There is increasing interest in extreme-ultraviolet (EUV) laser-based lamps for sub-10-nm lithography operating in the region of 6.6 nm. A collisional-radiative model is developed as a post-processor of a hydrodynamic code to investigate emission from resonance lines in Kr, Gd, and Tb ions under conditions typical for mass-limited EUV sources. The analysis reveals that maximum conversion efficiencies of Kr occur at 5 x 10(10) W/cm(2), while for Gd and Tb it was similar or equal to 0.9%/2 pi sr for laser intensities of (2-5) x 10(12) W/cm(2)

Masnavi, Majid

Parchamy, Homaira

Richardson, Martin C.

Szilagyi, John

English

University of Central Florida (UCF): STARS (Showcase of Text, Archives, Research & Scholarship)

University of Central Florida STARS Faculty Bibliography 2010s Faculty Bibliography 1-1-2013 Laser-plasma source parameters for Kr, Gd, and Tb ions at 6.6 nm Majid Masnavi University of Central Florida John Szilagyi University of Central Florida Homaira Parchamy University of Central Florida Martin C. Richardson University of Central Florida Find similar works at: https://stars.library.ucf.edu/facultybib2010 University of Central Florida Libraries http://library.ucf.edu This Article is brought to you for free and open access by the Faculty Bibliography at STARS. It has been accepted for inclusion in Faculty Bibliography 2010s by an authorized administrator of STARS. For more information, please contact STARS@ucf.edu. Recommended Citation Masnavi, Majid; Szilagyi, John; Parchamy, Homaira; and Richardson, Martin C., "Laser-plasma source parameters for Kr, Gd, and Tb ions at 6.6 nm" (2013). Faculty Bibliography 2010s. 4381. https://stars.library.ucf.edu/facultybib2010/4381 Appl. Phys. Lett. 102, 164102 (2013); https://doi.org/10.1063/1.4802789 102, 164102© 2013 AIP Publishing LLC.Laser-plasma source parameters for Kr, Gd,and Tb ions at 6.6 nmCite as: Appl. Phys. Lett. 102, 164102 (2013); https://doi.org/10.1063/1.4802789Submitted: 08 January 2013 . Accepted: 08 April 2013 . Published Online: 22 April 2013Majid Masnavi, John Szilagyi, Homaira Parchamy, and Martin C. RichardsonARTICLES YOU MAY BE INTERESTED IN Spectral irradiance of singly and doubly ionized zinc in low-intensity laser-plasma ultravioletlight sourcesJournal of Applied Physics 121, 033303 (2017); https://doi.org/10.1063/1.4973848Estimation of optimum density and temperature for maximum efficiency of tin ions in discharge extreme ultraviolet sourcesJournal of Applied Physics 101, 033306 (2007); https://doi.org/10.1063/1.2434987Rare-earth plasma extreme ultraviolet sources at 6.5–6.7 nmApplied Physics Letters 97, 111503 (2010); https://doi.org/10.1063/1.3490704Laser-plasma source parameters for Kr, Gd, and Tb ions at 6.6 nmMajid Masnavi, John Szilagyi, Homaira Parchamy, and Martin C. RichardsonThe Townes Laser Institute, College of Optics and Photonics, University of Central Florida,4000 Central Florida Blvd., Orlando, Florida 32816, USA(Received 8 January 2013; accepted 8 April 2013; published online 22 April 2013)There is increasing interest in extreme-ultraviolet (EUV) laser-based lamps for sub-10-nm lithographyoperating in the region of 6.6 nm. A collisional-radiative model is developed as a post-processor of ahydrodynamic code to investigate emission from resonance lines in Kr, Gd, and Tb ions under conditionstypical for mass-limited EUV sources. The analysis reveals that maximum conversion efficiencies of Kroccur at 5 1010 W=cm2, while for Gd and Tb it was ’0:9%=2psr for laser intensities