2.1.

X-Ray Measurement

Our SPO sample was prepared at the coating facility dedicated for the Athena mirror production.^12,13 The sample has a length and width of 110 and 49 mm, respectively. A 10-nm thick iridium thin film coating was deposited using DC magnetron sputtering. The details of the sample preparation are described in Awaki et al. 2021.⁹

We measured the x-ray reflectivity of the SPO sample at BL20B2¹⁴ in SPring-8. The crystal plane of 311 of the Si double crystal monochromator¹⁵ was selected to monochromatize continuum x-rays in our experiment. The energy resolution ($\mathrm{\Delta }E/E$) of the available x-ray beam is $<10{}^{-4}$ in the energy range from 9000 to 15,000 eV, and the energy scale was calibrated by measurements of the Cu $K$-edge structure. We measured the intensity of a reflected x-ray on the SPO sample as well as the intensity of an incident x-ray and derived the reflectance $R$, defined as the ratio of the intensity of a reflected x-ray to that of the incident x-rays. Since the reflectance $R$ is described as a function of the energy $E$ of the incident x-ray and grazing angle $\theta$, we measured the reflectivity by performing angle and energy scans at fixed energies and fixed incident angles, respectively.

In the energy scans, three fine pitch scans with an incident angle of 0.2, 0.32, and 0.4 deg were performed around the energies of the iridium L-edges in steps of 1.5 eV to clarify the iridium $L$-shell structure of $f_1$ and $f_2$. The scanning energy ranges are 11 to 11.5 keV for $L_3$ edge, 12.5 to 13 keV for $L_2$ edge, and 13.2 to 13.7 keV for $L_1$ edge. Figure 1 shows the reflectance obtained in the energy scans. We can clearly see small oscillations in the post-edge region. These small oscillations are referred to as DAFS. Angle scans were performed at x-ray energies of 11, 12, and 14 keV, spanning the range of the iridium $L$-edges, specifically. The incident angle was scanned up to 1.5 deg in steps of 0.05 deg to measure the thickness of the iridium layer.

Fig. 1

Iridium $L$-edge structure of the reflectance obtained by the energy scan in steps of 1.5 eV.

2.2.

Estimation of the Atomic Scattering Factors

The reflectance of a single thin layer can be calculated using the refractive indices of the thin layer and the substrate. By fitting the measured data with a single thin layer model, we can estimate the parameters describing the iridium layer, specifically, the thickness of the iridium layer ($d$), interfacial roughness between the iridium layer and SPO substrate (${\sigma }_b$), and the surface roughness of the iridium layer ($\sigma$). However, the angle data points in the energy scan were not enough to estimate the parameters. Thus, the fit to the angle scan data was used to identify the parameters describing the iridium layer, specifically, $d$, ${\sigma }_b$, and $\sigma$. In this calculation, the loss of reflectance owing to roughness was considered as the Nevot–Croce factor,¹⁶ and the atomic weight and the corresponding mass density of iridium were taken as 192.22 and $22.421\mathrm{g}{\mathrm{cm}}^{-3}$,¹⁷ respectively. We employed an overlayer model, assumed as a hydrocarbon chain of the form ${\mathrm{CH}}_2$ with a density of $1{\mathrm{g}/\mathrm{cm}}^3$ (Graessle et al.⁸). The best-fit values were obtained from the angle scan. The details of the measurements are given in Awaki et al.⁹

In the fitting procedure of the energy scan data, $\sigma$, ${\sigma }_b$, and $d$ were set as constant at the weighted mean values of the best-fit values of the angle scan data ($\sigma =0.30\mathrm{nm}$, ${\sigma }_b=0.64\mathrm{nm}$, $d=10.01\mathrm{nm}$). The thicknesses of the overlayer were set to be 0.9 nm because we found that an overlayer thickness of 0.9 nm led to a better fit to the $f_2$ data reported by Henke et al.⁶ Figure 2 shows the derived $f_2$ near the iridium $L$-edges to clarify their structures.

Fig. 2

The atomic scattering factor $f_2$ near the $L$-edges. The dash-dotted lines indicate the energies (11215.7 $\pm 0.3\mathrm{eV}$, 12824.3 $\pm 0.9\mathrm{eV}$, and 13426.5 $\pm 0.6\mathrm{eV}$) of $L_3$, $L_2$, and $L_1$ edges, respectively.⁹ The gray line in the panels of $L_2$ and $L_3$ shows $\mu (E)$ (arb. unit) obtained by Clancy12.

