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Abstract
High resolution metrology of beam profiles is presently a major challenge at X-ray free electron lasers. We demonstrate a characterization method based on beam imprints in poly (methyl methacrylate). By immersing the imprints formed at 47.8 eV into organic solvents, the regions exposed to the beam are removed similar to resist development in grayscale lithography. This allows for extending the sensitivity of the method by more than an order of magnitude compared to the established analysis of imprints created solely by ablation. Applying the Beer-Lambert law for absorption, the intensity distribution in a micron-sized focus can be reconstructed from one single shot with a high dynamic range, exceeding 103. The procedure described here allows for beam characterization at free electron lasers revealing even faint beam tails, which are not accessible when using ablation imprint methods. We demonstrate the greatly extended dynamic range on developed imprints taken in focus of conventional Fresnel zone plates and spiral zone plates producing beams with a topological charge.
© 2017 Optical Society of America
1. Introduction
With the ongoing construction of X-ray free electron lasers (XFELs), a set of extremely brilliant light sources has become available to science. Along with the development of these lasers providing high photon fluences in the X-ray and extreme ultraviolet (EUV) regime, a variety of technical and scientific challenges arises. Among them, the precise characterization of focused photon beams remains a difficult task. Because of the very small dimensions and the extremely high fluence levels in the focus of such beams, a direct characterization using detectors is impossible due to lack of spatial resolution and insufficient beam hardness.
An elegant method to characterize the shape of intense laser beams by investigating ablated craters was introduced by Liu already in 1982 [1]. This method was then applied to study the ablation behavior of several polymers in the EUV regime [2] and has been introduced to XFELs some years ago by Chalupský, Juha and others [2]. Their pioneering work to characterize individual XFEL pulses is based on investigating the size and shape of craters formed by non-thermal ablation of poly (methyl methacrylate) (PMMA) [3]. By recording a series of single-shot ablation imprints at different fluence levels, the full intensity profile of highly brilliant XFEL beams can be reconstructed with a method referred to as F-scan [4]. The ablation imprint method can be applied to different materials for tailoring the ablation behavior to different energies and fluences [5]. It has been successfully used to characterize the transverse properties of focused beams on the nanometer scale [6]. By analyzing the shape of imprints at various positions along the optical axis, even the phase profile of the focused beam can be reconstructed [7]. Assuming that absorption occurs ideally according to the Beer-Lambert law [8] and that the ablation depth is directly related to absorbed photon dose, surface analysis of the imprint craters provides quantitative information about the penetration depth at which the remaining photon intensity drops below the ablation threshold [3]. This is generally the case for non-thermal ablation processes, which are referred to as photochemical models where electronic excitation leads to bond breaking, directly resulting in material loss of the molecular fragments. When the photon fluence reaches higher intensities, cascades of other effects start to play a significant role, such as photothermal ablation as result of bond breaking by photoexcitation and thermal heating, or highly non-linear mechanisms with different bond breaking energies of ground state and excited states [9–11]. The use of individual non-thermal ablation imprint craters to determine the intensity distributions is thus limited to a dynamic range from the ablation threshold to the onset of thermal ablation processes [3].
In this study, we demonstrate that we can access much higher dynamic ranges by developing the beam ablation imprints in organic solvents. The procedure is similar to grayscale lithography, which is a well-established method to produce continuous surface profiles with pre-defined depth in resist layers, such as PMMA [12–15]. Compared to the ablation-based approach, this reduces the intensity threshold remarkably and thereby enhances the dynamic range of the method by at least an order of magnitude. Irradiating polymer films with a focused XFEL beam and their subsequent development thus proves as a highly sensitive method for determining the intensity distribution in focus over a high dynamic range.
