Time-resolved spatial profiles of electron density and temperature in hydrogen plasmas induced by radiation from laser-produced tin plasmas for extreme ultraviolet lithography light sources

Figure 1(a) shows the configuration (or overview) of the Sn-LPP generation system. The origin of the x-axis (x = 0) is defined as the surface of the Sn plate.

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Sn-LPP was generated inside the vacuum chamber, which was evacuated to 10⁻² Pa or less. Hydrogen gas was introduced into the chamber to achieve a H₂ pressure (P_H2) of 50–200 Pa. The hydrogen flow rate was set to 50 sccm. To produce Sn-plasmas, the fundamental wave of Nd:YAG laser (Continuum, Surelite-II, wavelength 1064 nm, energy 200 mJ, pulse width 11.8 ns, repetition frequency 10 Hz) was used. The spot of the laser was 1 mm in diameter, and the intensity was 2.2 × 10⁹ W cm⁻². The solid Sn target (50 mm × 50 mm × 1 mm thickness) installed in the chamber was finely moved in the y- and z- directions at a constant speed (0.5 m s⁻¹) using a precision stage control system. The EUV energy from the plasma was measured using a calibrated EUV photodetector, which was composed of a spectral purify filter, a narrow-band EUV multilayer mirror, and a photodetector, each calibrated by Physikalisch-Technische Bundesanstalt. ^27–29) It was confirmed that the conversion efficiency (CE) from the laser pulse to the in-band EUV (13.5 nm ±1%) was 2%/2π sr, by using the detector. Figure 1(b) indicates a detail of a slit and a box inside the plasma chamber depicted in Fig. 1(a), with which the radiation from the Sn plasma achieving to the LTS measurement position can be limited, as described later in Sect. 3.1.1. Figure 1(c) is the side view of the vacuum chamber and the LTS system.

For the LTS measurements, the second harmonic of the Nd:YAG laser (Continuum, Surelite-II, wavelength 532 nm $\left(={\lambda }_{0}\right),$ laser energy 300 mJ, pulse width 8 ns, repetition frequency 10 Hz) was used as the probing laser. Two cylindrical lenses were used to focus the probing laser. The spot size at the measurement position was 5 mm in the z-direction and 0.2 mm in the x-direction, i.e. the laser intensity was 3.8 × 10⁹ W cm⁻² and a spatial resolution to the x-direction was 0.2 mm. To obtain spatial profiles of n_e and T_e, the Sn target, the box with the slit, and the driving laser were moved to the x-direction.

The timing of the plasma generation and the probing laser were synchronized using a delay pulse generator (Stanford Research Systems, DG-645). In this study, 0 ns (t = 0) was set as the time when the driving laser pulse reached its peak.

LTS signals at an angle of 90° with respect to the incident angle of the probing laser were collected and focused on the entrance slit of a custom-made triple grating spectrometer (TGS). As shown in Fig. 1(d), the TGS consists of six achromatic lenses (L1–L5, f = 220 mm; L6, f = 250 mm), a mirror (M1), three diffraction gratings (G1–G3, 2400 grooves mm⁻¹), an entrance slit (S1, width: 0.2 mm), an intermediate slit (S2, width: 0.2 mm), and a reverse slit (width: 0.5 mm) to block stray light, which is called as the laser-wavelength stop in this study. An intensified CCD (ICCD) camera (Princeton Instruments, PI-MAX4, quantum efficiency at λ₀ of 45%, 1024 × 1024 pixels, pixel size 13 μm × 13 μm, and gate width 5 ns) was used as the detector. A spectrum resolution of the TGS was 0.2 nm full-width at half-maximum and a sufficient stray-light rejection at ±0.3 nm from λ₀ were achieved. The time resolution of the measurement was 5 ns, which was determined by the gate width of the ICCD camera. To improve the signal-to-noise (S/N) ratio, the TS signals were spatially integrated over 5.2 mm along the probe laser (Y direction), and the TS signals from 1000 laser shots were accumulated.

As shown in Fig. 1(b), the radiation from the Sn plasma that can reach the measurement position was strictly limited using the box with the slit. This limitation was useful in suppressing noise due to radiation, as will be explained in detail in the next section.

