Dependence of ion charge-energy emission from Nd:YAG-laser-produced plasma on laser intensity in the $0.4 – 40 × 10 10$ W/cm² range

Extreme ultraviolet (EUV) light is utilized in the lithographic process to produce nanometer-sized features on silicon chips. Industrially, tin laser-produced plasmas (LPP) are used to produce 13.5 nm EUV light. The density, temperature, and morphology of the LPP are optimized for EUV production. However, ion emission from the LPP is also to be considered, as this adverse process is known to take a toll on EUV output from the source, e.g., by gradually tarnishing the performance of the surrounding EUV transport optics, for instance, by implantation and sputtering on their surface. Furthermore, all the laser energy transferred to ion kinetics is not available for EUV production and can therefore be considered to be wasted. One parameter of particular interest is the intensity of the laser pulses, where a higher intensity is associated with the generation of more ions with higher kinetic energies, which at some point may be no longer stopped by the buffer gases that are typically employed in industrial sources of EUV light to mitigate the impact of ion “debris.”

The parameter space of the LPP experiment is vast (drive laser wavelength, laser pulse morphology and intensity, target volume and morphology, single- or multi-laser-pulse schemes, etc.), and currently, systematic exploration is incomplete. Analytical work has produced valuable general insights into plasma expansion.^1–3 However, analytical work necessarily relies on highly idealized and simplified conditions and needs to be supported by dedicated numerical simulations and experiments. Existing experimental research examines the energy, charge state, and angular distributions of emitted ions for experimental parameters similar to those of nanolithographic EUV sources, using a variety of ion diagnostic tools. Such tools include electrostatic probes,^4,5 Faraday cups,^6–8 electrostatic analyzers,^7–11 retarding field analyzers,¹² and Thompson parabolas.⁶ Many studies observed anisotropy in the charge-integrated^{4,6,7,13–17} and charge-state-resolved ion emission into a buffer gas.⁹ Morris et al.,^10,11 O'Connor et al.,¹⁸ and Brandstätter et al.⁴ studied angle- and charge-state-resolved ion emission in a solid tin target experiment. They reported increasing ion charge states and increasing average kinetic energies for decreasing angles with respect to the direction of the incoming laser pulse. O'Connor et al.¹⁸ additionally measured increasing numbers of ions, average ion energies, and average charge states with increasing laser intensities. We recently combined absolute angle- and charge-state-resolved kinetic energy measurements on an industrially relevant tin-microdroplet-based plasma, expanding into the vacuum.¹⁹ More specifically, the anisotropy of the ion emission was investigated. The presence of a high-energy peak in the ion energy spectra was found to be more prominent for smaller angles with respect to the direction of the drive laser.¹⁹ Furthermore, our studies showed that the experimental ion energy spectra could be reproduced using a numerical single-fluid, single-temperature radiation hydrodynamic approach employing the code RALEF-2D.^19,20 Given the complexity of ion flow characterization, we previously performed proof-of-principle experiments. In these experiments, we simplified our approach by (i) focusing on just a single laser intensity and, moreover, (ii) by assessing only the overall mass flow and not the individual charge states contributing to it. To complement our previous work,^19,20 as well as that of Morris et al.^10,11 and O'Connor et al.,¹⁸ we here investigate experimentally the dependence of ion emission, including specifically the individual charge states, on laser intensity—an important parameter for the optimization of EUV light production and for the optimization of tin usage for EUV production and suppression of ion debris. Retarding field analyzers (RFAs) are employed to provide information on ion yield, energy, and charge state. Seven RFA detectors placed around the LPP are used to map the angular dependence of the ion emission. First, we recall the experimental setup used for ion detection at ARCNL and describe the explored parameter space. We present charge-state-resolved and charge-integrated ion energy spectra, where we highlight notable spectral features. Those features and their variation with increasing laser intensity are the main targets of our investigation. We interpret our findings from the perspective of hydrodynamic plasma expansion, performing power-law fits, and compare the results to plasma radiation hydrodynamics theory.

