Modeling of radiative properties of Sn plasmas for EUV source

Transcription

1 Modeling of radiative properties of Sn plasmas for EUV source Akira Sasaki Quantum Beam Science Directorate, Japan Atomic Energy Agency 8-1 Umemidai, Kizugawa-shi, Kyoto , Japan Atsushi Sunahara, Hiroyuki Furukawa Institute for Laser Technology Utsubohonmachi, Nishi-ku, Osaka , Japan Katsunobu Nishihara, Shinsuke Fujioka Institute of Laser Engineering, Osaka University 2-6 Yamadaoka, Suita, Osaka , Japan Takeshi Nishikawa Department of Electrical and Electronic Engineering, Okayama University 1-1 Naka 1-chome, Tsushima, Okayama , Japan Fumihiro Koike Physics Laboratory, School of Medicine, Kitasato University Kitasato, Sagamihara, Kanagawa , Japan Hajime Tanuma Department of Physics, Tokyo Metropolitan University 1-1 Mimaiohsawa, Hachioji, Tokyo , Japan 1

2 Abstract : In this study, atomic processes in Sn plasmas are investigated for application to extreme-ultra-violet (EUV) light sources used in microlithography. An atomic model of Sn is developed on the basis of calculated atomic data using the Hebrew University Lawrence Livermore Atomic Code (HULLAC). Resonance and satellite lines from singly and multiply excited states of Sn ions, which contribute significantly to the EUV emission, are identified. The wavelengths of the 4d 4f + 4p 4d transitions of Sn 5+ to Sn 13+ are investigated, because of their importance for determining the conversion efficiency (CE) of the EUV source, in conjunction with the effect of configuration interaction (CI) in the calculation of atomic structure. Results of calculation are compared with those of the charge exchange spectroscopy, measurement of the emission spectrum of the laser produced plasma EUV source, and the opacity measurement of a radiatively heated Sn sample. A reasonable agreement is observed between calculated and experimental EUV emission spectra obtained under the typical condition of EUV sources with the ion density and electron temperature of the plasma around cm 3 and 20eV, respectively, by applying wavelength correction to resonance and satellite lines. Finally, the spectral emissivity and opacity of Sn plasmas are calculated using a full collisional radiative (CR) model as a function of electron temperature and ion density. These data are useful for the radiation hydrodynamics simulation carried out to optimize the pumping condition of EUV sources. 2

3 1 Introduction Plasma extreme-ultra-violet (EUV) sources have been investigated extensively for application to next generation microlithography. Sn plasma, which shows a strong spectral emission at λ = 13.5 nm, has attracted considerable attention. Laser produced plasma (LPP), and discharge pumped plasma (DPP) sources have been studied. In order to obtain high output power of 180 W in a 2% bandwidth at λ = 13.5 nm with a high conversion efficiency (CE), the optimization of pumping conditions has been investigated, both experimentally and theoretically [1]. Especially, the radiation hydrodynamics simulation is found to be useful for investigating the emission spectrum and CE of EUV sources over a wide range of pumping conditions [2] [4]. It has been proposed that higher CE and output power of EUV sources can be realized by using a CO 2 laser as a pumping source and double pulse irradiation [5]. We develop an atomic model of Sn, which is used to obtain data on the equation of state and coefficients of radiative transfer such as spectral emissivity and opacity of Sn plasma for carrying out the radiation hydrodynamics simulation. We develop the model, by calculating atomic data using Hebrew University Lawrence Livermore Atomic Code (HULLAC) [6]. Recently, significant progress in the modeling of atomic processes of high-z ions has been achieved by the use of computational atomic data, including the modeling of Xe and Sn plasmas [7, 8]. In the case of Sn plasmas, it is found that efficient emission is obtained from 4d 4f and 4p 4d transitions of nearly 10 times charged ion [9]. It is also shown that the satellite lines arising from the multiply excited states contribute significantly to the emission and absorption of in the laser produced plasmas, for instance, in the high density spatial region near the target surface, and in the case that plasma has a large optical depth [10], which is preferred to increase EUV output power. In the present work, we show a computational method, which allows one to model emission including those from multiply excited states from the atomic ions with a complex structure. We develop the atomic model of Sn, through an investigation of the dependence of calculated averaged charge of the plasma and emission intensity on the atomic model [11]. On the other hand, accuracy of the wavelength of emission lines of Sn ions has particularly important, because of the requirement of narrow (= 2%) bandwidth of the emission, which is required by the Mo/Si multiplayer optics. The effect of configuration interaction (CI) has been shown to reduce the wavelength and width of 4d 4f and 4p 4d transitions [12]. However, the 3

4 calculated wavelength is still different from that observed in experiments [13], and correction is required for the modeling of the emission spectrum [7]. We determine the wavelength correction of the major emission lines through a theoretical analysis and a detailed comparison of results of different experiments. Eventually, it is shown that a reasonable agreement between the calculated and observed emission spectra is obtained. This paper is organized as follows. In section 2, the atomic model of nearly 10 times ionized Sn, which is of great interest in the development of EUV sources, is outlined. In section 3, the development of a full collisional radiative (CR) model of Sn plasma is discussed in terms of the selection of an appropriate set of atomic states and the calculation of the wavelength of emission lines. In section 4, the validation of the model is presented. Results of three different types of experiments such as charge exchange spectroscopy (CXS), measurement of the emission spectrum of EUV sources, and opacity measurement of a radiatively heated Sn sample, are compared. In section 5, results of the calculation including the spectral emissivity and opacity of the Sn plasmas are presented, which is followed by summary and conclusion in section 6. 2 Modeling of Sn ions In typical LPP EUV sources, a Sn droplet target is irradiated by CO 2 laser pulses, and plasmas with electron temperature of few tens of electron volts are produced [14, 15]. In the plasma, Sn atoms are ionized up to around 10 times charged state, which exhibit predominant emission in the EUV wavelength region. During the irradiation, the energy of laser is absorbed near the critical density surface, n e = cm 3, for CO 2 lasers with a wavelength of 10.6µm. The surface of the Sn target is ablated and coronal plasma is produced. The energy of the laser pulses is converted to thermal electrons and radiation. In the case of Sn plasmas, more than 50% of the pumping energy is converted to optical radiation [16], which implies that the radiative transfer has the significant effect determining the temporal and spatial features of Sn plasmas. Optimization of plasma condition is indispensable for the development of EUV sources, because although the conversion to optical radiation is efficient, the bandwidth (= 2%) is considerably narrow as compared to a typical Sn spectrum. The CE for EUV emission depends on various parameters such as wavelength, intensity, and pulse duration as well as the target conditions. Moreover, the effect of self absorption in Sn plasmas, which modifies the spectrum 4

