Opacity effects on soft X-ray spectra from highly charged lanthanide ions in laser-produced plasmas

We have observed soft X-ray spectra from highly charged ions of seven diﬀerent lanthanide elements with atomic numbers ranging from 60 to 70 in laser-produced plasmas (LPPs) using CO 2 and Nd:YAG laser systems, the wavelengths of which are 10.6 (cid:22) m and 1.064 (cid:22) m, respectively. The spectral feature drastically changes between the two types of LPPs due primarily to the diﬀerence in opacity. Narrowband quasicontinuum features arising from n =4{ 4 transitions, the centre wavelength of which systematically moves to shorter wavelength as the atomic number ( Z ) increases, are observed in the CO 2 LPPs, accompanied by sharp peaks coinciding with the strongest resonance lines of Pd-like ions for lower Z elements. In contrast, the quasicontinuum bands are broader and smoother in the Nd:YAG LPPs, appearing with bands of n =4{5 transitions on the shorter wavelength side. The results are also discussed based on comparisons with atomic structure calculations for ions with outermost 4d and 4f subshells. CO 2 and Nd:YAG LPPs. The results are qualitatively interpreted in terms of opacity eﬀects and comparisons with atomic structure


Introduction
Soft X-ray emission spectra from highly charged lanthanide ions are of particular interest for basic atomic physics as well as applications to short wavelength light sources. In the last decade, laser-produced plasmas (LPPs) of gadolinium (Gd) and terbium (Tb) have been extensively investigated as possible candi- 5 dates for light sources for semiconductor lithography in the wavelength range of 6-7 nm [1,2,3,4]. Emission spectra of these plasmas typically form a quasicontinuum band, or the so-called unresolved transition array (UTA) [5], Systematic studies of soft X-ray spectra from LPPs of lanthanide elements have been carried out so far in higher opacity conditions in which smooth broadband UTAs were recorded on photographic or microchannel plates [7,8]. In 15 general, the UTA spectral feature strongly depends on the opacity of the emitting plasma. In terms of the application to lithography, optically thin plasmas having lower density are more appropriate because of higher spectral efficiency for the required wavelength band. Therefore, several techniques have been explored to generate optically thin LPPs in the development of lithography at 20 13.5 nm using tin (Sn) plasmas [9,10]. The solutions include the use of longer wavelength lasers (e.g., CO 2 laser) because critical plasma density is inversely proportional to the square of laser wavelength.
Recently, soft X-ray spectra from CO 2 LPPs of Gd have been newly reported and higher spectral purity has been obtained in comparison with Nd:YAG 25 LPPs [11]. However, spectra from CO 2 LPPs of other lanthanide elements have not been reported yet. In this study, we have systematically observed soft X-ray spectra from highly charged ions of seven lanthanide elements with atomic numbers from Z=60 to 70 in CO 2 and Nd:YAG LPPs. The results are qualitatively interpreted in terms of opacity effects and comparisons with atomic structure 30 2 calculations.

Experimental
All the experimental data in this article have been measured at Utsunomiya University where shortpulse laser systems are available. An ultra-shortpulse Critical (cutoff) electron density n ec in an LPP is inversely proportional to the square of the laser wavelength λ L , n ec ≃ 1.1×10 21 λ −2 L , where n ec and λ L are in cm −3 and µm, respectively. Therefore, critical densities in CO 2 and Nd:YAG LPPs are estimated to be roughly 10 19 and 10 21 cm −3 , respectively.

