Nuclear Instruments and Methods in Physics Research B 315 (2013) 81–84

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Nuclear Instruments and Methods in Physics Research B

journal homepage: www.elsevier .com/locate /n imb

Quantitative evaluation of charge-reduction effect in cluster constituentions passing through a foil

0168-583X/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.nimb.2013.04.077

⇑ Corresponding author.E-mail address: chiba.atsuya@jaea.go.jp (A. Chiba).

A. Chiba a,⇑, Y. Saitoh a, K. Narumi a, K. Yamada a, T. Kaneko b

a Takasaki Advanced Radiation Research Institute, Japan Atomic Energy Agency (JAEA), 1233 Watanuki-machi, Takasaki-shi, Gunma 370-1292, Japanb Department of Applied Physics, Okayama University of Science, 1-1 Ridai-cho, kita-ku, Okayama-shi, Okayama 700-0005, Japan

a r t i c l e i n f o

Article history:Received 29 November 2012Received in revised form 26 March 2013Accepted 26 April 2013Available online 4 July 2013

Keywords:Carbon clusterAverage chargeInteratomic distance

a b s t r a c t

Swift cluster ions, which cause characteristic irradiation effects on a solid surface, have a possibility ofestablishing a new ion irradiation technique for high-sensitivity surface analysis and innovative surfacemodification. However, the mechanism of cluster irradiation effects has not been understood completely.We have focused on the charge reduction effect in some physical phenomena and performed a quantita-tive evaluation of the relationship between the charge state and the interatomic distance of the constit-uent ions moving in the solid. This technique is based on the refined analysis of the divergence angle ofthe constituent ions resulting from the foil-induced dissociation of the two-atomic molecular ion. Theresults derived from this analytical approach clearly showed the correlation between the average chargeand the interatomic distance of the constituent ions and implied that the average charge of the constit-uent ions emerging from the foil varies according to the interatomic distance at the instant of clusterdissociation.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

When a swift cluster ion bombards a solid, a high-density elec-tronic excitation field may be produced locally on the target sur-face, because the distance among atoms constituting the clusterion is comparable to that among atoms constituting the target.As a result, the cluster ion gives rise to irradiation effects that arenever observed under monatomic ion irradiation; therefore, thecluster ion beam has the potential of being a new tool in ion irra-diation techniques. For example, the irradiation effect of cluster ionbombardment, which enhances the emission yield of secondaryions containing many molecular ions, can be applied to second-ary-ion mass spectroscopy aimed at sensitive analysis of a solidsurface [1].

Cluster-irradiation effects are observed not only in the second-ary ion-/-electron emission under cluster impact [2,3], but also inthe energy loss [4,5] and average charge [6] of the cluster constit-uent ions passing through a thin foil. Several researchers studyingthe average charge, which is also topic of this study, have showedthat the average charge of cluster ions moving at more than theBohr velocity is smaller than that of the monatomic ions at thesame speed.

Physical phenomena caused by interaction between the clusterion and the solid cannot be completely explained by the

superposition of the existing theory describing an ion–solid inter-action. The mechanism of these phenomena observed in the energyloss and average charge of cluster constituent ions were describedby the several theoretical models considering the coherent stop-ping and Coulomb interaction in their correlated motion [7–9].The coherent stopping and the Coulomb interaction may varydepending on the unique parameters of the cluster, such as thestructure and interatomic distance. Such uncertainty more compli-cates the understanding of the mechanism of cluster-induced phe-nomena. We have so far demonstrated the significance of theseparameters via foil-transmission experiments in which the averagecharge of the cluster was measured, taking into account the clusterstructure and the interatomic distance of the incident cluster ionsto the foil [10,11]. Additionally, theoretical models explain thereduction of the cluster average charge as a result of the enhance-ment of the electron-binding energy of the constituent ions, pri-marily owing to the Coulomb interaction among them [10]. Thecharge state of an isolated ion moving in a solid determines thecoupling strength of the ion–target interaction, and hence, theinteratomic distance of the constituent ions, which relates closelyto their charges, is one of the most important parameters for a clar-ification of the mechanism of cluster irradiation effects. However,there are few experimental reports in which the average chargeof the constituent ions had been evaluated in relation to the inter-atomic distance, especially on the heavy ion clusters.

In a previous work [11], we have discussed the dependence ofcluster average-charge on the initial interatomic distance at the

82 A. Chiba et al. / Nuclear Instruments and Methods in Physics Research B 315 (2013) 81–84

instant of the foil-induced dissociation of Cþ2 ions. The main goal ofthis study will become a quantitative evaluation of the relationshipbetween the average charge and the interatomic distance of thecluster constituent ions moving in the solid. Therefore, the distri-butions of the interatomic distance for each combination of ioncharges at the foil exit are obtained by the trajectory simulationof the ions passing through the foil using the distributions of theinitial interatomic distance analyzed from the measured diver-gence angle of the constituent ions of 6-MeV Cþ2 ions after theypenetrate the foil.

