Ion distribution and ablation depth measurements of a fs-ps laser-irradiated solid tin target
M J Deuzeman, A S Stodolna, E E B Leerssen, A Antoncecchi, N Spook, T Kleijntjens, J Versluis, S Witte, K S E Eikema, W Ubachs, R Hoekstra, O O Versolato
IIon distribution and ablation depth measurements of a fs-ps laser-irradiatedsolid tin target
M.J.Deuzeman,
1, 2, a) A.S.Stodolna, E.E.B.Leerssen, A.Antoncecchi, N.Spook,
1, 3
T.Kleijntjens, J.Versluis, S.Witte,
1, 5
K.S.E.Eikema,
1, 5
W.Ubachs,
1, 5
R.Hoekstra,
1, 2 and O.O.Versolato Advanced Research Center for Nanolithography (ARCNL), Science Park 110, 1098 XG Amsterdam,The Netherlands Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen,The Netherlands Van der Waals-Zeeman Instituut, University of Amsterdam, Science Park 904, 1098 XH Amsterdam,The Netherlands FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands Department of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam,The Netherlands (Dated: 5 January 2017)
The ablation of solid tin surfaces by an 800-nanometer-wavelength laser is studied for a pulse length range from500 fs to 4.5 ps and a fluence range spanning 0.9 to 22 J/cm . The ablation depth and volume are obtainedemploying a high-numerical-aperture optical microscope, while the ion yield and energy distributions areobtained from a set of Faraday cups set up under various angles. We found a slight increase of the ion yieldfor an increasing pulse length, while the ablation depth is slightly decreasing. The ablation volume remainedconstant as a function of pulse length. The ablation depth follows a two-region logarithmic dependence onthe fluence, in agreement with the available literature and theory. In the examined fluence range, the ionyield angular distribution is sharply peaked along the target normal at low fluences but rapidly broadens withincreasing fluence. The total ionization fraction increases monotonically with fluence to a 5-6% maximum,which is substantially lower than the typical ionization fractions obtained with nanosecond-pulse ablation.The angular distribution of the ions does not depend on the laser pulse length within the measurementuncertainty. These results are of particular interest for the possible utilization of fs-ps laser systems in plasmasources of extreme ultraviolet light for nanolithography. I. INTRODUCTION
Ultrafast lasers, with pulse durations in thefemtosecond-picosecond range, are used in a wide rangeof applications, such as micromachining, thin film de-position, material processing, surface modification, andion beam generation . More recently, these lasershave attracted attention for their possible applicabilityin the field on tin-based plasma sources of extreme ul-traviolet (EUV) light for nanolithography. There theycould be used for generating a fine-dispersed liquid-metal target before the arrival of a high-energy main-pulse responsible for the EUV emission, enhancing laser-plasma coupling . The utilization of a fs-ps laser sys-tem could strongly reduce fast ionic and neutral debrisfrom EUV sources compared with nanosecond-pulses ,enabling better machine lifetime .Since the 1990s many experiments have been per-formed and models developed for laser-matter inter-action at this particular time scale. Target materi-als used are metals such as gold, silver, copper andaluminum , and non-metals such as silicon and metal oxides , among others . Most of thesestudies are conducted in a femtosecond pulse length rangefrom 50 fs up to approximately 1 ps and a pulse fluence a) Electronic mail: [email protected] up to 10 J/cm . In almost all studies the wavelengthof the laser is in the infrared, where commercial lasersystems are readily available. The focus is often eitheron ablation depth or ion distributions (energy, yield orangular), with a few exceptions such as the work of Toft-mann et al. which addresses both. A detailed study oflaser ablation of the relevant element tin, including bothdepth and ion emission distribution, has not yet beenperformed in the fs-ps domain. Such a study, however,is indispensable for exploring EUV plasma sources in theshort-pulse regime.In this work, we present a systematic study of thelaser ablation of a solid tin target by an 800-nanometer-wavelength laser. We determine the angle-resolved yieldand energy distributions of the produced plasma ionsthrough time-of-flight techniques. The