- Email: [email protected]
Absorption spectroscopy of an expanding laser produced lithium plasma in the extreme ultraviolet using the Dual Laser Plasma technique
Applied Surface Science 127–129 Ž1998. 686–691
Absorption spectroscopy of an expanding laser produced lithium plasma in the extreme ultraviolet using the Dual Laser Plasma technique William Whitty, John Costello, Eugene Kennedy, Christopher Moloney, Jean-Paul Mosnier ) School of Physical Sciences, Dublin City UniÕersity, GlasneÕin, Dublin 9, Ireland
Abstract We describe the essential features of the Dual Laser Plasma ŽDLP. vacuum ultraviolet photoabsorption spectroscopy technique and the characteristics of our DLP apparatus. We show that the time- and space-resolved capabilities of this technique are suited to the monitoring of the dynamics of expanding plasma plumes in the regime used for pulsed laser deposition of materials. Examples of spectra showing the spatial and temporal evolution of a lithium plasma expanding in vacuum are presented. A model based on a self-similar expansion for the plume is developed and used to analyse the shape of absorption lines. Measurements in the photoionisation continuum of Liq are also presented. q 1998 Elsevier Science B.V. PACS: 52.70 La; 32.70 Jz Keywords: Laser produced plasma; Extreme ultraviolet photoabsorption; Lithium
1. Introduction When the output of a Q-switched laser Žtypically, 1 J, 10 ns. is focused onto a solid target a hot, dense plasma is formed. Such plasmas constitute intense sources of vacuum ultraviolet ŽVUV. and X-ray radiation w1,2x. The laser plasma has thus gained acceptance as a standard laboratory-based pulsed source of short wavelength radiation w3x. The inherent time-resolved nature of the laser plasma light source is suited to the study of the dynamics of transient species, including laser plasmas themselves. The technique of probing the struc)
Corresponding author. Tel.: q353-1-704-5303; fax: q353-1704-5384; e-mail: [email protected].
ture and dynamics of a laser plasma using the light emitted by another laser plasma is known as the Dual Laser Plasma ŽDLP. photoabsorption technique w4x. DLP absorption involves probing the absorbing plasma in different conditions. Spectra of multiply or singly charged ions or neutrals are obtained when probing the plume in different spatio-temporal regimes, thus introducing selectivity of absorbing species. Most DLP experiments have hitherto been concerned with the study of fundamental aspects of the photoionisation process w5x. Photoabsorption is also a powerful analytical tool, finding application in the study of the processes governing pulsed laser deposition ŽPLD. of oxide superconducting thin films w6,7x. Yet, the interpretation of the optical absorption spectra of plasma
0169-4332r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 9 - 4 3 3 2 Ž 9 7 . 0 0 7 2 6 - 5
W. Whitty et al.r Applied Surface Science 127–129 (1998) 686–691
plumes is complex. Severe broadening and distortion effects, e.g., refraction w8x, alter the line shapes observed. A quantitative interpretation of such spectra thus requires a knowledge of the basic physical mechanisms involved in the plume, together with values of the relevant atomic parameters characterising the transitionŽs. in question. In this paper, we show that under certain conditions the quantitative interpretation of the Extreme UV ŽXUV. absorption spectra of laser plasmas is comparatively simpler. This is due to: Ž1. the broadening or distortion effects resulting from local plume conditions affect electronic inner-shells less severely than valence levels and thus the observed spectral broadening may even be purely instrumental, Ž2. refractive effects are minimised for probe frequencies much larger than the plasma frequency. The XUV absorption spectra presented here were obtained using the DLP technique, which has rarely been used to study the dynamics of the PLD process. Some recent DLP studies reported on the ablation of silicon w9,10x. In the following, we describe our DLP apparatus, present results showing the spatio-temporal evolution of a lithium plume and develop a model to analyse absorption line shapes. Finally, measurements in the photoionisation continuum of Liq are presented.
