Analysis of the x-ray spectrum emitted by laser-produced plasma of dysprosium

Transcription

1 Marcus et al. Vol. 24, No. 5/ May 2007/J. Opt. Soc. Am. B 1187 Analysis of the x-ray spectrum emitted by laser-produced plasma of dysprosium Gilad Marcus, Einat Louzon, Zohar Henis, and Shlomo Maman Soreq Research Center, Yavne, Israel Pinchas Mandelbaum Jerusalem College of Engineering, Ramat Beth Hakerem, 1035 Jerusalem, Israel Received November 14, 2006; revised January 22, 2007; accepted January 23, 2007; posted January 2, 2007 (Doc. ID 7611); published April 17, 2007 A detailed analysis of the x-ray spectrum Å emitted by laser-produced plasma of dysprosium (Dy) is given using ab initio calculations with the HULLAC relativistic code and isoelectronic trends. Resonance 3d 4p, 3d nf (n=4 to 7), 3p 4s, and 3p 4d transitions of Ni I-like Dy XXXIX and neighboring ion satellite transitions (from Dy XXXIV to Dy XL) are identified Optical Society of America OCIS codes: , INTRODUCTION Laser-produced plasmas of high-z elements are powerful sources of radiation in the x-ray region. Moreover, spectra of highly ionized heavy ions are actively under study for microlithographic light sources 1 and extreme ultraviolet (XUV) laser (e.g., Ref. 2). Our previous works have already dealt with the XUV spectra from lower-z rare-earth laser-produced plasmas: lanthanum, praseodymium, 3 and barium. 4 In the present work we perform a detailed analysis of the spectrum emitted from dysprosium laser-produced plasma. The present work fills the gap between the previous studies of lower-z lanthanide elements spectra 3 5 and the spectra of higher-z transition metal elements. 6 It confirms the isoelectronic trends observed in the previous works. In particular, the progressive transition from LS to jj coupling for the 3d 4f pseudocontinuum transitions array is confirmed. Burkhalter et al. 5 have described a spectrum of laser-produced plasma of dysprosium in their pioneering work. But only six lines pertaining to Ni I-like 3d 4p and 3d 4f transitions were given and identified there. 2. EXPERIMENT The laser-produced plasma is generated by the irradiation of intense short laser pulses on solid dysprosium targets. The laser generates 160 mj, 10 ps pulses at a repetition rate of 10 Hz. This laser is based on a Ti:sapphire oscillator generating 45 fs pulses at a wavelength of 800 nm and with a spectral width of 35 nm. The 45 fs pulses are stretched to about 200 ps and amplified through a regenerative amplifier and two successive fourpass amplifiers. After amplification the laser is recompressed to a pulse length of about 10 ps. The laser pulse is focused on the dysprosium target to a focal spot of about 100 m diameter, producing a laser intensity of W/cm 2. The plasma formed emits intense short bursts of x rays. The x rays were separated from the visible light with a 1 m Parylene-n film coated with 200 Å of aluminum. After the Parylene-n window, the x ray was dispersed by a rubidium acid phthalate (RAP) crystal and recorded on Kodak direct exposure film (DEF). This spectrum was digitally scanned with a 16-bit scanner. To obtain relative intensities, we scanned a Kodak step-density filter with the film and used the Kodak DEF calibration given in Ref. 7. We also took into account the variations in relative sensitivity of the film versus wavelength according to Ref. 7. The wavelengths were calibrated using known 1s np transition lines of H and He-like ions of magnesium, aluminum, and silicon targets. 3. THEORY The spectrum was analyzed by comparison of measured wavelength and intensities with ab initio computations. In some cases, we also used the regularities along the isoelectronic sequences using the previous published spectra. 