5 significantly, should be taken into account [17] [20]. The hydrodynamics simulation can be used to calculate the temporal and spatial evolution of the density and temperature of plasmas, as well as the emission spectrum and CE. However, the calculation of coupled plasma hydrodynamics, atomic processes, and radiative transfer is prohibitively difficult in the case of Sn plasmas, because the calculation may involve the determination of the population of a large number of atomic levels and the detailed spectral structure. On the other hand, in the case of LPP EUV sources, the pulse duration of the pumping laser as well as EUV emission (>10 ns) is considerably longer than the time taken for the ionization and excitation of Sn ions. Hence we determine hydrodynamic and radiation transport characteristics of Sn plasmas, by assuming steady-state of the atomic processes in the plasmas, using the emissivity and opacity of the plasmas, which are calculated separately, as a function of ion density and electron temperature [21, 22]. We develop a full CR model of Sn plasmas. Sn ions of charge state around 10 have a ground electron configuration of 4d N, where N is the occupation number of the 4d subshell. Figure 1 shows the schematic level diagram of Sn 10+, which has the ground configuration of 4d 4. The energy level is calculated using the HULLAC without considering CI. Sn ions have a large number of excited configurations. In order to develop the CR model, we have to select an appropriate set of levels. Instead of selecting individual configurations, we define a group of configurations, which have the same core configuration and one excited electron in an outer orbital such as 4d 3 nl. We note that the population of the states within a group strongly couple each other through fast collisional and radiative processes. Consequently, we determine number of groups to be included in the CR model, by increasing the number of groups until the convergence of the calculation with respect to the population and emission of the plasma is obtained. Figure 1 shows first 5 groups of configurations, 4d 3 nl, 4d 2 5snl, 4p 5 4d 4 nl, 4d 2 4fnl, and 4d 2 5pnl according to the order of their excitation energy of the states defined by the core configuration, i.e., 4d 3, 4d 2 5s,..., which can also be found from the energy of excited configurations of Sn 5+ to Sn 14+ shown in fig. 2. As shown in fig. 1 and 2, a strong EUV emission occurs primarily through resonant 4d 4f, 4d 5p, and 4d 5f transitions, and also through 4p 4d transition from inner-shell excited 5

6 states [23], from Sn ions with a charge around 10. It is shown that the excitation energy of 4d N 1 5l configurations increases as ion charge increases, whereas the excitation energy of 4d N 1 4f and 4p 5 4d N configurations is almost constant. This feature of 4 4 transitions are common for various atomic elements with Z 50 [24]. This also implies the potential of Sn ions for application as an efficient EUV emitter at λ = 13.5nm over a wide range of temperatures and densities. In addition to the resonant lines, transitions between excited configurations, such as spectator satellite lines corresponding to 4d 4f transitions with one spectator electron in an outer orbital, e.g., 4d N 1 nl 4d N 2 4fnl, and inner-shell satellite lines such as 4d N 1 4f 4d N 2 4f 2, 4d N 1 4f 4p 5 4d N 4f, and 4p 5 4d N 4f 4p 5 4d N 1 4f 2, as shown in fig.1, contribute significantly to the emission [10]. This suggests that in the atomic model of Sn, the level population should be calculated by considering a sufficient number of atomic levels, including 4d N 1 nl, 4d N 2 (4f 5p 5f)nl, and 4p 5 4d N nl configurations. 3 Development of the atomic model We develop the atomic model of Sn, including neutral Sn to Ar-like Sn (Sn 32+ ), to calculate the level population and the coefficients of radiative transfer covering the possible temperature (5 250eV ) and ion density ( cm 3 ) range of LPP EUV sources. We calculate the level population on the basis of non-relativistic detailed configuration accounting (DCA) using the atomic state averaged over configuration, because the relativistic effect is not significant in the case of low charge states of Sn, which is of a great interest for the development of EUV sources. We calculate the steady-state population of each atomic state by solving the following set of rate equations; dn i dt = j R ji N j k R ik N i = 0, (1) where N i is the population of the ith level and R ij and R ik correspond to the formation and destruction rate of the ith level, from the jth level and to kth level, respectively. We take a variety of atomic processes into account. We calculate the energy of the configuration averaged states using HULLAC without considering the effect of CI. We calculate rates of 6

7 radiative decay, electron collisional excitation, collisional ionization, and radiative recombination by using either HULLAC or empirical formulas. We calculate the rate of radiative decay using HULLAC. In the case of multiple excited configurations having the energy above the ionization limit, the rate of autoionization are also calculated using HULLAC, so that dielectronic recombination (DR) and excitation autoionization (EA) processes through those configurations to be included. On the other hand, we use empirical formulas, as a function of transition energy and electron temperature, for the calculation of the rate of the electron collisional ionization and radiative recombination [25]. We also use another empirical formula for the calculation of the rate of collisional excitation from the transition energy and oscillator strength. The rate of reverse processes such as electron collisional de-excitation and three-body recombination is determined by the detailed balance. This ensures that the present model reproduces the Saha-Boltzmann distribution of population in the limit of the local thermodynamic equilibrium (LTE). After the level population is determined, the emissivity and opacity are calculated by taking bound-bound, bound-free, and free-free transitions into account. The emissivity and opacity in the EUV wavelength region mainly originates from the bound-bound transitions. We calculate the bound-bound emissivity η ν and opacity κ ν of plasmas at the radiation frequency ν from the level population as and η ν = hν ul 4π N ua ul L (ν), (2) κ ν = hν ul 4π (N lb lu N u B ul ) L (ν), (3) where A and B are Einstein s coefficients, N u and N l denote the population of the upper and lower level of the transition, respectively. L (ν) is the spectral profile function. We calculate the spectral emissivity and opacity including the profile of each transition array. The emission lines of Sn ions sometimes refer to an unresolved transition array (UTA) [26], for which the averaged energy of lines, E UT A, and the width as the standard deviation E UT A are defined assuming a Gaussian distribution of lines, E UT A = (gi A ij ) E ij gi A ij, (4) 7

