Multiple pulse thermal damage thresholds of materials for x-ray free electron laser optics investigated with an ultraviolet laser

The high-intensity ultrashort coherent monochromatic radiation of hard x-ray free electron lasers (XFELs) promise to enable numerous scientific experiments.^1,2 The x-ray optics required to guide and shape an XFEL beam³ have to be able to withstand extreme radiation conditions.⁴ Since no appropriate light sources are available to test the damage resistance of these optics directly, design efforts and materials selection are primarily based on theoretical damage estimates.^5–7 Recent experiments on various inorganic bulk materials performed at 32 nm with the soft XFEL in Hamburg (FLASH) (Ref. 8) have shown that the single-pulse damage threshold is closely related to the melt threshold.⁹ It is possible that the multiple-pulse damage threshold, important for the high repetition rate of XFELs, may be limited by a different damage mechanism, for example, thermal fatigue⁷ or radiolysis.^10,11 A controlled multiple-pulse damage experiment at FLASH is difficult since the energies fluctuate widely from pulse to pulse.¹² In this paper we show that the thermal aspect of the multiple-pulse damage may be tested using longer-pulse optical lasers. We note that this approach builds on previous work using long-pulse optical lasers where it was found that the damage threshold is related to plastic deformation.^13–15 These experiments were performed on different materials and under different irradiation conditions (such as pulse length and spot size) compared to the current experiments.

At the XFEL Linac Coherent Light Source (LCLS), mirrors to deflect the x-ray beam will be operated at grazing incidence angles to achieve high reflectivity. For x-ray energies between 0.8 and 2 keV, the soft x-ray offset mirror system (SOMS) is being made of Si substrates coated with 50 nm of $B 4 C$⁠. The incidence angle is 13.9 mrad from the mirror surface. For x-ray energies between 2 and 25 keV, hard x-ray offset mirror system (HOMS) is being made of Si substrates coated with 50 nm SiC, and the grazing angle is 1.3 mrad.¹⁶ A fraction of the incoming photon beam is absorbed through photoionization within 10 nm of the surface. Photoelectrons are ejected primarily in the direction of the electric field vector of the incoming radiation,¹⁷ which is nearly normal to the mirror surface at LCLS. The inward directed electrons and electrons reflected by space-charge effects back to the mirror deposit their energy within 1000 nm of the mirror surface through electron impact ionization. Within a few picoseconds, the electrons equilibrate with the ions and recombine generating phonons.¹⁸ The heated region is believed to relax to a state of thermodynamic equilibrium within a few picoseconds. On longer timescales, of order 10 ns, it is anticipated that the heat dissipates by conduction. Due to thermal expansion, heating of the surface of the optics by the LCLS beam subjects the optics to repetitive thermal stress, which may lead to fatigue failure at fluences much lower than that required to cause damage on a single application of load.^7,19 In the theory presented in Ref. 7, the main determinant of the thermal stress is the temperature rise at the surface. The temperature profile is not important, so long as the depth of the heated region is much less than its transverse extent and the time of interest lies in between the sound crossing time and the thermal diffusion time.

We used a 308 nm ultraviolet (UV) laser at near-normal incidence to produce surface temperatures similar to those expected from an XFEL, with profiles that fit the criteria mentioned above. For Si and $B 4 C$-coated Si samples, the depth directly heated by the UV radiation is small (absorption depth $< 33 nm$⁠). By using long pulses (27 ns full width at half maximum) the energy has sufficient time to diffuse into the sample without overly heating the surface material. To compare the XFEL and UV cases, we have calculated temperature profiles using a Monte Carlo technique for the XFEL case²⁰ and a one-dimensional heat-flow model for the UV case.¹⁷ We consider two limiting cases for the LCLS optics. For the HOMS irradiated at 8267 eV, the depth at which the temperature rise drops to $1 / e$ of the surface value of 37 K is $0.40 μ m$⁠, while for the SOMS at 827 eV, the surface temperature rise is 34 K and the depth is $0.025 μ m$⁠. We compare these values to the heat penetration depths for UV irradiation at the end of the laser pulse (when the temperature is highest). The $1 / e$ depths are $1.1 μ m$ for pure Si and $0.81 μ m$ for $B 4 C$-coated Si. Therefore, the 27 ns UV pulse length gives thermal penetration depths similar to the hard x-ray case, while the penetration depth is much larger than for the soft x-ray case. Nevertheless, since the criterion for thermal fatigue failure depends primarily on the maximum surface temperature and the conditions concerning the timescales and length scales mentioned above are satisfied, we believe that the UV experiments are a valid test of the thermal fatigue mechanism.

