Analysis of extreme ultraviolet spectra of laser-produced Cd plasmas

Cite this Article

Bakhiet Mohammedelnazier, Su Maogen, Cao Shiquan, Min Qi, Sun Duixiong, He Siqi, Wu Lei, Dong Chenzhong. Analysis of extreme ultraviolet spectra of laser-produced Cd plasmas. Chinese Physics B, 2020, 29(7): 075203 Copy to clipboard

Permissions

Analysis of extreme ultraviolet spectra of laser-produced Cd plasmas

Bakhiet Mohammedelnazier^{1, 3}, Su Maogen^{1, 2, †}, Cao Shiquan¹, Min Qi¹, Sun Duixiong¹, He Siqi¹, Wu Lei¹, Dong Chenzhong^{1, 2, ‡}

1Key Laboratory of Atomic and Molecular Physics & Functional Material of Gansu Province, College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China

2Joint Laboratory of Atomic and Molecular Physics, Northwest Normal University and Institute of Modern Physics of Chinese Academy of Sciences, Lanzhou 730070, China

3Department of Physics, Faculty of Education, University of the Holy Quran and Islamic Sciences, P. O. Box 1459, Khartoum 14412, Sudan

† Corresponding author. E-mail: nwnu_sumg@163.com

dongcz@nwnu.edu.cn

Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0402300), the National Natural Science Foundation of China (Grant Nos. 11874051, 11904293, and 61965015), and the Special Fund Project for Guiding Scientific and Technological Innovation of Gansu Province, China (Grant No. 2019zx-10).

Abstract

In order to provide detailed information about Cd structure and gain more insight regarding ionization degrees and types of transition, as well as the understanding of the temporal evolution behavior of laser produced Cd plasmas, extreme ultraviolet spectra of laser-produced cadmium (Cd) plasmas have been measured in the 8.4–12 nm region using spatio-temporally resolved laser-produced plasma spectroscopy technique. Spectral features were analyzed by the Hartree–Fock (HF) method with relativistic correlations (HFR) using the Cowan code. The results showed that the 4p–5s resonance transition arrays from Cd⁹⁺ to Cd¹³⁺ merged to form intense lines in this spectral region. A number of new spectral features from Cd⁹⁺ and Cd¹⁰⁺ ions are reported in this study. Based on the assumption of a normalized Boltzmann distribution among the excited states associated with a steady-state collisional–radiative model, the plasma parameters were obtained by comparing the experimental and simulated spectra. As a result, we succeeded in reproducing the synthetic spectra for different time delays, which yielded good agreement with the experiments. The temporal evolution behaviors of electron temperature and electron density of plasma were also analyzed.

PACS: ;52.38.-r;;52.38.Mf;;52.50.-b;;52.50.Jm;

Keyword:;extreme ultraviolet spectra;;laser-produced plasmas;;collisional-radiative model;;cadmium;

Show Figures

1. Introduction

An accurate understanding of the evolution of laser-produced plasmas (LPPs) spectral structures would be very helpful to determine the radiation properties and hydrodynamic evolution of plasmas.^[1,2] There are direct applications in many areas of important research, such as nuclear fusion,^[3,4] astrophysics,^[5] laboratory plasmas as ion sources,^[6,7] and short wavelength light sources^[8] for extreme ultraviolet (EUV) lithography.^[9–11] Spectroscopic data concerning highly ionized fifth period atoms are important for work in tokamaks and some appear as impurities, such as zirconium and molybdenum.^[12] In the last decades, several theoretical and experimental studies on the 4p–5s transition of various elements have been widely studied through their isoelectronic sequences.^[13–17] In theoretical studies, the Hartree–Fock with configuration interaction (HFCI) method developed by Cowan^[18] and some other computer programs are commonly performed.

