Energy Level Structure of Sn${}^{3+}$ Ions

Abstract

Laser-produced Sn plasma sources are used to generate extreme ultraviolet (EUV) 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 Sn${}^{1+}$ - 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), 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 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 Sn${}^{3+}$ is confirmed and refined to 328908.4 cm${}^{-1}$ with an uncertainty of 2.1 cm${}^{-1}$. The relativistic Fock space coupled cluster (FSCC) calculation 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 FSCC, COWAN code calculations, and configuration interaction many-body perturbation theory (CI+MBPT), this behavior is shown to arise from interactions with doubly-excited configurations.

arXiv comment12 pages, 6 figures

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Cited by in corpus (2)

• Relativistic atomic structure calculations in support of spectroscopy
• Accurate determination of energy levels, hyperfine structure constants, lifetimes and dipole polarizabilities of triply ionized tin isotopes