2. Experimental details
We prepared PMMA films of approx. 1 µm thickness (950k molecular weight, spin-coated from an 8% solution in anisole at 3000 rpm) on silicon substrates as targets for irradiation. The EUV radiation from the FERMI free electron laser [16] (photon energy E = 47.8 eV, wavelength λ = 26.0 nm, pulse duration 50 fs) was focused by means of a Fresnel zone plate (FZP) having a diameter of 1.90 mm. The outermost zone width dr was 1.64 µm, resulting in a focal length f of 120 mm and a diffraction-limited Rayleigh spot size of 2.00 µm [17]. The FZP consisted of structures etched 230 nm deep into a 340 nm thick silicon membrane (provided by Norcada Inc.) The duty cycle, i.e. the ratio of line width to period, was adjusted to 60% to minimize the 0th diffraction order and thus to avoid the need of a central beam stop. The first order diffraction efficiency of the FZP (including absorption losses in the support membrane) can be calculated as 17% [18]. As all other diffraction orders are not focused in the focal plane, their intensity contribution can be neglected and thus an order sorting aperture was not required. Apart from a plane mirror to steer the beam, there are no additional X-ray optical elements in the beamline. The experimental setup is similar to the one described in reference [19].
Both focus position and attenuation were varied to find the optimum conditions for creation of ablation imprints and subsequent processing. For each focus position and attenuation setting, a set of 9 individual shots was recorded. The ablation imprints created in this way were analyzed using a Bruker Dimensions 3100 atomic force microscope (AFM) in tapping mode. The imprints were successively developed in two different procedures: (i) immersion in a 1:3 mixture of methyl isobutyl ketone (MIBK) and isopropyl alcohol (IPA) for 30 s, and then rinsed in IPA for 30 s; (ii) immersion in a 1:1 mixture of MIBK and IPA for 30 s, and then rinsed in water for 30 s. After each development, the imprints were characterized again under the AFM to observe the evolution of the imprints.
3. Reconstruction of intensity distributions
According to the Beer-Lambert law, the depth of non-thermally ablated imprints is related to the incident beam intensity by
with d(x,y) denoting the imprint depth, Ith the threshold intensity and lat the attenuation length. Note that non-thermal ablation is regarded as the regime where no additional effects play a role except for photon absorption [3, 11]. The attenuation length in our experiments was interpolated to 64.3 nm at 47.8 eV from experimental values reported for 38.7 eV (56.9 nm), 57.1 eV (69.9 nm) and 91.8 eV (175 nm) [2, 3]. The intensity map reconstructed in this way appears in units of the beam intensity normalized to the ablation threshold. The relative intensity is thus cut off at unity (where I0 ≤ Ith and d = 0). For development of the imprint, the threshold value corresponds to the minimum photon dose, i.e. the local beam intensity required to reduce the molecular chain length of the polymer sufficiently so that it is removed in the developer solution. The topography of the respective imprint revealed after development corresponds to the iso-dose surface of the threshold value, as illustrated in Fig. 1. Thus, the imprint depth represents the intensity distribution of the incident photons on a logarithmic scale. It should be noted that different solvent mixtures result in different strength for development, allowing for lowering the threshold of the development step. A good measure for the relative intensity of the shot which caused the respective imprint is the peak-to-threshold ratio at the center of the focal spot [3],Obviously, this ratio will increase with the lowered threshold intensity when developing the imprints, thus allowing to relate the threshold intensities as a function of p for ablation, development with the 1:3 MIBK: IPA mixture, and the 1:1 mixture: pabl, p1:3, and p1:1.
Fig. 1 Scheme illustrating the impact of the intensity threshold on the peak-to-threshold value and the imprint depth. The colored areas indicate the material that received a dose above threshold. With decreasing threshold, additional material, which has been exposed to lower intensities, will also be removed. The imprint depth thus corresponds to the iso-dose surface which is revealed upon ablation or development.