8 and [ g i A ij (E ij E UT A ) 2] E UT A =, (5) gi A ij where A ij and E ij are the radiative decay rate and energy, respectively, of each fine structure transition and g i is the statistical weight of the upper level. However, in the case of emission lines of Sn ions in the λ = 13.5nm band, a detailed spectral structure is observed, and moreover, this structure is found to have a significant effect on the efficiency. Therefore, we calculate the spectral profile function from the distribution of fine structure transitions for the strong lines. In the case of the EUV emission of Sn ions, the most important 4d 4f +4p 4d transition array consists of a large number of fine structure transitions. The number of fine structure lines is more than 10 3, except in the case ions, which have closed shell structure. Typical separation between fine structure lines is of the order of 1mÅ, which is smaller than the line width, determined by thermal Doppler broadening and Stark broadening. For a plasma temperature of 10eV and an effective life time of the upper state of emission of s 1, the line width is estimated to be approximately 5mÅ. Therefore, the energy of a photon emitted from one fine structure line can be redistributed through reabsorption by adjacent lines, and eventually, the emission spectrum will be determined by the spectral distribution of the transition array. Hence, we calculate the spectrum using an energy grid of 0.1 ev, by averaging the contribution of each fine structure transition within the grid. Weak lines as well as lines outside the EUV wavelength region are treated as a UTA. 3.1 Selection of set of atomic levels in the CR model Before calculating the level population of the state of plasma by solving the set of rate equations, we have to select an appropriate set of atomic levels. In the case of plasmas in LTE, the ratio between the abundance of the nth and (n + 1)th charge states, R n, is determined by the Saha equation as follows; ( ) 2πme k 3/2 Te 3/2 Q n + 1 R n = 2 h 2, (6) n e Q n where T e, and n e are the electron temperature and density. m e, h and k are the electron mass, Planck and Boltzmann constants, respectively. Q n is the partition function of the nth charge state given as 8

9 Q n = j ( g n,i exp E ) n,i, (7) kt e where E n,i is the energy of the ith level of the nth charge state [27]. In order to obtain the accurate ion abundance using eq. 6, R n should be accurately determined over all charge states, which in turn can be achieved by determining the accurate ratio of Q n between each pair of adjacent charge states. It has already been shown that even in the case of non-lte plasmas, the calculated ion abundance converges with the increase in the number of levels in the model [28]. This condition can be satisfied if one includes the low energy levels, which are likely to have a large population. We define a group of configurations by a set of states, which have the same core configuration, as shown in fig. 1. In the present model, the range of principal and orbital quantum numbers of states is set as n 8 and l 3, respectively. The groups of configurations are listed in table 1. In order to determine the number of groups to be included in the model, we investigate the convergence of the LTE emission intensity for each ion with respect to the number of groups of configurations. We show a result for Sn 10+ as an example. We assume LTE, because for which the upper limit of the effect of the population of the multiply excited configurations and satellite line emission is obtained. Figure 3 shows the calculated typical averaged charge of Sn plasmas as a function of electron temperature for different ion densities. It is indicated that in the case of n i = cm 3, and T e = 25eV, Sn +10 ions is likely to have a large population. Figure 4 shows the total statistical weight and partition function of a Sn 10+ ion, which are calculated using the set of energy levels shown in fig. 1. The partition function is calculated at T e = 30eV. The number of levels is apparently too small, if only the one electron excited configurations, 4d 3 nl, are included. On the other hand, if 5 groups of configurations are included, most of the levels below the ionization limit 200eV are included in the model. We then investigate the dependence of the emission intensity from Sn +10 into the energy range between 50 to 150eV on the number of groups of configurations as shown in fig. 5. In the case of T e 25eV, the emission intensity is found to be underestimated if only the one electron excited configurations 4d 3 nl are included. On the other hand, more than 70% of the emission can be included by considering 5 groups of configurations. The emission is found to increase significantly by including 4p 5 4d 4 nl and 4d 2 4fnl configurations, indicating the contribution of 9