3,4 Full intermediate coupling calculations, including configuration interactions for the transitions wavelength and gf values, were carried out using the HUL- LAC computer package. 8 These calculations were performed for lines belonging to the Ni-like Dy XXXIX (ground state 3p 6 3d 10 ) and for some well-resolved lines belonging to Co-like, Cu-like, and Zn-like ions (ground states 3p 6 3d,3p 6 3d 10 4s, and 3p 6 3d 10 4s 2, respectively). However, most of the observed spectral features are in fact unresolved transition arrays (UTA). UTAs arise from the coalescence of many lines into one or several broad unresolved arrays. The coalescence of the lines may arise from the limited instrumental resolution or from the physical broadening (Doppler, Stark, ) of close individual spectral lines. To compare an observed UTA with a computed transition array, it is useful to compute the two first moments of the computed array distribution: /07/ /$ Optical Society of America

2 1188 J. Opt. Soc. Am. B/ Vol. 24, No. 5/ May 2007 Marcus et al. 2 = g j A ji ji =, 1 g j A ji g j A ji ji 2, 2 g j A ji where A ji is the Einstein coefficient for spontaneous emission from level j to level i, g i is the statistical weight of the upper level, and ji is the wavelength of the transition from j to i. If the transition array splits into several subarrays, we can perform the summations for the wavelengths in the desired ranges to obtain the mean wavelength and variance of each subarray. Fig. 1. Recording of the x-ray spectrum in the 5.0 to 6.6 Å wavelength range emitted by a dysprosium laser-produced plasma. Labels refer to Table 1. Table 1. Results for Identified Transitions in the Spectrum of Dysprosium Laser-Produced Plasma in the Å Wavelength Range

3 Marcus et al. Vol. 24, No. 5/May 2007/J. Opt. Soc. Am. B 118 It must be stressed that closed formulas have been developed for the first two moments of a transition array, particularly for the cases where the transition array does not split into subarrays and for the case where one or several spin-orbit splitting interactions are the dominant features of the configuration, so that the transition array actually splits into several subarrays called SOSA (spinorbit-split array). 10 In the later case, the closed formulas were obtained by summation on the j j subspace of the configurations, and the results are valid where the j j coupling scheme applies. However, as shown in Ref. 3 particularly for 3d 4f Cu I-like transitions, for the dysprosium ions considered here, one is close neither to pure LS nor to j j coupling. For this reason, we did not use the UTA and SOSA formalism here. 4. RESULTS The results of the computations and the line identification are given in Table 1 for the wavelength range from 5.0 to 6.6 Å. The first column gives a label that identifies the line (or transition array) in Fig. 1. The next two columns display the experimental wavelength in angstroms and the relative line intensity in arbitrary units. The next three columns give the results of the theoretical calculations and identification: the isoelectronic sequence of the emitting Dy ions (I.S.) and the upper and lower levels for the line transition (upper and lower configurations for transition arrays). The last four columns give the transition wavelength in angstroms (the mean transition wavelength in the case of the transition array), the calculated Fig. 2. Experimental spectra superimposed with synthetic spectra showing the result of the computations of the 3d 3d 8 5f [Fig. 2(a)] and 3d 4s 3d 8 4s5f [Fig. 2(b)] transition array. The Ni-like 3d 10 3d 3/2 5f 