# Ni-Al Alloys as Alternative EUV Mask Absorber
## 4 Verification of Optical Constants  
In this section, we compare optical constants, calculated by Equation (1) with values from film characterization in Section 3, and by fitting EUVR measurement. The optical constants will be used in rigorous simulations to predict M3D impact in Section 5. The first set of \(n_{,K}\) is calculated using crystalline density and composition of Ni\({}_{x}\)Al\({}_{y}\) compounds from literature. The second set of optical constants is calculated based on bulk density and bulk composition obtained with XRR. These density and composition values are tabulated in Table 4. The third set of optical constants are calculated from fitting EUVR data, which were collected with PTB's soft X-ray radiometry beamline at BESSY II facility. The EUV reflectance of Ni\({}_{3}\)Al, NiAl and Ni\({}_{2}\)Al\({}_{3}\) was measured through wavelength and through incidence angle. The results have previously been reported in [50]. We fit the measured EUV reflectance with a three-layer stack model, consisting out of native oxide, bulk metal, and SiO\({}_{2}\) on Si-substrate. The fitting parameters consist out of layer thickness, and optical constants. The EUV reflectance fits are illustrated in the Supplementary Materials Figure S3; the resulting optical constants at 13.5 nm wavelength are tabulated Table 5. Figure 11 compares the optical constants obtained through literature, XRR, and EUVR. Figure 11: Optical constants of Ni\({}_{3}\)Al (full circle), NiAl (full triangle), Ni\({}_{3}\)Al (full square), and their surface oxide (open circle, triangle, square): calculated from crystalline density and nominal composition (blue), calculated from XRR measured bulk density and bulk composition (orange), and calculated from EUVR fitting (green). EUV reflectance shows higher \(\kappa\) with increasing Ni content and \(n\) closer to unity with increasing Al content. The extinction coefficients \(\kappa\) are very comparable between calculation based on literature, XRR, and EUVR. However, EUVR found the refractive coefficients \(n\) much closer to unity. The calculated optical constants of the Ni\({}_{x}\)Al\({}_{y}\) compounds lie linearly between those from the single elements Ni and Al, and is based on their tabulated atomic scattering factor f\({}_{i}\), which is very sensitive to absorption edges. Depending on the chemical state of the element, the absorption edge can shift through wavelength, resulting in different optical constants. Few elements have absorption edges near 13.5 nm EUV wavelength, one of which is Al. Metallic Al L2 absorption edge lies at 73.1 eV [51], corresponding to a wavelength of \(\sim\)17 nm, as illustrated in Figure 12a. Figure 12: (**a**) Absorption edges of elements between \(Z\) = 11 (Na) and \(Z\) = 30 (Zn) through wavelength. Data from Bearden and Burr [51]. Measured Al L2 absorption edge of (**b**) bulk, and (**c**) surface oxide of Ni\({}_{3}\)Al (blue), NiAl (orange), and Ni\({}_{2}\)Al\({}_{3}\) (green), compared to theoretical Al L2 absorption edge of elementary Al and crystalline Al\({}_{2}\)O\({}_{3}\) (black) respectively. The refractive coefficient is \(n\) represented by full lines, the extinction coefficient \(\kappa\) by dashed lines. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & **Bulk \(n\)** & **Bulk \(\kappa\)** & **Oxide \(n\)** & **Oxide \(\kappa\)** \\ \hline
**Ni\({}_{3}\)Al** & 0.9762 & 0.0630 & 0.9652 & 0.0242 \\
**NiAl** & 0.9863 & 0.0601 & 0.9691 & 0.0220 \\
**Ni\({}_{2}\)Al\({}_{3}\)** & 0.9936 & 0.0488 & 0.9681 & 0.0229 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Optical constants at 13.5 nm EUV wavelength obtained from fitting EUV reflectometry (EUVR) measurements. XPS measurements showed partially oxidized Al at the surface and in the bulk (cf. Figure 8). Higher binding energy of Al-O bonds compared to Al-Al, will shift the Al L2 edge towards higher energy and smaller wavelength. To verify this behavior, additional EUV reflectance was measured between 16 nm and 18 nm wavelength to determine the Al L2 absorption edge position.