending, which possibly originates from residual strain or crystal mounting, should be avoided. Furthermore, variations in thickness over an illuminated area, which could produce unwanted perturbations in wavefront and intensity for replica pulses, should be reduced. We propose applying silicon crystals, which are widely used as monochromators in the hard x-ray regime. Note that the ablation threshold (0.8 μJ/μm2) is higher than the fluence of direct XFEL beams (<0.02 μJ/μm2) [22]. Although ultrathin near-perfect silicon crystals were available using the silicon-on-insulator technology, the crystal orientation to be realized is limited to (111) [23]. An applicability to various orientations are important for controlling longitudinal coherence length or energy bandwidth at a wide range of photon energies. In this paper, we report a new method to fabricate the Bragg beam splitters. Ultrathin silicon single crystals were fabricated with a reactive dry etching method using atmospheric-pressure plasma that does not have selectivity of the crystal orientations. Evaluation results with coherent x-rays at SPring-8 are described.
2. Design and fabrication of Bragg beam splitters
Our target is to fabricate thin and strain-free crystals with uniform thickness distributions over the illuminated area. First, we discuss the optimal crystal thickness. Figure 1 shows reflectivity R and transmissivity T for the Si(511) reflection at the exact Bragg condition as a function of the crystal thickness t at a photon energy of 10 keV, which are evaluated with the dynamical theory of x-ray diffraction. The incident x-ray beam was assumed to be a monochromatic plane wave. As seen in Fig. 1, we obtain equal intensities for the two replica pulses at t = 7.1 μm. For reference, we show the transmissivity T0 at a detuned photon energy (Edet > 500 meV) from the exact Bragg condition. In this case, we can obtain high transmissivity (e.g., T0 > 0.75) with a thickness range of 7–23 μm. Note that this transmissivity largely depends on the photon energy because the Bragg angle changes (i.e., effective crystal thickness changes). For example, the crystal thickness should be below 15 μm for 8 keV x-rays. When we use lower order reflection, in addition, the optimal thickness becomes smaller because of smaller the Bragg angle and smaller the penetration depth.
Fig. 1 Reflectivity R (solid) and transmissivity T (dashed line) as a function of a crystal thickness t, calculated from the dynamical theory of x-ray diffraction for the Si(511) reflection operating in the symmetric Bragg geometry with a 10 keV monochromatic plane wave. The chain line shows the transmissivity T0 at a detuned photon energy (Edet > 500 meV). The inset shows the intrinsic reflectivity (solid line) and transmissivity (dot line) as a function of energy deviation ΔE for a thickness of 20 μm. The upper and lower dashed lines denote T0 and T, respectively. The bandwidth of the reflected beam is approximately 100 meV.
Second, thickness uniformity is important for suppressing intensity modulations and for avoiding wavefront distortion. We set an upper limit of an intensity variation and that of phase error to be 10% and (1/30)λ, respectively, which corresponds to a thickness variation being smaller than 500 nm peak-to-valley (P-V).
We describe the design of the beam splitter. To avoid bending, we designed a frame-shaped crystal, as shown in Fig. 2 . The thin area serving as a beam splitter is supported by a thick tapered frame. This taper angle sets the minimum Bragg angle θmin for which the transmission beam is usable. The corresponding maximum photon energy Emax is given hc/(2d sinθmin), here h is the Plank’s constant, c is the speed of light, and d is the lattice spacing of the reflection plane. We used 20° for the taper angle, which corresponds to Emax = 9.44, 17.34, and 18.88 keV for the Si(220), (511), and (440) reflections, respectively (d220 = 1.92 Å, d511 = 1.05 Å, and d440 = 0.96 Å). Under these conditions, the length of the foot-print on the crystal surface is approximately 600 μm, which accepts the XFEL beam with a diameter of 200 μm.
Fig. 2 Schematic of the frame-shaped crystal. The crystal size is 25 mm × 25 mm. The thin area with a diameter of 5 mm and thickness t is supported by a 1.5-mm-thick tapered frame with a taper angle of 20°.
The crystals were fabricated by a combination of mechanical grinding and plasma chemical vaporization machining (PCVM) [24] that is a reactive dry etching method using atmospheric-pressure plasma. Owing to the high pressure, ions with low kinetic energy and short mean free path are generated in the plasma, which suppress to induce lattice strains. Another advantage of this method is a capability to localize the processing area, down to several hundred μm diameter. Furthermore, we empirically found that PCVM using fluorine radicals etches the silicon target isotropically with a processing speed that is independent of crystal orientation [e.g., (111) or (511)]. We describe the fabrication process as follows. First, the frame-shaped figure is roughly prepared by mechanical grinding from a 1.5-mm-thick silicon plate. Next, PCVM is applied to remove the damaged layer created during the mechanical grinding and reduce the thickness of the thin area. Finally, variations in thickness were uniformed with computer-controlled (CC) raster scanning of the highly localized plasma. More details are described in Ref. [25].
