Soft x-ray spectra of cerium laser-produced plasmas

Laser produced plasmas (LPPs) are formed when high-power laser pulses are incident on a solid, liquid or gaseous target. They have been exploited for emission and absorption spectroscopy of atoms [1], ions [2] and molecules [3]. LPPs have been deployed in laser induced breakdown spectroscopy (LIBS) to measure surface quality, composition and contamination [4, 5].

In recent years LPPs have been developed as sources of extreme ultraviolet (EUV) and soft x-ray (SXR) radiation for applications including semiconductor processing [6] and microscopy on the nanoscale [7]. Tin plasmas formed on liquid microdroplets are the chosen source for EUV lithography applications and these sources, operating at 13.5 nm, entered industrial production in 2018 [8]. At shorter wavelengths between 2.33 nm and 4.40 nm, the K-edges of oxygen and carbon respectively, in the 'water window', liquid nitrogen jet targets [9] and solid targets [7] are being developed as sources for laboratory-scale SXR microscopes. The intense spectral feature at 13.5 nm in the tin LPP spectrum is an unresolved transition array (UTA), a result of 10⁵–10⁶ overlapping transitions in a narrow band typically 1 nm in width. The UTA was initially thought to primarily arise from resonance 4p⁶4d^N to 4p⁶4d^N−14f + 4p⁵4d^N+1 (4–4) transitions in open-4d subshell ions, in this particular case ranging from Sn¹⁰⁺ to Sn¹⁴⁺. However, it has been recently shown that the bulk of the emission originates from multiply excited 4–4 transitions in ions where there is reduced occupancy in the 4d subshell [10] which serves to broaden the UTA, thus resolving the observation that in a Sn LPP the width of the array was always greater than that predicted from consideration of resonance transitions alone. The effect of such transitions within a single stage was already demonstrated in charge exchange experiments [11]. In the elements from tin (Z = 50) to bismuth (Z = 83) this UTA shifts to shorter wavelength [12], reaching its narrowest profile at cerium (Z = 58), where it lies at 8.8 nm. The narrowness of this feature is attributable to the overlap between the 4d and 4f wavefunctions, reaching a maximum at cerium due to the contraction of the 4f wavefunction with increasing ionisation, the proximity of 4p–4d and 4d–4f transition energies and the relatively small spin orbit splitting of the 4p subshell [13].

Features due to n = 3–n = 4 and n = 4–n = 5 transitions dominate at shorter wavelengths in the LPP spectra of these elements. Unlike the 4–4 UTAs, these transition arrays shift to shorter wavelength with increasing ionisation, resulting in a series of modulations in the SXR spectrum. These features also shift to shorter wavelength with increasing atomic number. This provides the possibility to tune the emission characteristics of the plasma by choice of target element, in addition to varying the laser pulse parameters.

Recent studies of LPPs in the EUV/SXR spectral region illustrate n = 3–n = 4 and n = 4–n = 5 transitions in addition to n = 4–n = 4 arrays, as well as individual lines and groups of lines. Wu et al [14] report spectra, between 1.0 and 8.5 nm, of ytterbium plasmas formed by pulses from a neodymium aluminium-garnet (Nd:YAG) laser operating at the fundamental wavelength of 1064 nm. Transitions from the 4p and 4d subshells in ions ranging from Yb¹³⁺ to Yb³⁴⁺ are identified. Wu et al [15] report studies of holmium ions in the same spectral region using plasmas formed with Nd:YAG pulses of both 6 ns and 170 ps duration. Ionisation stages ranged from Ho¹⁷⁺ to Ho³⁶⁺, with n = 4–n = 4 and n = 4–n = 5 transitions dominant in the spectra. Lokasani et al [16] performed a study on samarium plasmas, formed with Nd:YAG pulses of 150 ps duration. n = 4–n = 4 and n = 4–n = 5 transitions were again the principal features in the spectrum, with ions observed ranging from Sm¹²⁺ to Sm³¹⁺. Li et al [17] presented analysis of hafnium and tantalum plasmas in the 1 to 7 nm region, formed with Nd:YAG pulses of 10 ns and 170 ps duration. With the 10 ns pulses the highest ion stages achieved were Hf²⁵⁺ and Ta²⁶⁺, both of which have a closed 4d subshell. Using the 170 ps laser pulses the 4d subshell was opened up in the ions in the plasma, as evidenced by the appearance of 4d–5p transitions. A significant enhancement of emission from the tantalum plasmas was observed using pre-pulses to preionise the solid target, leading to increased coupling of the main laser pulse into the target plasma. Sheil et al [18] analysed SXR emission from LPPs of dysprosium, erbium and thulium, formed with 1064 nm pulses of 6 ns duration from a Nd:YAG laser. The power densities on target ranged from 1.3 to 6.6 × 10¹² W cm⁻² yielding a maximum ion stage of Tm³²⁺. In addition to transition arrays, some single transitions along the Ag-like, Pd-like, Rh-like and Sr-like isoelectronic series were identified. An investigation by Churliov et al into gadolinium and terbium vacuum spark and LPP sources [19] identified 4d–4f and 4f–5d transitions in multiple ion stages, highlighting the UTA emission at 6.78 and 6.54 nm respectively. Both elements have been of interest as potential candidates for beyond EUV (BEUV) lithography in a technology to replace tin-plasma based tools with a shorter operating wavelength in the region of 6.7 nm [20, 21]. These, and other investigations concentrated on optimising the emission from Pd-like and Ag-like ions in the plasma [22].