The experimental setup (see Fig. 1) is thoroughly described in previous publications.^19,21,22 Here, we briefly summarize the key experimental parameters. The laser used to drive the tin plasma is a 10 Hz pulsed Nd:YAG laser operating at 1064 nm wavelength. The laser pulses have a Gaussian profile in both temporal and spatial co-ordinates. The spatial full-width-at-half-maximum (⁠ $FWHM x y$⁠) is 100 μm (the spatial profile has cylindrical symmetry), and the temporal full-width-at-half-maximum (⁠ $FWHM t$⁠) is either 8 or 10 ns. The pulse duration is here determined by the Q-switch delay of the laser, with the shorter 8 ns pulse length enabling larger pulse energies. Tin plasmas are generated in a vacuum chamber (maintained at approximately $10 − 7$ mbar) from liquid tin droplets having three diameters, namely, 17, 27, and 35 μm. For each droplet size, we set the total laser pulse energy to four values ranging from approximately 5 to 100 mJ for the 10 ns pulse length measurements (on 17- and 27-μm-diameter droplets), and from approximately 5 to 350 mJ for the 8 ns case (17- and 35-μm-diameter droplets). Note that the amount of laser light absorbed by the droplet and plasma not only depends on the initial size of the droplet but also on the radial expansion of the tin mass (either in the form of tin liquid or plasma) as the laser pulse is absorbed. Unless stated otherwise, the 27-μm-diameter droplets and 10-ns $FWHM t$ pulses are used. For this droplet size, the set laser pulse energies in a vacuum are 8, 25, 58, and 97 mJ, corresponding to laser intensities of approximately 6, 21, 48, and 80 GW/cm². This intensity range is relevant for laser pre-pulses that are used in the industry to pre-shape tin targets²³ before interacting with a more energetic main pulse.

The seven RFAs are placed at α = 30°, 41°, 64°, 90°, 120°, 139°, and 150° with respect to the direction of the incoming laser beam [in the current case of cylindrical symmetry, a single angle α suffices to describe the angular position of each RFA—Fig. 1(a)]. The distances from the LPP to the RFAs range from 296 to 420 mm. The distance to the LPP and the aperture size (5 mm in diameter) of the RFAs together define their solid angle of collection, for which the ion signal is corrected. The transmission of the devices is defined by that of the four-grid stack [Fig. 1(b)]. As discussed in Ref. 19, the full transmission lies between 41% and 83%, corresponding to the extreme cases of minimum and maximum mutual overlap of the grids. In the following, we take a transmission value of 62%, cf. Ref. 19. Two of the grids carry the retarding electric potential used for charge state unraveling. The purpose of each of the grids is discussed in detail in Ref. 22.

The raw RFA signal is amplified using a custom-built high-speed, large bandwidth trans-impedance amplifier with a gain of 25 kV/A.²² The ion signal reduces to the noise floor at very short (few ns) and very long (few hundred μs) time-of-flight values, with few ions arriving. In the charge-integrated kinetic energy distribution representation, the noise level scales with $E − 3 / 2$ effectively rendering the signal to have too low signal-to-noise for energies below about 10 eV and above a few keV (the specific values depend on experimental parameters), see also Ref. 22.

We examine the dependence of the ion energy spectra on laser intensity from tin LPPs produced from mass-limited droplet targets. Four laser intensities are set for each selected droplet diameter, ranging $0.4 × 10 10$ to $40 × 10 10$ W/cm².

Using our post-processing scheme,²² energy distributions are retrieved for each charge state observed in the LPP.

Figure 2 shows the variation of charge-state-resolved spectra with laser intensity at a 30° observation angle for the 27-μm-diameter droplet target. In the following, we restrict the low-energy bound to 100 eV for the sake of visual clarity. Following Ref. 24, we calculate the laser intensity using $I = ( 2 ln 2 / π ) 3 E L / ( FWHM x y 2 FWHM t )$⁠, where $E L$ is total laser pulse energy. First, we note that the (average) kinetic energy of the ions increases with increasing charge state. Similar observations were made in our studies,^21,22 however without any quantitative assessment, as well as in O'Connor et al.¹⁸ and Morris et al.¹¹ The former study reports a linear increase in the average ion kinetic energy with charge state.¹⁸ The increase in kinetic energy with charge state saturates around a few keV for higher charge states (z > 5 for the measurement presented in Fig. 2).