4. Results and discussion
Ablation imprints
Figure 2(a) shows an AFM image of a typical imprint crater formed by ablation resulting from a single EUV shot. Its topography shows a nicely shaped central dip at the focus position of the zone plate, and the first side maximum of the Airy disk. The center is 218 nm deep, corresponding to pabl = 30.1. It is worth mentioning that the intensity of the first side lobe of an ideal zone plate diffraction pattern is approx. 3.0% of its center maximum value [20]. In our case, the average intensity in this region amounts to 3.8% of the intensity at the center, which is close to the theoretical value. As shown in Figs. 2(b) and 2(c), the intensity in the focal plane can be calculated from the imprint topography according to Eq. (1). The reconstructed intensity distributions show a clean, circular focal spot with the first minimum at 2 µm from the center. The radial intensity distribution of a conventional zone plate and thus the local dose at a distance r from the optical axis in the focal plane can be calculated as
with the first-order Bessel function J1, the outermost zone width dr [17] [see Fig. 2(d)]. Thus, the radius of the first minimum corresponds to the numerically calculated value of 1.22 ⋅□dr for the theoretical diffraction-limited spot of a Fresnel zone plate with an outer zone width dr = 1.64 µm. The sharp edges of the crater point out that in our experiment the creation of ablation imprints follows the model described above. At fluences below ablation threshold, the PMMA film appears to be intact. Unlike the results reported on similar experiments for EUV radiation focused by mirrors [21], we do not observe any desorption of polymer material in the vicinity of the imprint crater. This is probably due to the fact that – unlike the investigated mirrors - the focal spot of our zone plates exhibits a sharp decline in intensity towards the first Airy disk minimum with very low beam tails.Fig. 2 (a) Atomic force micrograph of a non-thermally ablated single-shot imprint of the focal spot of a Fresnel zone plate in PMMA. The photon energy was 47.8 eV, corresponding to an attenuation length of 64.3 nm. (b) and (c) Reconstructed intensity above the ablation threshold as calculated from the Beer-Lambert law on a linear (b) and logarithmic (c) scale. (d) Numerically calculated intensity distribution above a threshold value of 2.3% of .
Taking a closer look at the sensitivity of the ablation method, we compared imprints obtained at different attenuator settings, i.e., different incident fluences. For this purpose, we reduced the energy per shot of the FEL in five steps from an average value of 7.3 µJ/shot to 0.3 µJ/shot, each time attenuating the XFEL beam with a combination of solid and gas attenuators by approximately a factor of two. Note that the pulse intensity jittered strongly during this experiment. The resulting average pulse energy in the first order focus spot is determined as 88, 42, 18, 8.4 and 3.6 nJ/shot taking into account the beamline transmission, zone plate efficiency and aperture size. Figure 3 shows the reconstructed intensity profiles along the imprint cross section in x-direction on a logarithmic scale. Knowing the intensity distribution of our Fresnel zone plate [see Eq. (3)], the local fluence can be calculated as its radial integral corresponds to the energy per shot (see y-axis on the right-hand-side). The statistical average of 28 imprints allows for determining the ablation threshold as 52 ± 8 mJ/cm2 at 47.8 eV.
Fig. 3 Intensity profiles of ablated imprints in PMMA obtained from individual shots with different pulse energies. As a natural property of an XFEL, the number of incident photons fluctuates from shot to shot. The values shown in the inset show the average pulse energies at the different attenuator settings. The shape of the profile corresponds to the theoretical intensity distribution of a Fresnel zone plate up to p = 20. At higher peak intensities, a slight dip evolves until the ablation imprint center becomes nonlinearly deeper above p = 40, indicating the inception of thermal ablation. The cross section of the imprint shown in Fig. 2 is indicated.
