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Abstract
We present a new nozzle design for an improved brilliance of laser-produced gas plasmas emitting in the soft X-ray and extreme ultraviolet spectral regime. A rotationally asymmetric gas jet is formed by employing two closely adjacent nozzles facing each other under the angle of 45°. The generated three-dimensional gas density distribution is tomographically analyzed using a Hartmann-Shack wavefront sensor. A comparison with numerical simulations accomplishes an optimization of the nozzle arrangement. The colliding gas jets create an optimized gas distribution with increased density, leading to a significant brilliance enhancement of the extreme ultraviolet, soft X-ray plasma.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Laboratory-scale laser-produced plasma (LPP) sources emitting in the extreme ultra-violet (EUV) and soft X-ray (SXR) spectral range have found a variety of applications in industry and research in recent years. Compact EUV sources are employed for various metrology purposes in the framework of the now already maturing EUV semiconductor microlithography, e.g. for actinic mask inspection, material testing, or optics and sensor characterization [1]. Due to the considerable brilliance improvement, table-top LPP sources can nowadays also afford high-resolution microscopy [2,3] and near-edge X-ray absorption spectroscopy (NEXAFS) [4–8] in the SXR spectral region, techniques that were almost exclusively restricted to synchrotron sources in the past. Depending on the application, various types of laser targets are employed for LPP sources, i.e. solids [9], liquid jets [10] or droplets [11], and gases [12,13], each type showing different advantages and drawbacks. Comparatively bright and small plasmas, with spatial extensions of several tens of micrometer, are generated using solid or mass-limited liquid targets. However, their main disadvantage is the inevitable production of debris, which can severely damage optical elements in the beam path. Possible debris mitigation schemes require considerable technical effort, adding a large amount of complexity to the system.
As an alternative, the use of gaseous targets emitted from pulsed nozzles enables the construction of rather compact, clean and long-term stable EUV/SXR sources, providing actually an inherent debris mitigation: Although the laser plasma is ignited very close to the nozzle, almost no debris is generated since the gas flow protects the nozzle against erosion from the plasma, accomplishing a clean and long-term stable operation and making these sources ideally suited for metrological applications. However, compared to solid or liquid targets, the achievable peak brilliance of a gas target plasma is definitely smaller. This is, on the one hand, due to the much lower density, leading to relatively large plasma sizes of several hundreds of µm. Additionally, the photon yield is reduced as the generated short wavelength radiation is partially absorbed by the surrounding target gas itself.
There have been several attempts to overcome these deficiencies of gas jet based LPP sources, without giving up their inherent advantages. Fiedorowicz et al. [14] developed a double-stream nozzle with an outer helium jet confining the main target gas jet, leading to smaller and brighter plasmas due to increased particle densities. Mey et al. [15] investigated the formation of a barrel shock during expansion of a supersonic jet into a moderate helium atmosphere, also enhancing the target particle density and therefore the brilliance of the plasma. Reabsorption effects can be reduced by choosing the optimum direction under which the generated short wavelength radiation is utilized [16]. However, in spite of these achievements, there is definitely still room for further improvements regarding the conversion efficiency from laser energy into EUV/SXR radiation.
It has been shown before that the shape of the nozzle strongly influences the density distribution in a gas jet, representing one of the key parameters for the formation of the laser plasma [17]. Thus, the objective of this work is an optimization of the gas density distribution for a further enhancement of the plasma brilliance. For this, a comprehensive characterization of the 3D density distribution is achieved from a tomographic analysis of wavefront distortions imposed by the gas jet on a collimated test beam. The good agreement between these experimental data and the results of computational fluid dynamic (CFD) simulations accomplishes an optimization of the nozzle geometry, indicating that the brilliance of the laser plasma is maximized by a high gas density with a steep gradient for reduced reabsorption of the plasma emission.
2. Gas jet optimization
A primary objective of this study is to investigate the influence of different nozzle geometries on the gas jet density distribution and the resulting soft X-ray and EUV emission from the plasma. For this purpose, an experimental setup was employed that has been described in detail elsewhere [12] and is only briefly addressed in the following.