Ryabtsev and Kononov^[19] systematically observed the spectra of Rh⁷⁺, Pd⁸⁺, Ag⁹⁺, and Cd¹⁰⁺ in 14–33 nm and about 100 lines in each spectrum from 4p⁶4d²–(4d5p + 4d4f + 4p⁵4d³) transitions were reported. Costello and O’Sullivan^[20] observed and analysed the spectra from highly ionized Cd LPPs in the 8–11 nm range emitted by 4p–5s transitions from Cd¹¹⁺ to Cd¹³⁺; the spectra were produced by focusing a ruby laser (1.5 J, 25 ns) pulse onto pure Cd and Cd(NO₃)₂ targets. Their analysis was based on Hartree–Fock and Dirac–Fock with Froese–Fischer and Grant codes.^[21,22] The analysis allowed the identification of a number of lines from 4p–5s transitions. However, a full description of the Cd spectrum in the 8–11.8 nm region remains unanalyzed to date.

This study analyzed the EUV spectra of Cd ions from LPPs. The overall objective was to provide detailed information about Cd structure and gain more insight regarding ionization degrees and types of transitions, as well as analyze the temporal evolution behavior. The 8.4–12 nm spectra produced from Cd ions are measured by using spatio-temporally resolved laser-produced plasma spectroscopy. Detailed atomic structure calculations were performed by the Hartree–Fok (HF) method with relativistic correlations (HFR) using the Cowan code. A number of new spectral features were identified from the experimental and calculated results. The collisional–radiative (CR) model^[23] was able to deduce the charge distribution, plasma parameters, and ion fractions for different ion stages of Cd LPPs.

2. Experiment

The experimental device is shown in Fig. 1. A detailed description of the experimental procedures has been previously reported.^[24] Briefly, a tightly focused 1064 nm Nd:YAG laser with a 10 ns pulse width was used to produce plasmas from a planar metallic Cd target. The EUV radiation was coupled to a 10 μm-entrance slit of a focal-length 1.0 m-grazing-incidence spectrometer, equipped with 600 grooves/mm grating. Spectra were acquired with a 40 mm diameter microchannel plate detector coupled, via a coherent fiber optic bundle, to a 1024× 255 pixel charge-coupled device (CCD). The microchannel gate width was 60 ns and the entrance slit width was 10 μm. The peak of the laser pulse on the target surface was defined as time zero for plasma production, as monitored by an oscilloscope.

	Figure Option View Download New Window
	Fig. 1. Schematic of an LPP experimental setup.

The target holder was positioned on a three-dimensional translation stage (0.1 mm resolution) to provide a fresh surface for each laser shot and avoid forming deep craters. A lens positioned on a linear translation stage with the same resolution could be moved along the laser beam direction for convenient adjustment of laser focusing. Spectra were recorded 0.5 mm from the target surface. Known lines from the LPPs spectra of highly charged Al and Si ions were used to calibrate the spectrometer wavelength. Figure 2 shows the measured emission spectra of the laser-produced Cd plasmas after different time delays, measured at a laser power density of 2× 10¹¹ W/cm². Spectral intensity along the wavelength range varied with increasing time delay. Several intense narrow peaks were observed at 8.95 nm, 9.42 nm, 10.25, 10.66 nm, and 11.49 nm with widths of ∼0.05 nm, 0.03 nm, 0.02 nm, 0.03 nm, and 0.02 nm, respectively.

	Figure Option View Download New Window
	Fig. 2. Time evolution of extreme ultraviolet spectra of Cd produced by a laser power density of 2 × 10¹¹ W/cm² at 0.5 mm from the target surface.