As samples, we fabricated Si(511) and (110) crystals. Surface profiles of the thin areas with CC raster scanning are shown in Figs. 3(a) and 3(b). The sizes of these areas are typically 2 mm × 2 mm. The profiles were measured by a phase-shift interferometric micrometer (ZYGO, NewView 200 HR). These profiles correspond to the variations in the crystal thickness because profiles on back side surface are extremely flat (<50 nm P-V). Figure 3(c) shows a line profile of the (511) crystal along the dot line AA’ in Fig. 3(a). The thickness variation is approximately 300 nm P-V, which would lead to a wavefront error of (1/50)λ and an intensity variation of less than 5%, which satisfies the criteria. We obtained much smaller variation for the (110) crystal. The surface roughness of both samples is below 0.2 nm rms in a 64 μm × 48 μm area on both sides, which is better than that with conventional solution etching method.
Fig. 3 Crystal surface profiles of thin areas with computer-controlled raster scanning for (a) (511) and (b) (110) crystals. Panel (c) shows the line profile along the 600 μm dot line AA’, in which the thickness variation is approximately 300 nm peak-to-valley.
3. Evaluation of crystalline perfection
3.1 Experimental setup
To evaluate the degree of crystalline perfection, we used plane-wave topography and diffractometry measurements at the 1-km-long beamline BL29XUL of SPring-8 [26]. The measured rocking curve Im is expressed as a convolution of an intensity distribution Iin of incoming x-rays and a reflectivity (transmissivity) distribution Rs (Ts) of the samples as a function of angle (θ) and wavelength (λ). The curve Im is given by
The dynamical theory of x-ray diffraction states that a thin perfect crystal operating in the Bragg geometry produces intensity oscillations in the rocking curves for the reflection and refraction branches. These oscillations, called the Pendellösung beats, are caused by interference between x-rays reflected from the entrance and the back side surface. The period of the Pendellösung beats, which provides information on the crystal thickness, is typically a few microradians. According to Eq. (1), measurement of the Pendellösung beats requires a highly monochromatic and collimated x-ray probe. So far non-dispersive highly-asymmetric geometry has been used to resolve the narrow features in perfect-crystal diffraction [21, 27]. In this study, we use an alternative approach that employs highly monochromatic and collimated x-rays from brilliant synchrotron sources [28].
Figure 4 shows a schematic of the setup. First, the x-ray beam from an undulator is reflected by a high-heat-load Si(111) double crystal monochromator (DCM). A four-bounced Si(444) reflection arranged in the (+, −, −, +) geometry is utilized for higher monochromatization in the experimental hutch 1 (EH1), 52-m downstream from the source. We achieved an energy resolution ΔE/E = 4.8 × 10−6 being smaller than the intrinsic energy width of 8.3 × 10−6 for the (511) reflection. Furthermore, we accomplished high angular resolution (better than 1 μrad) at the experimental hutch 4 (EH4) after the 1-km beam transport. Finally, the x-ray probe was delivered to the samples at the Bragg angle θB = 45°. The photon energy was 8.39 and 9.13 keV for the (511) and (440) reflection, respectively. The intensity of the x-ray beam reflected (refracted) from the samples were measured by PIN photodiodes, PIN1 (PIN2), and topographs of the reflection was taken by a CCD camera with 6 μm × 6 μm pixel size.
3.2 Results
The intensities reflected from the (511) and (110) crystals were measured with aperture sizes of 0.3 mm (horizontal) × 0.2 mm (vertical) and 0.5 mm (horizontal) × 0.2 mm (vertical), respectively. The Pendellösung beats are clearly observed, as seen in Figs. 5(a) and 5(b). The theoretical curves, which are shown in Figs. 5(a) and 5(b) as solid lines, were calculated assuming thicknesses of 6.9 and 6.6 μm, respectively. For both samples, the intensities of both the reflected and refracted beams well agree with the theoretical curves. The visibility of the Pendellösung beats, which depends on the thickness uniformity, of the (110) crystal is higher than that of the (511) crystal. This result well agrees with the fabrication results shown in Fig. 3. The Pendellösung beats were also obtained by topographic measurements [see Figs. 5(c)–5(e)] with larger apertures. When slightly changing the angular position, the contrast was reversed in the thin areas with CC raster scanning. The topograph on the Bragg condition [Fig. 5(e)] shows that intensity distribution was uniform in the thin area, which indicates the areas do not include observable lattice bending nor defects. The variations in thickness of the (511) and (110) crystals are measured to be 6.9–9.0 μm and 6.4–6.8 μm, respectively. Although the thickness variation of the (511) crystal is not fully suppressed, we found that the variation in an area illuminated by XFEL pulses (up to 0.6 mm in the optical direction) is considered to be sufficiently small as discussed in chapter 2.
