Laser-produced tin plasmas and gas-discharge xenon plasmas have been widely investigated because their compactness and high emissivity around 13.5 nm make them an attractive extreme ultraviolet light (EUV) source.^[1–5] In previous studies, tin spectra in the 13.5 nm region show a complicated spectral profile with a broad reabsorption band and several pronounced dips. The true spectral profiles of tin ions in optically thick plasmas are distorted to yield the observed profile by self-absorption features owing to the opacity effect.^[6] Meanwhile, the fact that more than tens of thousands of individual lines contribute to the quasi-continuum band or unresolved transition array (UTA) spectral profile in the EUV region presents a challenge to the accurate analysis of the EUV experimental spectra.^[7] Therefore, a high-resolution EUV spectrograph is an indispensable tool to accurately determine the radiation properties and to analyze the evolution of the short-wavelength plasma light sources. However, most spectrographs require accurate wavelength calibrations before each measurement.^[8–11]

The wavelength calibration of a spectrograph directly affects the spectral analysis. For example, grazing-incidence spectrographs disperse light with a grating while recording the spectrum with a charge-coupled device (CCD), and calibration is needed to determine the wavelength of each characteristic peak on the CCD. Each pixel of the detector corresponds to a specific wavelength, and calibration establishes the pixel–wavelength relationship. For wavelengths below 200 nm, the common calibration sources are hollow-cathode gas discharges,^[12] multiple-anode sources,^[13] and laser-produced plasmas (LPPs). Relative to LPPs, the other two sources are expensive and their calibration process is tedious.

LPPs have high densities and temperatures and consist of highly-charged ions. They emit intense radiation from the visible to x-rays,^[14–20] and are typically produced by a high-energy pulsed (e.g., Q-switched) laser focused on a solid target. Highly charged ions of several low Z elements, such as C,^[21] Si,^[22,23] Al,^[24,25] S,^[26] and O,^[27] have isolated spectral features in the EUV and soft-x-ray regions that offer good resolution and spectral characteristics typical of simple energy level structures. Therefore, they can be used as potential calibration sources for EUV spectrographs. However, due to the limited number of spectral lines from low Z elements in the EUV region, auxiliary calibration using isolated EUV spectra of middle Z elements is necessary.

In this paper, we demonstrate the wavelength calibration of a grazing incidence grating spectrograph with known spectral lines from C, Si, Al, and S LPPs. In addition, the EUV spectra of chromium (Cr) LPPs are analyzed to obtain spectral lines of highly charged ions for EUV wavelength calibration in the 6.5–15.0 nm range.

Details of the experimental setup for spatio-temporally resolved LPPs emission spectroscopy have been reported previously,^[28] and will be briefly described here. A Nd:YAG laser (PRO-350, Spectra-Physics) with a fundamental wavelength of 1064 nm and pulse width of 10 ns was used to produce plasmas in a vacuum chamber by tightly focusing the beam on a planar Cr target. The EUV radiation was coupled into the entrance slit of a 1.0 m focal length grazing incidence spectrograph (McPherson 310 G), equipped with a 600 grooves/mm grating. The dispersed spectra were detected with a 40 mm diameter micro channel plate (MCP) detector coupled via a coherent fiber-optic bundle to a 1024 × 255 pixel charge coupled device. The spectra were temporally resolved by gating the MCP with a negative voltage pulse (−2200 V) for a minimum width of 60 ns. The spectrograph covered the spectral region of 6.6–68 nm via a Rowland circle. Here, the spectral measured range was fixed over 6.5–15 nm, corresponding to resolving powers ( ) from 361 to 4286, respectively.

To obtain the dispersion function of the spectrometer, well-known lines from highly charged C, Al, Si, and S, and their higher-order diffractions were used to cover the whole wavelength range of interest, as shown by the symbols in Fig. 1(a). Several peaks were deconvoluted before wavelength calibration so that the relationship between the transition wavelength and peak pixel could be accurately determined. These included two Si peaks at 11.79 nm and 11.90 nm, two Al peaks at 12.52 nm and 13.05 nm, and three S peaks at 7.24 nm, 14.53 nm, and 14.63 nm, which have been indicated in Fig. 1. A total of twelve lines were used in the calibration with wavelength values taken from the National Institute of Standards and Technology (NIST) atomic spectra database (ASD).^[24] A parabolic polynomial was used to fit the pixel versus wavelength calibration, as plotted in Fig. 1(b). Multiple measurements and calibrations revealed that the calibration parameters were constant. This dispersion function was also used to calibrate the Cr spectra.