2. Experimental and results A diagram of the apparatus is given in Fig. 1. It comprises three parts: Ž1. the lasers and laser plasma sources, Ž2. the coupling toroidal optics and Ž3. the spectrometer and data acquisition system. A general description of the DLP system is given elsewhere w5x and here we only provide new or additional information relevant to the present paper. The source of continuum XUV radiation CS is created by a Nd:YAG laser Ž0.75 J, 15 ns. tightly focused onto a tungsten rod using a 100 mm uncorrected plano-convex lens ŽFL1.. The duration of the pulse of EUV radiation is about the duration of the laser pulse w11x. The absorbing plasma AP ŽFig. 1c. is created by a Nd:YAG laser Ž0.3 J, 15 ns. using a cylindrical lens FL2. The irradiance on target can be varied between 10 8 and 10 11 Wrcm2 . The firing sequence between the two lasers Ž DT . is controlled
687
Fig. 1. Ža. Diagram of apparatus in the horizontal plane: ŽCS. Continuum Source, ŽAP. Absorbing Plasma, ŽTM. Toroidal Mirror, ŽES. Entrance Slit, ŽGS. Grating Spectrometer ŽMCPrPDA. Microchannel PlaterPhotodiode Array, ŽRC. Rowland Circle, ŽOMA. Optical Multichannel Analyzer, ŽPC486. 486 Personal Computer, ŽDG. Digital Delay Generator. Žb. Diagram of apparatus in the vertical plane: Ž K x . Knife-edge along O x axis. Žc. Detailed view of plasma chamber: Ž D x . Distance above plane of sample target, Ž K z . Knife-edge along O z axis, ŽFL1. Focusing Lens 1, ŽFL2. Focusing Lens 2.
by a digital delay generator DG, the system jitter being less than 3 ns. The optical layout conforms with the configuration prescribed by Rense and Violett w12x to increase the efficiency of a grating spectrometer by removal of astigmatism with the help of a toroidal mirror TM. The radii of curvature of TM were chosen to produce spectral lines of uniform length on the Rowland circle RC. Thus, the system is capable of quasistigmatic imaging in the available 3–30 nm range provided by a 1200 linesrmm grating GS operated
688
W. Whitty et al.r Applied Surface Science 127–129 (1998) 686–691
axes, respectively. The spectral resolving power is of the order of 1500 at 150 eV photon energy before removal of instrumental broadening. The determination of the instrument function is of prime importance, as the true absorption profile mirrors the conditions existing in the plume Žsee Section 3 below.. The instrument function was estimated by measuring the profile of the Li 2q Lyman-b absorption line Ž108.845 eV. for which accurate values of the Doppler and Stark widths are computable w15x. A Lorentzian function of 0.105 eV FWHM centred at 108.845 eV accurately depicts the instrumental function. This value is comparable to typical Doppler and Stark widths of EUV lines in laser plasmas w15x. The present experimental results were obtained with a lithium plasma expanding in vacuum. The temporal and spatial evolution of Li 0 was mapped by integrating the spectrum of the optically thin absorption coefficient of the 1s 2 2s ™ 1s2s2p transition Žline A., at 58.92 eV, for varying distances above the target surface Ž D x . and time delays Ž DT . between the laser pulses. The resulting plot is shown in Fig. 2a. In the case of Liq, the same procedure under the same conditions was used for the 1s 2 ™ 1s2p transition Žline B. at 62.22 eV ŽFig. 2b.. The two vertical scales are not directly comparable since
Fig. 2. Ža. Temporal and spatial evolution of Li 0 species. Žb. Temporal and spatial evolution of Liq species.
at an 848 angle of incidence. Details on stigmatic imaging of laser produced plasmas in the EUV can be found in w13x. In order to determine the spatial resolving capability of our system, we carried out a detailed ray-tracing study using SHADOW 1 and a series of knife-edge measurements Žsee Fig. 1b and c.. The key idea is to determine the region of the continuum source and hence of the absorbing medium that effectively contributes to the final image on RC w14x. The dimensions of this region are found to be approximately 300 = 500 m m along the O x and O z
1
SHADOW is a software package developed and licensed by the University of Wisconsin Madison; for further reference see www.xraylith.wisc.edu.
Fig. 3. The Liq photoabsorption spectrum. Ža. Dotted line: measured at D x s 0.4 mm, DT s 30 ns; solid line: absorption spectrum resulting from model Žsee text.. Žb. Theoretical absorption coefficient.