Cerium ions have been the subject of multiple spectroscopic studies, typically using triggered vacuum sparks [23], tokamaks [24] and laser plasmas [25]. Many of these studies followed isoelectronic sequences as systematic trends greatly aided identifications and analysis. As with the bulk of the rare earth elements, cerium spectra in the EUV and SXR regions are complex, presenting large regions of quasi-continuum, modulated by UTA features, and interrupted by groups of lines and few strong individual lines. Here, the cerium target was irradiated at 532 nm in order to examine the spectra of higher density LPPs, specifically to investigate weaker transitions, whose intensity is expected to be enhanced by the higher density of emitting ions. However the increase in ion density also increases the plasma opacity for stronger transitions. Since the plasma electron temperature varies according to (λ² ϕ)ⁿ [26], where λ is the laser wavelength, ϕ is the power density and n = 0.6 for a simple collisional radiative (CR) equilibrium model, the reduced plasma electron temperature resulting from the reduced laser wavelength is somewhat compensated for by the tighter spot size, and hence the higher power density, obtained when 532 nm light is focused compared to 1064 nm light. Plasma opacity and the presence of multiple ion stages in the plasma increase the difficulty of the spectral analysis. In the current study varying the power density of the laser pulse incident on the target aided in the identification of lines and groups of features as they tend to rise and fall in intensity with changes in plasma electron temperature.

A plano-convex lens with a focal length of 50 mm was used to focus pulses from a Q-switched Continuum Surelite III Nd:YAG laser (full width at half maximum (FWHM) = 4.7 ± 0.15 ns), at normal incidence, onto a planar cerium target in vacuum (10⁻⁴ mbar). Some surface oxidation was present on the target, whose removal by mechanical means left a smooth, but not polished finish. The laser operated at its second harmonic with a wavelength of 532 nm and with a repetition rate of 10 Hz. Both the cerium target position, and that of the lens, were controlled under vacuum using motorised stages to both vary the distance between the lens and the target and to ensure a fresh area of target was presented for each shot. The pulse energy was kept constant at 155 ± 15 mJ. The distance between the lens and target was adjusted to vary the power density on target. The power density ranged from 8.6 × 10⁹–2.1 × 10¹³ W cm⁻².

The spectra were recorded at 45° to the target normal using a 0.25 m flat-field grazing incidence spectrometer with a 1200 grooves/mm Shimadzu grating equipped with a cooled, back-illuminated, x-ray ANDOR DX436-BN charge-coupled device (CCD) camera. The resolving power λ/Δλ is 195 at 2.878 nm [27]. Spectra from individual laser pulses were recorded between 1.5 and 15.5 nm and were corrected for background noise signals on the CCD camera. Lines from LPPs of carbon, copper and reaction bonded silicon nitride were used to perform a wavelength calibration. Previously identified lines in the spectrum of cerium, for example the 4f–5g and 5s–6p transitions in Ce¹¹⁺ [28], found in the current spectra were also used in the calibration. The calibration yielded maximum residuals of 0.0097 nm, while the pixel spacing in the CCD camera ranged from 0.005 nm per pixel at 2 nm to 0.009 nm per pixel at 12 nm.