After the first try of the LTS measurement, it was found that the strong bremsstrahlung radiation from the dense Sn plasmas produced at the target surface (n_e ∼ 10²⁵ m⁻³, average ionic charge ∼10) ²⁴⁾ easily overwhelmed the weak LTS signals. Figures 2(a)–2(c) depict typical relationships between the radiation and the LTS signals. Figure 2(a) was measured without the probing laser, i.e. the spectrum contains only the radiation from the Sn plasma. Note that the spectrum at −0.5 nm < Δλ < 0.5 nm was cut by the laser-wavelength stop installed in the TGS. Figure 2(b) was measured with the probe laser, i.e. the spectrum consists of both the radiation and the LTS. The LTS spectrum can be extracted by subtracting the spectrum of Fig. 2(b) from that of Fig. 2(a), as to be shown in Fig. 2(c). However, since the radiation signal was much larger than that of the LTS, the extracted LTS spectrum includes a significant statistical error. As a result, it is difficult to determine n_e and T_e accurately. To improve the S/N ratio, the box with the slit as shown in Fig. 1(b) was set inside the chamber, with which the radiation from the Sn plasma achieving to the LTS measurement positions (30 mm < x < 90 mm) was strictly limited. Using this box, the radiation spectrum [Fig. 2(d)] and the spectrum including both the radiation and the LTS signal [Fig. 2(e)] were measured again. As can be seen from these figures, the radiation signal was extremely reduced. Then, the extracted LTS signal became clear as shown in Fig. 2(f). After that, all the LTS results in this study were performed by using the box to improve the S/N ratio. In Fig. 3, the LTS spectrum shown in Fig. 2(f) is plotted in a logarithmic scale against ${\left({\rm{\Delta }}\lambda \right)}^{2},$ where ${\left({\rm{\Delta }}\lambda \right)}^{2}$ is proportional to the energy of the electrons. As shown in this figure, The LTS spectrum is linear at 0.5 nm² < ${\left({\rm{\Delta }}\lambda \right)}^{2}$ < 2 nm², i.e. the electron energy distribution function was Maxwellian in this energy range. The T_e was determined to be 0.8 eV by a Gaussian fitting curve. The n_e was determined to be 6.0 × 10¹⁷ m⁻³ by the signal intensity of the LTS spectrum. In the following sections, T_e and n_e were determined in the same manner.

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Figures 4(a) and 4(b) show the temporal evolutions of n_e and T_e at x = 50 mm and H₂ gas pressure of 200 Pa. We confirmed that there was no LTS signal when the chamber was in vacuum condition. In addition, it was also confirmed that there was no signal from hydrogen gas without the LPPs. As shown in these figures, both the n_e and T_e reached their peak values at t = 30 ns. At t > 30 ns, however, the temporal evolutions of n_e and T_e were different from each other completely; n_e was almost constant, whereas T_e decreased smoothly. The measurements were performed three times at t = 10 ns, six times at t = 20 ns, and one time for the other timings. For the results measured at t = 10 and 20 ns, the averaged values are plotted in Figs. 4(a) and 4(b), and the error bars illustrate the standard deviations of the measurements. For the other timings, uncertainties of the measured values were estimated to be at most within ±15%, which were determined by standard deviations of the parameters of the spectral fitting curves.

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Figures 5(a) and 5(b) depict the spatial profiles of n_e and T_e, respectively. For the measurements, the H₂ pressure was changed to 50, 100, and 200 Pa. The LTS was performed at the positions of x = 30, 50, 70, and 90 mm and at the time of t = 100 ns. Various fitting curves in Fig. 5(a) will be explained in the discussion part later.

