Energy-level structure of ${\mathrm{Sn}}^{3+}$ ions

Laser-produced Sn plasma sources are used to generate extreme ultraviolet light in state-of-the-art nanolithography. An ultraviolet and optical spectrum is measured from a droplet-based laser-produced Sn plasma, with a spectrograph covering the range 200–800 nm. This spectrum contains hundreds of spectral lines from lowly charged tin ions ${\mathrm{Sn}}^{1+}-{\mathrm{Sn}}^{4+}$ of which a major fraction was hitherto unidentified. We present and identify a selected class of lines belonging to the quasi-one-electron, Ag-like ([Kr]$4d^{10}nl$ electronic configuration), ${\mathrm{Sn}}^{3+}$ ion, linking the optical lines to a specific charge state by means of a masking technique. These line identifications are made with iterative guidance from cowan code calculations. Of the 53 lines attributed to ${\mathrm{Sn}}^{3+}$, some 20 were identified from previously known energy levels, and 33 lines are used to determine previously unknown level energies of 13 electronic configurations, i.e., $7p$, $(7,8)d$, $(5,6)f$, (6–8)$g$, (6–8)$h$, $(7,8)i$. The consistency of the level energy determination is verified by the quantum-defect scaling procedure. The ionization limit of ${\mathrm{Sn}}^{3+}$ is confirmed and refined to 328 908.4 ${\mathrm{cm}}^{-1}$, with an uncertainty of 2.1 ${\mathrm{cm}}^{-1}$. The relativistic Fock-space coupled-cluster (FSCC) calculations of the measured level energies are generally in good agreement with experiment but fail to reproduce the anomalous behavior of the $5d{}^{2}D$ and $nf{}^{2}F$ terms. By combining the strengths of the FSCC calculations, cowan code calculations, and configuration interaction many-body perturbation theory, this behavior is shown to arise from interactions with doubly excited configurations.

Figure 1

Schematic top view of the main components of the laser-produced plasma source from which the spectroscopic data were taken. For details see Sec. 2.

Figure 2

Experimentally obtained ${\mathrm{Sn}}^{\mathrm{q}+}$ spectra for laser energies of 0.5 mJ (blue; lower), 2 mJ (yellow; middle), and 10 mJ (green; upper). The observable increase in the background level is due to increased continuum emission from the plasma at higher laser energies. Spectra shown are taken without spectral filters and, thus, include second-order contributions.

Figure 3

Spectral intensity scaling as a function of the wavelength (vacuum; in nm) for varying laser energies. Here, the intensity is normalized to their (local) continuum background level, and unity is subsequently subtracted. The specific transitions shown are described in the text.

Figure 4

Normalized scaled intensities of Sni–Snv lines as a function of the laser energy. The same lines as presented in Fig. 3 are used. Other Sni–Snv lines show a similar dependence on the laser energy.

Figure 5

Quantum defect values as a function of the $1/n^{{*}^2}$ of the Sniv energy levels, for $l\le l_{\mathrm{core}}$ (top) and $l>l_{\mathrm{core}}$ (bottom). Quantum defects are calculated using Eq. (1) and the refined ionization limit of 328 908.4 ${\mathrm{cm}}^{-1}$. Black lines are linear fits of the data points where the lowest level is excluded (except for the $ni$ configuration).

Figure 6

Level diagram of ${\mathrm{Sn}}^{3+}$, drawn from 150 000 ${\mathrm{cm}}^{-1}$ to the ionization limit at 328 908.4 ${\mathrm{cm}}^{-1}$. The ground state $5s$, the $5p{}^{2}P$ term, and multiply excited configurations lying near the ionization limit are omitted, as transitions to these levels occur outside the detection range of this study. The levels determined in this study are shown in the boxed area. Other levels are based on Refs. [24] and [30].