W. Whitty et al.r Applied Surface Science 127–129 (1998) 686–691
Fig. 4. The absolute photoionisation cross-section of Liq as a function of photon energy. ŽTheoretical cross-section from Ref. w16x..
the two transitions have different oscillator strengths. The irradiance of the focused laser beam on target was estimated at 9 = 10 9 Wrcm2 . The relative absorption cross-section spectrum of Liq as a function of photon energy in eV is presented between 72 eV and 75 eV in Fig. 3a Ž D x s 0.4 mm, DT s 30 ns.. The observed lines correspond to the He-like resonance series 1s 2 ™ 1s np with n s 4, 5, 6 and 7. A synthetic absorption spectrum obtained from the corresponding theoretical absorption coefficients ŽFig. 3b. is also presented Žsee Section 3 for explanations.. Fig. 4 depicts the measured and theoretical cross-section curves for the 1s 2 ™ 1s ´ p photoionisation process between threshold Ž75.64 eV. and 130 eV Ž D x s 0.4 mm, DT s 30 ns..
689
5 for geometry.. A fixed observer in the laboratory frame looking at the plasma side-on will see Doppler shifted light proportionally to the sign and magnitude of the radial component of the instantaneous velocity Žif the line-of-sight is along the diameter of the plume. or the corresponding Õ Ž z . projection Žif the axis of observation is along a chord as in the figure.. It is assumed that the instantaneous velocity of an absorbing ion or atom at any point in the plasma can be represented by the sum of a thermal Doppler component which contributes the Gaussian component of the total line width and a streaming component which contributes a frequency shift. In this model, a photon of frequency n in the vicinity of an atomic resonance centred at n 0 will only be absorbed by those ions Žatoms. whose thermal and streaming velocities combine to give a frequency shift D n s n y n 0 along the path of the photon w18x. This frequency shift is equal to Õ nXsn0 1" Ž 1. c in the non-relativistic limit. In Eq. Ž1., Õ represents either Õ Ž r ., the radial component, or Õ Ž z . the z component with Õ Ž z . s Õ Ž r . = zrr. The minus sign corresponds to a velocity component away from the observer Žred shift. and the plus sign to a velocity component toward the observer Žblue shift.. Knowl-
ž
/
3. Analysis and discussion The spatio-temporal distribution maps of Fig. 2 give insight into the dynamics of the evolution of the lithium plasma. It can be seen that the Liq ions appear in the earlier stages of the plume expansion and are concentrated close to the target surface along its normal. Conversely, the population of neutral Li atoms appears to peak at a later stage of the expansion and tends to occupy a comparatively larger area. This observation is consistent with earlier detailed studies on the ion and velocity structure of a laser produced plasma w17x. The expansion is symmetric about O x with radial symmetry assumed in planes normal to O x Žsee Fig.
Fig. 5. Geometry of the plasma plume in a plane normal to the expansion direction.
W. Whitty et al.r Applied Surface Science 127–129 (1998) 686–691
690
edge of the variations of Õ Ž r . and Õ Ž z . as a function of r and z respectively is therefore required to predict the line profile. It has been shown that Õ Ž r . s kr Žand thus, Õ Ž z . s kz . where k is a positive constant which may vary with time and position Žalong O x . is an acceptable self-similar solution for the expansion of a laser plasma from a plane target w18,19x. The attenuation of radiation at frequency n incident on the expanding plasma with intensity I0n and emerging with intensity ILn is given by: ILn I0n
ž
qLr2
HyLr2 x Ž z . d z
s exp y
n
/
Ž 2.
where xn Ž z . is the absorption coefficient such that xn Ž z . s sn Ž z . N Ž z ., sn Ž z . is the total photoabsorption cross-section Ždiscrete or in the continuum. and N Ž z . is the number density of absorbers, introducing a spatial Ž z . dependence. In the case of a discrete transition between two levels labeled i and j respectively of weighted oscillator strength f i j the crosssection Žin m2 . is written as:
sn i j Ž z . s
1
p e2
4p´ 0
mc
ž /
f i jFn Ž z .