5/2 J=1 transitions are shown for reference. Fig. 3. Recording of the x-ray spectrum in the 6.8 to.2 Å wavelength range emitted by a dysprosium laser-produced plasma. Labels refer to Table 2. Table 2. Results for Identified Transitions in the Spectrum of Dysprosium Laser-Produced Plasma in the Å Wavelength Range No. exp Å I exp I. S. Upper Lower th (Å) ma gf g A ji Ni I 3p 3/2 3d 10 4d 5/2 J=1 3p 6 3d Cu I 3p 1/2 3d 10 4s4d 3/2 J=3/2 3p 6 3d 10 4s Zn I 3p 3/2 3d 10 4s 2 4d 5/2 J=1 3p 6 3d 10 4s Ga I 3p 3/2 3d 10 4s 2 4p4d 5/2 3p 6 3d 10 4s 2 4p Ni I 3p 1/2 3d 10 4s J=1 3p 6 3d Cu I 3p 1/2 3d 10 4s 2 J=1/2 3p 6 3d 10 4s Co I 3p 6 4 4f 5/2 5/2 3p p 6 4 4f 5/2 5/2 3p p 6 4 4f 5/2 7/2 3p Co I 3p 6 2 4f 5/2 3/2 3p p 6 4 4f 5/2 3/2 3p Ni I 3p 6 3d 8 4s4f 3p 6 3d 4s (15) Ni I 3p 6 4f 5/2 J=1 3p 6 3d Cu I 3p 6 3d 4s4f 3p 6 3d 10 4s (14) Ni I 3p 3/2 3d 10 4s J=1 3p 6 3d

4 110 J. Opt. Soc. Am. B/ Vol. 24, No. 5/ May 2007 Marcus et al. variance, in må in the case of the transition array, the gf value for the line transition, and the sum gj A ji in the case of the transition array. Figures 2(a) and 2(b) show an enlarged portion of the experimental spectrum (from 5.7 to 6.1 Å) superimposed with the calculated 3d 3d 8 5f [Fig. 2(a)] and 3d 4s 3d 8 4s5f [Fig. 2(b)] transition array. This wavelength range corresponds to features 12 and 13 in Table 1. Both calculated arrays have been shifted by 15 må toward longer wavelengths. Indeed, the discrepancy between the measured and the calculated wavelengths can arise from many factors. First, wavelengths are measured with an accuracy of about 5 må due mainly to reference wavelength limitations. Second, calculated wavelengths obtained by the HULLAC code have inherent inaccuracies that among others, arise, from the central field approximation and the introduction of only partial configuration interaction effects. Nevertheless, many previous spectroscopic studies of highly ionized heavy-ion spectra have been performed using the HULLAC ab initio calculations and have been confirmed by isoelectronic regularities. Thus there is no ambiguity in the identifications besides the blending. Clearly, the experimental spectrum cannot be reproduced by the Co-like 3d 3d 8 5f alone. The same kind of satellite transitions have been observed in the x-ray laser-produced spectra of heavier elements. 11 Figure 3 gives the spectrum obtained in the 6.8 to.2 Å wavelength range. This wavelength range includes a wide, intense, and nearly structureless feature around the Ni-like 3d 4f transitions. It partly saturated the recorded spectrum. This pseudocontinuum has been analyzed for laser-produced plasma of higher-z elements. 6 It is explained as a superposition of UTAs pertaining to 3d 4f transitions in the Dy 33+ to Dy 37+ isoelectronic from As I to Cu I. For each ionic species, the blending of the many lines arising from the 3d 4f transitions with different electron spectator configurations causes the coalescence of the lines into an unresolved emission band. These bands are shifted by about 50 må toward longer wavelengths when shifting from one ion (e.g., Dy 37+ )toits lower ionized neighbor (e.g., Dy 36+ ). Fig. 4. Calculated 3d 10 4p 2 3d 4p 2 4f transition array in the Zn-like Dy +36 and the two Gaussian curves used in the pseudocontinuum model. Table 3. Calculated Mean Wavelength, Variance and ga of the Subarrays for 3d 4f Transitions in Cu-like to As-like Dysprosium Transition Parameters 3d 10 4s n 4p m 3d 4s n 4p m 4f 3d 10 4s n 4p m 1 4d 3d 4s n 4p m 1 4d4f 3d 10 4s n 4p m 1 4f 3d 4s n 4p m 1 4d4f 2 3d 10 4s n 1 4p m+1 3d 4s n 1 4p m+1 4f Dy +37 n=1, m=0 1 Å Å Å ga 1.07(15) 4.83(15) 5.8(15) 3.0(15) Dy +36 n=1, m=1 1 Å Å Å ga 5.8(15).45(15) 8.81(15) 7.28(15) Dy +35 n=2, m=1 1 Å Å Å ga 2.5(15) 4.61(15) 5.70(15) 1.42(6) Dy +34 n=2, m=2 1 Å Å Å ga 6.75(15) 2.5(16) 3.18(16) 1.78(16) Dy +33 n=2, m=3 1 Å Å Å ga 8.54(15) 6.15(16) 7.71(16) 1.31(6)