3.1.

Comparison with the XANES Obtained from XAS

It is known that the absorption coefficient $\mu (E)$ of iridium near $L_2$ and $L_3$ edges contains three main features: (i) a sharp line feature known as “white line”^18,19 (hereafter WL), (ii) a step-like edge feature, and (iii) a small wave-like feature.^1,20 The scattering factor $f_2$ near $L_2$ and $L_3$ edges also shows these features (see Fig. 2). To confirm the similarity between $\mu (E)$ by Clancy12 and our result $f_2(E)$, the Clancy12 data (arb. unit) was scaled to fit our data and then overlaid on our data in Fig. 2. Both data were found to be similar, including the small wave feature in the energy $\mathrm{\Delta }E>50\mathrm{eV}$. The similarity suggests that (1) the fine structures of $f_2$ obtained from reflectance are consistent with XAFS obtained from XAS and (2) there is no apparent difference of optical characteristics between a thin iridium film formed by a DC magnetron sputter and an iridium powder with a purity of 99.99%.

The similarity to Clancy12 can also be seen in the best-fit parameters of $L3$. Comparing the best-fit parameters obtained by Awaki et al.⁹ with previous works,^1,20 the best-fit parameters (center energy and line width) of $L3$ WL were consistent with previous works^1,20 (see Table 1). Clancy12 also measured $L_2$ WL and estimated the branching ratio to be 3.2, which is larger than that of our result. In the fitting procedure by Clancy12, the line width of $L_2$ WL was fixed to the same line width as $L_3$ WL. Thus, we fitted the $L_2$ WL with the same line width as $L_3$ WL. The branching ratio is changed to $2.9\pm 0.4$, which is consistent with their result.

Table 1

L3 and L2 white lines.

3.2.

Fine Structures of the Scattering Factor f₂ Near L-Edges

There are two distinct peaks ($p1$ and $p2$ in Fig. 2) in the $f_2$ fine structures at $L_2$ and $L_3$-edges, and these peaks are also seen in the x-ray absorption near edge structure (XANES) results obtained by previous works.¹ Each peak was fitted with a Lorentzian model. The best-fit parameters are shown in Table 2. The center energy of each peak is represented by the energy $\mathrm{\Delta }E$ from the absorption edge. Since the center energies $\mathrm{\Delta }E$ and line widths of $p1$ in the $L_3$ edge are consistent with those of $p1$ in $L_2$ edge in the $1\sigma$ error region, p1 detected in $L_2$ edge is considered to be a transition to the same state as detected at $L_3$ edge. It would be the same for $p2$ as for $p1$. Sham²¹ studied the x-ray absorption fine structures at $L$-edges for 4d elements, Rh, Pd, and Ag, and there were prominent weak peaks at $˜20$ and $\sim 38\mathrm{eV}$ in their absorption spectrum at the $L$-edge for these materials. The two weak lines $p1$ and $p2$ in Fig. 2 would be assigned to peaks 2 to 4 ($\to pd$) and 5 ($\to df$) in Table 1 of Sham.²¹ To find branching ratios of these lines, we fixed both the center energies and the line width (${\mathrm{\Gamma }}_E$) of the two peaks at the weighted mean values ($\mathrm{\Delta }E=17.1$ and 31.8 eV, ${\mathrm{\Gamma }}_E=3.9$ and 4.6 eV for $p1$ and $p2$, respectively) and fitted $p1$ and $p2$ with a Lorentzian model. The branching ratio of $p1$ was larger than 2 but the error was large, while the branching ratio of $p2$ was consistent with 2.

Table 2

Best fit parameters of two peaks in L-edge structure.

On the $f_2$ fine structure at the $L_1$ edge, there are two prominent peaks at $\mathrm{\Delta }E={{12.2}^{+1.1}}_{-0.9}\mathrm{eV}$ and $\mathrm{\Delta }E={{42.0}^{+2.3}}_{-3.3}\mathrm{eV}$. The prominent lines are clearly seen in the $\mu$ of iridium the ${\mathrm{L}}_1$ edge in the Materials Data Repository. Although Sham²¹ studied the $L_1$-edge x-ray absorption properties of 4d noble metals, there were two clear peaks of absorption coefficient at about 18 and 40 eV from the $L_1$ edge in Fig. 8 of Sham,²¹ and these two peaks were associated with $2s\to p$, $pd$ and $2s\to f$, respectively. This assignment of the two peaks will be helpful to consider the $p1$ and $p2$ assignments found in the iridium $L_1$ edge, although we cannot eliminate the possibility that $p2$ might be similar to extended XAFS (EXAFS) due to the large line width of ${{11}^{+6}}_{-6}\mathrm{eV}$.