depth of the ab-lation crater was established in addition to the ion mea-surements using a high-numerical-aperture optical micro-scope. We varied the laser pulse length between 500 fsand 4.5 ps. In this pulse length range lies a transitionregime in which the transfer of laser energy from theheated electrons to the lattice starts playing a signifi-cant role . Recent work using ultrafast laser pulses toirradiate molten-tin microdroplets hinted at a dramaticchange in laser-metal coupling at 800 fs pulse length, re-sulting in a simultaneous sharp increase in droplet expan-sion velocity and a strong dip in the yield of fast ionicdebris . This makes it highly desirable to provide fur- a r X i v : . [ phy s i c s . p l a s m - ph ] J a n ther data in this pulse length regime. In our experiments,we additionally study the influence of pulse fluence in de-tail, covering a range from 0.9 to 22 J/cm , similar as inrefs. 10 and 31. At the high end of this fluence range,the total volume of ablated material reaches ∼ µ m ,which is similar to the volume of a tin droplet used instate-of-the-art plasma sources of EUV light and there-fore provides an interesting comparison. II. EXPERIMENTAL SETUP
A solid planar polycrystalline 99.999% pure tin targetwith a 1-millimeter-thickness is irradiated by a pulsed800-nanometer-wavelength Ti:Sapphire laser (CoherentLegend USP HE). The laser beam is incident on thetarget at normal incidence. The target and detectors iskept at a vacuum of 10 -8 mbar. The laser pulses have aGaussian-shaped temporal and spatial profile. All pulselengths presented in this work are the full-width at half-maximum (FWHM) of the pulse in time-domain. Thepulse duration has been changed between 500 fs and 4.5ps by varying the group velocity dispersion in the com-pressor of the amplified laser system. The resulting pulseduration was measured using a single-shot autocorrela-tor. The beam profile of the pulses are slightly elliptical,with a FWHM of 105 ± µ m on the long axis and 95 ± µ m on the short axis. The peak fluence, the maximumfluence attained in the center of the Gaussian pulse, iscalculated using these widths and the pulse energy. Thisfluence is varied with a λ /2 wave plate in combinationwith a thin-film polarizer, which leaves the spatial pro-file of the laser beam unchanged. The pulse repetitionrate of 1 kHz is reduced with pulse-picking optics to an FIG. 1. The outline of the setup (top view) used for theexperiments. The four dark black spots mark the positionsof the Faraday cups (FCs): one at 2 ◦ and three at 30 ◦ withrespect to the normal of the target. Two of the 30 ◦ -FCs andthe 2 ◦ -FC are in the horizontal plane, one of the 30 ◦ -FCs isout of plane. The laser beam (red), horizontally polarized, isincident on the target under normal angle. A schematic cut-through of a home-made FC is also shown. The outer guardshield has a diameter of 6 mm, the inner suppressor shield adiameter of 8 mm. The ion currents are obtained from thecollector cone. effective rate of 5 Hz to enable shot-to-shot data acqui-sition and controlled target movement between the laserpulses. The polarization of the laser light is horizontal(see Fig. 1). As the pulses are incident on the target atnormal incidence, no dependence on the polarization isexpected.Time-of-flight (TOF) ion currents are obtained fromFaraday cups (FCs) set up around the target, one at 2 ◦ from the surface normal and at a distance of 73 cm, twoat 30 ◦ and 26 cm (in horizontal and vertical position) andone at 30 ◦ and 24 cm (also in the horizontal plane). ThreeFCs are home-made and consist of a grounded outerguard shield, an inner suppressor shield, and a charge-collector cone (cf. inset in Fig. 1). A voltage of -100 Von the suppressor shield inhibits stray electrons enteringthe collector cone and secondary electrons, which maybe produced by energetic or multi-charged ions , fromleaving it. To further reduce the chance of stray elec-trons arriving at the collector, a bias voltage of -30 V isapplied to the collector cone itself. The other FC (at 30 ◦ and 24 cm) has a different design (model FC-73A fromKimball Physics) and can be used for retarding field anal-ysis. Checks with retarding grids using this FC indicatethat ions with energies below 100 eV, the vast majorityof the ions, are mostly singly charged. The charge yieldmeasured with a FC can thus be