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The n_e obtained in this study were in the range of 10¹⁷–10¹⁸ m⁻³. These values are much higher than those in the previous study, in which n_e of the order of 10¹⁴ m⁻³ was reported using the MCRS method. ¹⁷⁾ To confirm the validity of our results, we roughly estimated the electron density yielded through the photoionization process (n_{e_pi}) using the following equation: ¹⁷⁾

$$\begin{eqnarray}&&{n}_{{\rm{e}}\_{\rm{pi}}}=\displaystyle \frac{1.05{\sigma }_{{\rm{pi}}}{n}_{\alpha }{E}_{{\rm{EUV}}}}{2\pi {x}^{2}{E}_{{\rm{ph}}}},\end{eqnarray} \tag{ 3 }$$

where ${\sigma }_{{\rm{pi}}}$ is the ionization cross-section of H₂, ${n}_{\alpha }$ the background hydrogen density, ${E}_{{\rm{EUV}}}$ the EUV pulse energy, x the distance from the Sn plasma, and ${E}_{{\rm{ph}}}$ the photon energy of the EUV light. These values are listed in Table I. We assumed that 30% of the drive-laser energy was converted to radiations in a range of 10 nm to 20 nm wavelength, i.e. E_EUV = 0.06 J. This assumption is based on the measured in-band EUV (13.5 nm ± 1% wavelength) energy (4 mJ) and a previous study performed by George et al. ³⁰⁾ They measured absolute energy of radiation from Sn-LPPs in a wavelength range of 2–60 nm with various driving laser intensity. According to their results, the total energy in the "whole EUV range," which is defined as a wavelength range of 10–20 nm in this study, is estimated to be 15 times larger than that in the in-band EUV for our experiment condition, in which the intensity of the drive-laser was 2.2 × 10⁹ W cm⁻². Using the values listed in Table I, n_{e_pi} was calculated to 8 × 10¹⁶ m⁻³. The second process which should be considered is electron impact ionization. The single ionization energy of the hydrogen molecule is 15.4 eV. ³¹⁾ Therefore, the electron yielded through the photoionization can yield additional electrons through electron impact ionization. For example, a photon at λ = 13.5 nm having 92 eV energy can produce at most five additional electrons through electron impact ionization. Therefore, it is concluded that the order of n_e obtained by the LTS is reasonable.

With regard to T_e, only simulated values have been reported. The calculated T_e values are in the range of 0.5–4.8 eV. ³²⁾ Meanwhile, the value of T_e obtained in the experiment was 0.3–1.1 eV. Therefore, the measured T_e was on the same order as that calculated in a previous study.

Next, the temporal evolution of n_e is discussed. As shown in Fig. 4, the decay speed of n_e was much slower than that of T_e. This tendency is reasonable considering the timescales of recombination and diffusion processes. The order of the recombination time was 10² s, ¹⁹⁾ and the time scale of ambipolar diffusion ${\tau }_{{\rm{ab}}}$ can be evaluated from Eq. (4): ³³⁾

$$\begin{eqnarray}&&{\tau }_{{\rm{ab}}}={\left[{\left(\displaystyle \frac{2.405}{R}\right)}^{2}+{\left(\displaystyle \frac{\pi }{H}\right)}^{2}\right]}^{-1}\displaystyle \frac{1}{{D}_{\alpha }},\end{eqnarray} \tag{ 4 }$$

with R and H the radius and height of the vacuum chamber and ${D}_{\alpha }$ the ambipolar diffusion coefficient. Assuming that the photoionized hydrogen plasma is weakly ionized and T_e is matched higher than ion temperature T_i $\left({T}_{e}\gg {T}_{{\rm{i}}}\right),$ ${D}_{\alpha }$ can be calculated from the ion mobility ${\mu }_{{\rm{i}}}$ and T_e, ³⁴⁾

$$\begin{eqnarray}&&{D}_{\alpha }\sim {\mu }_{{\rm{i}}}\left\{\kappa {T}_{{\rm{e}}}/e\right\}\end{eqnarray} \tag{ 5 }$$

with $\kappa$ the Boltzmann constant, e the elementary charge, respectively. Under the condition of our experiment, ${\mu }_{{\rm{i}}}$ was estimated on the order of 1–10 m² V⁻¹ s⁻¹ for atomic-hydrogen ions (H⁺) and molecular hydrogen ions (H₂ ⁺). ³⁵⁾ Based on estimated ${\mu }_{{\rm{i}}}$ and T_e obtained in the experiment, the ${D}_{\alpha }$ was estimated in the order of 1–10 m² s⁻¹. As a result, ${\tau }_{{\rm{ab}}}$ was in the order of 10⁻⁵–10⁻⁴ s, which was much longer than the time range of the LTS. Meanwhile, the order of relaxation time between the electrons and hydrogen molecules was calculated to be 10⁻⁷ s based on the measured T_e; it is of the same order as the LTS measurement in this study. Therefore, it is concluded that the temporal evolution of n_e and T_e measured in this study is reasonable.