Ž 3.
in which Fn Ž z . is the normalised Atomic Frequency Response ŽAFR. function. The most versatile function depicting the AFR is a Voigt profile characterised by a Doppler width D n D and a Lorentzian width D n L . The explicit spatial dependence of the cross-section in ŽEq. Ž3.. arises from ŽEq. Ž1.. and in particular, the choice of Õ Ž z . s kz. We now apply the model just described to the case of the Rydberg series 1s 2 ™ 1s np Ž n s 4, 5, 6, 7. in Liq ŽFig. 3. for which accurate values of the oscillator strengths are known w20x. First, we note that the widths of these lines are comparable to the FWHM of the instrument function previously estimated. The broadening is therefore mostly instrumental. This implies that the experimental conditions belong to the low expansion velocity regime as defined in w18x, i.e., streaming plays a negligible role. For each of these transitions an absorption coefficient is generated using a Voigt profile for the L r2. Ž . AFR and a trial value of NL s HqŽ yŽ L r2. N z d z. An initial estimate for the width is obtained using the formulae given in Ref. w15x for the Doppler and Stark components. Natural line widths are negligible for
these transitions. A value for the transmission Ž2. is then computed and the procedure repeated over the full line profile. The synthetic transmission spectrum obtained is then convolved with the instrumental function and finally compared with the experimental one. The entire procedure is repeated until a satisfactory level of convergence between experiment and model is achieved simultaneously for all four transitions. At each iteration, the FWHM is allowed to vary differently for each transition, since Stark broadening depends on n Žprincipal quantum number., whereas the same value of NL is used for all four transitions. A theoretical absorption coefficient spectrum results from the fitting procedure ŽFig. 3b. as well as a value for NL . This is equal to ; 3 = 10 16 cmy2 in the conditions of Fig. 3a Ž D x s 0.4 mm, DT s 30 ns.. This corresponds to a ground state Liq density of ; 9 = 10 17 cmy3 for a plasma length of 0.3 mm and zero density gradient along the line-ofsight. These values are in good agreement with other plume density measurements or estimations w21x. The photoionisation cross-section for the 1s 2 q hn ™ 1s q ´ ey process in Liq can be accurately computed using the universal fitting formula of w16x. The corresponding curve is plotted in Fig. 4. A transmission measurement in this case directly provides a value for NL since the continuum cross-section does not depend on any particular line shape factor. We have measured the photoionisation continuum of Liq between 75.64 eV and 130 eV photon energies in conditions where the neutral population is negligible. The cross-section varies between 2.5 Mb and 0.75 Mb in this range which corresponds to a factor of 6 on the value of transmission. Thus, in order to carry out the measurements in a satisfactory absorbance regime over this energy range the length of the absorbing column was increased with increasing photon energies. All other experimental conditions were identical to those of Fig. 3. The entire range was recorded using six different positions of the detector along the Rowland circle with large overlaps between adjacent settings. For each setting, the best value of NL was obtained by a non-linear least square fit of the measured absorbance data to the analytical cross-section w16x. The excellent agreement between the curves ŽFig. 4. further confirms the high purity of the Liq content in the plume in the conditions used and also the accuracy of the theoreti-
W. Whitty et al.r Applied Surface Science 127–129 (1998) 686–691
cal cross-section. Assuming zero gradient in the Liq distribution along the line-of-sight, the NL values are converted to number density values averaging to ; 1 = 10 18 cmy3 . This value is in good agreement with the value obtained from modeling the discrete part of the spectrum Žsee above..
Acknowledgements The authors wish to thank Forbairt and the EU ŽHCM Programme. for financial support.
References w1x P.K. Carroll, E.T. Kennedy, G. O’Sullivan, Opt. Lett. 2 Ž1978. 72. w2x J. Balmer, C.L.S. Lewis, R.E. Corbett, E. Robertson, S. Saadat, D. O’Neill, J.D. Kilkenny, C.A. Back, R.W. Lee, Phys. Rev. A 40 Ž1989. 330. w3x E.M. Gullikson, J.H. Underwood, P.C. Batson, V. Nikitin, J. X-ray Sci. Technol. 3 Ž1992. 283. w4x J.T. Costello, J.-P. Mosnier, E.T. Kennedy, P.K. Carroll, G. O’Sullivan, Phys. Scr. T34 Ž1991. 77.