We performed damage experiments on uncoated (100) silicon wafers and on (100) Si wafers coated with 50 nm $B 4 C$ deposited using a DC-magnetron sputtering system.²¹ The same system will ultimately be used for the coating of the LCLS x-ray mirrors. Silicon was studied since it will be used in beam energy measurement systems and because damage processes in silicon are well understood,²² and $B 4 C$-coated silicon was studied since it comprises the surface for the LCLS soft x-ray offset mirrors.¹⁶ X-ray photoelectron spectroscopy on the $B 4 C$ samples aged for about 1 month indicated that the top 9 nm of the films contains $64 at . %$ B, $22 at . %$ C, and $13 at . %$ O, with the O concentration rapidly diminishing with increasing depth from the top surface. Rutherford backscattering measurements across the entire film thickness indicated a B-to-C ratio of 3.7, with 6% O present. The density of the sputtered films is $2.28 g / cm 3$⁠. By modifying the deposition parameters we generated two sets of $B 4 C$ coatings, one with a compressive stress of 2.3 GPa and top surface microroughness of 0.15 nm rms, and another one with a compressive stress of 1.2 GPa and top surface microroughness of 0.5 nm rms. The lower-stress $B 4 C$ coatings are similar to the coatings that will be used for the LCLS mirrors.

We exposed the samples to pulses from a Lambda Physik EMG-301 XeF excimer laser. The beam was shaped into a $4 × 4 mm 2$ square focal spot, and the exposure rate was 50 Hz.¹⁷ We measured the reflectivity of the irradiated spot using a 650 nm laser and a photodiode with a time resolution of better than 1 ns. This allowed us to detect the onset of melting in the Si samples because the reflectivity of molten silicon is substantially higher than for crystalline Si.²² The fluences were calibrated by assuming that the onset of melting occurs at $740 mJ / cm 2$⁠.¹⁷ The samples were placed in a vacuum cell with a base pressure of less than 10 mTorr in order to minimize surface oxidation and contamination.

We exposed the Si sample to (i) single, $10 1$⁠, $10 2$⁠, $10 3$⁠, and $10 4$ pulses at fluences of 95, 160, 400, 640, 800, and $1200 mJ / cm 2$⁠, (ii) single pulses at $1500 mJ / cm 2$⁠, and (iii) $10 5 pulses$ at fluences of 95, 160, 400, and $800 mJ / cm 2$⁠. Similarly, we exposed the $B 4 C$ samples to (i) single, $10 1$⁠, $10 2$⁠, $10 3$⁠, and $10 4$ pulses at fluences of 20, 40, 70, 100, 130, 160, and $180 mJ / cm 2$⁠, (ii) single pulses at 200, 240, and $300 mJ / cm 2$⁠, and (iii) $10 5 pulses$ at fluences of 20, 40, 100, and $160 mJ / cm 2$⁠. Exposure sets (i) and (ii) were repeated three times, whereas exposure set (iii) was only performed once.

We analyzed the exposed samples with a ZYGO NewView™ optical profiling microscope, which is sensitive to changes in surface height and in the refractive index, and with a scanning electron microscope (SEM). The lateral and vertical resolutions of the ZYGO are about $1 μ m$ and 1 nm, respectively. We consider a sample damaged if any changes on the surface of the sample were detected. The SEM analysis is more sensitive in detecting damage than the optical profiling microscope for the silicon samples in that the interferometrically determined damage sites are a subset of the damage sites determined by SEM. The onset of damage shows up as changes in the image contrast in the SEM of about 10%, consistent with the presence of different atomic elements. This may be due to alteration of the surface oxidation layer or oxidation and carbon deposition associated with the imperfect vacuum.²³ Therefore, the threshold fluences we report in this paper should be considered to be lower boundaries.

