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Sweeping-out-electrons effect under impact of large molecules and clusters
Nuclear Instruments and Methods in Physics Research B 193 (2002) 240–247 www.elsevier.com/locate/nimb
Sweeping-out-electrons effect under impact of large molecules and clusters E. Parilis
*
California Institute of Technology, 200-36, Pasadena, CA 91125, USA
Abstract This paper presents a review of one of the most intriguing effects of non-additivity under impacts of polyatomic molecules and clusters, observed up to now only in a variety of electronic energy loss phenomena: electron emission, luminescence, projectile charge state formation, electron–hole pairs generation and the high-energy part of sputtering under cluster impacts. The sublinear effects consist in decreasing yields per atom with increasing number of cluster constituents. The reduction is caused by the mechanism of sweeping-out-electrons that removes some electrons from the cluster trek in binary collisions between the front running cluster atoms and the target atoms, leaving fewer available for the tailing ones. In addition to the pioneering experimental studies performed at IPN, Orsay, these and similar effects were observed in many laboratories and are thought to be the expressions of a general mechanism. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 79.20.Rf; 36.40.)c; 34.50.Dy
1. Introduction After decades of studying the secondary emission under ion bombardment, the time had came to investigate the same processes under impacts of molecules and clusters. The first question was: are all the effects additive? Is there a dependence of the secondary yields per atom on the number of atoms in a cluster impinging the solid surface at the same velocity? Along with the linear phenomena, a group of non-linear effects has been discovered. They consist in an enhancement, in some cases very drastic, of the yield per atom, with increasing number of atoms in the cluster. All of them are
*
Tel.: +1-562-634-7417. E-mail address: [email protected] (E. Parilis).
connected to the nuclear stopping and could be regarded as a natural result of the synergetic action of the cluster constituents. What was puzzling and intriguing and yet not completely explained was the existence of some non-additivity effects, in which the total yield is sublinear, i.e. it is less than proportional to the number of atoms in the cluster. The extent of reduction increased with the increasing number of cluster constituents. It looked like the atoms were mutually blocking or screening each other, diminishing the resulting effect. All the sublinear effects were observed only in the electronic stopping related phenomena. They were discovered in different laboratories, studying the secondary electron emission, luminescence, and projectile charge state formation after passing through thin films. Clusters and polyatomic molecules in wide
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E. Parilis / Nucl. Instr. and Meth. in Phys. Res. B 193 (2002) 240–247
range of energies, from a few keV/atom to 4 MeV/ atom, were used as projectiles. It was supposed that the sublinear reduction is due to a sweepingout-electrons effect, consisting in removing some electrons from the cluster trek in binary collisions between the front running cluster atoms and target atoms, leaving fewer available for the rear ones.
2. Secondary electron emission A sublinear effect in the secondary electron emission from CsI under impacts of gold clusters Aun has been observed experimentally by the group of Le Beyec at IPN, Orsay [1]. The effect manifests itself in a decrease of the electron yield per one cluster atom cn ðEÞ=n with increasing number of atoms in the cluster n. The ratio Rn ¼ cn ðEÞ=nc1 ðEÞ, being a measure of the effect, is less than 1 and decreases from 0.75 to 0.5 with n increasing from 2 to 4 and the projectile energy E increasing from 0.5 to 4 MeV/atom. The mechanism of sweeping-out-electrons was proposed to explain this effect. The electron emission yield under n-atom cluster impacts equals cn ¼
n X
Nk1 qre kw;
ð1Þ
k¼1
It was reasonable to take for rs the same crosssection as for ionization, rs ¼ re . Another possibility is to take the cross-section just proportional to the electronic energy losses re ¼ ke ðdE=dxÞe =q, where ke (ions/eV) is the efficiency of the electronic energy losses ðdE=dxÞe for internal ionization in solid. Then the ratio re =prn2 could be replaced by dn ðdE=dxÞe with dn ¼ ke =qprn2 The Eq. (2) gave a good agreement with the experimental data [1]. The decrease of Rn ðEÞ with the energy is due to the increase of re ðEÞ and ðdE=dxÞe in this energy region. That it is not always so, is shown by the experiments with hydrogen clusters. A similar non-linear effect in electron emission from carbon films under hydrogen cluster impacts has been observed at Lyons by Billebaud et al. [3] (Fig. 1). They used cluster beams Hn with n ¼ 1–13 and energy E ¼ 20–150 keV/proton. The ratio Rn ðEÞ < 1 was increasing slightly with the energy E. The same calculations using Eq. (2) show a good agreement between experimental and theoretical functions Rn ðnÞ and Rn ðEÞ (Fig. 2). The values of the parameters used were: N0 ¼ 1, 3 , k ¼ 30 A , w ¼ 0:5. In this case, in q ¼ 0:11 at/A accordance with Eq. (2), the Rn ðEÞ increases with E because both c1 ðEÞ and ðdE=dxÞe decrease in the given energy region. The same group studying
where (N q)k1 is the number of available electrons after passage of (k 1)th projectile atom through the cross-section prn2 (where rn is the radius of the n-atom cluster); q is the atomic density of the solid; k is the secondary electron path length, w is the electron escape probability; re is the binary atom– atom or ion–atom collision ionization cross-section. It could be taken from the same experimental data as re ¼ c1 =kwN0 q or calculated from the theory [2]. The numbers of available electrons decrease in a geometrical progression ðN qÞk ¼ ðN qÞk1 (1 rs =prn2 ), depending on rs , the cross-section of electron sweeping out from the volume by one projectile atom. By summation the geometrical progression one gets Rn ¼ cn =nc1 n ¼ 1 1 rs =prn2 = nrs =prn2 :
ð2Þ
241
Fig. 1. Scheme of hydrogen cluster impact on carbon.