10 spectator satellite lines such as 4p 5 4d 3 nl(4p 4d) and 4d 2 4f 2 nl(4d 4f). At higher temperature, the emission increases by inclusion of still large number of configurations such as 4p 4 4d 5 nl and 4p 5 4d 3 4fnl, due to the increased contribution of inner-shell satellite lines. We repeat this analysis for each ion to confirm that the present method allows one to include a sufficient number of atomic states with low excitation energy and likely to populate for each charge state. Eventually, we determine the number of groups of configurations to be 5 for each charge state, for the calculation of the level population as well as the emissivity and opacity. 3.2 Calculation of the wavelength and intensity of emission lines We calcualte the the wavelength and profile of the emission lines by considering the effect of CI. Although the characteristic feature of a Sn spectrum is attributed to the CI between the upper states of the emission, 4d N 1 4f and 4p 5 4d N+1, there are more possible interacting configurations. We investigate the convergence of the calculated wavelength and transition probability of 4d 4f and 4p 4d transitions with an increase in the number of configurations. We create new configurations, by moving one electron in 4s, 4p, and 4d orbital to outer orbitals, to obtain 4d N 1 nl, 4p 5 nl and 4snl configurations, respectively. We find that the 4p 5 4f configuration has a considerable effect on the 4d 4f and 4p 4d transitions. We also investigate the CI with configurations generated by two electron substitution in the N-shell to determine the effect of 4p 4 4d N+2, 4p 4 4d N+1 4f, and 4p 5 4d N 1 4f 2. The effect of CI in the case of Sn 12+ is summarized in fig. 6. Results of calculation including up to 9 configurations, which have the significant effect of CI. We note that even we include more configurations created by another one of two electron substitution, change in the spectrum is small. A similar trend is observed in the results for other charge states. Figure 7 shows that energies of both 4d 4f and 4p 4d transitions increase 2 ev by including 4p 5 4f and 4p 4 4d 4 configurations and decrease 1eV and 4eV by including 4p 5 4d4f and 4d 4 4d 3 4f configurations, respectively. Interestingly, the averaged width of the transition array, which is calculated from the distribution of fine structure transitions using eq. 5, does not depend on the number of configurations. To calculate the emissivity and opacity of the plasma, the accurate wavelength, radiative rate, and spectral profile have to be determined not only for resonance lines but also satellite lines from multiple excited configurations. Unfortunately, it is difficult to obtain the convergence 10

11 of these values with respect to the effect of CI for all emission lines. In particular, in the case of ions with a half-filled 4d subshell, the number of fine structure levels is large, and the CPU time and memory size required for the computation exceed the capacity of present computers. Therefore, we decide that we calculate the wavelengths and radiative rates of emission lines using a relatively simple set of configurations such that including 4d N, 4d N 1 (4f 5p 5f), and 4p 5 4d N+1, and apply corrections based on comparisons with experiments, as described in the subsections 4.1 and Validation of atomic model through comparison with experimental results We validate the atomic model and atomic data to obtain reliable values of emissivity and opacity. In the case of lighter elements, atomic data has been evaluated through a detailed comparison between a number of calculations and experimental results. In contrast, the measurement of energy levels and rate coefficients has been carried out only for limited cases, due to the complexity of the atomic processes in Sn plasmas. We firstly verify calculated wavelength of resonance lines of Sn ions ranging from Sn 8+ through Sn 13+ by specially designed experiment based on CXS [29]. However, besides the resonance lines, the wavelength of satellite lines, which contribute significantly to the emission, has to be determined. Therefore after investigating the wavelength of emission lines theoretically, we also compare the calculated spectrum assuming LTE with that of EUV sources. Although, only a few experimental studies dedicated to the measurement of atomic data of Sn have been reported, a large number of experimental results for EUV sources are available. We correct the wavelength of emission lines to obtain a reasonable agreement between calculated and experimental spectra. In addition, we compare the calculated opacity of Sn with the measured opacity of the radiatively heated Sn sample. 4.1 Comparison of calculated emission spectrum with spectrum observed from CXS In the spectrum of an EUV source, emission lines from multiple charge states appear simultaneously in a same wavelength region. These lines overlap with each other. Therefore, the identification of an emission line from a specific charge state and its comparison with the calcu- 11

12 lated line is almost impossible. In CXS experiments, each single charge state of Sn ion is selected, and the emission spectrum after charge exchange collision with Xe and He is observed. In CXS, EUV spectra is measured within the wavelength range from 6 to 24 nm. Emission arising from 4d 4f, 4d 5p, and 4d 5f transitions for each charge state through Sn 7+ to Sn 20+ are measured separately. The spectral distribution of the total ga value of the combined 4d 4f + 4p 4d transition array is calculated and compared with the experimental spectrum of Sn obtained after the charge exchange collision with Xe, as shown in fig. 8 [30]. The theoretical and experimental spectra are found to be similar, except for the central wavelength for which calculated wavelength is systematically shorter than experiment. We find the amount of the wavelength shift using the least square method. We take the experimental emission intensity typically between 12 to 14nm, which corresponding to the 4d 4f + 4p 4d transition array, to determine the shift required to minimize the squared error. Averaged wavelength of transitions from Sn 8+ to Sn 13+ and shift are listed in table 2. It is found that difference between calculated and experimental wavelengths is within the range of 0.5 to 0.8 nm depending on the charge state. The averaged difference is 0.59 nm or 4.7 ev. A larger difference of 0.7 nm or 5.0 ev is obtained with the experimental data from the charge exchange collisions between Sn ions and He [31]. 4.2 Estimation of wavelength correction for satellite lines A comparison with CXS results suggests that the calculated wavelength of resonance lines of Sn ions should be shifted nm toward longer wavelengths. This suggests that wavelength of spectator satellite lines should also be shifted, because the wavelength of the spectator satellite lines should converge to that of the resonance line at the limit of the principal quantum number of the spectator electron n. We calculate the wavelength and transition probability of each spectator satellite line of 4d 4f, 4p 4d, 4d 5p, and 4d 5f transitions, using HULLAC taking the effect of CI into consideration, by including the configurations with same core, such as 4d N, 4d N 1 nl, 4p 5 4d N, 4d N 2 (4f 5p 5f)nl, and 4p 5 4d N 1 nl configurations. We also calculate the wavelength and transition probability of inner-shell satellite lines with a set of configurations obtained by removing one electron from 4s and 4p orbitals. 12