3.3.

Ratio of the Scattering Factor f₂ Between L₂ and L₃-Edges

The measured step size, which presents the depth of an edge, of the $L_3$ edge was twice that of the $L_2$ edge. Since the step-like edge features are associated with the $2p\to$ continuum transition, the ratio of the step size reflects the ratio, which is 1:2, of the initial core-electron states available for the $L_2$ ($2p_{1/2}$) and $L3$ ($2p_{3/2}$) processes. On the other hand, the WL, which is associated with $2p\to 5d$ transition, has a branching ratio $(L_3/L_2)>2$. We investigated how the ratio of the scattering factor $f_2$ ($L_3/L_2$) changes with energy offset from WL.

At first, we estimated a floor value of $f_2$ in the energy region of $\mathrm{\Delta }E$ from $-100$ to $-50\mathrm{eV}$, and then subtracted the floor value from the measured $f_2$. Next, the measured $f_2$ was smoothed by applying savgol_filter in python 3.8.2 with a window length of 5 and an order of 2 to reduce scattering of the ratio due to poor statistics. Figure 3 shows the $f_2$ after subtraction of the floor value and the ratio of $f_{2,L3}/f_{2,L2}$, where $f_{2,L3}$ and $f_{2,L2}$ are the $f_2$ at $L_3$ edge and $L_2$ edge, respectively. The solid line indicates the smoothed curve with savgol_filter. The energy $\mathrm{\Delta }{E}^{\prime }$ is the energy from the center energy of WL, because the uncertainty of the edge energy in our fitting results makes a discrepancy of the energy $\mathrm{\Delta }E$ between $L_2$ and $L_3$ regions, and then the discrepancy makes pseudo peaks in the ratio near WL. A typical $1\sigma$ error of the ratio at the energy $\mathrm{\Delta }{E}^{\prime }>0$ is 0.14.

Fig. 3

Ratio of the atomic scattering factor $f_2$ between $L_3$ and $L_2$. $\mathrm{\Delta }{E}^{\prime }$ is the energy from WL. (a) and (b) The solid lines show the values after smoothing, the dashed lines indicate the energy of $p1$ and $p2$ features, and the dashed-dotted lines indicate the $L$-edge energy.

The branching ratio around the energy of WL is about 2.4, which is significantly $>2$. The branching ratio remains large up to $\mathrm{\Delta }{E}^{\prime }\sim 7.5\mathrm{eV}$. This result is consistent with a larger line width of WL in $L_3$ than that in $L_2$. In the energy region $\mathrm{\Delta }{E}^{\prime }=8$ to 18 eV, the ratio is 2.1–2.2, which is slightly larger than 2. This result is also in agreement with the estimation of the results of the branching ratio of $p1$. Above 20 eV, the branching ratio becomes to be a mean value of 2.04 with a standard deviation of 0.05, which is consistent with the ratio of the density of states between $2p_{1/2}$ and $2p_{3/2}$.

3.4.

Fine Structures at ΔE >50 eV Seen in the Scattering Factor f₂

It is found that the $f_2$ structure of the $L_3$ data at $\mathrm{\Delta }E>50\mathrm{eV}$ is similar to that of the $L_2$ data (see Fig. 2). The similarity can also be seen in the constant ratio of $f_{2,L3}/f_{2,L2}$ at $\mathrm{\Delta }E>20\mathrm{eV}$ (see Fig. 4). The origin of the fine structure in EXAFS is the interference between the incoming and scattered photoelectron waves. The kinetic energy of a photoelectron wave is given by $E_K=h\nu -E_{\text{edge}}$, where $h\nu$ is the photon energy and $E_{\text{edge}}$ is the edge energy. Interference patterns should depend on $E_K$ because the wavelength of a photoelectron is related to $1/E_K$. Thus, the fine structure in EXAFS of $L_3$ is expected to be similar to that of $L_2$.