ofð2 5Þ  1012 W=cm2.VC 2013 AIP Publishing LLC [http://dx.doi.org/10.1063/1.4802789]Progress in the field of extreme-ultraviolet (EUV) li-thography based on 13.6 nm wavelength normal-incidence,Mo:Si multilayer mirror technology is advancing with thedevelopment of laser-based1 and discharge-based2 tin plasmasources. It is expected to be introduced into high-volumesemiconductor chip production in the next few years. Shorterwavelengths permit higher imaging resolution at lower nu-meral apertures (NAs). So in seeking pathways towards stillfiner feature sizes, interest is rising in the possibility of fabri-cating high reflective EUV mirrors based in LaN and B orBC. Theoretical reflection efficiencies ’80% have beenpostulated for these mirrors in the 6.6 nm region.3 The Feiglgroup3 estimates the highest efficiencies occurring in bandsat 6.6356 0.018 nm or 6.6756 0.015 nm, depending onwhether LaN/B4C or LaN/B multilayer mirrors are used.In this paper, we examine the emission spectra of laserplasma sources that would be efficient in this region. Inparticular, the rare-earth elements of gadolinium (Gd) andterbium (Tb) emit as intense unresolved transition arraysaround 6.6 nm. We report calculations using a model thatincludes a collisional-radiative (CR) solver4 and a modifiedone-dimensional hydrodynamic code MEDUSA5 coupled withan atomic code relevant to the conditions in mass-limitedlaser-based EUV sources.6,7The CR solver includes all of the electric dipole transi-tions among the most important singly excited-states config-urations in the Krð013Þþ;Gdð1026Þþ, and Tbð1028Þþ chargestates using detailed atomic data obtained from the relativis-tic Flexible Atomic Code (FAC) including the effect of con-figuration interactions.8 The latter, primarily accounting forthe effect of electron correlations among transitions with thesame principal quantum number, causes a strong spectralnarrowing. For other charge-states, we include only theirground states in the model. The in-band emission peaks aris-ing mainly from the 3d–4f transitions belong to the chargestates near the Kr10þ ion and the 4d–4fþ 4p-4d transitionsin the Gd20þ and Tb20þ charge states. Therefore, for exam-ple, 4p64dm; 4p64dm1nl, and 4p54dmþ1 configurations withn  6 and l  3 are included for Tb19þ through Tb28þ chargestates. The radiation transport is solved using the plane-parallel approximation for the case of a spatial grid, partition-ing the plasma source into cells such that all their propertiescan be considered uniform within each cell. Thus, theobserved spectral radiance of plasma at a wavelength k froma given cell i after successive loss by other cells j can bewritten as9Lki ðobsÞ ¼ Ski ½1 expðski ÞexpXjskj; (1)where S is the non-local thermodynamic equilibrium sourcefunction and s is the optical depth including the continuum.This is the contribution from a single cell i for a photon atwavelength of k. After summation over all cells along theline of sight, the total spectral radiance is estimated. Theeffect of radiation loss or opacity on the population distribu-tion in Eq. (1) is evaluated using the photon escape probabil-ity factor for the Voigt line profile as10pki ¼ bik 1skiXj¼1;j 6¼iSkjSkiMij; (2)where M is a function of optical depth.10 The function b isan escape factor for the cell i taking into account its ownreabsorption effect. The second term on the right hand sidedescribes the effect on the level populations in cell i due toradiation produced in all the other cells. Owing to a largenumber of excited states and iteration method to calculateopacity effect, we have removed a number of out-of-bandtransitions while keeping major in-band transitions in the CRsolver.To verify the emission line positions, we have comparedour calculated spectra for a homogeneous spherical Gd or Tbplasma having a radius of 50 lm (’ laser spot size) with anelectron temperature of 100 or 110 eV, respectively, and anion density of 1:4 1019 cm3 to experimental results cre-ated using planar-target laser-produced plasma11 as shown inFigs. 