13 Results of calculation for Sn 10+ are shown in fig. 9. As expected, the wavelength of the spectator satellite lines is slightly longer than that of the resonance line and approaches the wavelength of the resonance line as the principal quantum number of the spectator electron increases. In fig. 9, the effect of a spectator electron in 4f orbital is strong, resulting in a large difference of the transition energy and A value from those of the resonance. The emission from such configurations with double excitation in the n = 4 shell may contribute significantly to the EUV emission, because of their relatively low excitation energy and large statistical weight. The spectral profile of inner-shell satellite lines of Sn 11+ is shown in fig. 10. It is found that 4d 2 4f 4p 5 4d 3 4f and 4d 2 4f 4d 2 4f 2 transition arrays have a width of 6.4 and 4.7 ev, respectively, which are twice as broad as the corresponding 4d 4f and 4p 4d resonance lines. These spectral profiles may result in short wavelength tail (< 13nm) in the EUV emission, which is inconsistent with the feature of experimental spectrum. After the investigation of LTE spectrum, the magnitude of wavelength shift is set to be -10 ev for inner-shell satellite lines, as also discussed in following subsection. 4.3 Calculation of LTE spectra and comparison with EUV sources Using the present model, we calculate the population of configuration averaged levels, based on the calculated level energy from HULLAC firstly without CI. We in turn calculate the emissvity and opacity using A and B coefficient and L(ν) from calculations with CI. We note that the calculated transition energy of 4d 4f and 4p 4d transitions arrays, which mainly contribute to the EUV emission, is considerable smaller if calculated without the effect of CI. Furthermore, these transition arrays sometimes have a large spectral width of 10eV. Therefore, we correct the emissivity and opacity at the radiation frequency ν by assuming LTE over the fine structure levels and apply the correction to the population of the upper level as ( ) hν/e Eu N u (ν) = N u exp, (8) kt e where E u is the energy of the configuration averaged level, calculated without considering the effect of CI. If we consider a plasma sphere in LTE, the spectral emission intensity can be calculated 13

14 analytically from the spectral opacity of the plasma as [32] I ν = I νp [ 1 1 2τ 2 ν ( ) ] τ ν 2τν 2 exp ( 2τ ν ). (9) Although plasma used for the EUV source is in the non-equilibirium state with and is spatially non-uniform, the emission spectrum is sometimes similar to the spectrum calculated assuming LTE. This is due to the fact that to obtain the maximal efficiency and output power, conditions are selected so that the plasma to have the optical depth 1. As a result, the photo excitation brings the state of the plasma close to LTE. We calculate the LTE spectrum by changing the electron temperature, T e, ion density, n i, and size of the plasma, r. We apply the spectral profile of emission lines calculated using HULLAC taking into account the effect of CI by including 4d N, 4p 5 4d N+1, 4d N 1 nl, 4d N 2 (4f 5p 5f)nl, and 4p 5 4d N 1 nl configurations for each charge state. We compare the calculated spectrum with the experimental spectrum obtained by Tao [33], which was observed by irradiating a solid Sn target by 100 ns long CO 2 lasers pulse with an intensity of W cm 2. We determine the energy shift of the resonance and spectator satellite lines using the least square method. We find that the squared error minimizes if those lines are shifted by 3.1eV, while T e = 18eV, n i = cm 3 and r = 0.012cm. We also make comparison with an experimental result obtained by Fomenkov [14] and find a reasonable agreement using the same energy shift for emission lines at T e = 18eV, n i = cm 3 and r = 0.006cm. The results are shown in fig. 11. The spectrum obtained by Fomenkov is broader than that obtained by Tao indicating a slightly larger optical thickness. In the following calculations, we apply an energy correction of 3.1eV to the resonant 4d 4f and 4p 4d transitions as well as spectator satellite lines such as 4d 4f(nl) and 4p 4d(nl) transitions from Sn 5+ to Sn 13+ ions, to maintain consistency between the wavelengths of resonance and satellite lines. The energy shift of emission lines determined from the comparison of calculation with LTE emission spectra is smaller than those obtained from the comparison with CXS experiment. This may arise from the fact that CXS spectra may contain satellite lines, as pointed out by the comparison with spectra measured using Electron Beam Ion Trap (EBIT) [34]. CXS spectra, in which upper states are populated through a cascade after a charge exchange collision, is shown 14

15 to be broader, than EBIT spectra, in which the emission lines are excited only from the direct electron collision from the ground state. The averaged wavelength obtained from CXS is slightly longer than that obtained from EBIT. In addition, we apply the same energy correction to 4d 5p transitions of Sn 11+ and Sn 12+, because 4d N 1 5p configuration in these charge states also interacts with 4d N 1 4f and 4p 5 4d N+1 configurations due to the fact that the wavelength of the 4d 5p transition array is close to that of the 4d 4f + 4p 4d transition array. On the other hand, we apply -10eV of shift for the inner-shell satellite lines by comparing theoretical and experimental spectral profiles to reproduce the experimental cut off structure at the shorter wavelength region of the peak at λ = 13.5nm and obtain rather gentle slope at the longer wavelength region. The energies of resonance lines of Sn 5+ to Sn 13+ used in the following calculation of emissivity and opacity are summarized in table 3 along with transition energies calculated by White [7]. It is shown that for the 4d 4f and 4p 4d transitions from Sn 9+ to Sn 13+, both calculation agrees each other within 1%, except for the 4d 4f transition of Sn 9+ and Sn Comparison of opacity of radiatively heated Sn sample Furthermore, we compare the calculation and experimental results in terms of the transmission of the EUV radiation observed from a Sn sample [35] heated by thermal radiation with a temperature T R = 50eV. The averaged ion density and electron temperature are estimated to be cm 3 and 30eV, respectively. Results of comparison are shown in fig. 12. Although the difference determined from the least square method is smaller when a high temperature is used, the spectral structure, which shows the feature of emission from relatively lower charge states is similar by using a low temperature. This may be attributed to the inhomogeneity of the density and temperature inside the sample. 5 Calculation of radiative properties of Sn plasma 5.1 Dependence of LTE spectra on plasma temperature and size We calculated EUV spectra from the plasma in LTE changing the electron temperature and plasma size to obtain information for the optimization of plasma conditions, after selecting the atomic model and applying spectral the corrections. The temperature dependence of emission spectra is shown in fig. 13. The plasma ion density 15