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w5x E.T. Kennedy, J.T. Costello, J.P. Mosnier, J. Electron Spectrosc. Rel. Phen. 79 Ž1996. 283. w6x D.B. Geohegan, D.N. Mashburn, Appl. Phys. Lett. 55 Ž1989. 2345. w7x H.F. Sakeek, T. Morrow, W.G. Graham, D.G. Walmsley, Appl. Phys. Lett. 59 Ž1991. 3631. w8x A.H. El-Astal, T. Morrow, J. Appl. Phys. 80 Ž1996. 1156. w9x T. Ohyanagi, A. Miyashita, K. Murakami, O. Yoda, Jpn. J. Appl. Phys. 33 Ž1994. 2586. w10x T. Makimura, K. Murakami, Appl. Surf. Sci. 96–98 Ž1996. 242. w11x C.L. Cromer, J.M. Bridges, J.R. Roberts, T.B. Lucatorto, Appl. Opt. 24 Ž1985. 2996. w12x W.A. Rense, T. Violett, J. Opt. Soc. Am. 57 Ž1959. 139. w13x G. Tondello, Opt. Acta 26 Ž1979. 357. w14x C. Moloney, J.P. Mosnier, to be published, 1998. w15x G. Bekefi, C. Deutsch, B. Yaakobi, in: G. Bekefi ŽEd.., Principles of Laser Plasmas, Wiley, New York, 1976, p. 549. w16x D.A. Verner, G.J. Ferland, K.T. Korista, D.G. Yakovlev, Ap. J. 465 Ž1996. 487. w17x F.E. Irons, R.W.P. McWhirter, N.J. Peacock, J. Phys. B 5 Ž1972. 1975. w18x F.E. Irons, J. Phys. B 8 Ž1975. 3044. w19x R.A. Al-Wazzan, C.L.S. Lewis, T. Morrow, Rev. Sci. Instr. 67 Ž1996. 85. w20x D.A. Verner, E.M. Verner, G.J. Ferland, Atom. Data Nucl. Data Tables 64 Ž1996. 1. w21x E. Jannitti, P. Nicolosi, P. Villoresi, F. Xianping, Phys. Rev. A 51 Ž1995. 314.
Absorption spectroscopy of an expanding laser produced lithium plasma in the extreme ultraviolet using the Dual Laser Plasma technique William Whitty, John Costello, Eugene Kennedy, Christopher Moloney, Jean-Paul Mosnier ) School of Physical Sciences, Dublin City UniÕersity, GlasneÕin, Dublin 9, Ireland
Abstract We describe the essential features of the Dual Laser Plasma ŽDLP. vacuum ultraviolet photoabsorption spectroscopy technique and the characteristics of our DLP apparatus. We show that the time- and space-resolved capabilities of this technique are suited to the monitoring of the dynamics of expanding plasma plumes in the regime used for pulsed laser deposition of materials. Examples of spectra showing the spatial and temporal evolution of a lithium plasma expanding in vacuum are presented. A model based on a self-similar expansion for the plume is developed and used to analyse the shape of absorption lines. Measurements in the photoionisation continuum of Liq are also presented. q 1998 Elsevier Science B.V. PACS: 52.70 La; 32.70 Jz Keywords: Laser produced plasma; Extreme ultraviolet photoabsorption; Lithium
1. Introduction When the output of a Q-switched laser Žtypically, 1 J, 10 ns. is focused onto a solid target a hot, dense plasma is formed. Such plasmas constitute intense sources of vacuum ultraviolet ŽVUV. and X-ray radiation w1,2x. The laser plasma has thus gained acceptance as a standard laboratory-based pulsed source of short wavelength radiation w3x. The inherent time-resolved nature of the laser plasma light source is suited to the study of the dynamics of transient species, including laser plasmas themselves. The technique of probing the struc)
Corresponding author. Tel.: q353-1-704-5303; fax: q353-1704-5384; e-mail: [email protected].
ture and dynamics of a laser plasma using the light emitted by another laser plasma is known as the Dual Laser Plasma ŽDLP. photoabsorption technique w4x. DLP absorption involves probing the absorbing plasma in different conditions. Spectra of multiply or singly charged ions or neutrals are obtained when probing the plume in different spatio-temporal regimes, thus introducing selectivity of absorbing species. Most DLP experiments have hitherto been concerned with the study of fundamental aspects of the photoionisation process w5x. Photoabsorption is also a powerful analytical tool, finding application in the study of the processes governing pulsed laser deposition ŽPLD. of oxide superconducting thin films w6,7x. Yet, the interpretation of the optical absorption spectra of plasma
0169-4332r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 9 - 4 3 3 2 Ž 9 7 . 0 0 7 2 6 - 5
W. Whitty et al.r Applied Surface Science 127–129 (1998) 686–691
plumes is complex. Severe broadening and distortion effects, e.g., refraction w8x, alter the line shapes observed. A quantitative interpretation of such spectra thus requires a knowledge of the basic physical mechanisms involved in the plume, together with values of the relevant atomic parameters characterising the transitionŽs. in question. In this paper, we show that under certain conditions the quantitative interpretation of the Extreme UV ŽXUV. absorption spectra of laser plasmas is comparatively simpler. This is due to: Ž1. the broadening or distortion effects resulting from local plume conditions affect electronic inner-shells less severely than valence levels and thus the observed spectral broadening may even be purely instrumental, Ž2. refractive effects are minimised for probe frequencies much larger than the plasma frequency. The XUV absorption spectra presented here were obtained using the DLP technique, which has rarely been used to study the dynamics of the PLD process. Some recent DLP studies reported on the ablation of silicon w9,10x. In the following, we describe our DLP apparatus, present results showing the spatio-temporal evolution of a lithium plume and develop a model to analyse absorption line shapes. Finally, measurements in the photoionisation continuum of Liq are presented.