2.1 Experimental setup
The plasma source consists of a piezoelectric nozzle that enables the generation of a pulsed gas jet (topen = 1 ms) which expands into a vacuum environment of 10−5 mbar, providing a target for a focused (f = 100 mm) short pulse laser (Innolas, Nd:YAG, λ = 1064 nm, τ = 6 ns, pulse energy 600 mJ, 10 Hz). As a result of the high laser peak power a highly ionized plasma is generated that emits short wavelength radiation. Krypton and xenon are used as target gases for broadband emission in the SXR and EUV spectral region, respectively. As demonstrated recently, emission under an angle of 20° referred to the incoming laser beam results in minimized reabsorption by the surrounding target gas [16]. Thus, plasma size, spatial distribution and intensity can be monitored under 20° with a pinhole camera (pinhole diameter 50 µm, phosphor-coated CCD chip Sony ICX285, pixel size 6.45 µm, 1280 × 1024 pixels). For the SXR range a thin aluminum foil (thickness 200 nm) in front of the pinhole ensures that mainly radiation < ∼5 nm is registered. The transmission of the aluminum filter at higher wavelengths (> 20 nm) is not relevant due to the low emission of the krypton laser plasma in this regime [18].
Spectrally resolved analysis of the EUV emission around 13.5 nm is performed with an EUV spectrometer. It consists of a 100 µm entrance slit, an aberration-corrected Variable Line Spacing (VLS) diffraction grating (Hitachi, 1200 grooves per mm, arm length 237 mm) and a back-thinned CCD camera (TPI, Pixis XO 1024B, 13 µm pixel size, 1024 × 1024 pixels), cooled to −70 °C for reduced intrinsic thermal noise. A 150 nm zirconium foil is applied to block visible light. Narrowband EUV radiation (λ = 13.55 nm ± 0.25 nm) is obtained using a Mo/Si multilayer mirror and a zirconium filter, allowing the determination of absolute source brilliance with a calibrated photodiode (IRD, SXUV 100) [16].
To visualize and quantitatively determine the density distribution of the expanding gas jet a Hartmann-Shack (HS) wavefront sensor is utilized, recording the wavefront distortion of a collimated probe beam (λ = 520 nm) induced by the jet (see Fig. 1). The wavefront sensor consists of a CCD camera behind a microlens array with a pitch of 150 µm. A spatial resolution of 45 µm is achieved by projecting the wavefront deformation in the xy-plane onto the sensor using a lens with a magnification factor of 3.33. Due to the density dependent change of the refractive index n, the initially plane wavefront w of the probe beam is deformed by the jet according to:
Fig. 1. Schematic drawing of the laser-induced plasma source. The plasma is monitored under an angle of 20° referred to the laser beam. Quantitative evaluation of the gas jet density is performed with a Hartmann-Shack wavefront sensor.
Thus, measurement of the wavefront distortion allows the determination of the refractive index distribution within a rotationally symmetric gas jet [15]. In order to retrieve 3D information in case of a non-axisymmetrical jets, a tomographic technique is used measuring under different azimuthal observation angles φ. For this purpose, the nozzle is rotated from 0° up to 180° in 5° steps around the y-axis. A filtered backprojection based on the inverse Radon transform including a Ram-Lak filter is used to reconstruct the spatially resolved refractive index distribution n(x,y,z). Refractive index n and number density of the target gas N are related by the Lorentz-Lorenz formula [19]:
with the polarizability α of the gas particles. Thus, it is possible to reconstruct the 3D gas density distribution of the expanding jet (see Fig. 3).The achievable number density in a gas jet is proportional to the reservoir pressure p0 and the minimum nozzle diameter Amin [20]. A linear pressure dependence has indeed been demonstrated in a previous paper [16]. Measurements of the gas density distribution according to Eq. (2) were now compared with simulation results of a finite volume method described in the following. With the help of this code, the influence of geometrical parameters like opening diameter and shape of the nozzle were investigated. It was already shown [17] that a conical nozzle results in a more directed gas jet compared to a cylindrical one. The optimal opening angle α was experimentally found to be approximately 7°, motivating the so far utilized standard nozzles S1, with diameters of 300 µm to 550 µm and a length of 1 mm.
Fig. 2. Simulated 3D krypton gas density distribution for different single and double conical nozzles at fixed distances from the nozzle exit (applied pressure 20 bar).
Fig. 3. Comparison of measured (left) and simulated (right) gas density distribution for the double nozzle D3 with an applied pressure of 20 bar krypton.
2.2 Simulations
In order to create a highly brilliant plasma and to avoid nozzle erosion it is especially desirable to generate a strongly directed gas jet with a high density relatively far away from the nozzle. Optimizing the nozzle design for an improved gas jet opens up many geometrical degrees of freedom. To study the influence of each parameter for different designs we set up a steady-state 3D simulation using the software ANSYS Fluent. To define the turbulent flow, the shear stress transport (SST) k-ω model, based on solving Reynolds-averaged Navier-Stokes equations on a discrete grid is applied [21–23]. The turbulence behavior of the flow is described by the turbulent kinetic energy k and the specific dissipation rate ω, whereby the SST formulation ensures a more accurate freestream behavior [24]. Here, Krypton approximated as ideal gas is used as medium. The Sutherland viscosity model [25] is deployed to describe the temperature dependence of the viscosity. The model structure consists of a gas reservoir with a pressure inlet defined as total pressure with a value of 20 bar. This is followed by the nozzle with adiabatic wall behavior and a subsequent cylinder volume, serving as a pressure outlet with a value of 10−5 bar. For the calculation an implicit density based solver with solution steering is chosen. This ensures, at the expense of accuracy, the output of a converged solution by using a blending (75%) between the first and second order of discretization.