regarded as a directmeasure of the ion yield. In the conversion from a TOF-to a charge versus the ion energy-signal, the signal is cor-rected for the non-constant relation between bin size inthe time- and in the energy-domain using S E = | dtdE | S t = t E S t , (1)in which S E and S t are the signals in respectively the en-ergy domain and the time domain, and t and E respec-tively denote the TOF and the ion energy. Signals arecorrected for the solid angle of the detectors and for thefinite response RC -time of the circuit. The total chargeyields are determined by integrating the charge over thefull spectrum. Unless otherwise specified, we use the av-erage of the total charge yield for the three 30 ◦ -FCs.To enable depth measurements and to prevent severetarget modification by the laser, which would influencethe measurements, the target is moved after every 30pulses. The first pulses on a fresh spot on the targetgenerate signals with a small TOF, indicative of lightelements or high-energy tin atoms. Early studies, em-ploying ion energy analyzers, identify these pulses aslight elements contaminations . Energy-dispersive X-ray spectroscopy measurements reveal that areas on ourtin target unexposed to laser light contain a substantialamount of oxygen and other low-mass elements, such ascarbon and nitrogen. These elements are only barely vis-ible, if at all, for an irradiated target area. Therefore,we conclude those fast ion peaks correspond to contam-ination of the surface by low-mass atoms. To avoid theinclusion of this contamination in the results, spectra andcharge yields are considered only after cleaning the sur-face by the first nine shots. In the experiments, we aver-age over five shots (shots no. 10-14) per target positionas well as over 30 separate target positions, i.e. 150 shotsin total. Shots later than shot no. 14 are excluded fromour analysis to prevent target surface modification ef-fects, which become apparent in the measurement of iondistributions after 20 shots (with a conservative safetymargin). We verified that these effects do not change thedepth of the hole and confirmed the linear dependence ofthe depth on the number of shots for the first 30 shots.Following the charge yield experiments, the target isinspected by means of an optical microscope. The micro-scope has a 50x imaging objective with a numerical aper-ture (NA) of 0.42, yielding a depth of focus of 3 µ m andenabling the determination of crater depth by straight-forward optical inspection of a selected number of holes.The same microscope, equipped with a 5x imaging objec-tive and a motorized stage for automated focus scanningto provide a complete picture of the hole, is used foran automated ablation volume determination by meansof the focus variation technique which combines theimages acquired by the microscope with computationaltechniques to provide 3D reconstructions of the ablatedsample surfaces. A 2D Gaussian fit to the reconstructedsurface profile is performed, and the integral of the fittedcurve then provides an estimate of the ablated volume. III. RESULTS & DISCUSSIONPulse length dependence
Fig. 2 shows the charge-per-energy signal for twoFCs for varying pulse lengths, ranging 500 fs to 4.0 ps.Most of the charge is due to relatively low-energy ions,in the range of 10-100 eV. The peak energy (the energyof the maximum yield) does not substantially changefor changing pulse length and is located near 30 eV.Most of the ions are directed backwards with respect tolaser beam, i.e. normal to the surface of the target, inline with the model of Anisimov et al. of the ion plumedynamics during laser ablation . The ratio of totalcharge yield of the 30 ◦ -FCs to the yield of the 2 ◦ -FC isconstant in the investigated pulse length range at a valueof 0.14 (see Fig. 3), implying an angular distributionwhich does not depend on the pulse duration.Rates of multiphoton ionization processes, in whichmultiple photons are directly absorbed by a single atom,are heavily dependent on the laser intensity. For laserintensities above 10 W/cm , multiphoton ionization isdominant in laser ablation . The maximum examinedpeak intensity in this work is 4 . × W/cm , at a peakfluence of 22 J/cm and with a pulse length of 500 fs.Therefore, we expect that multiphoton ionization has anegligible role in the laser ablation and that the ablationand ionization in the