Fig. 4

Prediction of reducing the error in $f_1$ value using the $f_2$ estimated from $\mu$. As a small error in $\mu$ was expected, $f_2$ was fixed on the best-fit value.

We supposed that the fine structure of the $L_1$ data is also similar to that of the $L_3$ data, but we did not see a clear similarity. If we shift the energy of the $L_1{f}_2$ data by $+20\mathrm{eV}$, we may see a weak similarity between the $f_2$ fine structures of $L_3$ and $L_1$.

4.1.

Measurement of the Atomic Scattering Factors

We have demonstrated that the $f_2$ fine structure obtained from the reflectance is similar to the XANES results obtained using XAS. This confirms the relationship between $f_2$ and $\mu$ and shows that $f_2$ can be estimated from $\mu$. Estimating $f_2$ from $\mu$ may lead to reducing the time for the ground calibration of an x-ray mirror because the detailed structure of $f_2$ near the absorption edge is measured without a fine energy scan of the reflectance. In addition, because $\mu$ is accurately determined via XAS, the error margin in $f_1$ value obtained using $\mu$ is small. We demonstrate this possibility by fixing $f_2$ in our data. Figure 4 shows the error of $f_1$ when $f_2$ was fixed. It is found that the error in the $f_1$ value decreased by 0.3 to 0.8 times. As the critical angle for iridium at 12 keV is $\sim 0.385\mathrm{deg}$, the x-ray reflectivity at an incident angle of 0.4 deg at an energy of 12 keV or less is not sufficiently low (Fig. 1). Thus, the uncertainty in the $f_1$ value is large when $f_2$ is set to a free parameter. Using $\mu$ may be worthwhile when using data wherein the incident angles are close to or below the critical angle.

4.2.

XAFS Measurement

Our result suggests that the 10-nm-thick iridium formed by the DC magnetron sputtering device has almost the same optical property as that of iridium powder. This result indicates that a study of XAFS is possible with a thin layer instead of powder.

The reflectance measurements will be useful for fine structure research on thin atomic layer samples that are difficult to do with XAS technique. For thin films, the absorption coefficient is estimated by measuring the intensity of a fluorescence line (fluorescence XAFS measurements^22,23). However, the self-absorption effect causes distortion in the measured spectra in fluorescence line, and a correction for this distortion is needed.²² In addition, a sufficient intensity of fluorescence line is required to obtain $\mu$ with a high signal-to-noise ratio. Our reflectance measurement is an alternative method to estimate the absorption coefficient. The similarity between $f_2$ and $\mu$ suggests that the effects observed in the fluorescence XAFS measurements are small.

We have provided the fine structures of $f_2$ in the energy region $\mathrm{\Delta }E<50\mathrm{eV}$ from iridium L-edges ($L_3,L_2$, and $L_1$). The properties of the two peaks are similar to those of $4d$ material obtained by Sham 1985. We have also calculated the ratio $f_{2,L3}/f_{2,L2}$ in the energy range $\mathrm{\Delta }{E}^{\prime }=0\sim 150\mathrm{eV}$. The ratio is about 2.4 in the energy range $\mathrm{\Delta }{E}^{\prime }<7.5\mathrm{eV}$, and as the photon energy increases, the ratio decreases; at the energy $\mathrm{\Delta }{E}^{\prime }>20\mathrm{eV}$, the ratio comes to the mean value of $\sim 2$, which is consistent with the ratio of the density of states between $2p_{1/2}$ and $2p_{3/2}$.

The origin of the fine structure in EXAFS is the interference between the incoming and scattered photoelectron waves. Thus, each fine structure in the EXAFS region can be compared because we obtained the $f_2$ fine structures of the $L$-edges ($L_3,L_2$, and $L_1$). The $f_2$ fine structure of ${\mathrm{L}}_2$ is, as expected, similar to that of $L_3$, but the $f_2$ fine structure of $L_1$ is not similar to that of $L_3$. If we shift the energy of the $L_1{f}_2$ data by $+20\mathrm{eV}$, we may see a weak similarity between the $f_2$ fine structures of $L_3$ and $L_1$. This shift may be because of the difference between the $L_1$ transition ($\to 6p$) and the $L_2/L_3$ transition ($\to 5d$). Detailed analysis using high quality data is required to investigate the fine structures of iridium $L$-edges.