1. Introduction

Ever since their discovery more than 100 years ago, x-rays have been an extremely useful tool for the exploration of atomic, electronic and spin-structure in condensed matter. The evolution of pertinent light-sources, from x-ray tubes to current generation synchrotrons, is marked by the ever increasing ability to produce shorter, yet more intense x-ray pulses. Since the development of free electron lasers (FEL), fluences of several J/cm² on the sample for a single sub-100 femtosecond (fs) pulse can be reached in the soft x-ray and extreme ultraviolet regime. This is of particular interest as the number of photons per coherence volume now can greatly exceed unity, thus enabling nonlinear multi-photon processes at ever shorter wavelengths [1]. Such effects are well known for optical frequencies, where their study drives whole research fields and has found a multitude of applications in industry. The prospect to observe the fundamental effects, such as stimulated emission, multi-photon and wave-mixing phenomena at x-ray wavelengths is one of the main interests in current FEL-based research [2–7].

Especially when studying non-linear phenomena, it is vitally important to have an accurate knowledge of the number of photons per unit area and time accepted by the sample. Since experiments on solids are typically destructive in a focussed single FEL pulse, this is a nontrivial task. Frequent sample alignment in combination with shot-to-shot variation of pulse intensity and pointing direction are recurring challenges in high-fluence FEL experiments with respect to fluence characterization.

In the present work, we demonstrate the use of specially designed, low-efficiency curved gratings to enhance and extend the fluence-monitoring capabilities in experiments with XUV and soft x-ray pulses. (For simplicity we will refer to this spectral range only as XUV in the remainder of the article.) The concept is compatible with samples that need to be placed on a supporting membrane, such as Si, Si₃N₄ or parylene. In our case, the samples were developed to study the resonant scattering of 59.6 eV photons from magnetic domains forming in a multilayer thin-film. We detect scattered photons in transmission, resolving the momentum transfer on a 2D pixelated (CCD) detector, as sketched in Fig. 1.

 

Fig. 1 Schematic sketch of the experiment. A sample membrane on a movable silicon chip (green) is aligned to the incident XUV beam (red). Each membrane is structured with a curved grating reference that scatters a well-defined fraction of the incident photons onto the detector. The curvature is not discernible in the small image frame of the scanning electron micrograph inset. The structure under study (blue) is deposited on the back of the sample chip. After passing the sample, the intense zero-order light is blocked by a beamstop (black cross). The scattered intensity (light red cone) is detected on a 2D pixelated detector and carries the scattering signal from the fluence monitor grating (white spots in upper left and lower right corner) and from the sample under study (bright ring).

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Note that it is typically impossible to capture the directly transmitted XUV pulse as an integral intensity reference. In most FEL experiments this intensity exceeds the detector’s dynamic range and will even ablate and destroy it. The standard method to measure the FEL pulse intensity prior to a sample is via gas monitor detectors [8]. More recently, concepts that utilize diffractive transmission gratings in order to split off a small fraction of the beam for diagnostic purposes have been developed. This also allows for spectral analysis of the FEL beam via inspection of the grating’s different diffraction orders [9,10]. In the case of soft x-ray monochromator beamlines, the monochromator’s diffraction orders that are not transported to the experiment can be used in a similar fashion [11]. Due to space constraints, however, none of the mentioned concepts are typically located immediately upstream of the sample. As a result, they do not account for losses in subsequent optical elements such as refocussing optics. Furthermore, for samples smaller than the beam size, they cannot provide information on which part of the beam was intercepted by the sample. Neither can intensity variations within the illuminated sample area be detected. Note that overfilling a small sample with a larger beam is common practice in fluence dependent measurements in order to approximate a “flat” illumination over the entire sample area that is probed.

The concept presented here overcomes these limitations without the need for additional measurement equipment. By adding suitable, low-efficiency grating structures to the supporting membrane, we are able to measure the fluence accepted by the sample. Appropriately designed grating structures even allow for spatially resolved fluence measurements of the XUV pulses, as we will show below.

2. Concept and grating design

Our approach aims to fulfill a specific purpose for XUV scattering experiments in transmission for samples on a supporting membrane: to provide a measure of the incident photon intensity that is actually accepted by the sample. To achieve this, the whole of the sample membrane is used as a diffraction lattice with a grating structure, which in our case is created by focussed ion beam (FIB) milling. It is designed such that its scattering signature in reciprocal space does not overlap with the intrinsic scattering signal of the sample under study. Furthermore, the grating efficiency has to match the sample’s scattering cross-section so as not to exceed the limited dynamic range of the detector, allowing for simultaneous measurement in the same exposure.