surface is dominated by electron impact mechanisms . These mechanisms are dependenton the total energy put in the system and not on theintensity, barring potential larger heat conduction lossesfor longer pulse lengths . The relative insensitivityof our observations to the length of the laser pulse inthe studied range confirms that laser intensity itself, ata given fluence, does not play a dominant role.Fig. 2 also shows that ion yields increase with pulselength for all ion energies. The upper panel of Fig. 4shows the total charge collected on the 2 ◦ -FC togetherwith the ablation depth for each pulse length. The chargeyield increases linearly from 3.2 µ C/sr at a pulse lengthof 500 fs to 3.9 µ C/sr at 4.0 ps. In contrast, the ab-lation depth exhibits the opposite trend. It decreasesfor increasing pulse length from 2.4 (500 fs) to 2.1 (4.0ps) µ m/shot. However, the ablation volume is constant(see lower panel of Fig. 4), within the measurement un-certainties, because of an increase in hole radius com-pensates decreasing depth. The increase in accumulatedcharge does therefore neither have its origin in an increase Yield ( m C/keV sr)
E n e r g y ( k e V ) o o FIG. 2. Charge yields as a function of the ion energy forthe 2 ◦ -FC (upper set of lines) and one of the 30 ◦ -FCs (lowerset of lines). Five pulse lengths are shown: 500 fs (black),1.2 ps (red), 2.0 ps (blue), 3.0 ps (green) and 4.0 ps (orange).The measurements were performed with a constant peak flu-ence of 17 J/cm . Ratio 30o-FCs:2o-FC
P u l s e l e n g t h ( f s )
FIG. 3. The ratio of the yields of the 30 ◦ -FCs to the 2 ◦ -FCversus the pulse length. The black line depicts the averageratio for all pulse lengths. of ablated material (cf. Fig. 4), nor in a broadening ofthe angular ion distribution (cf. Fig. 3). A possible ex-planation could be local screening of the laser light byvapor absorption . For longer pulses, more and moreablated material (ions, electrons, and neutral particles)will partially block the target surface from these laserpulses. Instead of ablating the surface, this laser lightwill be absorbed by the vapor. For gold, Pronko andcoworkers used numerical simulations to show that thefraction of laser light absorbed by vapor increases from0 to almost 20% between 100 fs and 10 ps, respectively.This results in a decrease of the amount of ablated ma-terial because part of the laser light does not reach thetarget, while the vapor may be further ionized.Concluding, we find that a longer pulse length resultsin a gradual increase in ionization, but a gradual decreasein the ablation depth at the center. The total amount ofablated material did not change. We observe no indica-tions of a maximum or minimum such as found by Vi-nokhodov et al. . This could possibly be attributedto the difference in target morphology in the compari-son: Vinokhodov reported on results obtained on liquidtin droplets, whereas our work focuses on planar solid tintargets. The angular ion yield distribution is constant inthe pulse length range of 500 fs to 4.0 ps. For the ob-served range, shortening the pulse length results in fewerions. Peak fluence dependence
In addition to the pulse duration, experiments for avarying pulse fluence are conducted. These measure-ments are performed at 1.0 and 4.5 ps pulse length. Fig.5 shows the ion spectra at 2 ◦ and 30 ◦ angle for all exam-ined pulse fluences. The bulk of the ions have low energy,with a broad peak around 30 eV. More charge is collected (cid:12) (cid:18) (cid:25) (cid:28) (cid:19) (cid:5) (cid:27) (cid:19) (cid:24) (cid:28) (cid:1) (cid:2) m (cid:22) (cid:3) (cid:1) (cid:14) (cid:20) (cid:18) (cid:21) (cid:17) (cid:1) (cid:8) (cid:24) (cid:4) (cid:13) (cid:11) (cid:1) (cid:2) m (cid:11) (cid:5) (cid:27) (cid:26) (cid:3) (cid:10) (cid:16) (cid:21) (cid:15) (cid:28) (cid:20) (cid:24) (cid:23) (cid:1) (cid:30) (cid:24) (cid:21) (cid:29) (cid:22) (cid:18) (cid:1) (cid:2) (cid:7)(cid:6) (cid:9) (cid:1) (cid:31) (cid:22) (cid:9) (cid:5) (cid:27) (cid:19) (cid:24) (cid:28) (cid:3) P u l s e l e n g t h ( f s )