5 Marcus et al. Vol. 24, No. 5/May 2007/J. Opt. Soc. Am. B 111 Table 2 gives the identification of the lines or transition arrays appearing in this wavelength range. The 3d 4f pseudocontinuum has been analyzed for laser-produced plasmas of higher-z elements in Ref. 6. For the elements considered there, it was shown that j j coupling SOSA formulas were not applicable to the 3d 4f transitions for the calculation of the mean wavelengths of the subarrays in contradistinction to the 3d nf n 4 case, where it showed excellent agreement with the experiment. 11 For lower-z rare-earth spectra, 3 the 3d 4f pseudocontinuum showed one single peak corresponding to LS coupling. The intermediate case of Dy is treated in the following way: For each ionization state from Dy +33 (As-like, ground 3d 10 4s 2 4p 3 ) to Dy +37 (Cu-like, ground 3d 10 4s), the four lowest transitions arrays with different 4s n 4p m spectator configurations were calculated. A representative calculation for the 3d 10 4p 2 3d 4p 2 4f transition in the Zn-like Dy +36 is shown in Fig. 4: The transition array s Einstein coefficients concentrate in two separate peaks with a relative ga value ranging from 10 to 2. For each transition array, we calculated the mean wavelengths ( 1 and 2 ) and variance (which was found approximately equal for the two peaks). The results of these calculations are given in Table 3. Each transition was introduced in the following model by two Gaussian curves with FWHM of 2.35, mean wavelengths of 1 and 2, and relative amplitudes of 10 and 2. Each of the four transitions into one specific ionic state was given a relative weight of 0.4 3d 10 4s n 4p m 3d 4s n 4p m 4f, 0.3 3d 10 4s n 4p m 1 4d 3d 4s n 4p m 1 4d4f, 0.2 3d 10 4s n 4p m 1 4f Fig. 5. Synthetic spectrum showing the result of the modeling of the 3d 4f pseudocontinuum. Fig. 6. Recording of the x-ray spectrum in the.0 to 10.2 Å wavelength range emitted by a dysprosium laser-produced plasma. Labels refer to Table 4. Table 4. Results for Identified Transitions in the Spectrum of Dysprosium Laser-Produced Plasma in the 10.2 Å Wavelength Range No. exp Å I exp I. S. Upper Lower th (Å) gf Co I 4 4p 3/2 J=5/ Co I 2 4p 3/2 J=3/ Co I 2 4p 3/2 J=3/ Co I 2 4p 3/2 J=5/ Co I 4 4p 3/2 J=5/ Co I 4 4p 3/2 J=7/ Ni I 3d 8 4s4p 3d 4s.44(A) Ni I 3d 8 4s4p 3d 4s.560(B) Co I 2 4p 1/2 J=5/ Co I 2 4p 1/2 J=3/ Ni I 3d 8 4s4p 3d 4s.612(C) Ni I 3d 8 4s4p 3d 4s.668(D) Ni I 3d 8 4s4p 3d 4s.747(E) NI I 3p 6 4p 3/2 J=1 3p 6 3d Cu I 4s 2 4d 5/2 J=3/2 3d 10 4p 3/ Cu I 4p 3/2 0 J=5/2 3d 10 4p 3/ Cu I 4s 3 4p 3/2 J=3/2 3d 10 4s F NI I 3p 6 4p 1/2 J=1 3p 6 3d Cu I 4p 1/2 3 4p 3/2 J=3/2 3d 10 4p 1/ Cu I 4p 1/2 2 4p 3/2 J=1/2 3d 10 4p 1/ Cu I 4p 3/2 2 J=5/2 3d 10 4p 3/ Cu I 4p 1/2 4p 3/2 J=3/2 3p 10 4p 3/ Cu I 4p 1/2 4p 3/2 J=5/2 3p 10 4p 3/ Cu I 4s 2 4p 1/2 J=5/2 3d 10 4s Zn I 4s 2 4p 3/2 J=1 3d 10 4s

6 112 J. Opt. Soc. Am. B/ Vol. 24, No. 5/ May 2007 Marcus et al. 3d 4s n 4p m 1 4f 2, and 0.1 3d 10 4s n 1 4p m+1 3d 4s n 1 4p m+1 4f. The resonant transitions 3d 10 3d 4f (of the Ni-like ion) and 3d 10 4s 2 3d 4s 2 4f (of the Zn-like ion) were introduced with an experimental width corresponding to =2 må. The final synthetic spectrum as given in Fig. 5 was obtained by adding the contribution of each ionic state with a relative weight of 0.4 Dy 38+, 0.8 Dy 37+,1 Dy 36+,1 Dy 35+, 0.6 Dy 34+, and 0.4 Dy 33+. It gives the best agreement with the experimental spectrum. A more elaborate modeling