A Theoretical Collisional-Radiative Framework for Modeling the Highly Charged Sn¹⁵⁺ Ion: Electron Impact Excitation and Radiative Property Calculations

Shivam Gupta^1*, Chun-Tse Wu², Yao-Li Liu¹, Shih-Hung Chen²

¹Institute of Space and Plasma Sciences, National Cheng Kung University, Tainan-City, Taiwan
²Deaprtment of Physics, National Central University, Zhongli, Taiwan

* Presenter:Shivam Gupta, email:gshivam475@gmail.com

The development of laser-produced plasma (LPP) extreme ultraviolet (EUV) light sources is critical for high volume manufacturing lithography [1-2]. Among several EUV light sources, tin (Sn) has emerged as the most favorable 13.5 nm EUV light emitter. This emission primarily from Sn⁵⁺ to Sn¹⁵⁺ ions, appears in unresolved transition arrays (UTAs) due to spectral line blending from adjacent charge states, complicating spectroscopic investigations. The calculation of conversion efficiency (CE) of an LPP-EUV light source is sensitive to the precision of the radiative data, including line positions and intensities, used in the simulations. Comprehensive benchmarking of the atomic structure, transition, and electron collision parameters involved in the code is therefore necessary for the development of a predictive plasma modeling framework. In light of this, the EUV emission spectra from different tin ions is theoretically computed through detailed atomic structure and collisional-radiative (CR) model calculations. Currently, atomic structure and electron-collision data for multiply charged tin ions (Sn⁸⁺-Sn¹⁵⁺) are relatively scarce, primarily due to the complex electronic structures resulting from strong electron correlation among a large number of active electrons in the open 4d subshells. This complexity makes it difficult to establish accurate energy levels and other critical atomic parameters.

To address this gap, this study focuses on calculating the atomic-ion structure parameters of the Sn¹⁵⁺ ion, alongside providing fine structure-resolved electron impact excitation (EIE) cross-section data. The atomic structure data will be obtained using the relativistic multi-configuration Dirac-Hartree-Fock (RMCDHF) and relativistic many-body perturbation theory (RMBPT) methods, integrated within the flexible atomic code (FAC) [3]. We consider electron excitation from the ground state of Sn¹⁵⁺ (4p⁵, J=3/2), incorporating a range of odd and even electron configurations. Using the FAC, we calculate excitation energies, transition probabilities, and oscillator strengths. These wave functions are then used to construct a transition matrix (T-matrix) for excitation cross-section computations, with a relativistic distorted wave (RDW) method applied to calculate cross-sections at electron energies up to 3.5 keV. The results are integrated into a collisional-radiative plasma model, accounting for fine structure levels, electron impact excitation, ionization, radiative decay, and reverse processes such as electron impact de-excitation and three-body recombination. To validate our calculations, we compare the theoretical line emissions from Sn¹⁵⁺ within the 12–20 nm range with EBIT measurements, confirming the reliability of our atomic structure and collision data. The detailed results on electron impact excitation and plasma properties will be presented and discussed at the conference.

References:
[1] J. Scheers et al, Physical Review A, 101, 062511 (2020).
[2]O. O. Versolato, J. Opt., 24, 054014 (12pp) (2022).
[3] M. F. Gu, Can. J. Phys. 86, 675 (2008).

Keywords: Plasma Diagnostic, Collisional-Radiative Model, Laser Produced Plasma, Atomic Structure Calculation, Electron Impact Cross-Sections