FIG. 4. (upper) Total charge yield at the2 ◦ -FC (open circles, right axis) and the depth at thecenter of the holes (closed squares, left axis) as a functionof pulse length. The measurements were performed at aconstant peak fluence of 17 J/cm . (lower) The ablationvolume obtained from the focus variation technique as afunction of pulse length at the same constant peak fluence.The error bars indicate 1-standard deviation of the mean oneither side. Two data points where no reliable estimationwas possible are excluded. as the pulse fluence increases for all ion energies. Particu-larly noticeable is the increase in the yield of high-energyions. The yield at 40 eV ion energy increases approxi-mately 10 times, whereas that at 400 eV increases by afactor of about 300, comparing the signals on the 2 ◦ -FCfor the highest (22 J/cm ) and the lowest (2.6 J/cm )peak fluence (cf. Fig. 5). For the 30 ◦ -FCs an additionalshoulder at a higher ion energy (several hundred eV) isvisible. This shoulder shifts towards higher energies forincreasing pulse energy. At the high end of the fluencerange the larger low-energy peak attains such heights andwidths that the high-energy shoulder becomes indistin-guishable from it. This high-energy feature is also visiblein other ablation experiments with pulse durations in thefs-ps range and has been ascribed to the occurrenceof an ambipolar field, resulting from a space-charge layerformed by electrons above the surface. This field acceler-ates some of the ions towards higher energies. It increaseswith temperature and the gradient of electron density .Nolte and coworkers showed that the ablation depthhas a logarithmic dependence on the laser fluence forpulse lengths up to a few ps. Typically two regions arepresent: a low-fluence region, in which the optical pene-tration of the laser light defines the ablation, and a high-fluence region, in which the electron thermal diffusion isleading. The low-fluence region has a smaller ablationdepth than the high-fluence region. The precise locationof the boundary between these regions is dependent onthe target material and the laser characteristics. In both (cid:5) (cid:11) (cid:7) (cid:15) (cid:10) (cid:9) (cid:1) (cid:17) (cid:12) (cid:9) (cid:14) (cid:8) (cid:1) (cid:2) (cid:18) (cid:5) (cid:4) (cid:13) (cid:9) (cid:6) (cid:1) (cid:16) (cid:15) (cid:3) o (cid:5) (cid:11) (cid:7) (cid:15) (cid:10) (cid:9) (cid:1) (cid:17) (cid:12) (cid:9) (cid:14) (cid:8) (cid:1) (cid:2) (cid:18) (cid:5) (cid:4) (cid:13) (cid:9) (cid:6) (cid:1) (cid:16) (cid:15) E n e r g y ( k e V ) o FIG. 5. Charge yield as a function of the ion energy for the2 ◦ -FC (upper panel) and one of the 30 ◦ -FCs (lower panel)for increasing peak fluence, from 2.6 to 22 J/cm in steps of1.8 J/cm at a constant pulse length of 1.0 ps. (cid:11) (cid:16) (cid:23) (cid:26) (cid:18) (cid:1) (cid:2) (cid:28) (cid:21) (cid:5) (cid:25) (cid:18) (cid:22) (cid:26) (cid:3) (cid:10) (cid:18) (cid:14) (cid:24) (cid:17) (cid:16) (cid:1) (cid:27) (cid:19) (cid:16) (cid:20) (cid:15) (cid:1) (cid:7) (cid:22) (cid:4) (cid:12) (cid:10) (cid:1) (cid:2) (cid:28) (cid:10) (cid:5) (cid:25) (cid:24) (cid:3) (cid:13) (cid:14) (cid:26) (cid:19) (cid:22) (cid:1) (cid:8)(cid:6) (cid:22) (cid:4) (cid:12) (cid:10) (cid:25) (cid:9) (cid:7) (cid:22) (cid:4) (cid:12) (cid:10) P e a k f l u e n c e ( J / c m ) FIG. 6. (upper) The ablation depth at 1.0 (filled squares)and 4.5 ps (open circles) as a function of the peak pulsefluence. The lines represent fits of equation 2 through thedata. Points at 6 J/cm are included in both fit ranges.Thresholds are 0.44 (1.0 ps) and 0.38 J/cm (4.5 ps) for thelow fluence region and 3.0 (1.0 ps) and 2.4 J/cm (4.5 ps)for the high fluence region. As a reference these thresholdsare also shown below (middle) Total charge yields for the2 ◦ -FC at 1.0 (filled squares) and 4.5 ps (open circles). Theerror bars are smaller than the symbol size. (lower) Theratio of the yields of the 30 ◦ -FCs to that of the 2 ◦ -FC at1.0 (filled squares) and 4.5 ps (open circles). The data pointat 0.9 J/cm is omitted due to low signal quality. regions, the depth follows the generic equation D = a ln (cid:18) FF thr (cid:19) , (2)in which D is the ablation depth, a the ablation constant, F the laser fluence and F thr the threshold ablation flu-ence.We measured the depth of the hole at its center as afunction of the peak fluence (see the upper panel of Fig.6). For both pulse lengths, the results show a clear log-arithmic dependence separated in two regions, with thehigh-fluence region starting around 6 J/cm . A fit of theresults for the low-fluence region shows that, within theuncertainties of the measurements, the ablation constantand