3. Atomic structure calculations and analysis

In earlier studies,^[20] only 36 lines in the 8.0–11 nm range have been reported and identified as the 4p–5s resonance transitions of Cd¹¹⁺, Cd¹²⁺, and Cd¹³⁺; other lines between 11–12 nm are unknown. To determine new features and confirm prior identifications, calculations of the 4p–5s transitions from Cd⁹⁺ to Cd¹³⁺ were carried out by HFR using Cowan’s codes.^[18]

In these calculations, the electrostatic Slater–Condon F^k, G^k, and R^k integrals were reduced to 95%, the spin–orbit parameter ζ was retained, and the configuration interaction effects were considered. The calculations predicted that 4p–4d and 4d–4f configurations would enhance the 4p–5s transitions in Cd⁹⁺ to Cd¹¹⁺. The study also showed that important interactions affecting the 4s²4p^k-15s configurations in Cd¹²⁺ and Cd¹³⁺ ions were 4s²4p^{k – 1}nd, 4s¹4p^knf, 4s²4p^{k – 1}ms, and 4s4p^kε p, in view of the important effects on the wavelengths and spectral line intensities. Note that n = 4–7, m = 6–7, and ε = 5–7 and k took the values of 6 (Cd¹²⁺) and 5 (Cd¹³⁺). To compare the spectra obtained from the experiment with theoretical output, the transition lines were calculated by convolving each line with a 0.05 eV full width at half maximum (FWHM) Gaussian profile. It should be noted that the same parameters were assumed for each ion. The most intense peak in the 10.63–10.69 nm region was from a mixture of the Cd⁹⁺ and Cd¹⁰⁺ stages.

To evaluate the accuracy of the present calculations, a comparison between the results obtained in Ref. [20] and the present work is summarized in Tables 1–3. The similarity between a measured spectrum and calculated wavelengths helped the identification of the spectral lines. As can be seen in Tables 1 and 2, our calculations are consistent with calculations in Ref. [20]. The difference in the wavelengths had an error of approximately ⩽ 0.04 nm in most cases. Additionally, our calculation predicted new lines for Cd¹¹⁺, specifically,²D_5/2–(³P) ²P_3/2, ²D_3/2–(¹D) ²D_3/2, ²D_5/2–(³D) ²D_3/2, and ²D_5/2–(¹P) ²P_3/2 transitions at 10.1 nm, 10.19 nm, 9.42 nm, and 8.51 nm, respectively. These lines showed a relatively high transition probability to the ground level, but had not been reported previously. Meanwhile, 20 levels were previously identified for Cd¹¹⁺. All levels of 4p–5s configurations in Cd¹¹⁺ to Cd¹³⁺ reported in Ref. [20] were confirmed and some additional levels were established. The wavelengths were revised in this analysis and the values of the levels were also changed slightly. Furthermore, the ground configuration of Cd¹¹⁺ was 4p⁶4d ²D_5/2,3/2 and the investigated 4p⁵4d5s configuration had 23 levels. The most excited states found were 4p⁶4d–4p⁵nd (n = 4–6), 4p⁶4d–4p⁵4dε s (ε = 5–7), and 4p⁶4d–4p⁶mf (m = 4–6). Additionally, Cd¹²⁺ had six p-electrons forming a completely filled shell. Its excited state was obtained by excitation of one of the 4p electrons into 4p⁵ns and 4p⁵md. The 4p–5s excitation gave only two levels. The ground state of Cd¹³⁺ was 4s²4p^{5 2}P_3/2,1/2 with ²P_3/2 lying deepest. The even excited states corresponded to 4p⁴ns and 4p⁴nd configurations. Eight levels were obtained in the 4p–5s transition.

Table 1.

Comparison of the calculated wavelengths for resonance lines of the 4p⁶4d–4p⁵4d5s transition in Cd¹¹⁺ ion.

Table 2.

Comparison of the calculated wavelengths for resonance lines of the 4p⁶–4p⁵5s and 4p⁵–4p⁴5s transitions in Cd¹²⁺ and Cd¹³⁺ ions.

Table 3.

Comparison of the calculated energy levels of 4p⁶4d, 4s²4p⁶, 4s²4p⁵, 4p⁵4d5s, 4s²4p⁵5s, and 4s²4p⁴5s arrays of Cd¹¹⁺, Cd¹²⁺, and Cd¹³⁺ ions. The levels are designated in LS coupling scheme.