Figure 2 shows a compilation of simulated density distributions for four nozzle geometries at different distances to the nozzle exit. As expected, in comparison to the standard nozzle S1 mentioned above, the enlarged nozzle S2 leads to a higher gas density, but also to a flat density gradient and a distribution widely spread over much larger volume, with possibly negative reabsorption effects for the emitted SXR radiation. To overcome this problem, a geometry is simulated in which two nozzle openings are placed at an angle θ to each other. Besides this tilt, further design parameters to be optimized are size, shape and distance between the two nozzles. With the nozzle combination D1 (θD1 = 12°, distance between nozzle exits 220 µm), the inlet and outlet cross section area is kept equivalent to the single nozzle S1. At D2, two standard nozzles S1 are tilted by θD2 = 45° to each other with an exit gap of 100 µm. For this design, the number density is locally increased in a specific distance to the nozzle due to the interaction of the two expanding gas jets. The colliding jets create an azimuthally varying density distribution with a steep density gradient, presumably minimizing reabsorption of the emitted plasma radiation.
Based on these results, further simulation studies for an optimized nozzle geometry were conducted, leading finally to a design with two opposing, roughly Laval-shaped nozzles (D3, see Fig. 3). Of course, it had to be demonstrated that such relatively complicated shapes are manufacturable with reasonable effort.
2.3 Nozzle fabrication
Various nozzle geometries were manufactured in house with an excimer laser (Lambda Physik, COMPex 150T, λ = 248 nm, pulse energy 250 mJ, τ = 25 ns, repetition rate 50 Hz). Nozzles were produced by percussion drilling into tungsten plates (1 mm thickness, 5 mm diameter) under on-line control with a video microscope. For this, a circular aperture is projected onto the plates with a demagnification factor of 10 resulting in an energy density of 5 J/cm2. The laser drilled exit diameter is actually smaller than the entry diameter resulting in a conical shape of the nozzle hole. The cone angle α can be influenced by varying focal length of the imaging lens, energy density, repetition rate and the number of pulses. In addition, by tilting the tungsten plate about an angle β, also nozzle holes can be produced which are not perpendicular to the surface. For production of the D3 design, the nozzle plate is flipped after the main drilling and processed from the other side, generating the Laval-like shape.
3. Brilliance improvement
3.1 Soft X-ray emission
In order to verify the simulation results, the comparison of measured and simulated gas density distributions for nozzle D3 is presented in Fig. 3. Overall there is a very good qualitative agreement regarding the propagation characteristics and density distribution of the jet flow. The collision of the two gas jets results in a region with increased density as compared to nozzle S1. In particular, a rotationally asymmetric gas distribution with azimuthally dependent density gradient is formed. The absolute deviation in number density between measurement and simulation may be caused by simulation inaccuracies regarding the assumed continuum approximation and time-independent solution.
In order to determine the optimum angle of incidence of the laser beam with respect to the nozzle orientation, nozzle D3 is rotated in 5° steps from ϕ = 0° to 180° (due to mirror symmetry) around its center. Thereby the focal position of the incident laser beam is adjusted for maximum plasma emission brightness at each measuring point. The resulting angular dependent plasma brightness is shown in Fig. 4(a) for distances between nozzle exit and plasma of 1 mm and 1.5 mm, respectively. For comparison, the brightness of the so far used standard nozzle S1 is also plotted in the diagram. For nozzle D3 the plasma brightness depends strongly on the angle ϕ, showing maxima at 70° and 150° and minima at 20° and 110°. The reason becomes apparent when looking at Fig. 4(d), where the density distribution is superimposed with the incident laser beam, plasma position and SXR viewing angle. Angular positions with maximum plasma brightness benefit from an area of low density in the gas distribution, minimizing reabsorption of the emitted plasma radiation. Furthermore, the steep density gradient ensures a more efficient coupling of the laser radiation, resulting in a smaller plasma size compared to the standard nozzle S1 [see Figs. 4(b), 4(c)].