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Fig. 2. Sublinear effect in electron emission under Hn impacts on carbon. Solid lines – calculation, points – experiment [3].
electron emission from C under Aun impacts observed a decrease in R3 from 0.85 to 0.77 with E increasing from 150 to 500 keV/at and a decrease from R3 ¼ 0:85 to R9 ¼ 0:65 at E ¼ 150 keV/at [16]. Susuki [4] of Osaka Kyoiku University studied the vicinage effect (the influence of the neighboring cluster atoms) in secondary electron emission from a (0 0 1) SnTe surface induced by hydrogen clusters H2 and H3 and found the ratios Rn to decrease from R2 ¼ 0:95 to 0.85 and from R3 ¼ 0:9 to 0.8 with the energy increase from 7 to 12 keV/amu. Both values of Rn and their energy dependence are in a good agreement with a calculation using Eq. (2). Ritzau and Baragiola [5] of the University of Virginia found a molecular effect in secondary electron emission in the backward direction from carbon foils under 0.5–50 keV/amu H2 , CO, N2 and O2 ion bombardment. In a study by Veje [6] a similar effect has been observed for electron emission induced by HeH compared to the sum of electron yields for H and He at the same velocity (Fig. 3). Recently Borisov and Mashkova [7] of Moscow University observed a molecular effect in the electron emission from graphite, chromium and gold under N2 with the energy 15–34 keV. The ratios R2 , they found, fit Eq. (2). A sublinear effect in kinetic electron emission from CsI under impacts of very slow (the velocity v ¼ 5 105 –7 106 cm/s) and large (the mass
Fig. 3. Molecular effect in electron emission under HeH impacts [6].
M ¼ 1182–66 430 amu) biomolecules has been reported by the Orsay group [8]. The electron yield for biomolecules of the same velocity was found to be roughly proportional to M 0:69 which means a lack of additivity in electron emission by projectile atoms. The data on electron yield by single atoms were not available. Given that the bioorganic molecules have very close elemental composition, one can take the mass of the biomolecule LHRH (M ¼ 1182 amu) as unity, n ¼ 1. Then for INSULIN (M ¼ 5733 amu) n 5, for TRYPSIN (M ¼ 23 296 amu) n 20 and for ALBUMIN (M ¼ 66 430 amu) n 56, approximately (Fig. 4). One can calculate from the experimental data the ratios Rn ¼ cn =nc1 with c1 being the electron emission yield for LHRH. The ratios were equal to Rn ¼ 0:25–0:75 and decreased with both n and v increasing. This is a typical sublinear effect described very well by the same equations. The simple rule M 0:69 that would give cn / n0:69 and Rn / n0:31 does not reflect in full the mass dependence of the electron emission (Fig. 5).
3. Luminescence under molecular ion bombardment As both luminescence under ion bombardment and ion induced electron emission are due solely to electron energy deposition, one should expect a similar sublinear effect in light emission from solids under cluster impacts. Indeed a group of Texas
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Fig. 4. Scheme of electron ejection from CsI under impact of biomolecules. r5 and r20 are the cluster radii. A typical chain structure of the biomolecules is shown in the window.
out-electrons, and the same formalism was applied to calculate it [9]. The formula for the reduction factor Rnm , has been generalized for heteroatomic clusters containing n atoms of type a and m atoms of type b, n Rnm ðv; xÞ ¼ 1 1 dnm ð dE=dxÞa ð1 dnm ðdE=dxÞb Þm = ndnm ð dE=dxÞa þ mdnm ð dE=dxÞb ; ð3Þ
Fig. 5. Sublinear effect in kinetic electron emission from CsI under impacts of large (M ¼ 1182–66 430 amu) biomolecules [8]. The mass of LHRH is taken as 1. The horizontal lines represent the M 0:69 rule.