For z = 1, we find that increasing laser pulse energy barely affects the energy distributions. At most, it causes a small increase in the spectral intensity of the charge-resolved spectra. All z = 1 spectra exhibit a monotonically decreasing yield with increasing kinetic energy, and the distributions most probably peak below 100 eV. For the lowest multiply charged ions (⁠ $z =$ 2–4), we report a clearly peaked energy distribution, with an asymmetrical widening of the spectra in the direction of higher energies with increasing laser pulse energy. Distributions of this kind are typically modeled by so-called “shifted Maxwell–Boltzmann–Coulomb (MBC) distributions,”^18,25–27 where the apparent “shifting” of these Maxwell–Boltzmann-esque distributions to high kinetic energies is attributed to (i) adiabatic expansion in the Knudsen layer^28,29 and (ii) the formation of an accelerating voltage in the plasma that accelerates ions to energies proportional to their charge state.²⁷ A much simpler picture of ion acceleration in these plasmas is provided by quasi-neutral hydrodynamics,^20,30 where ion acceleration (and thus the location of the peak positions) originates from gradients in the plasma pressure $∇ p = ∇ ( p e + p i ) = ∇ [ ( z + 1 ) n i k T ]$⁠, where $p e ( ion )$ are the electron (ion) contributions to the pressure and z, T, and $n ion$ are the average charge state, plasma temperature, and ion density, respectively. In essence, hot and dense plasma regions generate high charge states and correspondingly high plasma pressures, spatial gradients of which form the basis for (charge-state-specific) ion acceleration.

With increasing laser energy, an additional high-energy peak emerges in the spectra. With increasing laser pulse energy, the energy corresponding to this second peak increases steadily, and its intensity decreases [Fig. 2(c)]. For higher charge states (z > 4), the relative spectral intensity of the second peak with respect to the first peak grows with increasing laser intensity, eventually becoming dominant with respect to the first peak. This can be seen in the spectra shown in Figs. 2(d) and 2(e), for $E L = 97$ mJ, where the relative spectral intensities of the first and the second peak switches between z = 4 and 5. For a given laser pulse energy, the second peaks have the same energy for all charge states. Moreover, as charge state increases, the energy of the first peak converges to that of the second peak; they eventually merge into a single peak, for instance, for z = 7, in the case of the 97 mJ pulse in Fig. 2(g).

Energy spectra for z = 1–8 are displayed in Fig. 3 for all seven observation angles for a 27-μm-diameter droplet illuminated by a 97 mJ laser pulse. A few immediate observations can be made. We note that at the back side (⁠ $α > 90 °$⁠), one collects about twice the amount of low charge states (⁠ $z =$ 1–3) as at the front side (⁠ $α < 90 °$⁠) for any pulse energy, while the front side generates a greater amount of high charge states (z > 3). Moreover, for high charge states (z > 3), spectra captured at small angles (⁠ $α ≤ 90 °$⁠) peak at higher energies than those captured at large angles (⁠ $α > 90 °$⁠).

Next, we note that the shape of the spectra transforms with decreasing angle and increasing charge state: gradually, a shoulder appears on the high-energy side of the distributions. This effect can be seen clearly in Fig. 3(d), where the spectra peak around 600–700 eV, while a second peak feature emerges around 1.5–2 keV. The signal intensity of this second peak decreases by three orders of magnitude with increasing detection angle from 30° to 150°.

The second, high-energy peaks observed in Figs. 2 and 3 correspond to the high-energy features found in charge-integrated distributions $dN / d E$ observed in our previous study.¹⁹ The presence of this peak was explained by a bunching phenomenon: in short, the absorption of the peak intensity of the laser pulse by the plasma generates a fast and dense expansion shell, propagating anisotropically toward small observation angles (⁠ $α < 120 °$⁠). This shell pushes all the slower material in its front as it expands in a vacuum, giving rise to high-energy peaks in charge-integrated spectra. Here, we find that the bunching is made up of different—relatively high—charge state ions. The absence of a second high-energy peak in $d N z / d E$ at large angles (⁠ $α > 120 °$⁠) was also observed in charge-integrated spectra.¹⁹ Additional features visible at even higher energies (around 1 keV) in Figs. 2(a), 2(b), 3(a), and 3(b) lie at noise level (here around $2 × 10 6$ eV/shot/sr), and no significance can currently be attributed to their observation. Gaps found in the ion spectra such as the ones observed in Fig. 2 are caused by the logarithmic representation of the y-axis, whereby negative values (originating from noise) cannot be represented.

From the viewpoint of plasma expansion governed by radiation hydrodynamics, i.e., expansion driven mostly by plasma pressure gradients in a hot-and-dense neutral fluid, a view that is strongly supported by our previous findings,^19,20 we may reason that the local characteristic sonic speed provides a meaningful measure of the detected ion energies. The experimentally observed scaling is not linear with charge state, hinting, taking a hydrodynamic view, that the detected ions are generated in regions of the tin plasma of different local temperatures T.

In addition to the strong scaling of the first peak with charge state, we observe a near-constant value of the energy of the second peak for charge states $z =$ 2–6. However, this value increases strongly with increasing laser intensity. The horizontal lines in Figs. 4(a)–4(e) show the increasing average position of the second peak with increasing laser intensities.