Our results showed that the highest emission lines from gf-values belong to Cd¹⁰⁺ ions. Moreover, calculations of the emission line wavelengths for highly ionized Cd⁹⁺ to Cd¹⁰⁺ were in close agreement (the error was 0.01 nm or less) with experimental values. According to the J selection rules, the 4p⁵4d³5s and 4p⁵4d²5s excited configurations of Cd⁹⁺ and Cd¹⁰⁺ permitted 1860 lines in Cd⁹⁺, extending from 8.78 nm to 12.60 nm; 371 transition lines to the ground level of Cd¹⁰⁺ were in the 8.62–11.47 nm region, but many were weak. Only transition lines with gf-values greater than 0.1 and agreement with the measured spectrum are listed in Tables 4 and 5.

Table 4.

Measured and calculated wavelengths, weighted oscillator strengths (gf), and weighted transition probabilities (gA) for the strongest lines from the 4p⁶4d³–4p⁵4d³5s transition in Cd⁹⁺ ion.

Table 5.

Measured and calculated wavelengths, weighted oscillator strength (gf), and weighted transition probabilities (gA) for the strongest lines from the 4p⁶4d²–4p⁵4d²5s transition in Cd¹⁰⁺ ion.

Moreover, the ground levels of Cd⁹⁺ and Cd¹⁰⁺ possessed an open 4d, and the exciting configurations contained open ns, np, εf, and εd (n = 5–7, ε = 4–6) subshells; hence, there exist many hyperfine degenerate energy levels when they couple with the electrons of other shells. The ground configurations (4p⁶4d³, 4p⁶4d²) of Cd⁹⁺ and Cd¹⁰⁺ had 19 and 9 levels, respectively, while the 4p⁵4d³5s and 4p⁵4d²5s configurations had 212 (Cd⁹⁺) and 90 (Cd¹⁰⁺) levels. The predicted energy levels resulting from the 4p–5s resonance transitions of Cd⁹⁺ and Cd¹⁰⁺ are listed in Tables 6 and 7. In these tables, the energy levels of the ground states (4p⁶4d³, 4p⁶4d²) and excited states (4p⁵4d³5s, 4p⁵4d²5s) of Cd⁹⁺ and Cd¹⁰⁺ were established. Figure 3 shows the calculated energy levels of the 4p^k4dⁿ (k = 5, 6 and n = 0–3) configurations and the spread of 4p⁵4dⁿ5s configurations in Cd⁹⁺ through Cd¹³⁺ below 160 eV.

	Figure Option View Download New Window
	Fig. 3. Schematic overview of the calculated energy levels of the 4p^k4dⁿ (k = 5, 6 and n = 0–3) configurations in Cd⁹⁺ through Cd¹³⁺. The vertical bars at the top show the spread of 4p⁵4dⁿ5s configurations below 160 eV.

Table 6.

The predicted energy levels of 4p⁶4d³ and 4p⁵4d³5s arrays of Cd⁹⁺ ion. The levels are designated in LS coupling scheme.

Table 7.

The predicted energy levels of 4p⁶4d² and 4p⁵4d²5s arrays of Cd¹⁰⁺ ion. The levels are designated in LS coupling scheme.

4. Comparison between theoretical and experimental spectra

The variation in wavelengths as a function of charge state is the most important feature to compare with experimental data. The 4p–5s resonance transition arrays of mixtures of Cd⁹⁺ to Cd¹³⁺ result in emission peaks and are responsible for the structures. This characteristic feature was readily observed and identified in the measured spectra. The dominant contributions were from Cd⁹⁺ and Cd¹⁰⁺.