Fig. 4. (a) Angular dependency of plasma intensity (Krypton, p0 = 20 bar, averaged over 100 pulses) for different distances between nozzle and laser focus for double nozzle D3 and standard single nozzle S1 and related plasma images (b, c) taken with the pinhole camera. (d) Overlay of the double nozzle openings, its measured density distribution (D3, 1 mm nozzle distance) and the incoming laser as well as the outgoing soft X-ray beam for maximum plasma brightness (ϕ = 70°).
The measured plasma characteristics for different nozzles are compiled in Table 1 indicating that the enlarged nozzle S2 provides no considerable improvement regarding plasma brightness, which is due to a stronger reabsorption as discussed in section 2.2. With nozzle D3, however, a significant increase in plasma brightness is achieved, along with a considerable reduction of the plasma size. For a larger plasma-nozzle distance of 1.5 mm, which is preferred for reduced nozzle erosion and long-term stability, the brightness increases by a factor of ∼3. The plasma brightness per source area, being important e.g. for imaging applications, improves even by a factor of 8 for this distance.
Table 1. Measured plasma characteristics under 20° referred to the incoming laser beam for different nozzle geometries and distances (Krypton, p0 = 20 bar, averaged over 100 pulses)
3.2 EUV emission
The described optimized nozzle design was also tested in the EUV spectral range using xenon as target gas. Figure 5(a) displays the xenon emission spectra recorded for nozzles S1 and D3 under selected observation angles [cf. Figs. 5(b) and 5(c)] together with Zr filtered pinhole camera images of the plasma [Fig. 5(d)]. In fact, the double nozzle D3 reveals a significant increase in intensity. In particular, a redistribution of the spectrum is observed, favoring the emission around 13.5 nm at the expense of the 11 nm peak. In a weakened manner this behavior is also found for single nozzle S1 under an observation angle of 20°. It is presumably caused by the steeper density gradient for the optimized geometry, leading to a more efficient laser heating of the plasma and a reduced reabsorption of EUV radiation.
Fig. 5. (a) Normalized xenon emission spectra in the EUV spectral range (p0 = 15 bar, nozzle distance 1.2 mm) accumulated over 100 pulses for different source configurations (b, c) and corresponding plasma images captured separately with a pinhole camera (Zr filtered, average 100 pulses) (d).
Table 2 gives an overview of the intensities emitted in the narrowband EUV wavelength range of λ = (13.55 ± 0.26) nm, as obtained by the Zr filtered pinhole camera behind a MoSi mirror for different gas pressures. In accordance with the spectroscopic data the plasma brightness for nozzle D3 is considerably higher than for S1 (both in backward direction, i.e. 20° w.r.t. the incident laser beam). Overall, an increase in brightness of up to a factor of 2 is observed, rising to ∼2.5 when the source area is taken into account. Even an increased distance of 1.5 mm between plasma and nozzle still provides a higher brightness compared to the single nozzle. A brilliance measurement at λ = 13.5 nm for a plasma distance of 1.2 mm (p0 = 15 bar) results in a source peak brilliance of 1.43 × 1017 photons/(s × mm2 × mrad2 × 3.8% BW) for a plasma pulse duration of 5 ns [26].
Table 2. Narrowband pinhole camera measurements [λ = (13.55 ± 0.26) nm] of the Xenon plasma for nozzle configurations S1 and D1 at different gas pressures and plasma distances d to the nozzle, recorded under 20° referred to the incident laser beam.
4. Conclusion
Although EUV/SXR plasmas generated from gas targets are less brilliant due to lower particle densities as compared to liquid or solid targets, such sources are of particular interest for metrological applications due to their cleanliness, simplicity and compactness. In order to optimize gas jet based plasma sources we have characterized the 3D density distribution of expanding jets for different nozzle configurations by tomographically analyzing the wavefront distortion of a test beam. The experimental results showed a very good agreement with numerical simulations. Thus, it was possible to predict density distributions for a larger number of nozzle geometries, avoiding time-consuming nozzle fabrication and experimental testing.
As an optimum geometry with respect to density enhancement and shape, i.e. in particular the density gradient, a design with two opposing, roughly Laval-shaped nozzles was discovered, which could be manufactured by excimer laser percussion drilling. This double orifice arrangement was characterized and tested, yielding indeed a higher plasma brightness even for larger nozzle distances as compared to the previously used nozzle. This is obtained, on the one hand, by a higher gas density, on the other hand by reduced reabsorption in the non-axisymmetrical density distribution.
Funding
Deutsche Forschungsgemeinschaft (434531747); Bundesministerium für Wirtschaft und Energie (ZF4060503DF8); European Cooperation in Science and Technology (CA17126).
Disclosures
The authors declare no conflicts of interest.
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