Fig. 1.

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	Fig. 1. Experimental spectra and wavelength calibration. (a) Spectral profile analysis based on known spectral lines of laser-produced C, Si, Al, and S plasmas, (b) polynomial fitting.

To avoid line shifts and to reduce opacity effects on the spectral profiles, the entrance slit width was set to , and the MCP gate width was set to 60 ns. Figure 2(a) shows a spectrum in the 6.5–15.0 nm range produced with a laser intensity of 2.0 ×10¹¹ W/cm². The spectrum was recorded at a location 1.5 mm away from the target surface and at a 55-ns time delay. To obtain accurate values of the central wavelengths and intensities, each peak was decomposed into Gaussian peaks by single- or multi-peak fitting methods. As displayed in Fig. 2(b), 36 preliminary lines were obtained according to the symmetry of the spectral peak profiles.

Fig. 2.

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	Fig. 2. Laser-produced Cr plasmas spectrum in the 6.5–15 nm wavelength range: (a) experimental spectrum and (b) decomposed lines.

From the perspective of atomic structure analysis, the experimental peaks in the spectra were identified via the NIST database and Hartree–Fock calculations of the Cowan RCN, RCN2, and RCG suites with configuration interaction codes and the flexible atomic code (FAC).^[29–31] For the energy levels, wavelengths, weighted oscillator strengths, and transition probabilities, the excited-state basis contained 3s²3p⁵3d4s/4d (for Cr⁵⁺), 3s²3p^kns, 3s²3p^knd (n = 4,5, k = 5 for Cr⁶⁺, k = 4 for Cr⁷⁺, k = 3 for Cr⁸⁺, k = 2 for Cr⁹⁺, and k = 1 for Cr¹⁰⁺). To optimize the output, the Slater–Condon integrals (F^k, G^k, and R^k) were reduced to 87%, while the spin parameter ((ξ) was retained. In comparison, the emission lines could be identified from the 3p–4s, 4d, 5d transitions lines of Cr⁵⁺–Cr¹⁰⁺ ions.

In the experimental and simulated comparative analysis, a steady-state collisional-radiative model was used to calculate the ion fractions at different ionization stages as a function of electron temperature and electron density.^[32] Figures 3(a) and 3(b) plot the ion fractions of Cr⁵⁺–Cr¹⁰⁺ ions as a function of electron temperature assuming an electron density N_e=6.4×10²⁰ cm⁻³, and as a function of electron density assuming an electron temperature T^e=28.2 eV, respectively. It is apparent that the electron temperature in the 15–43 eV range and the electron density in the 10¹⁹–10²¹ cm⁻³ range can produce Cr⁵⁺–Cr¹⁰⁺ ions.

Fig. 3.

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	Fig. 3. Cr plasma charge-state ion fractions as a function of (a) electron temperature and (b) density. The vertical dashed lines show the relative ion fraction of different charge-state at an assumed electron temperature and electron density.

In order to reproduce the experimental spectra and find the relationships between the experimental conditions and plasma parameters, a series of simulated spectra as a function of T_e and N_e have been obtained and compared with the experimental spectrum. Here, the total emission line profile was obtained by weighting and summing the corresponding Boltzmann factors and ion fractions for each ion and by convolving each line with a Gaussian function with a full width at half maximum (FWHM) of 0.09 nm. After comparison, a simulated spectrum closer to the experimental profile could be obtained. Usually, a minimum value among the deviations was less than 5%. This means that the best estimated value of the plasma temperature and electron density was obtained. Figure 4 shows the comparisons among the experimental spectrum and simulated spectra for an electron temperature of 28.2 eV and an electron density of 6.4×10²⁰ cm⁻³. Figure 4(a) shows the experimental spectrum recorded at a location 1.5 mm away from the target surface and at a 55 ns time delay. Figures 4(b) and 4(c) show the simulated spectra based on the atomic data from Cowan and FAC calculations, respectively. To realize mutual benchmark of Cowan and FAC calculations, the simulated spectra in Figs. 4(b) and 4(c) were obtained based on the same ion fractions and energy level populations. The inset bar chart shows the calculated ion fractions as a function of ionization stage. It can be seen by comparison that there is good agreement between the experimental and two simulated spectra, especially for wavelengths and intensities of intense lines from dominant ions. The respective fractional contributions of Cr⁵⁺–Cr¹⁰⁺ ions were about 2.8%, 22.8%, 40%, 25.6%, 5.3%, and 3.5%.