16 is cm 3. At a low temperature, a broad peak near λ = 14nm is accompanied by peaks of the 4d 5f transitions from lower charge states. As temperature increases, the spectrum becomes narrow, and intense emissions at λ = 13.5nm are observed. The averaged charge of the plasma at T e = 15, 17, 19, and 21eV is 8.6, 9.4, 10.1, and 10.8, respectively. Figure 14 shows that the spectrum becomes broad as the plasma size increases. This is caused by the increase in the optical thickness of the plasma. It is found that intensity at the peak becomes almost equal to the Planck radiation in the case of r = 0.8mm. Thus, the optimization should be carried out to have both a sufficiently large plasma size to obtain maximal radiation intensity, and a relatively small optical depth to maintain narrow emission spectrum to obtain high CE. 5.2 Calculation of spectral emissivity and opacity of Sn plasmas Finally, we calculate the radiative properties of Sn plasmas. Firstly, we calculate the steady-state level population and averaged charge of plasmas using the CR model. Secondly, we calculate the emissivity taking into consideration the detailed spectral profile of emission lines as well as wavelength correction for the emission lines. The results are shown in fig. 15. The averaged charge is used to determine the electron density in the hydrodynamics simulation and subsequently to calculate the conductivity as well as absorption coefficient. The internal ionization energy is useful for determining the specific heat of plasmas. The results show that the calculated averaged charge is same as that reported previously [28]. The spectral efficiency, i.e., the ratio of emission power inside the 2% bandwidth at λ = 13.5nm to the total emission power has more structure, with islands of temperature and density region, in which relatively higher efficiency is obtained. However, the maximal spectral efficiency is generally obtained under plasma conditions, for the averaged charge z = 10, and the efficiency decreases as density increases because of the broadening of the emission lines by increased satellite line contribution. 6 Conclusion We have developed an atomic model of Sn through detailed theoretical and experimental investigations of the emission properties of Sn plasmas in the EUV wavelength region. We have found that the 4d (4f 5p 5f) and 4p 4d resonance and satellite lines of Sn 5+ to Sn 13+, including 16

17 spectator satellite lines and inner-shell satellite lines between multiple excited configurations, mainly contribute to the emission. Although, complex Sn spectra can be modeled using calculated atomic data, the accuracy of calculation is not always satisfactory for the calculation of the emission spectrum and subsequent optimization the EUV sources. We have also determined the wavelength correction for the emission lines through the comparison of results of different experiments, and finally obtained a reasonable agreement between calculated and experimental results. However, still very few results of the direct measurement of atomic data and radiative coefficients of the plasma is reported, which may limit the accuracy of the simulation. Further researches on modeling atomic radiation processes in plasmas is required for the development of light sources in the UV to x-ray wavelength region. Acknowledgement A part of this study was carried out under the auspices of the Leading Project promoted by MEXT and Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (JSPS). One of the authors (A.S.) is grateful to Dr. M. Yamagiwa, Dr. A. Yokoymama, Dr. T. Kimura, Dr. S. Kawanishi, and Dr. T. Tajima of the Kansai Photon Science Institute, Japan Atomic Energy Agency, for their support and encouragement, and Dr. T. Kato, T. Kagawa, R. More, H. Nishimura, S. Fujioka, and Y. Izawa for their useful discussions. References [1] EUV Sources for Lithography, edited by V. Bakshi, 2005 SPIE press. [2] A. Cummings, G. O Sullivan, P. Dunne, E. Sokell, N. Murphy, J. Whoite, K. Fahy, A. Fitzpatrick, L. Gaynor, P. Hayden, D. Kedzierski, D. Kilbane, M. Lysaght, L. McKinney, and P. Sheridan, J. Phys. D37, 2376 (2004). [3] J. White, P. Dunne, P. Hayden, F. O Reilly, and G. O Sullivan, Appl. Phys. Lett. 90, (2007). [4] J. White, A. Cummings, P. Dunne, and G. O Sullivan, J. Appl. Phys. 101, (2007). [5] K. Nishihara, A. Sunahara, A. Sasaki, M. Nunami, H. Tanuma, S. Fujioka, Y. Shmada, K. Fujima, H. Furukawa, T. Kato, F. Koike, R. More M. Murakami, T. Nishikawa, V. Zhakhovskii, 17

18 K. Gamata, A. Takata, H. Ueda, H. Nishimura, Y. Izawa, N. Miyanaga, and K. Mima, Phys. Plasmas 15, (2008). [6] A. Bar-Shalom, M. Klapisch, and J. Oreg, J. Quant. Spectrosc. Radiat. Transf. 65, 91 (2001). [7] J. White, P. Hayen, P. Dunne, A. cummings, N. Murphy, P. Sheridan, and G. O Sullivan, J. Appl. Phys. 98, (2005). [8] N. R. Böwering, M. Martins, W. N. Partlo, and V. Fomenkov, J. Appl. Phys. 95, 16 (2004). [9] M. Poirier, T. Blenski, F. de Gaufridy de Dortan, and F. Gilleron, J. Quant. Spectrosc. Radiat. Transf. 99, 482 (2006). [10] A. Sasaki, K. Nishihara, M. Murakami, F. Koike, T. Kagawa, T. Nishikawa, K. Fujima, T. Kawamura, and H. Furukawa, Appl. Phys. Lett. 85, 5857 (2004). [11] J. G. Rubiano, R. Florido, C. Bowen, R. W. Lee, and Y. Ralchenko, HEDP 3, 225 (2007). [12] W. Svendsen and G. O Sullivan, Phys. Rev. A50, 3710 (1994). [13] F. G. Dortan, J. Phys. B40, 599 (2007). [14] I. V. Fomenkov, D. C. Brandt, A. N. Bykanov, A. I.Erashov, W. N. Partlo, D. W. Myers, N. R. Böwering, N. R. Farrar, G. O. Vaschenko, O. V. Khodkykin, J. R. Hoffman, C. P. Chrobak, S. N. Srivastava, D. J. Golich, D. A. Vidusek, S. D. Dea, and R. R. Hou, Proc. SPIE, Alternative Lithographic Technologies, 7271, (2009). [15] Y. Ueno, G. Soumagne, A. Sumitani, and A. Endo, Appl. Phys. Lett (2007). [16] T. Kawamura, S. Sunahara, K. Gamada, K. Fujima, F. Koike, H. Furukawa, T. Nishikawa, A. Sasaki, T. Kagawa, R. More, T. Kato, M. Murakami, V. Zhakhovskii, H. Tanuma, T. Fujimoto, Y. Shimada, M. Yamaura, K.Hashimoto, S. Uchida, R. Matsui, Y. Tao, M. Nakai, K. Shigemori, S. Fujioka, K. Nagai, T. Norimatsu, H. Nishimura, K. Nishihara, N. Miyanaga, and Y. Izawa, Proc. SPIE 5374, 918 (2004). [17] H. Tanaka, A. Matsumoto, K. Akinaga, A. Takahashi, and T. Okada, Appl. Phys. Lett. 87, (2005). 18