Fig. 1. Divergence angular distributions for each product of charges qi � qj ofconstituent ions resulting from foil-induced dissociation of 6-MeV Cþ2 ions, passingthrough a 80-Å-thick amorphous carbon foil. The measurement and calculationresults are indicated by the open squares with error bar and the histogramsexpressed in the solid line, respectively. R2 is the coefficient of determination.

2. Experiment and results

The experiment is based on the simultaneous measurement ofthe divergence angle and the charge state of the constituent ionsdissociated from a Cþ2 ion passing through a foil with an accuratelyknown thickness. The 80-Å-thick amorphous carbon foil (ArizonaCarbon Foil Co., Inc.) was adopted after taking into considerationthe condition that the energy straggling of the ions is as small aspossible and that they reach the equilibrium charge. The thicknessof the foil was evaluated correctly by the energy-loss measurementusing He+ beam and the wavelength measurement using opticalcoherence technology. The incident Cþ2 ions lose several electronswithin a few atomic layers from the foil surface and immediatelydissociate due to a mutual Coulomb repulsion between their con-stituent ions. The range of distance between the constituent ionsis increased continuously in accordance with their charges. Afterthe ions penetrate the foil, they are analyzed based on their chargeusing the electric field of the deflection plates located behind thefoil. The spatial positions of the ions are detected by a micro-chan-nel plate (MCP) equipped with a phosphor screen. The positions ofthe constituent ions arriving at the MCP are indicated in the phos-phor screen as luminance points. The distribution of luminancepoints on the screen is stored as image data on an event-by-eventbasis. The charge state of each ion is estimated from the position ofits luminance point. In order to measure the divergence angle ofthe constituent ions, it is necessary to know their spatial positionswithout the deviation by the electric field of the deflection plates.Therefore, the hypothetical positions of the constituent ions on thescreen are estimated from their observed positions and charges.The divergence angle h of constituent ions can be defined as d/L,for an L much larger than d, where d and L are the distance betweentwo hypothetical positions and distance between the foil and thedetector, respectively. Using this system, which had a high angularresolution (1.4 � 10�4 rad (FWHM)), we obtained a simultaneousmeasurement of the divergence angles and charge state of the con-stituent ions with considerable accuracy at the rate of about 10events per second. A detailed description of the measurement sys-tem is shown in Ref. [11]. After analyzing the images of about180,000 events, obtained from current experimental condition,the average charge of the 6-MeV Cþ2 ions is 3.12 ± 0.01, and thecharge states from 2e to 4e accounts for approximately 98% ofthe entire charge. As a result, we obtained 6 patterns of the diver-gence-angular distributions for all possible combinations of threecharge states (shown as open squares in Fig. 1).

3. Trajectory simulation model and data analysis

A pair of dissociated constituent ions moves in the mediumwith increasing interatomic distance owing to the mutual Coulombpotential proportional to the product of their charges. The trajecto-ries of the constituent ions would be affected by the energy loss ofthe ions, the multiple elastic scattering with target nuclei, and theion induced potential (wake) other than the variation of theircharges via electron-capture and -loss processes. Such

perturbations of the constituent ions therefore increase with theirdwell time in the medium. Under the present experimental condi-tions, i.e., a foil thickness of 80 Å and a Cþ2 ion velocity of6.94 � 106 m/s, the dwell time is estimated to be no more than1 fs; therefore, the contribution from energy loss, multiple scatter-ing, and wake potential will not be very important to simulate theion trajectories. Further, it is considered that charge fluctuation ofthe ions dose not influence the ion trajectories much because mostof their charges are distributed in the narrow range from 2e to 4eand because the mutual Coulomb repulsion between ions is atten-uated due to the screening effect by target electrons. On the otherhand, it should be considered that the trajectories of the ions aresignificantly varied with the fluctuation in the initial interatomicdistance rint at the instant of foil-induced dissociation. Accordingto the calculation based on the screened Coulomb potential forthe 6-MeV Cþ2 ion passing through a 80-Å-thick foil, under theassumption that the mean distance of rint and the charge statesof the constituent ions moving in the foil are respectively 1.27 Å[12] and 3e, the distance rext between the ions at the foil exit in-creases to 1.35 Å. Therefore, the fluctuation in rint correspondingto the molecular vibration associated with some electronic excita-tions is much larger than the difference between rint and rext. Theinteratomic distance between the constituent ions after they pen-

Fig. 2. (a) Distributions D(rint)qi � qj for initial interatomic distances of the constit-uent ions at the instant of foil-induced dissociation of 6-MeV Cþ2 ions, calculated foreach product of their charges qi � qj when they emerged from a carbon foil of 80 Åthickness. (b) Simulated distributions of the interatomic distance of the constituentions at the foil exit, corresponding to each D(rint)qi � qj. The magnitude of eachdistribution is proportional to the yield ratio (shown in parentheses).

Fig. 3. Average charge of the constituent ions moving in a carbon foil, analyzed for6-MeV Cþ2 ions incidence, as a function of the interatomic distance. Dashed lineindicates the experimental result of average charge for C+ ions, penetrating at thesame speed as the Cþ2 ions, shown in Ref. [11].