threshold are the same for both pulse lengths. Theablation constant is 0.3 µ m for both pulse lengths, whilethe ablation thresholds are 0.44 and 0.38 J/cm for 1.0and 4.5 ps, respectively. In the high-fluence region thethresholds are found to be 3.0 and 2.4 J/cm for 1.0 and4.5 ps, respectively. Such a decrease of the threshold isin agreement with the numerical simulations of Pronkoet al. . The ablation constant is slightly higher for the1.0 ps case at 1.2 µ m, against the 1.0 µ m found for 4.5ps.These ablation thresholds for tin are similar to thosefound with a similar experimental approach for iron byShaheen et al. with 0.23 and 2.9 J/cm for the low-and high-fluence regions, respectively (for a lower pulselength of 130 fs). In comparison to other metals suchas gold, silver, aluminum and copper, tin has higherthresholds . The high-fluence threshold of gold,for example, is reported to be 0.9 J/cm at roughly 150fs and 1.7 J/cm at almost 800 fs . The theoreti-cally expected ablation thresholds are dependent on tar-get properties, such as optical penetration depth, thermalconductivity, and density , and laser properties suchas the pulse duration . This large parameter spacemakes our experimental findings particularly valuable, asno straightforward predictions can be made.The charge yield at the 2 ◦ -FC (middle panel of Fig.6) increases for increasing pulse fluence, from the noiselevel below 0.1 to 4.1 (1.0 ps) and 5.2 µ C/sr (4.5 ps).A noticeable difference with the results for the ablationdepth is the higher ”threshold” above which apprecia-ble ionization is apparent in our measurements. At thelower fluences, the temperature of the surface is too lowto generate an observable amount of ions and mostly neu-tral particles are emitted. Above a certain fluence ionsare generated and the charge yield gradually increasesabove that fluence, following a roughly linear or loga-rithmic dependence. The charge yield results for bothpulse lengths are very similar. In agreement with theabove discussed pulse length results, the yield for the 4.5-picosecond pulses is slightly higher. As the charge yieldat a certain angle is determined by several factors whichare not necessarily constant for the pulse fluence, such asthe volume of ablated material, angular distribution, and ionization fraction, there are no clear expectations for thefluence dependence. For these same reasons, a good com-parison between studies in the available literature is alsodifficult to realize. Toftmann and coworkers find a lin-ear dependence for the total yield up to 2 J/cm whereasAmoruso et al. find a logarithmic dependence up to3 J/cm .While changing the pulse length does not influence theangular ion distribution, the pulse fluence certainly does.The lower panel of Fig. 6 shows the ratio of the 30 ◦ -FCyields to the 2 ◦ -FC yield for both pulse lengths. The ra-tio increases from 0.02 near threshold to almost 0.2 at thehighest fluence. At the lower fluences the ratio is fairlyconstant but it increases rapidly for higher fluences, indi-cating a rapidly broadening of the angular distribution.There is no appreciable difference between the ratios forthe 1.0- and 4.5-picosecond signals.Following Anisimov’s model , the angular distribu-tion of the plasma vapor from laser ablation in terms ofthe yield Y ( θ ) per unit surface at a certain polar angle θ with respect to the yield at 0 ◦ is described by Y ( θ ) Y (0) = (cid:20) ( θ )1 + k tan ( θ ) (cid:21) / , (3)assuming cylindrical symmetry around the targetnormal and introducing the parameter k . This formulais adjusted to the hemispherical case from the seminalplanar surface case . A large value of the scaling param-eter k indicates that the angular distribution is sharplypeaked in the direction along the target normal, while a k equal to 1 describes a fully isotropic distribution. Thevalues of k can be obtained from the charge yield ratiosdepicted in Fig. 6 (lower panel) and are plotted in Fig.7 (upper panel). We find that k decreases from roughly8 to 3 in the examined fluence range. A similar study onthe ablation of silver found similarly large values for k (6.2 and 4.0 depending on the axis of the elliptic spotsize) at 500 fs pulse length and a fluence of 2 J/cm .This same study reports values for k between 2 and 3for ns-pulses, similar to studies of Thestrup et al. in thenanosecond-range . Those studies