Figure 1(a) shows a damage map of silicon as a function of laser fluence and the number of pulses. In single-pulse exposures, we did not observe damage up to the maximum fluence of $1500 mJ / cm 2$⁠, which is approximately twice the melt fluence. This is consistent with near-epitaxial regrowth of solid silicon upon cooling, resulting in a near-perfect surface finish. Damage becomes visible only upon exposure to ten or more pulses. We observed damage in silicon below the melting fluence for $10 4$ pulses or more. At $10 4$ pulses the damage threshold lies between 400 and $640 mJ / cm 2$⁠, i.e., 54% to 86% of the melt fluence; the threshold at $10 5$ pulses lies in the same range. These results suggest that the melting threshold is a good indicator (i.e., a lower bound) for single-shot damage but that multiple-pulse damage can occur below the melting threshold in silicon. For up to $10 5$ pulses, the threshold is still greater than 50% of the melt fluence. We observed evidence for mechanical damage, i.e., cracks seen in the ZYGO microscope, only in one experiment at $1200 mJ / cm 2$ and $10 4$ pulses.

For the $B 4 C$ films, both SEM and optical profilometry agree on the identification of the damage sites, see Fig. 1(b). We found that the film stress does not have a significant effect on the damage resistance. The calculated melting threshold for the $B 4 C$ films is $560 mJ / cm 2$⁠, lower than for silicon since the reflectivity of $B 4 C$ is only 9%, whereas the reflectivity of Si is 59% and the thermal conductivity of $B 4 C$ is lower. We also found this value to be relatively insensitive to the assumed material properties of $B 4 C$⁠. Varying the values for the thermal conductivity and heat capacity by a factor of 2 in the simulations changes the melting threshold by $< 30 %$⁠. Since the melting temperature of Si is significantly lower than that of $B 4 C$⁠, our simulations show that the Si underlying the $B 4 C$ layer reaches the melting temperature for $380 mJ / cm 2$⁠. Figure 1(b) shows that single-pulse damage occurs even below the melting threshold (32%–36% of melting), suggesting that other damage mechanisms such as thermal-stress effects, phase changes, or photochemical processes may be dominant in this temperature regime. For multiple-pulse exposures, our results show that damage occurs at even lower fluences of 18%–23% of the melting threshold for $10 4$ and $10 5$ pulses. We did not observe evidence for mechanical damage in $B 4 C$⁠.

Figure 1 shows that the damage threshold decreases approximately logarithmically with the number of pulses so that it cannot simply be described by the cumulative fluence. Similar results were found in previous work^13–15 for different materials and under different irradiation conditions. The behavior is consistent with typical fatigue failures¹⁹ and is inconsistent with mechanisms that scale with the integrated fluence such as single photon photochemical processes.¹⁰ 

Table I summarizes the damage threshold doses (energy densities) that we observed in our UV experiments, the dose to which LCLS optics will be exposed, and damage thresholds calculated from models suggested in the literature. For Si, the observed damage threshold is 6–11 times larger than the calculated fatigue damage threshold, and a factor of 44–74 times larger than the worst case dose to which the LCLS mirrors would be exposed. For $B 4 C$ films, the observed damage threshold is comparable to the calculated fatigue damage threshold and a factor of 14–22 times larger than the worst case dose for the LCLS mirrors. These results suggest that Si mirrors would be more damage resistant than $B 4 C$⁠. However, $B 4 C$ is still preferred for the SOMS since its damage threshold is still well above the expected exposure and its spectral response extends to 2 keV, while Si cuts off above 1.84 keV due to its K-edge.

In summary, we have performed multiple-pulse experiments to determine the damage threshold of materials that are likely to be used for XFEL optics. We have found that in bulk silicon the melting threshold is generally a good indicator for single-pulse thermal damage. For $B 4 C$ films, single-pulse damage occurs somewhat below the melting threshold. For both bulk silicon and $B 4 C$ films we have found that the damage threshold decreases with increasing number of pulses and that it lies below the melting threshold. We have studied up to $10 5$ pulses per exposure site, which is small considering the exposure rate at LCLS at full operation of about $10 7$ pulses per day. More experiments with a larger number of pulses are needed to quantify this effect.

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344. This work was performed for the LCLS project at SLAC.