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The laser beams were introduced into a target chamber via a plano-convex lens to be focused onto a planar target made of pure lanthanide metals with Z=60, 62, 64, 65, 66, 68 and 70. The focal spot sizes are estimated to be 80 and 60 µm for the CO 2 and Nd:YAG lasers, respectively.
Time-and space-integrated soft X-ray emission spectra from the LPPs were 50 recorded in the wavelength range of 2-10 nm with a flat-field grazing incidence spectrometer equipped with a 2400 grooves/mm grating and a back-illuminated soft X-ray CCD camera (Andor Technology). The spectral resolution was typically better than 0.005 nm. Single-shot spectra were recorded for the Nd:YAG LPPs, while 40 identical shots were accumulated to obtain one spectrum for the 55 CO 2 LPPs due to weaker intensity. UTA peak positions expected from the quasi-Moseley's law [12,13] are marked by triangles. recently been proposed [12,13], given by  Fig. 1 (a).

Sharp peaks in CO 2 LPPs
The earlier work on a CO 2 LPP of Gd suggests that the sharp peak originates from the strongest resonance transition 4d 10 1 S 0 -4d 9 4f 1 P 1 of Pd-like Gd 18+ 85 overlapped with 2 F-2 D doublet lines of Ag-like Gd 17+ [11]. In this work, we have compared the measured wavelengths of the sharp peaks in Fig. 1 (a) with those of the Pd-like resonance lines reported previously [14,15] and calculated ab initio with the Flexible Atomic Code (FAC) code [16]. The results are summarized in Table 1 showing that the measured wavelengths for Z=60-66 are in very good 90 agreement with the literature values. This indicates that charge states around Pd-like ions are dominant emitters in the CO 2 LPPs for lower Z lanthanide elements. As shown in Fig. 1 (a), this peak is unseen for Er and Yb with Z of 68 and 70, respectively. The absolute intensities of the overall soft X-ray emission were very weak for Er and Yb as mentioned in the previous section. 95 These results imply that the CO 2 laser intensity in the present setup is too low to produce Pd-like ions for these higher Z elements having higher ionization energies.
The calculated wavelengths listed in Table 1 are systematically shifted to shorter wavelengths by 0.14-0.43 nm from the present or earlier measurements.

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This is probably because of the difficulty in the calculation of effective potential energy including complex correlation among N shell electrons for an inner 4d subshell excited configuration such as 4d 9 4f.
In the Nd:YAG LPPs, the sharp peaks of the Pd-like resonance lines completely disappeared, and broader and smoother UTA features are observed as 105 shown in Fig. 1 (b). When the laser energy is reduced to one order lower than the maximum, these features of the n=4-4 UTA are maintained though the emission intensity decreased over the entire spectral range. The doppler or other broadenings for each single spectral line are negligible because they are estimated to be much smaller than the instrumental width of the spectrometer.

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Therefore, these features are primarily attributable to higher opacities in the Nd:YAG LPPs in which strong self-absorption of the resonance lines occurs due to higher plasma density limited by n ec in the emitting region. and some of lower charge states calculated with FAC code [16]. The calculated resonance transition types are 4d-4f (red), 4p-4d (blue), 4d-5p (light blue), 4d-5f (orange) and 4f-5g (green). The line strengths have been normalized for each type of transition to its maximum. Table 1: Comparison of the wavelengths of the sharp peaks in CO 2 LPP with the reported and calculated wavelengths of Pd-like resonance line 4d 10 1 S 0 -4d 9 4f 1 P 1 . The ab initio calculation has been performed with FAC code [16]. References: a- [14]

Comparisons with calculations
In order to interpret the difference in the spectral feature, the measured Nd 10+ -Nd 13+ include one or two 5s electrons because of 4f orbital collapse [17].
As shown in Fig. 2

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We have recorded a series of soft X-ray spectra from highly charged lanthanide ions with Z=60-70 in CO 2 and Nd:YAG LPPs having different opacities. As a result of the large difference in critical plasma density between the 9 two types of LPPs, Pd-like resonance lines strongly dominate the spectra in the CO 2 LPPs, while smooth broadband UTA features are observed in the Nd:YAG

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LPPs. The intensity ratios of n=4-5 emissions to n=4-4 emissions are much larger in the Nd:YAG LPPs than in the CO 2 LPPs because of the effects of larger opacities and collisional excitations.