1(a) and 1(b). For these conditions, the average ioniccharge state for Gd is 18.5 and 19.2 for Tb plasmas. Usingthe FAC code, it is found that the calculated spectra are inapproximately agreement with the experimental spectraaround the mirror in-band region after a global displacementof 0.18 and 0.1 nm toward longer wavelength is introducedfor Gd and Tb, respectively. The calculated spectra areslightly shorter in wavelength due to the configuration inter-action effects and overestimation of the ab initio exchange0003-6951/2013/102(16)/164102/3/$30.00 VC 2013 AIP Publishing LLC102, 164102-1APPLIED PHYSICS LETTERS 102, 164102 (2013)Slater integrals, as investigated for a few elements includingtin and xenon targets in 13.6 nm lithography tool.12,13 Theeffect of instrumental broadening in the Voigt line profilewas not included. The calculations underestimate the out-of-band emission, in particular, on the longer wavelength sidedue to the limited number of emission lines treated in themodel and the assumption of a single electron temperatureand density for the transient plasma in experiment.To investigate the in-band conversion efficiency (CE),the CR solver is used as a post-processor of the MEDUSA code.The space and time histories of the plasma are calculated fora 20 lm diameter liquid cylindrical Kr jet target and forspherical Gd or Tb solid targets having a radius of 10 lm,each irradiated by a 1064 nm Gaussian laser pulse havingfull-width at half maximum (FWHM) of 8.5 ns. The idealgas equation-of-state was used for liquid Kr and the modifiedThomas-Fermi model for Gd and Tb. Typical ion densitiesand electron temperatures as a function of time and spaceobtained from these simulations of the interaction for a peaklaser pulse intensity of 2 1012 W=cm2 for the spherical Gdtarget are shown in Figs. 2(a) and 2(b). In this simulation,the ionization process is calculated using the Saha model.The time and space histories of the plasma parameters arefirst calculated using the MEDUSA code and they were thenused to recalculate electron density using the CR. The EUVspectrum, integrated over time and space, was obtained byallowing the CR solver to run for 50 ns, after which timethere was little predicted emission.The integrated spectral radiant energies for Kr, Gd, andTb at different laser intensities are shown in Figs. 3(a), 3(b),and 3(c), respectively. The in-band region of a LaN/B4Cmirror (6.6356 0.018 nm) is shown for reference. The liquiddensity of Kr is assumed to be 2:4 g=cm3. Figure 3(a) showsintegrated spectra per unit length of the Kr cylindricaltarget at intensities of (I) 5 1010 and (II) 3 1011 W=cm2.Although inert-gas targets are attractive since they producenegligible debris, however, these preliminary calculationsshow that the strongest spectral emission peaks of Kr arelocated outside the in-band region. However, comparison toexperimental spectra may be necessary to verify the posi-tions of these emission lines. Figures 3(b) and 3(c) show theintegrated spectra for Gd and