2. Experimental and results A diagram of the apparatus is given in Fig. 1. It comprises three parts: Ž1. the lasers and laser plasma sources, Ž2. the coupling toroidal optics and Ž3. the spectrometer and data acquisition system. A general description of the DLP system is given elsewhere w5x and here we only provide new or additional information relevant to the present paper. The source of continuum XUV radiation CS is created by a Nd:YAG laser Ž0.75 J, 15 ns. tightly focused onto a tungsten rod using a 100 mm uncorrected plano-convex lens ŽFL1.. The duration of the pulse of EUV radiation is about the duration of the laser pulse w11x. The absorbing plasma AP ŽFig. 1c. is created by a Nd:YAG laser Ž0.3 J, 15 ns. using a cylindrical lens FL2. The irradiance on target can be varied between 10 8 and 10 11 Wrcm2 . The firing sequence between the two lasers Ž DT . is controlled
687
Fig. 1. Ža. Diagram of apparatus in the horizontal plane: ŽCS. Continuum Source, ŽAP. Absorbing Plasma, ŽTM. Toroidal Mirror, ŽES. Entrance Slit, ŽGS. Grating Spectrometer ŽMCPrPDA. Microchannel PlaterPhotodiode Array, ŽRC. Rowland Circle, ŽOMA. Optical Multichannel Analyzer, ŽPC486. 486 Personal Computer, ŽDG. Digital Delay Generator. Žb. Diagram of apparatus in the vertical plane: Ž K x . Knife-edge along O x axis. Žc. Detailed view of plasma chamber: Ž D x . Distance above plane of sample target, Ž K z . Knife-edge along O z axis, ŽFL1. Focusing Lens 1, ŽFL2. Focusing Lens 2.
by a digital delay generator DG, the system jitter being less than 3 ns. The optical layout conforms with the configuration prescribed by Rense and Violett w12x to increase the efficiency of a grating spectrometer by removal of astigmatism with the help of a toroidal mirror TM. The radii of curvature of TM were chosen to produce spectral lines of uniform length on the Rowland circle RC. Thus, the system is capable of quasistigmatic imaging in the available 3–30 nm range provided by a 1200 linesrmm grating GS operated
688
W. Whitty et al.r Applied Surface Science 127–129 (1998) 686–691
axes, respectively. The spectral resolving power is of the order of 1500 at 150 eV photon energy before removal of instrumental broadening. The determination of the instrument function is of prime importance, as the true absorption profile mirrors the conditions existing in the plume Žsee Section 3 below.. The instrument function was estimated by measuring the profile of the Li 2q Lyman-b absorption line Ž108.845 eV. for which accurate values of the Doppler and Stark widths are computable w15x. A Lorentzian function of 0.105 eV FWHM centred at 108.845 eV accurately depicts the instrumental function. This value is comparable to typical Doppler and Stark widths of EUV lines in laser plasmas w15x. The present experimental results were obtained with a lithium plasma expanding in vacuum. The temporal and spatial evolution of Li 0 was mapped by integrating the spectrum of the optically thin absorption coefficient of the 1s 2 2s ™ 1s2s2p transition Žline A., at 58.92 eV, for varying distances above the target surface Ž D x . and time delays Ž DT . between the laser pulses. The resulting plot is shown in Fig. 2a. In the case of Liq, the same procedure under the same conditions was used for the 1s 2 ™ 1s2p transition Žline B. at 62.22 eV ŽFig. 2b.. The two vertical scales are not directly comparable since
Fig. 2. Ža. Temporal and spatial evolution of Li 0 species. Žb. Temporal and spatial evolution of Liq species.