found a decreasing k for increasing fluence, similar to our findings in thefs-ps-range. Additionally, they generally found that iondistributions from nanosecond-laser ablation are muchbroader than those of femtosecond-laser ablation. Fortin, studies with ns-long pulses indeed found similarlybroad angular ion distributions .To obtain the total charge yield Y total of all ions emit-ted from a pulse in terms of the yield at 0 ◦ , and k , weintegrate equation 3 over the relevant half hemisphereresulting in Y total = 2 πY (0) k . (4)The results of the total yield are shown in Fig. 7. Forthe examined fluence range, the total yield increases from k (cid:7) (cid:18) (cid:20) (cid:8) (cid:16) (cid:1) (cid:9) (cid:14) (cid:8) (cid:19) (cid:13) (cid:11) (cid:1) (cid:21) (cid:15) (cid:11) (cid:16) (cid:10) (cid:1) (cid:3) (cid:23) (cid:5) (cid:4) (cid:6) (cid:18) (cid:17) (cid:15) (cid:22) (cid:8) (cid:20) (cid:15) (cid:18) (cid:17) (cid:1)(cid:12) (cid:19) (cid:8) (cid:9) (cid:20) (cid:15) (cid:18) (cid:17) (cid:1) (cid:3) (cid:2) (cid:4) P e a k f l u e n c e ( J / c m ) FIG. 7. (upper) The value of k of the angular distribution (cf.equation 3) versus the peak fluence for 1.0 (filled squares) and4.5 ps (open circles) pulse length. The value of the dashed linerepresents the value of k for which the distribution is isotropic.(middle) The total charge yield over the whole hemisphere outof the target plane for 1.0 (filled squares) and 4.5 ps (opencircles), obtained using k and the total charge yield of the 2 ◦ -FC (cf. equation 4). (lower) The ionization fraction for 1.0(filled squares) and 4.5 ps (open circles), obtained with thetotal charge yield and the ablation volume. The error barsindicate the 1-standard deviation of the mean, as obtainedfrom error propagation (cf. Fig. 6). near-zero to ∼ µ C, corresponding to 2 × ions, as-suming singly-charged ions. The combination of increas-ing charge yield measured at the 2 ◦ -FC and a broadeningangular distribution results in a very rapidly increasingtotal charge yield. The total charge yield combined withthe volume measurements enable the determination ofthe ionization fraction, i.e., the amount of elementarycharge per atom (see lower panel of Fig. 7). Experimentsin the fs-range, on other elements than tin, report ioniza-tion fraction values of 1% at 2 J/cm (at 500 fs pulselength) to ∼ at 5 J/cm (50 fs). We find similarvalues, reaching 5 and 6% in our fluence range for 1.0 and4.5 ps respectively. This is significantly lower than theionization fraction of several 10% observed in nanosecondlaser ablation (at fluences of ∼ ) . IV. CONCLUSIONS
We have studied the influence of two laser parameterson the ion charge yield and energy distribution, as well asthe ablation depth and volume. A high-energy ion peak isvisible for low fluences, in agreement with the availableliterature. Variation of the pulse duration from 500 to4000 fs results in a small increase of the ion charge yield,while the ablation depth decreases slightly. A possibleexplanation is the screening of the target by the plasmaplume. The total ablation volume remains constant. In-terestingly, we do not observe the abrupt changes in ei-ther depth or ion yield that were hinted at in refs. 10 and31. The ion yield angular distribution does not changeappreciably as a function of pulse length. The ablationdepth follows a two-region logarithmic dependence onlaser pulse peak fluence, in agreement with the existingtheory. We find ablation thresholds of 0.44 (at a pulselength of 1.0 ps) and 0.38 J/cm (4.5 ps) for the low-fluence region and 3.0 (1.0 ps) and 2.4 J/cm (4.5 ps) forthe high-fluence region, close to literature values for othermetallic elements. The ”threshold” at which ionizationis apparent is higher, from there on the ion charge yieldincreases in step with fluence. The angular distributionis sharply peaked backwards along the target normal atthe lower fluences, but rapidly broadens for the higherfluences. The total ionization fraction increases gradu-ally and monotonically with the fluence to a maximumof 5-6%, which is substantially lower than typical valuesfor nanosecond-laser ablation. These results are of partic-ular interest for the possible utilization of fs-ps laser sys-tems in plasma sources of EUV light for next-generationnanolithography. ACKNOWLEDGEMENTS
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