Fig. 5 Measured rocking curves for (a) (511) and (b) (110) crystal. Intensities of reflected and refracted x-rays and the calculations are shown as red, blue circles and solid lines, respectively. Uppers and lowers of (a) and (b) show on logarithmic and linear scales, respectively. (c–e) topographs of (110) crystal. (c), (d), and (e) were taken at θ = −4, −3, and 0 arcsec corresponding to a peak, valley of the Pendellösung beats, and the exact Bragg condition, respectively. The scale bars in the topographs show a length of 1 mm on the crystal surface. Solid rectangles represent the foot-print of x-ray beam for the rocking curve measurement in (b). The dashed rectangle in (e) shows the thin area processed with computer-controlled raster scanning.
4. Discussion
We fabricated a 6.9-μm-thick Si(511) crystal with high crystalline perfection. We here investigate the expected performance of the autocorrelator proposed in Ref. [18], by assuming that the Laue beam splitters used there is replaced by our Bragg beam splitters. In the autocorrelator, each replica pulse undergoes the same number of reflections and transmissions: three reflections by thick crystals, one reflection and one transmission by thin crystals. We calculated throughputs of both branches as a function of energy difference δE, where δE = Eupper − Elower, with Eupper and Elower being the central photon energy of the x-rays propagating upper and lower branches, respectively. The incident beam was assumed to an 8.388 keV plane wave with a bandwidth ΔE/E of 1.0 × 10−3 reflected by a Si(111) DCM (ΔE/E = 1.3 × 10−4). In this calculation, Eupper was set to E. The calculated results are shown in Fig. 6(a) . The throughputs for original XFELs of 0.18% and 0.20% were obtained for the upper and lower branches, respectively, at δE = 100 meV, which is regarded as a “two-color” experimental condition. This can be easily realized with SASE XFEL incidence, which has a broad bandwidth of ΔE/E > 1.0 × 10−3. These throughputs improve to 0.28% and 0.33% when the thickness increases to 15.0 μm, as seen in Fig. 6(a). Note that the small difference of throughputs between upper and lower branches is caused by the spectral profile of the Si(111) reflection used for the DCM.
Fig. 6 Throughputs of upper branch (red lines) and lower branch (blue lines) of the autocorrelator as a function of photon-energy deviation. The bandwidths of incident XFEL are (a) 1.0 × 10−3 FWHM and (b) 1.0 × 10−5 FWHM at a photon energy of 8.388 keV. The solid and dashed lines show the results with crystal thickness of 6.9 μm and 15.0 μm, respectively. The right axis of (a) shows throughput after Si(111) double-crystal monochromator.
In the “one-color” condition (δE = 0 meV), the throughput decreases to 0.12% even for t = 6.9 μm due to the reduced penetration depth at the exact Bragg condition, as discussed in chapter 2. In this case, a self-seeded XFEL scheme [29, 30] is highly useful for improving the efficiency. Assuming the bandwidth to be ΔE/E = 1.0 × 10−5 FWHM, the throughputs drastically increase to 8.4% for the 6.9-μm-thick crystals, as shown in Fig. 6(b). It is 2.7 times higher than that for the 15.0-μm-thick crystals.
5. Summary
We present a new fabrication method of the Bragg beam splitters with atmospheric-pressure plasma and the evaluation results of the crystalline perfection with coherent x-rays at SPring-8. Measured topographs and rocking curves show that the crystals can be used as beam splitters without perturbations of wavefront and intensity of XFEL beams. We also investigate the expected performance of the autocorrelator proposed in Ref. [18] with replacement of the Laue beam splitters by the presented Bragg beam splitters. The throughput after Si(111) DCM improves to 0.8% from 0.3%. The Bragg beam splitters provide a 100 times higher throughput for an original XFEL until the availability of a monochromatic XFEL, such as a self-seeded XFEL. In future, we should improve the process accuracy in order to fabricate thinner crystals, which extend the range of applications, e.g., realizing the 1:1 split for the lower order reflection. Furthermore, we plan to examine the performance of the Bragg beam splitters on the XFEL condition.
Acknowledgments
This study was partially supported by the Proposal Program of SACLA Experimental Instruments of RIKEN and the Global COE Program from the Ministry of Education, Sports, Culture, Science and Technology, Japan. The use of BL29XUL at SPring-8 was supported by RIKEN.
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