According to Eq. (3), electron density will be inversely proportional to the square of the distance x due to decreases of the photon flux. However, as shown in Fig. 5(a), the measured dn_e/dx were smaller than −2, i.e. the decaying ratio of n_e is more rapidly than that expected from Eq. (3). Note that the decaying of the EUV radiation through the absorption by hydrogen is negligible, e.g. the absorption length, which is calculated as 1/(n _α σ_pi), is around 3 m when H₂ pressure is 200 Pa, and the absorption ratio at x = 90 mm is less than 3%. To explain the measured n_e profiles, we considered photoionization processes by VUV radiation, whose absorption cross-section is much larger than that of the EUV region as shown in Table II. ³⁶⁾ It has been reported that Sn-LPPs yield not only EUV but also broadband VUV radiations. ^21,22) Gambino et al. measured CEs of radiations to the EUV and the VUV regions. ²²⁾ Although their experiment was performed with a higher laser intensity (6.9 × 10¹⁰–1.24 × 10¹¹ W cm⁻²) than that in our experiment (2.2 × 10⁹ W cm⁻²), we referred to their results. Table III shows the CEs in each wavelength region, which were used to discuss our LTS results. Figure 6 shows revised calculated curves and the LTS results, which are the same as that shown in Fig. 5(a). The revised curves were produced as follows: first, n_e measured at x = 30 mm was used as the initial values for the calculation. Second, using the photo-absorption cross-section σ_pi(λ) in Table II, n_{e_pi} in Eq. (3) were calculated for each wavelength region. Third, electrons produced by electron impact ionization processes were added in the same manner explained in the Sect. 3.2.1. As shown in Fig. 6, the n_e profiles are well explained by the revised curves.

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Next, the S/N ratio before and after the emission suppression is discussed. The dominant noise is expected to be the statistical shot noise both before and after Sn plasma emission suppression, and this noise is determined by the square root of the number of photoelectrons. ³⁷⁾ The total shot noise is expressed as ${\left({p}_{{\rm{LTS}}}+{p}_{{\rm{emission}}}\right)}^{0.5},$ and the S/N ratio is determined by ${p}_{{\rm{LTS}}}/{\left({p}_{{\rm{LTS}}}+{p}_{{\rm{emission}}}\right)}^{0.5},$ where ${p}_{{\rm{LTS}}}$ is the number of LTS photoelectrons and ${p}_{{\rm{emission}}}$ is the number of emission photoelectrons. As shown in Fig. 3, the LTS signal intensity was estimated to be one-half of ${\rm{\Delta }}\lambda$ = 0 nm at ${\rm{\Delta }}\lambda$ = 1.12 nm. The total number of photoelectrons of the LTS signal detected by the photo cathode per laser shot was 27, which was estimated from the configuration of the optical system used described in the Sect. 2.2. Because the scattered light intensity per CCD pixel was small, CCD pixels were combined (binned) over 9 CCD pixels in the wavelength direction and 401 pixels in the Y-direction of the space, to improve the S/N ratio. As a result, the region of 9 pixel × 401 pixel (108 μm × 5.2 mm) was used as a single light receiving region. The number of LTS photons counted at ${\rm{\Delta }}\lambda$ = 1.12 nm was 0.6 per laser shot. The signal was integrated over 1000 laser shots; therefore, the total number of LTS photons at ${\rm{\Delta }}\lambda$ = 1.12 nm was 600. Similarly, the number of photons emitted at this wavelength was 22 per laser shot without Sn plasma emission suppression, and the integrated value over 1000 laser shots was 2.2 × 10⁴. In this case, the shot noise was 152, and the S/N ratio was 4.0. On the other hand, when light emission was suppressed, the number of photons emitted at ${\rm{\Delta }}\lambda$ = 1.12 nm was 0.053 per laser shot, and the integrated value over 1000 laser shots was 53. In this case, the shot noise reduced to 25.6, and the S/N ratio improved to 23.