A&M University observed a reduction, with n and E increasing, in the number of photons per atom emitted from CsI bombarded with polyatomic þ þ þ projectiles Hþ n , (NaF)n N ðn ¼ 1; 2Þ, Na , Cs2 I þ and Cs at impact energy E ¼ 5–30 keV. The effect has been attributed to the mechanism of sweeping-
2 with dnm ¼ ke =qprnm , where rnm is the cluster radius, and ke (ions/eV) is the efficiency of the electronic energy losses ðdE=dxÞe for internal ionization and creation of electron–hole pairs in the solid. The formula has been refined by taking into account that the energy to be spent to remove an electron increases by a factor 1 þ dnm ðdE=dxÞe due to charging the volume with every single atom passing through it. Unlike electrons, that can escape the solid only from a thin layer, the photons come out from the depth, and the luminescence yield should be integrated along the path. For Hn , the lightest among the projectiles, the lateral straggling of the trajectory had to be taken into account. This formula could be applied also to the electron
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emission under heteroatomic clusters of the type used in [5,6]. The calculated ratio Rnm < 1 decreases with the number of atoms in the cluster and projectile energy in a good agreement with the experiment. In the same year Koch, Tuszynski, Tomaschko and Voit in Oldenburg and Erlangen [10] have studied the photon emission under 1 MeV carbon cluster Cn ðn ¼ 2–10) impacts. They found that the luminescence exhibits a very strong sublinear effect ranging from Rn ¼ 0:9–0.6 for CsI to Rn ¼ 0:5–0.2 for POPOP.
4. Charge state of cluster atoms passing through thin foils The most recent manifestation of the sweepingout-electrons mechanism was found by the same group of IPN, Orsay, having studied the charge state of fast atoms passing through solids [11]. They have observed the mean charge state qn of carbon atoms, passing through a thin carbon foil ) with energy 1, 2 and 4 MeV/at, (s ¼ 100–2000 A in clusters Cn (n ¼ 3, 5, 8 and 10), being smaller than the mean charge q1 of a single carbon atom C1 passing through the same foils with the same velocity. The curves Rn ðsÞ < 1, show an explicit decrease with n and increase with the increasing path in the solid s, approaching Rn ¼ 1 at large s, or a decrease with the exit energy E, which was calculated using the SRIM code. It means that the closer are the clusters to the point of entrance into the solid, the larger is the vicinage effect of diminishing the charge state. The curve for q1 ðsÞ, which is the equilibrium charge qe ðEÞ of a single carbon atom, formed in competing electron capture and loss collisions, can be obtained from the same experiment. It is very important that the experimental value qe ðsÞ proved to be proportional to the electronic energy loss ðdE=dxÞe and to follow its trend in all three explored energy ranges: qe ðsÞ ¼ kðdE=dxÞe , for energy with k 1 ¼ 66:67, 58.3 and 45.5 eV/A regions 1, 2 and 4 MeV/at respectively, that reflects some differences in the mechanisms of electron stripping around the maximum of ðdE=dxÞe .
