Time- and space-resolved optical Stark spectroscopy in the afterglow of laser-produced tin-droplet plasma

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Time- and space-resolved optical Stark spectroscopy in the afterglow of laser-produced tin-droplet plasma

J. Scheers, R. Schupp, R. Meijer, W. Ubachs, R. Hoekstra, and O. O. Versolato

Phys. Rev. E 102, 013204 – Published 9 July 2020

Abstract

The afterglow emission from Nd:YAG-laser-produced microdroplet-tin plasma is investigated, with a focus on analyzing Stark effect phenomena and the dynamical evolution of the plasma. Time- and space-resolved optical imaging spectroscopy is performed on 11 lines from Sn i–iv ions, in the 315–425-nm wavelength range. Stark shift-to-width ratios serve as the basis for unambiguous experimental tests of atomic physics theory predictions. Experiment and theory, where available, are found to be in poor agreement, and are in disagreement regarding the sign of the ratio in several cases. Spectroscopic measurements of the Stark widths in tandem with Saha-Boltzmann fits to Sn i and Sn ii lines, establish the evolution of the local temperature and density of the plasma afterglow, 20–40 ns after the end of the 15-ns-long temporally box-shaped laser pulse. A clear cool-down from $\sim 2$ to 1 eV is observed of the plasma in this time window, having started at $\sim 30$ eV when emitting extreme-ultraviolet (EUV) light. An exponential reduction of the density of the plasma from $\sim 10^{18}$ – $10^{17} e^{-}$ ${cm}^{- 3}$ is observed in this same time window. Our work is relevant for understanding the dynamics of the decaying, expanding plasma in state-of-the-art EUV nanolithography machines.

Received 2 May 2020
Accepted 15 June 2020

DOI:https://doi.org/10.1103/PhysRevE.102.013204

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Atomic spectra Laser-plasma interactions Plasma production & heating by laser beams, laser-foil, laser-cluster Stark effect

Atomic, Molecular & OpticalPlasma Physics

Authors & Affiliations

J. Scheers ^1,2, R. Schupp ¹, R. Meijer ^1,2, W. Ubachs ^1,2, R. Hoekstra ^1,3, and O. O. Versolato ^1,2,*

¹Advanced Research Center for Nanolithography, Science Park 110, 1098 XG Amsterdam, The Netherlands
²Department of Physics and Astronomy, and LaserLaB, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
³Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands

^*versolato@arcnl.nl

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Vol. 102, Iss. 1 — July 2020

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Images

Figure 1
Schematic layout of the experimental setup. Panel (a): Geometry of the optical system to project plasma emission onto the fiber array. The here relevant fiber cores are labeled a–d. Panel (b): ICCD image capturing emission of Sn i (at $λ = 326$ nm) and Sn ii (at $λ = 328$ nm) lines from seven fiber cores, covering an approximately 0.9 mm spatial extent of the plasma as a function of wavelength, at time $t = 50$ ns. Transitions are detailed in Table 1. Panel (c): Time-resolved spectra from fiber core b, covering the temporal evolution from 25 to 75 ns.
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Figure 2
Time-resolved spectra of selected lines belonging to Sn i–iv. Transitions are detailed in Table 1. Lines are individually normalized to their respective maximum in time. Spectra shown are from plasma light captured by fiber core c, some $+ 250$ $μ m$ from the initial droplet position (see Fig. 1). Details of the individual transitions are given in Table 1. Time is relative to the first moment of the 15-ns-long laser pulse hitting the droplet.
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Figure 3
Lorentzian widths against line shifts as obtained from fitting Voigt functions (with the respective Gaussian component inferred from nearby calibration lines) of the lines shown in Fig. 2. The shift is given with respect to literature values for the line position, listed in Table 1. The results from the three fiber cores b, c, and d are shown (see Fig. 1). The error bars represent one standard deviation of the fit uncertainties. Solid straight lines represent linear fits to the data.
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Figure 4
Color map of the average charge state $\bar{z}$ as a function of electron density and temperature from FLYCHK calculations [71] in LTE. The solid (near diagonal) lines indicate the solutions allowed by a Saha-Boltzmann fit to Sn i and Sn ii lines, performed for each time step for fiber core b (see Fig. 1). The dashed (near vertical) lines indicate allowed solutions for the electron densities (as a weak function of $T$ ) as inferred from the width of the Sn ii $5 s 5 p^{2}^{2} D_{3 / 2} – 5 s^{2} 4 f^{2} F_{5 / 2}$ transition at the 328-nm line using the experimental input from Ref. [54] (see main text). The intersections of solid and dashed lines identify unique solutions for electron density and temperature. Time is relative to the first moment of the 15-ns-long laser pulse hitting the droplet.
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Figure 5
Plasma electron density determined from measurements taken at fiber core b (see Fig. 1) as a function of time (relative to the first moment of the 15-ns-long laser pulse hitting the droplet). The densities are calculated using the experimental Stark width in the case of Sn ii [54], and theoretical widths from Sn i [52], Sn iii [51], and Sn iv [59] taken at their $T = 1$ eV values; details are given in Table 1. Uncertainty estimates combine uncertainties on the input parameters (a 20% error margin is assumed where no value was provided), with statistical ones and a constant 0.05 nm uncertainty that captures systematic deviations seen, e.g., in Fig. 3. The solid black line results from an exponential fit to the 328-nm data of Sn ii. The inset in panel (a) shows 328-nm data also from fiber cores a and d (see Fig. 1). Panels (b), (c), and (d) show the densities as derived from lines of Sn i, Sn iii, and Sn iv, respectively, from fiber core b. The black lines are identical to the one shown in panel (a).
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