A simple regular grating, i.e. parallel lines and spaces, produces a scattering intensity under a polar angle θ and an azimuthal angle φ. θ and φ are directly related to the grating’s periodicity g and orientation of the lines in the sample plane, respectively. Here, we consider the first diffraction order:

Where θ and the wavelength λ translate to a momentum transfer

Choosing these parameters, the scattered beam can be aimed at arbitrary positions on the CCD detector (Fig. 1). By continuously varying the periodicity g and the orientation angle φ, a well-defined area on the CCD can be illuminated by the diffracted beam, i.e. the diffraction peaks can deliberately be broadened. This yields a reliable and readily accessible measure of the incident pulse over the grating area. For a given diffraction order, the grating efficiency and the transmission of the sample itself factor into the detected intensity.

Our aim is to generate a scattering signature with a well-defined position and an even intensity profile in reciprocal space. We find that this is achieved best by gratings with a height profile h(x, y) according to Eq. (3), oriented at an angle relative to the nontransmissive silicon facets bordering our Si₃N₄ membrane. This diagonal orientation is advantageous over horizontal or vertical alignment as it avoids overlap with the strong scattering streaks from the edges of the usually rectangular sample membrane.

We define the grating shape and its height profile as

The double vertical lines denote rounding to the nearest integer number and “÷” is the modulo operator. The sample area on the membrane is defined by 0 ≤ x ≤ 1, 0 ≤ y ≤ 1. The distortion is controlled by the parameter d while the total number of grating periods is p. In Fig. 2, we simulate the scattering by calculating the power spectrum to illustrate the influence of the parameters. The grating is FIB-milled to a square area of size l. We will specify all investigated gratings using the three parameters (p, d, l) for the remainder of the paper. The actual height of the grating grooves generated depends on FIB parameters and the membrane material. It is accounted for by the factor c in Eq. (3). Typical groove depths for our experiments are below 5 nm.

 

Fig. 2 a) – c): Example lattices illustrating the real-space distortion effect of increasing the distortion-parameter d. The generated gratings are regular for d = 0, and have variable curvature and periodicity for d > 0. For demonstration purposes, the gratings shown here are distorted much more than in the actual experiments. d) – f): Influence of lattice parameters p and d on the scattering signature. With increasing number of periods, the scattering pattern shifts towards higher scattering angles. At the same time its size changes as the distortion parameter d is a relative value. f): For increasing d, the scattering signature stays in place with its size extending. Consequentially, the scattered intensity per pixel decreases. The shown lattices and power spectra can be scaled arbitrarily, hence no absolute physical scale can be given.

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Given the optical constants in the XUV regime of the thin Si₃N₄ membranes used here, the gratings act as absorption gratings with negligible phase contrast. Their scattering efficiency remains constant even under very high pulse fluences, provided the pulse length is short enough such that the diffraction signal is collected prior to any grating modification or destruction. With the sub-100 fs pulses generated by current generation of XUV FEL sources, this assumption is valid [12].

3. Fabrication

The gratings are milled into thin Si₃N₄ membranes with a focused ion beam (FEI Helios NanoLab 600). We are able to reliably structure whole membrane windows as thin as 30 nm with sizes ranging from 30 μm × 30 μm up to 250 μm × 250 μm. For even larger membranes, the gratings can be milled with open spaces, i.e. covering the membrane only partially with variable amounts of spacing in between the structured areas, as demonstrated in Sec. 5. Without the necessity of any additional lithographic steps, rapid prototyping of different grating designs and the manufacture of hundreds of samples for destructive experiments is viable.

We prepare our gratings with an acceleration voltage of 30kV and adapt the beam current and dwelltime to achieve a processing time of less than 120s for a single membrane. In the case of our 35 μm × 35 μm membranes, milling a single grating takes about 90 s using a beam current of 72pA. The gratings are milled very shallow, with a topographic peak-to-valley amplitude of only 2 nm to 3 nm as measured by atomic force microscopy (not shown). The bare, 30 nm thick Si₃N₄ membranes we use show no sign of charge build-up during the milling process, which would rapidly decrease the spatial resolution. We expect that for significantly thicker membranes a conductive coating will become necessary.

We simulated the Ga-ion penetration into a Si₃N₄ layer using the “Stopping And Range of Ions in Matter” [13] software package. The distribution of ions at 30 keV peaks around 20 nm, but extends up to 60 nm which significantly exceeds our membrane thickness of 30 nm. Consequentially, a modification of the actual sample layer on the backside of the membrane is to be expected for sensitive samples due to ion-implantation. The gratings thus have to be fabricated prior to the deposition of our magnetic multilayer samples on the membrane. This will likely be the case in most XUV experiments in transmission geometry, where thicker substrates are impractical due to their high absorption.