of the pseudocontinuum is beyond the frame of the present work. However, one can observe from Table 3 that the neighboring ionization states give rise to emission bands about 65 må from one another. The overall width of the continuum is a function of the number of emitting ionization states. The contribution of the different configurations within one ionization state causes the filling of the gap between each band because of some little shift of the mean wavelength for the different transition array contributions from the same ionization state. Other factors can cause filling of the gap, for example, configuration mixing 12 and contribution of dielectronic recombination processes. 13 Finally, Fig. 6 shows the measured spectrum in the 10.2 Å wavelength range, and the identifications are given in Table 4. Here one also has to include the satellite transitionarray of the 3d 4s 3d 8 4s4p kind to allow coherent identification of the.observed features. 5. CONCLUSION In this work, a detailed analysis of the x-ray spectrum emitted from the laser-produced plasma of dysprosium has been given. Resonance 3d nf n=4 7 and 3p 4s,4d transitions of the Ni-like Dy XXXIX ion have been identified. Satellite transitions or transition arrays belonging to ions from Dy XXXIV to Dy XL have also been observed. REFERENCES 1. B. W. Smith, ed., Optical Microlithography XVII, Proc. SPIE 5537 (SPIE, 2004). 2. R. Smith, G. J. Tallents, J. Zhang, G. Eker, S. McCabe, G. J. Pert, and E. Wolfrum, Saturation behavior of two x-ray lasing transitions in Ni-like Dy, Phys. Rev. A 5, R47 R50 (1). 3. A. Zigler, P. Mandelbaum, J. L. Schwob, and D. Mitnik, Analysis of the x-ray spectra emitted by laser-produced plasma of highly ionized lanthanum and praseodymium in the 8.4 to 12.0 Å wavelength range, Phys. Scr. 50, 61 7 (14). 4. R. Doron, M. Fraenkel, P. Mandelbaum, A. Zigler, and J. L. Schwob, X-ray spectrum emitted by laser-produced barium plasma in the 8 to 13.5 Å wavelength range, Phys. Scr. 58, 1 24 (18). 5. P. G. Burkhalter, D. G. Nagel, and R. R. Whitlock, Laserproduced rare-earth x-ray spectra, Phys. Rev. A, (174). 6. M. Klapisch, P. Mandelbaum, A. Zigler, C. Bauche-Arnoult, and J. Bauche, The unresolved 3d 4f transitions in the x-ray spectra of highly ionized Tm and Re from laser produced plasma, Phys. Scr. 34, (186). 7. P. D. Rockett, C. R. Bird, C. J. Hailey, D. Sullivan, D. B. Brown, and P. G. Burkhalter, X-ray-calibration of Kodak direct exposure film, Appl. Opt. 24, (185). 8. A. Bar-Shalom, M. Klapisch, and J. Oreg, HULLAC, an integrated computer package for atomic processes in plasma, J. Quant. Spectrosc. Radiat. Transf. 71, (2001).. C. Bauche-Arnoult, J. Bauche, and M. Klapisch, Variance of the distributions of energy levels and the transition arrays in atomic spectra, Phys. Rev. A 20, (17). 10. C. Bauche-Arnoult, J. Bauche, and M. Klapisch, Variance of the distributions of energy levels and of the transition arrays in atomic spectra. III. Case of spin-orbit-split arrays, Phys. Rev. A 31, (185). 11. N. Tragin, J. P. Geindre, P. Monier, J. C. Gauthier, C. Chenais-Popovics, J.-F. Wyart, and C. Bauche-Arnoult, Extended analysis of the x-ray spectra of laser-irradiated elements in the sequence from tantalum to lead, Phys. Scr. 37, (188). 12. P. Mandelbaum, J. F. Seely, A. Bar-Shalom, and M. Klapisch, Effect of configuration mixing on 3d 4f transitions in highly ionized Ga-, Zn-, and Cu-like ions, Phys. Rev. A 44, (11). 13. C. Bauche-Arnoult, J. Bauche, E. Luc-Koenig, J.-F. Wyart, R. M. More, C. Chenais Popovics, J. C. Gauthier, J. P. Geindre, and N. Tragin, Dielectronic recombination process in laser-produced tantalum plasmas, Phys. Rev. A 3, (18).