19 [18] T. Higashiguchi, N. Dojyo M. Hamada W. Sasaki, and S. Kubodera, Appl. Phys. Lett. 88, (2006). [19] T. Okuno, S. Fujioka, H. Nishimura, Y. Tao, K. Nagai, Q. Gu, N. Ueda, T. Ando, K. Nishihara, T. Norimatsu, N. Miyanaga, Y. Izawa, and K. Mima, Appl. Phys. Lett. 88, (2006). [20] P. Hayden, A. Cummings, N. Murphy, G. O Sullivan, P. Sheridan, J. White, and P. Dunne, J. Appl. Phys. 99, (2006). [21] A. F. Nikiforov, V. G. Novikov, V. B. Uranov, and A. Iacob, Quantum-Statistical Models of Hot Dense Matter: Methods of Computation and Equation of State, Birkhäuser, Boston, [22] A. Cummings, G. O Sullivan, P. Dunne, E. Sokell, N. Murphy, and J. White, J. Phys. D. 38, 604 (2005). [23] W. Svensden and G. O Sullivan, Phys. Rev. A50, 3710 (1994). [24] G. O Sullivan and P. K. Caroll, J. Opt. Soc. Am. 71, 227 (1981). [25] M. Itoh, T. Yabe, and S. Kiyokawa, Phys. Rev. A35, 233 (1987). [26] C. Bouche-Arnoult, J. Bouche, and M. Klapisch, Phys. Rev. A31, 2248 (1985). [27] Ya. B. Zelfdovich and Y. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Academic Press, [28] A. Sasaki, A. Sunahara, K. Nishihara, T. Nishikawa, K. Fujima, F. Koike, and H. Tanuma, HEDP 5, (2009). [29] H. Tanuma, H. Ohashi, E. Shibuya, N. Kobayashi, T. Okuno, S. Fujioka, H. Nishimura, and K. Nishihara, Nucl. Inst. and Meth. Phys. Res. B235, 331 (2005). [30] H. Ohashi, to be published. [31] H. Ohashi, H. Tanuma, S. Fujioka, H. Nishimura, A. Sasaki, and K. Nishihara, J. Phys. Conf. Ser. 58, 235 (2007). 19

20 [32] M. Murakami, J. X-ray Sci. & Tech. 2, 127 (1990). [33] Y. Tao, M.S. Tillack, K. L. Sequoia, R. A. Burdt, S. Yuspeh, and F. Najamabadi, Appl. Phys. Lett (2008). [34] H. Ohashi, S. Suda, H. Tanuma, S. Fujioka, H. Nishimura, K. Nishihara, T. Kai, A. Sasaki, H. A. Sakaue, N. Nakamura, and S. Ohtani, J. Phys. Conf. Ser. 163, (2009). [35] S. Fujioka, H. Nishimura, K. Nishihara, A. Sasaki, A. Sunahara, T. Okuno, N. Ueda, T. Ando, Y. Tao, Y. Shimada, K. Hashimoto, M. Yamaura, K. Shigemori, M. Nakai, K. Nagai, T. Norimatsu, T. Nishikawa, N. Miyanaga, Y. Izawa, and K. Mima, Phys. Rev. Lett. 95, (2005). 20