4. Scattering experiments

We first performed scattering experiments at the UE112-PGM beamline at the BESSY II synchrotron radiation source to characterize and test different grating designs. The 35 μm × 35 μm membranes were FIB-structured and a magnetic multilayer thin-film was deposited on the opposite membrane side via magnetron sputtering. The [Co(4Å)/Pt(8Å)]₁₂ multilayer deposited has out-of plane magnetic anisotropy. At remanence with no external magnetic field present, such samples exhibit a labyrinth pattern of ferromagnetic domains, magnetized parallel or antiparallel to the sample normal [14]. Depending on the magnetic conditioning history, a 2D disordered labyrinth configuration or a (partially) aligned stripe orientation of the domains can be obtained. The photon energy was tuned to the Co M_2,3-edge at 59.6 eV (20.8 nm). At this energy, the magnetic layer’s domain structure acts as an absorption grating due to the x-ray magnetic circular dichroism effect, giving rise to a resonant magnetic scattering signal [15–17].

The scattering from the magnetic domain structure and from the FIB milled grating in the Si₃N₄ membrane were recorded simultaneously on a back-illuminated CCD detector (2048 pixel × 2048 pixel, 13.5 μm pixel size) placed 50 mm downstream of the sample. In this geometry, the maximum recordable momentum transfer is 84 μm⁻¹. The exposure time was chosen such that the highest measured intensity stays below the detector’s saturation level, approximately corresponding to 3000 photons per pixel at 59.6 eV photon energy. In Figs. 3(a) and 3(b), two SAXS images of gratings with different distortion values are shown along with their simulated scattering signature, in order to demonstrate how the grating parameters can be adapted to the experimental requirements. The simulated scattering is the two-dimensional power-spectrum of the gratings, cropped to the amount of reciprocal space that is recorded in the experiment. As seen in the simulations, the curved grating parameters were chosen such that the first diffraction order is “smeared out” into a square area. The reciprocal space distribution of simulated and measured diffraction from the curved gratings is in very good agreement. Note that in 3(b), the intensity of the grating diffraction is modulated by the underlying magnetic scattering signal.

 

Fig. 3 a), b): XUV scattering patterns of test samples to illustrate intensity matching by varying the distortion parameter d. A central cross-shaped beamstop blocks the directly transmitted light. The magnetic domains are partially aligned, giving rise to the two arc-shaped scattering lobes in the upper-left and lower-right quadrant, respectively. In these examples the scattering contributions of magnetic domains and curved grating overlap. This can be avoided either by aligning the domains perpendicular to the grating or with a different grating periodicity. Exposure times are 15 s in a) and 5 s in b). c): Scattering pattern of a single 100 mJ/cm² FEL shot on a sample with magnetic layer and well-matched grating. In all experiments the photon energy is 59.6 eV. Images d) to f) are simulated scattering patterns obtained by calculating the power-spectrum of the fabricated gratings, neglecting the existence of a magnetic domain structure.

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In terms of intensity, the first diffraction order of the weakly curved grating, shown in Fig. 3(a) clearly dominates the scattering on the CCD and necessitates a short illumination time. This leads to an unnecessarily noisy magnetic signal or, if the illumination time is increased regardless, the loss of the intensity normalization due to the saturation behavior of the detector. The stronger distorted example in Fig. 3(b) shows greatly improved intensity matching between the resonant magnetic scattering signal and the reference diffraction provided by the grating. Here, the grating efficiency almost equals the magnetic scattering cross-section, making optimal use of the detector integration time.

In addition to the preparation experiments at BESSY II, we have carried out a destructive single shot experiment at the FERMI@Elettra free electron laser facility, using the DiProI end-station. Figure 3(c) displays the scattering pattern of a 100 mJ/cm² single-shot at 59.6 eV photon energy on a magnetic sample with a curved reference grating that is matched in scattering intensity as well as momentum transfer to the magnetic domain structure under study. The scattered intensities differ between the magnetic structure and the grating by less than a factor of two and both scattering contributions are well separated on the detector. This allows to simply integrate over different regions of interest on the detector in order to obtain the respective signal strength. The absolute number of incident photons can not readily be determined from these intensities since the absolute value of the grating efficiency is a priori unknown. However, when investigating fluence-dependent, non-linear effects, reliable information on relative fluence changes over a large fluence range are already extremely valuable. An absolute calibration is possible, prior to destructive experiments, via an at-wavelength measurement of the grating efficiency [18,19].