To complete our simulations, the ion fractions of different stages as a function of electron density and electron temperature were calculated based on a steady-state CR model.^[23] To the best of our knowledge, calculations of highly ionized Cd based on a CR model have not been studied previously. Figures 4(a) and 4(b) show the ion fractions of Cd⁹⁺ to Cd¹³⁺ as a function of electron temperature for an electron density N_e = 5× 10²⁰ cm^–3 (Fig. 4(a)), and as a function of electron density for an electron temperature T_e = 35 eV (Fig. 4(b)). From these results, it is clear that T_e within 22–35 eV and N_e in the 1× 10¹⁹ cm^–3 to 5× 10²¹ cm^–3 range can be expected to produce Cd⁹⁺ to Cd¹³⁺ ions. For a number of lines (N) within 8.4–12 nm, an accurate identification would not be possible because only some data were sorted for comparison. The total synthetic emission profile was calculated by I_tot = Σ_i gf_i,k F_iP_i,k Γ_i,k, where gf_i,k is the oscillator strength, F_i is the ion fraction, P_i,k = exp (–ΔE/kT) is the Boltzmann factor, and Γ_i,k is the associated Lorentzian profile function. For simplicity, we used the emission spectrum measured after 40 ns time delay as an example (Fig. 4). In Fig. 4, an experimental spectrum is compared with the simulation results obtained for an electron temperature of 34 eV and an electron density of 7× 10²⁰ cm^–3.

	Figure Option View Download New Window
	Fig. 4. Ion fractions for different ion stages as a function of (a) electron temperature and (b) electron density.

There was good agreement when the dominant fractional contribution rose with values of 6% (Cd⁹⁺), 23% (Cd¹⁰⁺), 40% (Cd¹¹⁺), 28% (Cd¹²⁺), and 1% (Cd¹³⁺) (see column chart insert in Fig. 5(a)). Figure 5(b) also presents the line profiles from Cd⁹⁺ to Cd¹³⁺ by assuming a normalized Boltzmann distribution among the excited states for the same conditions mentioned above. The same procedure was used to simulate the spectra after other time delays (Fig. 6). The comparison between the experimental and the simulated spectra yielded the relationships between the experimental conditions and plasma parameters. Figure 7 depicts the temporal evolution of the ion fractions of Cd⁹⁺ to Cd¹³⁺ at time delays ranging from 20 ns to 70 ns to gain a deeper understanding of the temporal characteristics of the ionized stages of highly charged ions from the Cd LPP spectra. The initial fraction at 20 ns was dominated by Cd¹¹⁺ that gradually increased with increasing time delay (Fig. 7). However, with a time delay of 20 ns, the ion fractions of Cd¹²⁺ and Cd¹⁰⁺ were very close. For Cd¹²⁺, the fractions increased until 30 ns and then decreased gradually, whereas Cd¹⁰⁺ showed the opposite pattern. It was noted that with an increasing time delay, Cd¹¹⁺ and Cd¹⁰⁺ ions become more important after 30 ns. Moreover, the fractions of Cd⁹⁺ and Cd¹³⁺ ions were approximately constant along this sequence of time delays and had lower contributions.

	Figure Option View Download New Window
	Fig. 5. Comparisons between the experiment (black line) recorded after 40 ns time delay and simulated spectra (red line). The column chart insert in (a) displays the ion fractions of Cd⁹⁺, Cd¹⁰⁺, Cd¹¹⁺, Cd¹²⁺, and Cd¹³⁺.

	Figure Option View Download New Window
	Fig. 6. Comparison between the measured (grey fill) and simulated (black lines) spectra after various time delays.

	Figure Option View Download New Window
	Fig. 7. Temporal behavior of the Cd⁹⁺ to Cd¹³⁺ ion fractions.

Figures 8 and 9 show the evolution of electron temperature and electron density with time delays from 20 ns to 70 ns, respectively. Their fitting relations are given in their respective graphs. The T_e is the electron temperature; N_e is the electron density; and t is the delay time. It was clear that the electron temperature displayed an exponential decay from 36 eV to 30 eV with increasing time delay. The electron density exhibited a sharp maximum at 20 ns and then a sharp decay to 30 ns with a more gradual decay thereafter. The decay of the electron temperature and electron density explains the free expansion behavior of LPPs in vacuum near the target surface.