Fig. 4.

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	Fig. 4. Comparison between measured and simulated spectra: (a) experimental spectrum, (b) Cowan simulated spectrum, and (c) FAC simulated spectrum.

Table 1 summarizes the observed and identified wavelengths, as well as other transition data that could be used for spectral simulations and comparative analysis. The data are arranged in order of wavelength, while the experimental wavelengths obtained by deconvolution are listed in the fourth column. The identified wavelengths obtained from the NIST database and calculated from FAC and Cowan codes are listed in the fifth to seventh columns. The final two columns give the transition probabilities from the FAC and Cowan calculations, which may be useful for future measurements of lifetimes and plasma spectra.

Table 1.

Table 1.

Table 1. Summary of measured and calculated data. The same number with different postscripts (in the first column) denotes the blending lines, the “*” indicates the new lines. . Index Ion Classification Wavelength/nm Transition probability Exp. NIST Calc. (FAC) Calc. (Cowan) gA(FAC)/1010 gA(Cowan)/1010 1* Cr10+ 3s23p2 3P1-3s23p15d3P2 6.73±0.02 6.71 6.70 40.9 36.9 2* Cr10+ 3s23p2 3P1–3s23p15d3P0 6.94±0.02 6.94 6.94 38.9 40.4 3* Cr10+ 3s23p2 1D2–3s23p15d3F2 7.49±0.05 7.47 7.50 4.00 4.29 4 Cr10+ 3s23p2 3P0–3s23p14d3D1 8.05±0.07 8.10 8.06 8.06 9.98 9.87 5 Cr10+ 3s23p2 1D2–3s23p14d2F3 8.17±0.06 8.21 8.21 8.23 24.9 11.8 6* Cr9+ 3s23p3 4S3/2–3s23p24d2P1/2 8.62±0.04 8.62 8.61 5.89 6.20 7* Cr9+ 3s23p3 2P3/2–3s23p24d2D5/2 9.02±0.02 9.01 9.02 3.28 3.96 8* Cr8+ 3s23p4 3P1–3s23p34d3P0 9.18±0.03 9.19 9.20 2.56 2.13 9a* Cr8+ 3s23p4 1D2–3s23p34d1D2 9.33±0.07 9.31 9.35 2.36 2.20 9b Cr8+ 3s23p4 3P1–3s23p34d3D2 9.38±0.07 9.43 9.43 9.45 1.85 1.73 10a Cr8+ 3s23p4 1D2–3s23p34d1D2 9.62±0.05 9.65 9.64 9.64 1.26 1.19 10b Cr8+ 3s23p4 3P2–3s23p34d3D3 9.71±0.06 9.72 9.71 9.68 2.59 2.37 10c Cr8+ 3s23p4 3P2–3s23p34d3D2 9.80 9.74 9.77 2.54 2.67 11 Cr10+ 3s23p2 1P1–3s23p14s3P1 9.93±0.05 9.95 9.92 9.93 22.8 21.7 12a Cr7+ 3s23p5 2P3/2–3s23p44d2D5/2 10.19±0.07 10.25 10.22 10.23 3.84 3.94 12b* Cr7+ 3s23p5 2P3/2–3s23p44d2P1/2 10.26 10.26 5.09 5.19 13 Cr7+ 3s23p5 2P3/2–3s23p44d2D5/2 10.53±0.05 10.57 10.54 10.54 4.48 4.16 14 Cr7+ 3s23p5 2P1/2–3s23p44d2D3/2 10.64±0.04 10.67 10.66 10.63 6.99 6.11 15a Cr9+ 3s23p3 2D5/2–3s23p24s2P3/2 10.95 ± 0.04 10.98 10.94 10.95 3.50 2.59 15b Cr9+ 3s23p3 2D3/2–3s23p24s2P1/2 11.01±0.06 11.04 11.03 11.02 5.21 4.84 15c Cr9+ 3s23p3 2P3/2–3s23p24s2D5/2 11.11 11.10 11.10 3.89 3.50 16* Cr9+ 3s23p32D3/2–3s23p24s4P1/2 11.20±0.05 11.22 11.19 3.29 2.18 17 Cr9+ 3s23p3 2P1/2–3s23p24s2P1/2 11.39±0.03 11.37 11.40 11.37 3.34 2.33 18 Cr6+ 3s23p6 1S0–3s23p54d1P1/2 11.51±0.05 11.54 11.50 11.51 4.99 4.46 19a Cr6+ 3s23p6 3P1–3s23p54d3D0 11.61±0.07 11.67 11.61 11.62 4.29 4.46 19b* Cr6+ 3s23p6 1S0–3s23p54d3P1 11.67 11.66 4.48 6.11 20 Cr8+ 3s23p4 3P1–3s23p34s3D2 11.91±0.05 11.93 11.90 11.91 1.04 1.05 21 Cr8+ 3s23p4 1D2–3s23p34s1D2 12.10±0.06 12.13 12.09 12.12 2.57 2.42 22 Cr8+ 3s23p4 1S0–3s23p34s1P1 12.26±0.04 12.27 12.26 12.27 3.73 3.54 23 Cr7+ 3s23p5 2P3/2–3s23p44s2S1/2 12.47±0.04 12.42 12.47 12.49 3.11 2.94 24* Cr5+ 3p63d2D5/2–3p53d4d2D5/2 12.73±0.03 12.74 12.71 26.3 28.7 25* Cr5+ 3p63d2D5/2–3p53d4d2P3/2 12.92±0.03 12.91 12.94 37.1 35.5 26 Cr7+ 3s23p5 2P3/2–3s23p44s2P1/2 13.19±0.02 13.23 13.21 13.23 2.85 2.78 27* Cr5+ 3p63d1 2D3/2–3p53d4s2P1/2 13.72±0.02 13.73 13.77 40.9 36.9 28* Cr6+ 3s23p6 1S0–3s23p54d3P2 14.15±0.02 14.15 14.13 3.01 2.85 29 Cr6+ 3s23p6 1S0–3s23p54d1P2 14.59±0.06 14.65 14.63 14.65 2.83 2.64