21 Table 1: Groups of configurations of Sn 7+ to Sn 13+, having a same core configuration with one excited electron in outer orbital. The excitation energy of the core configuration increases from top to bottom. Sn 7+ Sn 8+ Sn 9+ Sn 10+ Sn 11+ Sn 12+ Sn 13+ 4p 6 4d 6 nl 4p 6 4d 5 nl 4p 6 4d 4 nl 4s 2 4p 6 4d 3 nl 4s 2 4p 6 4d 2 nl 4s 2 4p 6 4dnl 4s 2 4p 6 nl 4p 6 4d 5 5snl 4p 6 4d 4 5snl 4p 6 4d 3 5snl 4s 2 4p 6 4d 2 5snl 4s 2 4p 6 4d5snl 4s 2 4p 5 4d 2 nl 4s 2 4p 5 4dnl 4p 6 4d 5 5pnl 4p 6 4d 4 5pnl 4p 5 4d 5 nl 4s 2 4p 5 4d 4 nl 4s 2 4p 5 4d 3 nl 4s 2 4p 6 5snl 4s4p 6 4dnl 4p 6 4d 5 4fnl 4p 6 4d 4 4fnl 4p 6 4d 3 5pnl 4s 2 4p 6 4d 2 4fnl 4s 2 4p 6 4d4fnl 4s 2 4p 6 4fnl 4s 2 4p 4 4d 2 nl 4p 5 4d 7 nl 4p 5 4d 6 nl 4p 6 4d 3 4fnl 4s 2 4p 6 4d 2 5pnl 4s 2 4p 6 4d5pnl 4s 2 4p 6 5pnl 4s 2 4p 5 4fnl 4p 6 4d 5 5dnl 4p 6 4d 4 5dnl 4p 6 4d 3 5dnl 4s 2 4p 6 4d 2 5dnl 4s 2 4p 6 4d5dnl 4s 2 4p 6 5dnl 4s 2 4p 5 5snl 4p 6 4d 5 6snl 4p 6 4d 4 6snl 4p 6 4d 3 6snl 4s4p 6 4d 4 nl 4s4p 6 4d 3 nl 4s4p 6 4d 2 nl 4s 2 4p 5 5pnl 4p 6 4d 4 5s 2 nl 4p 6 4d 3 5s 2 nl 4p 6 4d 2 5s 2 nl 4s 2 4p 6 4d 2 6snl 4s 2 4p 6 4d6snl 4s 2 4p 4 4d 3 nl 4s4p 5 4d 2 nl 4p 6 4d 5 6pnl 4p 6 4d 4 6pnl 4p 6 4d 3 5fnl 4s 2 4p 6 4d 2 5fnl 4s 2 4p 5 4d 2 5snl 4s 2 4p 5 4d5snl 4s 2 4p 5 5dnl 4p 6 4d 5 5fnl 4p 6 4d 4 5fnl 4p 6 4d 3 6pnl 4s 2 4p 6 4d5s 2 nl 4s 2 4p 6 4d5fnl 4s 2 4p 5 4d4fnl 4s4p 6 4fnl Table 2: Comparison of calculated and experimental averaged wavelength in nm of combined 4d 4f + 4p 4d transition array of Sn 8+ to Sn 13+. The differences (wavelength shift) for which squared error is minimized is also listed. ion λ calc. λ exp. shift Sn Sn Sn Sn Sn Sn Table 3: Energy E [ev ] and radiative decay rate A [ s 1 ] for resonant 4d 4f, 4p 4d, 4d 5p, and 4d 5f transitions of Sn ions. Numbers in parentheses are the average energy of the transition array from calculations by White [7]. 4d 4f 4p 4d 4d 5p 4d 5f ion E A E A E A E A Sn (63.61) (80.67) Sn (71.26) (75.78) Sn (78.62) (82.38) Sn (83.55) (86.70) Sn (86.46) (89.13) Sn (89.39) (90.90) Sn (91.84) (92.60) Sn (92.80) (92.94) Sn (92.46) (93.29)

22 Figure 1: Energy level diagram of Zr-like Sn (Sn 10+ ). 5 lowest groups of configurations, 4d 3 nl, 4d 2 5snl, 4p 5 4d 4 nl, 4d 2 4fnl, and 4d 2 5pnl, are shown, along with the ionization limit of each configurations. The arrows indicate transitions in the EUV wavelength region. Transitions between excited states are indicated using dotted lines. Figure 2: Energy of excited configurations of Sn ions and their dependence on ion charge. The configuration of the excited states is labeled with respect to the ground state. 22

23 Figure 3: Averaged charge of Sn plasmas in LTE as a function of ion density and electron temperature. Figure 4: (a) Total statistical weight and (b) partition function of Sr-like Sn (Sn 12+ ) as a function of the excitation energy of the level is indicated in the horizontal axis. Results for different number of groups (1, 5, and 30) of levels in the model are shown. 23

24 Figure 5: Emission intensity from Sn 10+ per ion as a function of number of groups of configurations included in the model for (a) T e = 20eV, (b) 25eV, and (c) 30eV. 24

25 Figure 6: Spectral distribution of combined 4p 4d + 4d 4f transitions of Sn 12+, calculated by increasing the magnitude of the effect of CI. Configurations in the calculations are increased from the bottom to top. The bottom line graph corresponds to the result of calculation including minimal set of configurations; 4d 2, 4d4f, and 4p 5 4d 3, and calculations are performed adding new configuration(s) indicated at the left side of the figure. 25

26 Figure 7: (a) Energy of 4d 4f (closed circles) and 4p 4d (open circles) of Sn 12+ from the ground state, calculated by increasing the effect of CI. (b) Width of combined 4p 4d+4d 4f transition array, calculated by increasing the effect of CI. Configurations included in the calculations are same as those in fig.3. Figure 8: Comparison of the spectral distribution of calculated ga(4d 4f + 4p 4d) and experimental spectrum obtained from CXS for (a) Sn 11+, (b) Sn 10+, and (c) Sn 9+. Calculation is carried out using HULLAC, including the ground configuration 4d i, and excited configurations such as 4d i 1 (4f 5p 5f) and 4p 5 4d i+1 configurations. 26

27 Figure 9: Calculation of (a) energy and (b) radiative lifetime of 4d 4f (open circles) and 4p 4d (closed circles) transition arrays. Values for resonance line of Sn 11+, indicated by res. and satellite lines of Sn 10+ with one spectator electron in outer orbital are shown at the side of the graph. Figure 10: Spectral distribution of ga of resonance and inner-shell satellite lines of Sn

28 Figure 11: Comparison of experimental (thick dotted line) and theoretical (thin solid line) Sn emission spectra assuming LTE, from (a) Tao [33] and (b) Fomenkov [14]. Figure 12: Comparison between theoretical and experimental transmission of Sn plasmas. Results of calculation for two different temperature, at (a) 26eV and (b) 36eV are shown. 28

29 Figure 13: Temprature dependence of the emission spectra from Sn plasma in LTE. n i = cm 3, radius of the sphere r = 0.2mm. T e for each case is shown in the graph. Figure 14: Dependence of the emission spectra from Sn plasma in LTE on the size of the plasma. n i = cm 3, T e = 19eV. Radius of the sphere, r for each case is shown in the graph. 29

30 Figure 15: Calculated (a) averaged charge, (b) ionization energy [ev/ion], (c) spectral efficiency, (d) in-band emissivity [W cm 3 ], and (e) in-band opacity [cm 1 ] of Sn plasmas for a range of electron temperatures and ion densities, T e = 5 250eV and n i = cm 3. The dotted line in the graph of spectral efficiency (c) corresponds to the condition where the averaged charge is