Atomic structure calculations using the Cowan code [29] were undertaken to aid identification of the features in the spectra. Multiple configurations were included in the input to account for configuration interaction. For spectra of open 4f subshell ions, i.e. below Ce¹²⁺, configurations listed in table 1 were included along with the corresponding 4d–4f excited state, with the exception of those lying above the ionisation potential of the relevant ion, which are identified with an asterisk*. For Ce⁹⁺, Ce¹⁰⁺ and Ce¹¹⁺, extra configurations were included to account for higher-lying excited states. For spectra of open 4d shell ions, that is Ce¹²⁺ to Ce ²¹⁺, configurations of the type 4p⁶4d^k , 4p⁶4d^k−15s¹, 4p⁶4d^k−1np¹ (n = 5–7), 4p⁶4d^k−1nf¹ (n = 4–7), 4p⁵4d^k+1, 4p⁵4d^k ns¹ (n = 5–7), 4p⁵4d^k nd¹ (n = 5–7), 4p⁶4d^k−25s¹5p¹, 4p⁶4d^k−25s¹nf¹ (n = 4, 5) were included for k = 1–10, except 4p⁵4d^k+1 where k ranged from 1 to 9, and 4p⁶4d^k−25s¹5p¹, 4p⁶4d^k−25s¹nf¹ where k ranged from 2 to 10.

For Ce²²⁺ to Ce²⁷⁺ configurations of the type 4s²4p^k , 4s²4p^k−1np¹ (n = 5, 6), 4s¹4p^k 5s¹, 4s¹4p^k 4d¹, 4s²4p^k−14f¹, 4s²4p^k−1ns¹ (n = 5–7), 4s²4p^k−1nd¹ (n = 4–7), 4s¹4p^k+1, 4s¹4p^k 5p¹ were included for n = 1–6 except for 4s¹4p^k+1 which was included for n = 1–5.

Transitions from n = 6 and n = 7 levels are not expected to appear in the spectra presented here since their collisional ionisation lifetime is significantly shorter than that for radiative decay, but were included for completeness of the overall calculation. For the bulk of the ions the calculations were run with the electrostatic integrals, F^K , G^K and R^K , scaled to 85% of their ab initio values while the spin–orbit integrals, ζ, were maintained at 99% [18]. However, for spectra up to Ce XII, and for Ce XIII the integrals were scaled at 75% and 81% respectively, with the spin–orbit integral unchanged. These scalings resulted in the best fit of the strongest 4d–4f line in each of these spectra, the latter of which, at 8.92 nm, has already been identified as 4d¹⁰(¹S₀)–4d⁹4f(¹P₁) by Churilov [25]. The synthetic spectra seen in figures 2 and 3 were formed using the gA values obtained from the Cowan calculations. The gA values were obtained for each transition within an ion, then convolved with a Gaussian with a FWHM value representative of the resolution of the spectrometer. Any values below 0.01% of the maximum were removed to reduce computational demands while maintaining the shape of the spectrum. The gA values of each transition for each ion stage were then normalised to the maximum gA value.

A simple CR plasma model [26] shows that the bulk of the incident laser radiation is absorbed close to the critical density of the plasma, which is approximated as 10²¹/λ (μm) cm⁻³. The 2nd harmonic of the Nd:YAG laser has a wavelength of 532 nm, leading to a critical plasma density of 4 × 10²¹ cm⁻³. The shorter wavelength also leads to cooler plasmas than those formed with 1064 nm fundamental Nd:YAG pulses, the electron temperature having a dependence on λ^1.2. The increased density of plasmas formed with 532 nm radiation enhances the influence of weaker transitions on the spectrum and can lead to absorption effects playing a larger role in the observed spectrum.

Spectra of cerium LPPs at three representative power densities (2.1 × 10¹⁰ W cm⁻², 2.0 × 10¹¹ W cm⁻² and 1 × 10¹³ W cm⁻²) are shown in figure 1 in the range 1.8 to 12 nm. These correspond to electron temperatures (T_e) of 9 eV, 33 eV, and 347 eV respectively calculated according to [26] with average ionisation states of 5⁺, 8⁺ and 18⁺ respectively. However, there are limitations to this calculation. Firstly, the calculated T_e only applies to a relatively small region of the plasma, in general the rest of the plasma is at a lower temperature. Also to be noted is that the spectra here are time integrated over the lifetime of the plasma and hence also record photons emitted from the plasma as it formed, and also as it expands and cools. This results in a significant radiation emission from ions lower than the electron temperature would suggest. Hot spots in the beam can lead to higher power densities than estimated from simple calculations based on pulse energy and duration alone. In addition, multiphoton ionisation processes can also occur within LPPs and result in the production of higher ionisation stages than would be expected by electron temperature alone. For example, optimal emission from the UTA at 13.5 nm (92 eV) in tin LPPs occurs for T_e ≈ 30–50 eV [30, 31]. A power balance model [32] predicts a lower electron temperature than the simple CR model, for example, at a power density of 1 × 10¹³ W cm⁻² it predicts an electron temperature of slightly above 100 eV for a plasma formed with 532 nm radiation. Moreover, from figure 3, emission from ions at least up to Ce²¹⁺ are seen to contribute to the overall emission.