at an 848 angle of incidence. Details on stigmatic imaging of laser produced plasmas in the EUV can be found in w13x. In order to determine the spatial resolving capability of our system, we carried out a detailed ray-tracing study using SHADOW 1 and a series of knife-edge measurements Žsee Fig. 1b and c.. The key idea is to determine the region of the continuum source and hence of the absorbing medium that effectively contributes to the final image on RC w14x. The dimensions of this region are found to be approximately 300 = 500 m m along the O x and O z
1
SHADOW is a software package developed and licensed by the University of Wisconsin Madison; for further reference see www.xraylith.wisc.edu.
Fig. 3. The Liq photoabsorption spectrum. Ža. Dotted line: measured at D x s 0.4 mm, DT s 30 ns; solid line: absorption spectrum resulting from model Žsee text.. Žb. Theoretical absorption coefficient.
W. Whitty et al.r Applied Surface Science 127–129 (1998) 686–691
Fig. 4. The absolute photoionisation cross-section of Liq as a function of photon energy. ŽTheoretical cross-section from Ref. w16x..
the two transitions have different oscillator strengths. The irradiance of the focused laser beam on target was estimated at 9 = 10 9 Wrcm2 . The relative absorption cross-section spectrum of Liq as a function of photon energy in eV is presented between 72 eV and 75 eV in Fig. 3a Ž D x s 0.4 mm, DT s 30 ns.. The observed lines correspond to the He-like resonance series 1s 2 ™ 1s np with n s 4, 5, 6 and 7. A synthetic absorption spectrum obtained from the corresponding theoretical absorption coefficients ŽFig. 3b. is also presented Žsee Section 3 for explanations.. Fig. 4 depicts the measured and theoretical cross-section curves for the 1s 2 ™ 1s ´ p photoionisation process between threshold Ž75.64 eV. and 130 eV Ž D x s 0.4 mm, DT s 30 ns..
689
5 for geometry.. A fixed observer in the laboratory frame looking at the plasma side-on will see Doppler shifted light proportionally to the sign and magnitude of the radial component of the instantaneous velocity Žif the line-of-sight is along the diameter of the plume. or the corresponding Õ Ž z . projection Žif the axis of observation is along a chord as in the figure.. It is assumed that the instantaneous velocity of an absorbing ion or atom at any point in the plasma can be represented by the sum of a thermal Doppler component which contributes the Gaussian component of the total line width and a streaming component which contributes a frequency shift. In this model, a photon of frequency n in the vicinity of an atomic resonance centred at n 0 will only be absorbed by those ions Žatoms. whose thermal and streaming velocities combine to give a frequency shift D n s n y n 0 along the path of the photon w18x. This frequency shift is equal to Õ nXsn0 1" Ž 1. c in the non-relativistic limit. In Eq. Ž1., Õ represents either Õ Ž r ., the radial component, or Õ Ž z . the z component with Õ Ž z . s Õ Ž r . = zrr. The minus sign corresponds to a velocity component away from the observer Žred shift. and the plus sign to a velocity component toward the observer Žblue shift.. Knowl-
ž
/
3. Analysis and discussion The spatio-temporal distribution maps of Fig. 2 give insight into the dynamics of the evolution of the lithium plasma. It can be seen that the Liq ions appear in the earlier stages of the plume expansion and are concentrated close to the target surface along its normal. Conversely, the population of neutral Li atoms appears to peak at a later stage of the expansion and tends to occupy a comparatively larger area. This observation is consistent with earlier detailed studies on the ion and velocity structure of a laser produced plasma w17x. The expansion is symmetric about O x with radial symmetry assumed in planes normal to O x Žsee Fig.
Fig. 5. Geometry of the plasma plume in a plane normal to the expansion direction.