Next, we study the laser-intensity dependence of the positions of the two peaks. In Figs. 5(a)–5(e), the same spectral maxima are shown for each charge state, now as a function of laser intensity for each of the seven angles at which ion kinetic energies were measured.

Overall, the effect of increasing the laser intensity is an increase in the first or merged peak energy. Moreover, as seen in Fig. 3, it is apparent that the first peak energy (full markers) decreases with observation angle α for all intensities and charge states. For a given pulse intensity, the peak kinetic energy increases with charge state, up to 4 or 5, at which point the first peak merges with the higher-energy second peak (open markers). In all instances of overlapping first and second peaks, there is a systematic bias in the recovery of the peak position due to the overlap of the two peaks of different amplitude and widths, referred to as line pulling. This may generate a slight overestimation of the first peak position and an underestimation of that of the second peak.

We fit power-law models (⁠ $A z I B z$⁠, dotted black and green lines, respectively) to the positions of the charge-resolved first and second peaks (separately) from Figs. 5(a)–5(e), and report, in the inset of Fig. 5(f), the exponents for the first peak (⁠ $B 1 , z$⁠) and second peak (⁠ $B 2 , z$⁠) for each charge state (colored markers). The values of $B 1 , z$ and $B 2 , z$ averaged over all available angles are calculated for each charge state and shown in Fig. 5(f) (black and green lines and triangles, respectively).

The first peak scaling exponent $B 1 , z$ increases steadily from approximately 0 up to a value of 0.25 from z = 2 to 6, at which point the first peak has merged with the high-energy second peak. The scaling exponent of the second peak positions $B 2 , z$ varies between 0.5 and 0.8, with an average value of 0.67 (green dotted line).

The scaling exponents $B 2 , z$ for z < 6 take similar values; this is explained by the common bunching behavior of the underlying ions. We also expect those scaling exponents to be similar to that of the peaks found in charge-integrated spectra, which were observed in an earlier study.¹⁹ This point is specifically addressed later in Sec. III B.

We note that whereas the ion kinetic energy spectra show a very strong dependence on the emission angle, the power-law scalings extracted from the spectra show a relatively weak angular dependence. Overall, the same trends were observed in experiments with droplet targets of different diameters. We hypothesize that although the one-sided laser heating drives strong anisotropies,¹⁹ the unique link between temperature, charge state, and kinetic energy that is effectively captured in the power-law representation should indeed be independent of the observation angle under conditions of radial flow. Furthermore, study is required to more comprehensively explain the results for the individual charge states and may involve particle-in-cell (PIC) numerical modeling.

The RFA charge-integrated energy distributions $dN / d E$ are obtained by adding up the charge-resolved energy distributions of all charge states present in the experiment. Those distributions are akin to, and can be readily compared with, the flow velocity distributions obtained from hydrodynamic simulations such as the ones generated by the code RALEF-2D, and give access to the momentum and energy of the plasma ions.

Figures 6(a)–6(g) show measured pulse-energy-dependent ion energy spectra for a 27-μm-diameter droplet and a 10 ns pulse duration. For ease of comparison, the spectra at minimum, medium, and maximum observation angle α are presented for the pulse energy extrema of 8 and 97 mJ in panel (h). First, we observe a spectral shift to higher energies with increasing laser energy at all angles. Second, at large angles (⁠ $α ≥ 90 °$⁠), we note an increasing number of ions with increasing laser energy. O'Connor et al. presented similar findings for the front-side (⁠ $α < 90 °$⁠) emission using a planar target of solid tin.¹⁸ A high-energy peak is also observed in spectra with an observation angle smaller than 120°. This peak is formed by the accumulation around the same kinetic energy of ions with charge state $z ≤ 4$⁠, as seen in Sec. III A. The peak was reported,^21,22 and its physical origin examined^19,20 before—but only for a single laser intensity case. As the observation angle α increases, the peak loses its prominence and gradually fades into the smooth monotonously decaying background ion signal beyond $α > 120 °$⁠.