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Striking differences in the spectra are evident. As a general trend emission at shorter wavelengths is associated with higher ion stages. Lines from the spectra of O⁶⁺ (1.86 nm and 2.16 nm) and O⁷⁺ at 1.89 nm [33] appear at the higher power densities. These lines provide both wavelength calibration and an indication of plasma electron temperature, as the ionisation potentials of O³⁺, O⁵⁺ and O⁶⁺ are 77 eV, 138 eV and 739 eV respectively. Absorption due to a thin layer of carbon deposited on the grating of spectrometer is evident at 4.2 nm, corresponding to the carbon K-edge (figure 4).

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Kawasaki et al [32] discuss the effect of 532 nm compared to 1064 nm irradiation on the power loss processes within heavy element LPPs. While they concentrated on bismuth (Z = 83) LPPs, it would be expected to be applicable for other heavy element LPPs. Assuming equal pulse durations, the most notable difference is that at the lower power densities kinetic energy loss dominates for plasmas formed from 532 nm while radiation losses dominates for the higher power density plasmas. For 1064 nm radiation loss dominates for all but the lowest power density plasmas. A lower electron temperature is expected for an LPP formed using a wavelength of 532 nm compared to a wavelength of 1064 nm.

Before discussing the spectra, it is important to recall that the spectra of the lanthanides are, in general, complicated by the effects of 4f contraction with increasing ionisation that leads to 4f and 5p and subsequently 4f and 5s electron binding energy crossings. This leads to irregularities in the composition of the ground state configuration and strong configuration interaction between configurations containing different numbers of 5p and 4f electrons typically near the 6th ion stage and 4f and 5s electrons near the 15th [34]. Calculations with configuration interaction show that the configuration average energies of all but two configurations of the type (5s5p4f)^q , where q ranges from 8 in Ce⁴⁺ down to 1 in Ce¹¹⁺, are within 100 eV of the ground state of the ions Ce⁴⁺ to Ce¹⁰⁺, as shown in table 1. In a photoabsorption experiment on Ce⁴⁺ ions [35] strong absorption due to the 4d¹⁰–4d⁹4f ¹S-¹P transition was not observed. In its place structure due to overlapping 4d–4f transitions from a large number of 5pⁿ 4f^m states was seen, which varied with pulse energy due to the differences in excited state populations produced at different electron temperatures. As shown in table 1, the ground configuration in each ion stage is seen to contain only 5p or 5s electrons. However, transitions involving low-lying configurations containing 4f electrons are expected to be observed due to their proximity to the ground state and the fact that a Boltzmann distribution leads to a sizeable population of ions, in these metastable states especially, in light of their high multiplicity arising from the presence of 4f electrons.

The spectra are discussed in six separate sections, labelled (a) through (f), to highlight the families of transitions that occur in plasmas formed at varying power densities.

4.1. Region A: 10.0–12.0 nm

4.2. Region B: 9.1–10.0 nm

4.3. Region C: 8.5–9.1 nm

4.4. Region D: 6.0–8.5 nm

4.5. Region E: 4.4–6.0 nm

4.6. Region F: 1.5–4.4 nm

In summary, XUV emission spectra of Ce laser-produced plasmas were recorded using a 5.5 ns, Nd:YAG laser operating at the second harmonic wavelength of 532 nm. Power densities on-target ranged from 8.6 × 10⁹–2.1 × 10¹³ W cm⁻², generating a variety of spectra containing emission from ions between Ce⁵⁺ and Ce²⁵⁺. The spectra reflect a general trend of increasing ionisation with increasing power density on target. 4d–4f transitions dominate the spectra in the 8–12 nm region while Δn = 1 transitions from 4p and 4d configurations are evident at shorter wavelengths. The spectra show a high degree of similarity with laser plasma spectra of other rare-earth elements, however, the denser plasmas formed with the 532 nm laser pulses reveal higher intensity to the long-wavelength side of the 4d–4f UTA.

EW was supported by the Irish Research Council (EPSPG/2016/89).

The data that support the findings of this study are available upon reasonable request from the authors.