Comparing single-shot damage thresholds of boron carbide and silicon at the European XFEL

The damage threshold fluences of silicon (Si) and boron carbide (B4C)-coated Si at 1 keV and 9 mrad grazing incident angle are compared. Results show that B4C has a damage threshold approximately twice that of Si, highlighting the advantages of using B4C coatings for enhanced durability.


Introduction
X-ray free-electron laser (XFEL) facilities have the capability to produce high-brightness X-rays, enabling novel experiments to be performed (Tschentscher et al., 2017).The optical components of XFEL beamlines, such as mirrors and crystals, are constantly exposed to extremely intense photon beams concentrated in an ultrashort pulse duration (fs) -a situation that could easily cause irreversible damage to their surfaces, leading to compromised performance or to an unusable state altogether.A critical question therefore needs to be askedwhat is the maximum pulse fluence that a grazing-incidence FEL mirror can withstand under continuous photon impingement with MHz repetition rate at an accelerator-based light source such as the European XFEL (EuXFEL).
To address this question, we conducted grazing-incidence damage experiments for uncoated silicon substrates and B 4 C coated substrates, using the EuXFEL facility and in particular its soft X-ray beamline at 1 keV photon energy.We chose silicon as the substrate and B 4 C as the surface coating as this combination is most commonly used at soft X-ray FELs beamlines (Mazza et al., 2012;Tavakkoly et al., 2022).A higher damage threshold fluence for the B 4 C coating is expected due to its good thermal properties, high melting point, low density and high reflectivity.
Previous studies have explored the damage threshold of similar materials under various conditions.For instance, experiments with uncoated silicon under normal incidence at 10 keV reported a damage threshold fluence, F th , of 0.78 mJ mm À 2 (Koyama et al., 2015).At a grazing angle of 22 mrad and 0.9 keV, silicon exhibited an F th of 0.014 mJ mm À 2 (Krzywinski et al., 2018).Another study at 5.5 keV and an incident grazing angle of 11.4 mrad found a threshold fluence of 0.052 mJ mm À 2 (Koyama et al., 2016).For bulk B 4 C at normal incidence and 0.83 keV photon energy, the threshold fluence was 0.027 mJ mm À 2 (Hau- Riege et al., 2010).Moreover, a 50 nm B 4 C coating on a silicon substrate at 7 keV and an incident grazing angle of 4 mrad exhibited a damage threshold of 24 mJ mm À 2 (Aquila et al., 2015).
In this paper, we investigate the damage threshold of uncoated silicon and B 4 C coating for a grazing-incident angle of 9 mrad.The results of these experiments will provide critical insights into the durability and performance limits of these materials under extreme conditions, which is essential for optimizing the design and operation of XFEL beamlines.

Experimental setup
The experiment was conducted at the Small Quantum Systems (SQS) instrument at the EuXFEL (Mazza et al., 2012).The facility delivered X-ray pulses with an average pulse energy of approximately 4.7 mJ and pulse duration of 25 fs at a photon energy of 1 keV.The samples analyzed in this study were a polished silicon wafer without any coating and a similar silicon substrate coated with B 4 C.The samples' dimensions were 29.8 mm in length, 19.8 mm in width and 1830-1870 mm in thickness, with a 50 nm-thick B 4 C layer.
Samples were irradiated at a grazing angle of 9 mrad, which is typically used for B 4 C coated mirrors at soft X-ray beamlines.This angle is below the critical angle of 32 mrad at 1 keV (https://henke.lbl.gov/tmp/xray1041.dat).
The experimental setup is shown in Fig. 1.A gas attenuator was used to adjust the pulse energy and therefore the fluence.The maximum deliverable pulse energy to the samples was 1.8 mJ.An X-ray gas monitor (XGM) detector recorded the incident pulse energy for each damage measurement (Mazza et al., 2012).The shot-to-shot pulse energy fluctuation was measured to be 5%.
A pair of Kirkpatrick-Baez (KB) optics was utilized to focus the beam, resulting in a spot size with an effective area of 1590 mm 2 .In this experimental setup, two cross chambers were used, one for the sample and the other, at 700 mm downstream from the first chamber, for the YAG screen.The YAG screen in the second chamber was used to track the direct beam and its reflection.
At each different attenuation settings, 43 damage measurements were taken at a grazing angle of 9 mrad.Fig. 2 illustrates a representative set of damaged craters.

Analysis and results
In order to obtain the threshold fluence, the first step is to determine the corresponding energy for damage threshold (Dastjani Farahani et al., 2011;Koyama et al., 2015).We measured the areas of the damaged spots in grazing-incidence irradiation for this purpose.
When the beam has a perfect Gaussian shape, we can determine the threshold energy by fitting the area of the damaged spot to the logarithm of the pulse energy.The maximum pulse energy at which damage does not occur is determined by the point of intersection in the linear fit (Liu, 1982;Aquila et al., 2013).For non-Gaussian beams, the threshold energy is determined by minimizing the meansquare distance between experimental data points and a  function of the beam profile in a plot of normalized fluence against the beam area.The beam function is determined using the procedure described by Chalupsky ´et al. (2009Chalupsky ´et al. ( , 2010)), Here, S represents the area of the ablation contour, and f (S) denotes the normalized fluence.We measured the damaged area for each pulse energy.Fig. 3 presents a plot of normalized fluence versus measured damaged area, with the red curve depicting the beam profile.As a result of our studies the determined threshold energies for silicon and B 4 C are 261 mJ and 549 mJ, respectively.
Finally, to retrieve the threshold fluence F th , one needs to determine the beam effective area.According to Chalupsky ´et al. (2010), the effective area A eff is determined by a method of ablation imprints and is defined by a relation between fluence and pulse energy, F = E pulse /A eff .It was found to be 1590 mm 2 .As a result, the threshold fluence (F th = E th /A eff ) is 0.16 mJ mm À 2 for Si and 0.34 mJ mm À 2 for B 4 C.

Conclusion
Single-shot damage measurements were conducted on Si and B 4 C-coated Si to determine the damage threshold fluences.At 1 keV with a 9 mrad grazing angle, below the critical angle, the damage threshold fluence was determined to be 0.16 mJ mm À 2 for Si and 0.34 mJ mm À 2 for B 4 C.As expected, B 4 C has a damage threshold approximately twice that of Si.

Figure 1
Figure 1Schematic of the experimental setup.AT: attenuator; XGM: X-ray gas monitor.

Figure 3
Figure 3 Normalized fluence versus damaged area at 1 keV.Each damaged area was measured for every pulse energy, with the red curve representing the beam profile.(Top) Silicon with threshold energy of 261 mJ.(Bottom) B 4 C with threshold energy of 549 mJ.