When comparing the shape of the imprints with the theoretical beam profile in the focal plane of a Fresnel zone plate as shown in the upper part of Fig. 1, it becomes obvious that the relation of incoming intensity and imprint depth follows the Beer-Lambert law below pabl < 20, before this simple model breaks down as discussed in Section 1 [11]. In the region of pabl = 20 – 40, the behavior is still very close to the non-thermal ablation model, merely the center of the craters seem to be slightly shallower than expected. At higher fluences, the imprint center appears much deeper than anticipated whereas the outer edges still maintain their typical shape up to pabl ≈40. This indicates the presence of additional effects and thus imposes a limit for beam profiling using non-thermal ablation imprints. Whereas ablation is still a powerful method to map the maxima of the intensity distribution, it obviously does not provide sufficient dynamic range to record the beam tails in the very same imprint. In the case of an ideal zone plate diffraction pattern, the intensity profile above 3% of the peak intensity covers mainly the central spot, neglecting the majority of photons distributed in the side lobes of the diffraction pattern, which account for 16.2% of the integrated intensity [20]. More commonly used X-ray optics, such as a FZP combined with a central beam stop, suffer even more from this effect due to their increased side maxima.
Development of the exposed polymer
As described above, the maximum applicable fluence yielding a linear response in PMMA layers is limited to pabl < 20. This severely limits the dynamic range of the method. However, the molecular structure of the polymer is already changed at much lower absorbed doses compared to those required for ablation. The deposition of radiation doses in PMMA leads to a change in imprint depth after development in organic solvents. We thus developed the imprints after recording of their ablated topography using the procedure described in Section 2. With increasing developer strength, each development step removed additional material and thus deepened the craters [see Figs. 4(a) and 4(b)]. The information contained in the imprint shown in Fig. 2 is thus extended so remarkably that traces of the fourth side maximum of the Airy disk can be visualized, with a theoretic intensity below, i.e., corresponding to p > 1000 [20]. For the strongest imprints with peak fluences beyond the threshold for non-thermal ablation, we even observed up to seven side maxima (not shown here). In addition, the iso-dose surface in the center of these craters also deviates from the form described in Eq. (3). However, the experimental data does allow a more precise analysis of this effect, leaving the quantitative characterization of craters beyond non-thermal ablation subject to further investigation.
Fig. 4 (a) Atomic force micrographs of the single-shot imprint shown in Fig. 2 as ablated, and after two development steps. (b) 3-D cuts through the AFM images. (c) Cross section through the intensity profiles of the ablated imprint (black), and after development in 1:3 and 1:1 mixtures of MIBK:IPA (red and blue). The first minimum is found at ± 2.00 µm, and the peak-to-threshold ratios are determined as 30, 61, and 345.
Comparing the reconstructed intensity profiles from developed to those of purely ablated imprints shows that the sensitivity can be increased by an order of magnitude, improving the peak-to-threshold ratio from pabl = 30 to p1:3 = 61 and p1:1 = 345 using the 1:3 and 1:1 MIBK:IPA solvent mixtures for development [see Fig. 4(c)]. The threshold values thus are reduced from 52 mJ/cm2 to 25 mJ/cm2 and 4.5 mJ/cm2, respectively. This trend is in sound agreement with the reported threshold values at 91.8 eV for non-thermal ablation (~30 mJ/cm2) [3] and development with the 1:1 mixture of MIBK and IPA (3.6 mJ/cm2) [15].