Table 1. Summary of measured and calculated data. The same number with different postscripts (in the first column) denotes the blending lines, the “*” indicates the new lines. .

Only transition probabilities from the FAC and Cowan calculated results are listed in Table 1 because of the absence of transition probabilities in the NIST ASD. A total of 29 peaks were classified, including 14 new lines. The peaks were attributed to 3p–4d, 5d, and 3p–4s transitions from Cr⁵⁺–Cr¹⁰⁺ ions. The intense sharp peaks at 8.62 nm and 9.02 nm were attributed to the 3s²3p^{3 4}S_3/2–3s²3p²4d²P_1/2 and 3s²3p^{3 2}P_3/2–3s²3p²4d²D_5/2 transitions of Cr⁹⁺, respectively, the peaks at 9.18 nm and 12.26 nm were attributed to the 3s²3p^{4 3}P₁–3s²3p³4d³P₀ and 3s²3p^{4 1}S₀–3s²3p³4s¹P₁ transitions of Cr⁸⁺, respectively, the sharp peak at 10.64 nm was attributed to the 3s²3p^{5 2}P_1/2–3s²3p⁴4d²D_3/2 transition of Cr⁷⁺, and the peak at 11.51 nm was attributed to the 3s²3p^{6 1}S₀–3s²3p⁵4d¹P_1/2 transition of Cr⁶⁺. Figure 5 shows a parabolic polynomial by fitting the pixel versus wavelength calibration using the lines of highly-charged Cr ions. This dispersion function was also used to calibrate the Cr spectra. With adequate resolution, these lines could be used for EUV spectrograph calibration.

Fig. 5.

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	Fig. 5. Fitting the pixel vs. wavelength calibration using the lines of highly-charged Cr ions.

Laser-produced Cr plasma radiation in the EUV region was investigated as an EUV wavelength calibration source. EUV emission spectra of Cr⁵⁺–Cr¹⁰⁺ ions over 6.5–15.0 nm were acquired via spatio-temporally resolved emission spectroscopy. Using the line information from the NIST ASD and from Cowan and FAC calculations, the peaks were identified as 3p–4d, 3p–5d, and 3p–4s transitions of Cr⁵⁺–Cr¹⁰⁺ions. By using a normalized Boltzmann distribution among the excited states and a steady-state collision radiation model, the electron temperature and electron density and the charge states in the plasma were investigated. The Cowan and FAC simulation results agreed very well with the experimental spectra. In conclusion, the results indicate that relatively isolated lines of highly charged Cr ions can be used for EUV wavelength calibration.