Tb spherical targets at inten-sities of (I) 2 1012, (II) 6 1012, and (III) 1013 W=cm2.These calculations show that the spectral emission from Gdtarget drops in the region of k  6:7 nm, while strongestemission peaks of Tb plasma are close to in-band mirrorregion for high laser intensities, which is for high plasmatemperatures. The Tb spectrum becomes broader as thecharge-state increases beyond Tb19þ.The CE calculated as a percentage [(%) of the incidentlaser energy, emitted into 2p steradian]¼ (Pin-band radiantenergy in 2psr/total input laser energy) 100 against 1064nmFIG. 1. Comparison between the calculated and measured spectra:11 (a) the Gdand (b) the Tb spectra produced in laser-based EUV sources. Experimentalspectra reproduced with permission from Churilov et al. Phys. Scr. 80, 045303(2009). Copyright 2009 Institute of Physics. The spectra calculated for homoge-nous spherical Gd and Tb plasmas having a radius of 50lm, with an iondensity of 1.4 1019 cm3 and electron temperatures of 100 and 110 eV,respectively. In the experiment, each planar target is irradiated by 1064nm laserpulse intensity’ ð5 8Þ  1011 W=cm2.FIG. 2. Surface plot of the ion density (a) in logarithmic scale and electron tem-perature (b) as a function of time and space obtained from the MEDUSA simulationof interaction of a Gaussian laser pulse having FWHM of 8.5ns with peak inten-sity of 2 1012 W=cm2 for Gd spherical target having a radius of 10 lm.FIG. 3. The integrated spectral radiant energy: (a) a cylindrical liquid jet Krtarget having a diameter of 20lm irradiated with 1064 nm Gaussian laserpulse intensities of (I) 5 1010 and (II) 3 1011 W=cm2. (b) The sphericalGd target having a radius of 10 lm irradiated with 1064 nm laser pulse inten-sities of (I) 2 1012 and (II) 6 1012 W=cm2. (c) The spherical Tb targethaving a radius of 10 lm irradiated with 1064 nm laser intensities of(I) 2 1012, (II) 6 1012, and (III) 1013 W=cm2. The in-band region of aLaN/B4C mirror (6.6356 0.018 nm) is shown for reference.164102-2 Masnavi et al. Appl. Phys. Lett. 102, 164102 (2013)laser intensity is shown in Fig. 4. The CE in Fig. 4(a) is cal-culated for the LaN/B4C mirror (6.6356 0.018 nm) and inFig. 4(b) for the LaN/B mirror (6.6756 0.015 nm). A maxi-mum conversion efficiency of ’0:2%=2psr is expected forthe krypton plasma at a laser intensity of 5 1010 W=cm2.The calculation shows that the strongest peaks of the Gdspectra do not match the in-band mirror regions. However, acomparison between calculated Gd spectra to a sophisticatedexperimental spectra against thickness of target14 revealsthat we may need only a global displacement of our calcu-lated spectra by 0.1 nm toward longer wavelength instead of0.18 nm as shown in Figs. 1(a) and 3(b). In this case, the CEof Gd increases as shown by the hollow squares in Figs. 4(a)and 4(b). The calculated optimum laser intensity region tomaximize CE of Gd is in approximately agreement to theexperimental result presented in Ref. 16. It is expected thatwith a decrease in initial density of Gd or Tb, the maximumCE enhances compared to the solid density targets due to thelower opacity effects as investigated for tin in 13.6 nm li-thography tool.6,15 To better characterize features of Gdspectra, a detailed comparison between calculation and theexperimental spectra14 will be published elsewhere. Figure 4shows that the mass-limited spherical Tb target irradiated bya 1064 nm Gaussian laser pulse intensity of 5 1012 W=cm2gives the CE as high as ’0:9%=2psr.One of the authors (M.M.) gratefully