	Figure Option View Download New Window
	Fig. 8. Temporal behavior of electron temperature.

	Figure Option View Download New Window
	Fig. 9. Temporal behavior of electron density.

5. Conclusion and perspectives

The EUV emission spectra of Cd⁹⁺ to Cd¹³⁺ ions from laser-produced plasma were measured in the 8.4–12 nm region using a temporally and spatially resolved laser-produced plasma technique. The spectra dominated by a great number of lines from 4p–5s were analyzed using HFCI codes. A number of new features were identified for the first time and were tentatively assigned. Based on a steady-state CR model, plasma parameters were obtained for different ion stages by comparing experimental and simulated spectra. The simulated results for different time delays were in good agreement with the experimental spectra. In addition, the temporal evolution of electron temperature and electron density for Cd LPPs, and exponential decay of electron temperature and electron density were also described in this study. The results are helpful for astrophysics and plasma laboratory.

Reference

[1]	Su M G Min Q Cao S Q Sun D X Hayden P O’Sullivan G Dong C Z 2017 Sci. Rep. 7 1
[2]	Su M G Wang B Min Q Cao S Q Sun D X Dong C Z 2017 Phys. Plasmas 24 013302
[3]	Yoshikawa M Pease R Callen J Witkowsi S Velikhov E 1985 Plasma Physics and Controlled Nuclear Fusion Research Vienna IAEA 37 38
[4]	Meyer-ter-Vehn J 2009 Plasma Phys. Control. Fusion 51 124001
[5]	Shigemori K Kodama R Farley D R Koase T Estabrook K G Remington B A Ryutov D Ochi Y Azechi H Stone J Turner N 2000 Phys. Rev. 62 8838
[6]	Peacock N J Pease R S 1969 J. Phys. D: Appl. Phys. 2 1705
[7]	Monchinsky V A Kalagin I V Govorov A I 1996 Laser Part. Beams. 14 439
[8]	Gwyn CW Stulen R Sweeney D Attwood D 1998 J. Vac. Sci. & Tech. 16 3142
[9]	Aota T Tomie T 2005 Phys. Rev. Lett. 94 015004
[10]	Banine V Y Koshelev K N Swinkels G H 2011 J. Phys. D: Appl. Phys. 44 253001
[11]	Danylyuk S Loosen P Bergmann K Kim H Juschkin L 2013 J. Micro/Nanolith. Mems Moems. 12 033002
[12]	McCracken G M Stott P E 1979 Nucl. Fusion 19 889
[13]	Even-Zohar M Fraenkel B S 1972 J. Phys. B: At. Mol. Phys. 5 1596
[14]	Carroll P K Costello J T O’Sullivan G 1986 Phys. Scr. 33 226
[15]	O’Sullivan G Costello J T Carroll P K 1984 J. Phys. B: At. Mol. Phys. 17 345
[16]	Chaghtai M S Rahimullah K Khatoon S 1976 Phys. Scr. 14 281
[17]	Even-Zohar M Fraenkel B S Cowan R D 1974 J. Phys. B: At. Mol. Phys. 7 5
[18]	Cowan R D 1981 The Theory of Atomic Structure and Spectra Berkeley University of California Press 456 465
[19]	Ryabtsev A N Kononov E 2011 Phys. Scr. 84 015301
[20]	Costello J T O’Sullivan G 1984 J. Phys. B: At. Mol. Phys. 17 4477
[21]	Charlotte Froese C 1978 Compur. Phys. Commun. 14 145
[22]	Grant I P McKenzie B J Norrington P H Mayers D F Pyper N C 1980 Comput. Phys. Commun. 21 207
[23]	Colombant D Tonon G F 1973 J. Appl. Phys. 44 3524
[24]	Cao S Q Su M G Min Q Sun D X O’Sullivan G Dong C Z 2018 Phys. Plasmas. 25 023304