A. Chiba et al. / Nuclear Instruments and Methods in Physics Research B 315 (2013) 81–84 83

etrate the foil, i.e., in vacuum, drastically increases in relation to rext

and the product of their charges qi � qj, owing to pure Coulombrepulsion without screening effect. Thus, the important parametersdetermining the divergence angle of the constituent ions in vac-uum are rint, which strongly govern the distance rext; the productof charges qi � qj; and the orientation angle of the incident Cþ2ion. If the charge state of the constituent ions is correlated withtheir interatomic distance, rint would have a significant effect onthe product of charges qi � qj; therefore, it is considered that thedivergence-angular distributions for each product of charges qi � qj

have an individual probability distribution of rint, i.e., D(rint)qi � qj.In this trajectory simulation, D(rint)qi � qj were approximated

according to a log-normal distribution function. The divergence-angular distributions for all possible combinations of charges from2e to 4e were reproduced by optimizing, as fitting parameters, thevariables in the log-normal function defined as the followingequation,

DðrintÞqi�qj ¼1ffiffiffiffiffiffiffi

2pp

rðrint � r0Þexp

�½lnðrint � r0Þ � l�2

2r2

( ); ð1Þ

where the mean value is expressed as expðlþ r2=2Þ þ r0 and r0 de-notes the minimum value of rint. The orientation angle relative tothe direction of motion of the incident Cþ2 ions was set randomly,where it ranged from 0� to 180�. The ion trajectories in the foil werecalculated stepwise in time intervals of Dt = 5 � 10�18 s. Themomentum of the ion in each step was determined taking into ac-count the screened Coulomb potential, multiple elastic scatteringwith target nuclei, wake potential, and the energy loss of the ion.The screening length is defined as t/xp, where t is the velocity ofthe ions and xp is the plasma frequency for amorphous carbon(�hxp ¼ 23:4 eV). The Moliere potential was used to describe theinteractions between the ions and the target nuclei, and the coher-ent dynamics response of the target electrons [13] was used to esti-mate the wake potential. The energy loss and the charge state of theion were calculated, respectively, by the SRIM code [14] and a clus-ter average-charge theory taking into account the Coulomb interac-tion of the ions, described in Ref. [7]. The repulsion force betweenthe ions in vacuum was exerted solely by the Coulomb potentialwithout screening effect.

The calculation results corresponding to the product of chargesqi � qj, are normalized by the total events so that they can be accu-rately compared with the experimental results; these results areshown as a histogram in Fig. 1. When the theoretical model appliesthe log-normal function to the probability distribution of the inter-atomic distance of the Cþ2 ions incident on the foil, the divergence-angular distributions of the constituent ions after foil penetrationare well reproduced, as shown by the coefficient of determinationR2 indicated in the same figure. D(rint)qi � qj for each qi � qj and thedistributions of the interatomic distance of the constituent ions atthe foil exit, corresponding to each D(rint)qi � qj, are represented inFig. 2(a) and (b), respectively. The magnitude of D(rint)qi � qj is pro-portional to the yield ratio (indicated in parentheses) for the com-bination of charges qi and qj. Distributions expressed as ahistogram in Fig. 2(b) were obtained from D(rint)qi � qj by the trajec-tory simulation of the ions moving in the foil; the magnitude ofthese distributions is also equal to that of D(rint)qi � qj.

When the ions emerge from the foil, they are assumed to keeptheir charges because the edge effect or the surface effect can beconsidered mostly negligible under this experimental conditionin which the interaction time between the ions and the rear surfaceof the foil is very short. Therefore, Fig. 2(b) indicates the chargefraction for the distance between the ions moving in the foil. Final-ly, the average charge of the constituent ions moving in the foil wasrepresented as a function of their interatomic distance, as shown inFig. 3. For comparison, an experimental result of the average

charge of 3.44 for C+ ions, penetrating through the foil at the samespeed as the Cþ2 ions, shown in Ref. [11], is also plotted as a dashedline. The effect of charge reduction for cluster ions is expected todecrease with increasing the interatomic distance of the constitu-ent ions, so it is reasonable that the average charge obtained for Cþ2ions comes close to that of the experimental result for Cþ2 ions.

4. Summary

We performed, via foil-transmission experiments using Cþ2 ions,the quantitative evaluation of the relationship between the clusteraverage charge and the interatomic distance of the constituent ionsmoving in a solid. In the trajectory simulation, the divergence-angular distributions of the constituent ions after the ions pene-trate the foil were well reproduced by describing the fluctuationin the interatomic distance of the incident Cþ2 ions by a log-normaldistribution function. The charge state of the ions appeared to be

84 A. Chiba et al. / Nuclear Instruments and Methods in Physics Research B 315 (2013) 81–84

directly related to the interatomic distance at the instant of clusterdissociation. These results will provide genuine guidance forunderstanding the behavior of the cluster ions in a solid.

Acknowledgments

The authors gratefully acknowledge the crew of the 3-MV Tan-dem accelerator of JAEA/Takasaki for their technical support in theexperiments. This work was partially supported by the Inter-orga-nizational Atomic Energy Research Program in an academic collab-orative agreement between the JAEA and the University of Tokyo.

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