acknowledgesProfessor A. N. Ryabtsev for providing us the experimentaldata presented in Figure 1.1D. C. Brandt, I. V. Fomenkov, M. J. Lercel, B. M. La Fontaine, D. W. Myers,D. J. Brown, A. I. Ershov, R. L. Sandstrom, A. N. Bykanov, G. O.Vaschenko, N. R. Bawering, P. Das, V. B. Fleurov, K. Zhang, S. N.Srivastava, I. Ahmad, C. Rajyaguru, S. D. Dea, W. J. Dunstan, P. Baumgart,T. Ishihara, R. D. Simmons, R. N. Jacques, R. A. Bergstedt, P. I. Porshnev,C. J. Wittak, M. R. Woolston, R. J. Rafac, J. Grava, A. A. Schafgans, andY. Tao, Proc. SPIE 8322, 83221I (2012).2H. Meiling, W. de Boeij, F. Bornebroek, N. Harned, I. de Jong, P. K€urz,M. Lowisch, H. Meijer, D. Ockwell, R. Peeters, E. van Setten,J. Stoeldraijer, C. Wagner, S. Young, and R. Kool, Proc. SPIE 8322,83221G (2012).3S. Yulin, T. Feigl, V. Nesterenko, M. Schurmann, M. Perske, H. Pauer, T.Fiedler, and N. Kaiser, in Proceedings of the InternationalEUVL Symposium, Miami, 17 October 2011, International SEMATEC,http://www.sematech.org/meetings.4M. Masnavi, M. Nakajima, E. Hotta, and K. Horioka, J. Appl. Phys. 103,013303 (2008).5J. P. Christiansen, D. E. T. F. Ashby, and K. V. Roberts, Comput. Phys.Commun. 7, 271 (1974).6S. A. George, K. Hou, K. Takenoshita, A. Galvanauskas, and M. C.Richardson, Opt. Express 15, 16348 (2007).7M. Richardson, C. S. Koay, K. Takenoshita, C. Keyser, S. George,M. Al-Rabban, and V. Bakshi, in EUV Sources for Lithography, edited byV. Bakshi (SPIE, Bellingham, WA, 2005).8M. F. Gu, Astrophys. J. 582, 1241 (2003).9P. K. Patel, J. S. Wark, D. J. Heading, A. Djaoui, S. J. Rose, O. Renner,and A. Hauer, J. Quant. Spectrosc. Radiat. Transf. 57, 683 (1997).10M. Elitzur and A. A. Ramos, Mon. Not. R. Astron. Soc. 365, 779 (2006).11S. S. Churilov, R. R. Kildiyarova, A. N. Ryabtsev, and S. V. Sadovsky,Phys. Scr. 80, 045303 (2009).12C. Bauche-Arnoult, J. Bauche, J. F. Wyart, and K. B. Fournier, J. Quant.Spectrosc. Radiat. Transf. 65, 57 (2000).13R. D’Arcy, O. Morris, H. Ohashi, S. Sudo, H. Tanuma, S. Fujioka,H. Nishimura, K. Nishihara, C. Suzuki, T. Kato, F. Koike, andG. O’Sullivan, Phys. Scr. T144, 014026 (2011).14S. Fujioka, H. Nishimura, M. Miyake, T. Ugomori, M. Yoshida, andH. Azechi, in Proceedings of the International Workshop on EUV and Softx-ray Sources, Dublin, Ireland, 2011.15A. Sasaki, K. Nishihara, A. Sunahara, H. Furukawa, T. Nishikawa, andF. Koike, Appl. Phys. Lett. 97, 231501 (2010).16T. Cummins, T. Otsuka, N. Yugami, W. Jiang, A. Endo, B. Li,C. O’Gorman, P. Dunne, E. Sokell, G. O’Sullivan, and T. Higashiguchi,Appl. Phys. Lett. 100, 061118 (2012).FIG. 4. The CE (% in 2psr) for the Kr (circle), the Gd spectra shifted by0.18 nm to longer wavelength (square), the Gd spectra shifted by 0.1 nm tolonger wavelength (hollow square), and the Tb (solid line) against a1064 nm Gaussian laser pulse intensity having FWHM of 8.5 ns: (a) calcu-lated for in-band region of a LaN/B4C mirror (6.6356 0.018 nm) and (b) forin-band region of a LaN/B mirror (6.6756 0.015 nm).164102-3 Masnavi et al. Appl. Phys. Lett. 102, 164102 (2013)

Laser-plasma source parameters for Kr, Gd, and Tb ions at 6.6 nm

Majid Masnavi

John Szilagyi

Homaira Parchamy

Martin C. Richardson

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Applied Physics Letters

Laser-plasma source parameters for Kr, Gd, and Tb ions at 6.6 nm

https://stars.library.ucf.edu/cgi/viewcontent.cgi?article=5380&amp;context=facultybib2010

Laser-plasma source parameters for Kr, Gd, and Tb ions at 6.6 nm

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