W. Whitty et al.r Applied Surface Science 127–129 (1998) 686–691
690
edge of the variations of Õ Ž r . and Õ Ž z . as a function of r and z respectively is therefore required to predict the line profile. It has been shown that Õ Ž r . s kr Žand thus, Õ Ž z . s kz . where k is a positive constant which may vary with time and position Žalong O x . is an acceptable self-similar solution for the expansion of a laser plasma from a plane target w18,19x. The attenuation of radiation at frequency n incident on the expanding plasma with intensity I0n and emerging with intensity ILn is given by: ILn I0n
ž
qLr2
HyLr2 x Ž z . d z
s exp y
n
/
Ž 2.
where xn Ž z . is the absorption coefficient such that xn Ž z . s sn Ž z . N Ž z ., sn Ž z . is the total photoabsorption cross-section Ždiscrete or in the continuum. and N Ž z . is the number density of absorbers, introducing a spatial Ž z . dependence. In the case of a discrete transition between two levels labeled i and j respectively of weighted oscillator strength f i j the crosssection Žin m2 . is written as:
sn i j Ž z . s
1
p e2
4p´ 0
mc
ž /
f i jFn Ž z .
Ž 3.
in which Fn Ž z . is the normalised Atomic Frequency Response ŽAFR. function. The most versatile function depicting the AFR is a Voigt profile characterised by a Doppler width D n D and a Lorentzian width D n L . The explicit spatial dependence of the cross-section in ŽEq. Ž3.. arises from ŽEq. Ž1.. and in particular, the choice of Õ Ž z . s kz. We now apply the model just described to the case of the Rydberg series 1s 2 ™ 1s np Ž n s 4, 5, 6, 7. in Liq ŽFig. 3. for which accurate values of the oscillator strengths are known w20x. First, we note that the widths of these lines are comparable to the FWHM of the instrument function previously estimated. The broadening is therefore mostly instrumental. This implies that the experimental conditions belong to the low expansion velocity regime as defined in w18x, i.e., streaming plays a negligible role. For each of these transitions an absorption coefficient is generated using a Voigt profile for the L r2. Ž . AFR and a trial value of NL s HqŽ yŽ L r2. N z d z. An initial estimate for the width is obtained using the formulae given in Ref. w15x for the Doppler and Stark components. Natural line widths are negligible for
these transitions. A value for the transmission Ž2. is then computed and the procedure repeated over the full line profile. The synthetic transmission spectrum obtained is then convolved with the instrumental function and finally compared with the experimental one. The entire procedure is repeated until a satisfactory level of convergence between experiment and model is achieved simultaneously for all four transitions. At each iteration, the FWHM is allowed to vary differently for each transition, since Stark broadening depends on n Žprincipal quantum number., whereas the same value of NL is used for all four transitions. A theoretical absorption coefficient spectrum results from the fitting procedure ŽFig. 3b. as well as a value for NL . This is equal to ; 3 = 10 16 cmy2 in the conditions of Fig. 3a Ž D x s 0.4 mm, DT s 30 ns.. This corresponds to a ground state Liq density of ; 9 = 10 17 cmy3 for a plasma length of 0.3 mm and zero density gradient along the line-ofsight. These values are in good agreement with other plume density measurements or estimations w21x. The photoionisation cross-section for the 1s 2 q hn ™ 1s q ´ ey process in Liq can be accurately computed using the universal fitting formula of w16x. The corresponding curve is plotted in Fig. 4. A transmission measurement in this case directly provides a value for NL since the continuum cross-section does not depend on any particular line shape factor. We have measured the photoionisation continuum of Liq between 75.64 eV and 130 eV photon energies in conditions where the neutral population is negligible. The cross-section varies between 2.5 Mb and 0.75 Mb in this range which corresponds to a factor of 6 on the value of transmission. Thus, in order to carry out the measurements in a satisfactory absorbance regime over this energy range the length of the absorbing column was increased with increasing photon energies. All other experimental conditions were identical to those of Fig. 3. The entire range was recorded using six different positions of the detector along the Rowland circle with large overlaps between adjacent settings. For each setting, the best value of NL was obtained by a non-linear least square fit of the measured absorbance data to the analytical cross-section w16x. The excellent agreement between the curves ŽFig. 4. further confirms the high purity of the Liq content in the plume in the conditions used and also the accuracy of the theoreti-
W. Whitty et al.r Applied Surface Science 127–129 (1998) 686–691
cal cross-section. Assuming zero gradient in the Liq distribution along the line-of-sight, the NL values are converted to number density values averaging to ; 1 = 10 18 cmy3 . This value is in good agreement with the value obtained from modeling the discrete part of the spectrum Žsee above..
Acknowledgements The authors wish to thank Forbairt and the EU ŽHCM Programme. for financial support.
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