In the following, we look into the energy of the high-energy peak for forward emission angles (⁠ $α ≤ 120 °$⁠) as a function of the employed laser intensity. We determine the position of the peak using a combination of direct numerical peak finding in $dN / d E$ and looking for minima in $d 2 N / d E 2$ (as before, the Python package scipy and its threshold-based peak finding routine is used here). The central peak energy shifts with laser intensity, which is shown in Figs. 7(a)–7(e) for the five relevant angles (recall that the peak is observed only for $α ≤ 120 °$⁠), all four laser pulse energies, and all three droplet diameters of 17, 27, and 35 μm. To probe any influence of the small difference in pulse duration (related to the Q-switch delay settings, see above), two 17 μm droplet diameter measurements are investigated, one using an 8 ns $FWHM t$ and the other a longer 10 ns $FWHM t$ laser pulse.

We observe a consistent power-law-like dependence (⁠ $A α E B α$⁠) of the high-energy peak position on laser intensity, with little deviation from the fitted power laws [dashed black lines in Figs. 7(a)–7(e)]. We find no significant differences between the short- and long-pulse cases for the 17-μm-diameter droplet. The exponents $B α$ of the power-law fits are shown in Fig. 7(f). For each of the (a)–(d) panels, we also fit power-law functions to data subsets containing three out of the four data sets to assess the fit uncertainty. For each angle α, the difference between the maximum and minimum power-law exponents thus obtained define the (systematic) error bars for $B α$ as shown in Fig. 7(f). In all spectra, there is a sub-linear dependence of the high-energy peak position with laser intensity, with exponents $B α$ ranging from 0.55 to 0.75, and an average $B ¯ α = 0.67 ( 5 )$⁠, weighted by the corresponding uncertainty.

The expected value of the power-law exponent is remarkably close to the average angle-averaged experimental values of 0.67(5) reported in Fig. 7(f), for three different droplet target diameters. This finding supports the interpretation of the ionic emission from the LPP in terms of hydrodynamic plasma expansion. Moreover, the angle-averaged scaling exponent $B ¯ α$ of the peak in the charge-integrated spectra matches precisely that of the second, high-energy peak in charge-resolved spectra obtained in Sec. III A. This finding corroborates the formation of the peak in $dN / d E$ through a bunching phenomenon.

Once again, we note that despite the remarkable differences observed in spectra taken at different angles, the power-law scaling obtained by tracking features in the ion energy distribution presents a rather constant value over the angles [cf. Fig. 7(f)]. This observation holds for all studied set droplet sizes.

The ion emission from tin laser-produced plasma is characterized experimentally as a function of laser pulse intensity. Energy, charge state, and emission angle of the ions are obtained using seven retarding field analyzers. Charge-resolved ion energy spectra reveal the existence of two distinct peaks in the kinetic energy distribution of individual charge states. The kinetic energy of the first peak is found to smoothly scale (superlinearly) with ion charge state, hinting—from a hydrodynamics viewpoint on the expansion process—that the detected charge states are generated at different local temperatures. The second peaks found in charge-resolved distributions $d N z / d E$ combine, leading to the feature in the charge-integrated energy distributions $dN / d E$ reported previously,^19,20 corroborating the formation of the peak in $dN / d E$ through a bunching phenomenon. The energy corresponding to this second, high-energy peak is found to scale at all angles with $I 0.67 ( 5 )$⁠, in good agreement with empirical scaling laws derived from hydrodynamic theory of plasma expansion. This scaling relation exhibits strong isotropy, whereas the underlying ion energy spectra themselves are highly anisotropic. Our findings underpin previous interpretations^19,20 of the peaked features in the kinetic energy distributions and, with the wide laser range of laser intensities characterized in the current work, enable predicting their energy as a function of laser intensity under conditions relevant to nanolithography light sources.

The authors thank Duncan Verheijde for his support in understanding and improving the RFA electronics. They also thank Jorijn Kuster for the indispensable software support of our experimental setups. This work has been carried out at the Advanced Research Center for Nanolithography (ARCNL). ARCNL is public–private partnership with founding partners UvA, VU, NWO-I, and ASML, and associate partner RUG. This project has received funding from European Research Council (ERC) Starting Grant No. 802648. This publication is part of the project New Light for Nanolithography (with Project No. 15697) of the research program VIDI, which is (partly) financed by the Dutch Research Council. This work made use of the Dutch National e-Infrastructure with the support of the SURF Cooperative using Grant No. EINF-2947.

The authors have no conflicts to disclose.

Lucas Poirier: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Supervision (equal); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). Adam Lassise: Conceptualization (equal); Methodology (equal); Writing – review & editing (equal). Ronnie Hoekstra: Conceptualization (equal); Supervision (equal); Writing – review & editing (equal). John Sheil: Conceptualization (equal); Methodology (equal); Writing – review & editing (equal). Oscar Oreste Versolato: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Supervision (equal); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal).

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