5. Beam profiling and alignment

We developed a composite, “tiled” grating design to facilitate easy sample alignment with respect to the incident x-ray beam and to obtain a reliable estimate of the beam intensity profile within an illuminated sample membrane. Fig. 4(a) shows an SEM image of a tiled grating, made up of individually oriented segments of a few micrometer size each. All individual segments are designed as outlined above. They have the same line periodicity, thus scattering under the same polar angle. However, each segment’s grating is aligned to a different azimuthal angle. This produces two scattering spots on the detector (plus and minus first scattering order) for every grating tile, as seen in Fig. 4(b).

 

Fig. 4 a): Scanning electron micrograph of a section of patterned Si₃N₄ membrane. A single grating (dark) only covers an area of 7.5 μm × 7.5 μm in order to reduce milling time and the space between the gratings is not patterned. The actual grating structure of lines and grooves, as seen in Fig. 1, is not discernible in this magnification. b): Scattering pattern of a 250 μm × 250 μm membrane with 6 × 6 segmented gratings, illuminated by multiple XUV FEL shots. The bright ring near the center of the image is the XMCD scattering signal of the magnetic sample layer. Each pair of centro-symmetric spots on the outer ring corresponds to a different grating. c): False color intensity map of the sample illumination as measured by the segmented grating. Values are linearly interpolated between the 6 × 6 grating positions. d): Intensity map of the FEL spot obtained by scanning a 30 μm × 30 μm square aperture over the beam in 20 μm steps and recording the transmitted intensity with a photodiode. The white frame marks an area of the same size as the sampled area in c).

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The recorded 2D diffraction intensity map immediately allows assessment of the beam position and profile. Since all gratings share the same periodicity and were FIB-milled in parallel with the same parameters, we expect their scattering efficiency to be equal as well. We can therefore extract a relative photon intensity map from the scattering spots and the known positions of their respective grating tile. This is demonstrated on a sample with 6 × 6 grating segments. The extracted intensities are shown as a 2D false color map in Fig. 4(c). Here, an attenuated, non-destructive FEL-beam is used, integrating multiple shots. The membrane size is 250 μm × 250 μm in this case, and deliberately relaxed focussing is used in the beamline.

To validate the fluence mapping obtained in this way, we scan the FEL beam with a 30 μm × 30 μm square aperture and measure the transmitted intensity with a photodiode. The results, shown in Figs. 4(c) and 4(d), are in good agreement, taking into account that the aperture scan extends over a larger region. The intensities measured by the grating spots not only allow us to extract the beam profile in a single measurement, but eliminate any uncertainty towards sample alignment and temporal stability of the beam focus during the exposure time as it is recorded simultaneously with the sample’s actual scattering signal of interest. Especially in FEL experiments, with usually very tight schedules, this is a considerable advantage. While the time for sample preparation is increased, the actual experiment is simplified and made significantly more robust. Note that especially in the study of phenomena which are non-linear in the XUV fluence, the possibility for a simultaneous characterization of the fluence distribution on the sample is typically crucial for the interpretation of the data.

Depending on the needs of the experiment, the number of grating tiles can be increased to offer better spatial resolution. For beam alignment however, a low number of tiles is sufficient and offers a better trade-off with respect to the signal-to-noise ratio.

We anticipate samples featuring such a tiled grating design to be especially useful in x-ray pump/ x-ray probe experiments. Here, the important prerequisite of ensuring the spatial overlap of both x-ray beams will be simplified to separately aligning both beams to yield the same, readily identifiable, scattering signature of the tiled grating.

6. Conclusion

In summary, we demonstrated a flexible and tailorable fluence monitor and beam profiler concept for integration into transmission-type scattering samples. Our grating design is especially useful in single and multi-shot FEL experiments. It is compatible with standard scattering setups using 2D detection. No changes to the experimental setup are necessary and the fluence information is recorded from the actual shots that have been incident on the sample area without any temporal overhead when carrying out the experiment. The obtained intensity values are by default relative to a characterization measurement, however, calibration of each individual grating at low fluence is possible in order to yield absolute photon numbers. All additional work for sample nanostructuring takes place in the sample design and preparation stage, where time constraints apply to a much lesser degree than at the FEL beamline. Via composite gratings, spatial resolution in fluence monitoring can be achieved even in single-shot experiments and we expect composite curved gratings to be of particular use in x-ray pump/ x-ray probe experiments in the future.