Theoretical investigation on extreme ultraviolet radiative opacity and emissivity of Sn plasmas at local-thermodynamic equilibrium

Abstract

Sn is the material for an extreme ultraviolet (EUV) light source working at 13.5 nm, therefore the radiative properties of Sn plasma are of great importance in designing light source. The radiative opacity and emissivity of Sn plasma at local thermodynamic equilibrium are investigated by using a detailed-level-accounting model. In order to obtain precise atomic data, a multi-configuration Dirac-Fock method is used to calculate energy levels and oscillator strengths of <inline-formula><tex-math id="M3">\begin{document}${\rm{Sn}}^{6+}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M3.png"/></alternatives></inline-formula>-<inline-formula><tex-math id="M4">\begin{document}${\rm{Sn}}^{14+}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M4.png"/></alternatives></inline-formula>. The electronic correlation effects of <inline-formula><tex-math id="M5">\begin{document}$4{\rm d}^m\text{-}4{\rm f}^m$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M5.png"/></alternatives></inline-formula>(<inline-formula><tex-math id="M6">\begin{document}$m=1, 2, 3, 4$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M6.png"/></alternatives></inline-formula>) and <inline-formula><tex-math id="M7">\begin{document}$ 4\mathrm{p}^n\text{-}4\mathrm{d}^n $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M7.png"/></alternatives></inline-formula>(<inline-formula><tex-math id="M8">\begin{document}$n=1, 2, 3$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M8.png"/></alternatives></inline-formula>) are mainly considered, which dominate the radiation near 13.5 nm. The number of fine-structure levels reaches about 200000 for each ionization stage in the present large-scale configuration interaction calculations. For the large oscillator strengths (> 0.01), the length form is in accord with the velocity form and their relative difference is about 20%–30%. The calculated transmission spectra of Sn plasma at 30 eV and 0.01 g/cm³ are compared with the experimental result, respectively, showing that they have both good consistency. The radiative opacity and emissivity of Sn plasma at the temperature in a range of 16–30 eV and density in a scope of of 0.0001–0.1 g/cm³ are investigated systematically. The effects of the plasma temperature and plasma density on radiation characteristics are studied. The results show that the radiative properties near 13.5 nm are broadened with the increase of density at a specific temperature, while it is narrowed with the increase of temperature for a specific density. The present investigation should be helpful in designing and studying EUV light source in the future.