With the sensitivity increase after developing the imprints demonstrated, we investigated the beam profiles of several diffractive lenses in detail. In particular, we used conventional FZPs and similar lenses with zones designed as spirals. Whereas a FZP shows the intensity distribution of an Airy disk [Eq. (3)], spiral zone plates produce first-order focus spots which exhibit a phase vortex and a torus-shaped intensity distribution. Whereas the intensity distribution in the focal plane of a zone plate can be described using the Fraunhofer approximation, this is not immediately obvious for a spiral zone plate. However, we found that numerical comparisons of Fraunhofer and Fresnel approximations [22] show excellent agreement. In that sense, our spiral zone plates behave sufficiently similar to a lens to justify the use of the Fraunhofer approximation. The intensity distribution of a spiral zone plate can thus be described using the hypergeometric function 1F2 [22, 23]:
with the focal length f, the zone plate radius R, the topological charge, i.e. the number of spiral arms m, the wave vector k.Figure 5 shows a comparison of the diffraction pattern of the FZP (a) and the spiral zone plate (b). The latter optical element creates a tightly focused beam with a torus-shaped intensity distribution in its focus. It carries an orbital angular momentum and produces a phase singularity in their center of its focal plane [23, 24]. Utilizing the newly introduced technique, we can map the intensity distribution of such a spiral zone plate in a wide dynamic range, from maximum intensity to the 4th pair of side maxima. The peak-to-threshold ratio exceeds 1000 in this case, demonstrating successful beam profiling over three orders of magnitude. Moreover, the reconstructed intensity distribution again reflects exactly the theoretical diffraction pattern of the spiral zone plate in the focal plane, which has been calculated according to Eq. (4), including the intensity variations of even and odd side maxima.
Fig. 5 (a) Schematic illustration of a conventional Fresnel zone plate, its numerically simulated diffraction pattern, and its experimentally determined intensity distribution in the focal plane, as reconstructed from a developed imprint in PMMA. (b) Pattern, simulated and reconstructed intensity distribution of a spiral zone plate. The torus shape of the beam profile in the focal plane is clearly visible, as well as the distinct appearance of the side maxima. All intensity distributions are shown on a logarithmic scale.
5. Conclusions and outlook
We successfully demonstrated the adaption of grayscale lithography to characterize the intensity distribution of a focused EUV beam from a seeded FEL over a dynamic range exceeding 1000 in a single shot. By developing PMMA films which have been exposed to an EUV beam, the ablation imprint method can be extended by more than an order of magnitude in sensitivity and dynamic range. This approach becomes particularly appealing for beam characterization in XFEL experiments, where the shot-to-shot stability is often an issue. In this way, even challenging beam geometries can be effectively characterized completely from peak to faint beam tails taking advantage of the outstanding sensitivity of this method. We expect that the dynamic range can even be extended by another order of magnitude using more sensitive chemically amplified resists used in EUV lithography instead of PMMA [25–27]. The method of developed imprints is particularly well suited for investigations in the EUV and soft X-ray range. At higher photon energies, the attenuation length in PMMA increases, making the imprints deeper until at some point they can no longer be investigated by AFM. Extending the method to harder radiation would therefore require the use of heavier resist materials with sufficiently high absorption.
It should be noted that the dose required for development of the structures can also be accumulated. In contrast to the formation of ablation imprints which relies on photon absorption on an extremely short time scale, the method can thus be applied in exposures with much lower photon flux over a longer time, for instance at a synchrotron. In addition, the lateral resolution of atomic force microscopy is much higher than achievable with the pixel size of any two-dimensional detector, allowing the intensity distribution mapping at the nanometer scale. We therefore expect that this method can be successfully adapted for profiling EUV and soft X-ray beams in other state-of-the-art microscopy and spectroscopy techniques, for instance in applications such as angle-resolved photoelectron spectroscopy.
Funding
EU-H2020 Research and Innovation Programme (654360 NFFA-Europe); EU-H2020 Research and Innovation Programme (701647 Marie Skłodowska-Curie grant).
Acknowledgments
Atomic force microscopy was performed at the Scanning Probe Microscopy Laboratory of PSI. Rolf Schelldorfer is gratefully acknowledged for technical support during AFM measurements. We acknowledge the support of Enrico Allaria, Laura Foglia, Nicola Mahne, Michele Manfredda, Riccardo Mincigrucci, Najmeh Mirian, Eléonore Roussel, Alberto Simoncig, Simone Spampinati, and the LKO team at university of Nova Gorica during the experiment at Fermi. Thomas Lippert is acknowledged for fruitful discussions on ablation mechanisms.
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