One can introduce a variable rðsÞ ¼ ðdE=dxÞe = ðJ qÞ ¼ qe ðsÞ=ðJ qkÞ, which has a meaning of the cross-section of producing one positive charge, and J is the mean energy needed for this. It could be estimated as J ¼ 2Ri Vi =qe þ Ee qe where Vi are the carbon ionization potentials: V1 ¼ 10:6 eV; V2 ¼ 26:05 eV and V3 ¼ 50:4 eV, the factor 2 reflects the symmetry of the C–C collisions, and Ee ¼ 5–10 eV is the average energy of the stripped electrons. For J ¼ 64:96 eV which is compara2 , a value that is ble with k 1 one gets r ¼ 25:6 A reasonable for the region of maximum stripping and ionization. To verify the applicability of the mechanism, one has to calculate the total charge Qn ¼ nqn of a n-atom carbon cluster, where qn is the equilibrium charge of one atom, passing through the solid within a cluster. The foil thickness was much larger than the charge equilibrium path, s se , so qn depended only on the exit energy E. Each of the front running cluster atoms, forming its charge in binary collision with target atoms, increases the ionization energy of the cluster, that equals Vn ¼ V þ Qn e2 =rn , by a factor 1 þ rðsÞ=prn2 ¼ 1 þ dn 1 ðdE=dxÞe , where dn ¼ ðprn2 J qÞ and V is the ionization energy of one atom. In the mean time the number of target atoms available for stripping collisions with the same cross section is reduced by 1 dn ðdE=dxÞe . The total charge Qn is a sum of a geometrical progression with the factor (1 dn ðdE=dxÞe )/(1 þ dn ðdE=dxÞe ) and the ratio Rn equals Rn ¼ qn =q1 ¼ Qn =ðnq1 Þ n ¼ 1 1 dn ð dE=dxÞe = 1 þ dn ð dE=dxÞe ð4Þ = 2ndn ð dE=dxÞe = 1 þ dn ð dE=dxÞe : The Eq. (4) gives an increase of Rn with increasing path s, caused both by decreasing ðdE=dxÞe and by increasing separation of the cluster atoms rn due to Coulomb repulsion. The corresponding differential equation, Md 2 rn =dt2 ¼ ðn 1Þq2 e2 =ern2 ;
ð5Þ
connects the radial acceleration with the electrical force, acting on each carbon atom with charge q from the rest of the cluster atoms (n 1), charged q each, e is the dielectric constant, which takes ac-
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count of the Coulomb force screening. The charge qðv; sÞ of a single carbon atom C1 is a variable depending on the velocity v and distance s, qðv; sÞ ¼ qe ðvÞ½1 expð s=s0 Þ ;
ð6Þ
where qe ðvÞ is the equilibrium charge of C1 in carbon. The equilibrium charge path length pa. rameter s0 is known to equal approximately 20 A As the calculations show, the separation rn ðsÞ does not depend very much on s0 , because in the experiments in hand the thickness of the foils and the total path were much larger s s0 . We can take qðvÞ ¼ qe ðvÞ depending only on the exit velocity v or exit energy E ¼ Mv2 =2. With t ¼ s=v the differential equation for radial motion in s is d2 rn =ds2 ¼ ðn 1Þq2e e2 =2Eern2
ð7Þ
with the initial conditions rn ¼ rno and drn =ds ¼ 0 at s ¼ 0, where rno is the radius of the carbon cluster. The radius of the group of carbon atoms after passing the charge equilibrium distance s0 , where q ¼ qe is close to rno . As the carbon cluster size and shape are unknown, it is natural to assume that rno ¼ 1=3 ð3n=4pqÞ , i.e. rno / n1=3 . Here q is the atomic 3 , the initial density of carbon. With q ¼ 0:1 at/A ; radii of the clusters are: r3o ¼ 1:92 A; r5o ¼ 2:28 A r8o ¼ 2:67 A; r10o ¼ 2:88 A. It is well understood that this formula cannot be used for fullerenes or ring-shaped molecules. If the radii rno are known, they can be used in the formulae above. Resolving the differential equation (7) one gets the functions Rn ðsÞ for different n. The dielectric constant for carbon with the density 2.2 g/cm3 for the frequency m ¼ v=s ¼ 1013 1014 s1 is equal to e ¼ 1:67. The result of the calculation [12,13] is shown in Fig. 6, where the calculated curves Rn ðsÞ are compared to the experimental ones. It is seen, that the sequence of the curves, their mutual distance and the general trend with s agree well with the experiment.
5. Electronic sputtering The process of sweeping out electrons should affect also the electronic sputtering under highenergy cluster impacts. The number of ionized atoms Ni left after each consecutive cluster atom
Fig. 6. Charge state ratio qn =q1 versus foil thickness s. Points – experiment [11], dashed lines – calculation [12,13].
has passed the charged trek cylinder is diminished by a factor 1 ri =prn2 , where ri is the ionization cross-section and rn is the cluster radius. The yield Yn is known to be proportional to the square of the number of ionized atoms Yn / Ni2 and, therefore, to ½ðdE=dxÞe 2 . The corresponding ratio Rn ¼ Yn =nY1 n 2 ¼ 1 1 ri =prn2 = nri =prn2
ð8Þ
is <1 and should decrease with the projectile energy per atom E and the number of cluster constituents n. To describe the non-linearity one uses usually the ratio enm ¼ mYn =nYm ¼ Rn =Rm enn1
ðn > mÞ or
¼ ðn 1ÞYn =nYn1 ¼ Rn =Rn1
ðm ¼ n 1Þ: ð9Þ
According to the above enn1 < 1 and decreases with E, but increases with n. Indeed, in the experiments on sputtering by 102 –104 keV/at Aun clusters [14] it was observed, that the ratios enn1 (n ¼ 2–4) sharply decrease with E and could be projected both to cross the line enn1 ¼ 1 and to change to the opposite the sequence of the curves
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E. Parilis / Nucl. Instr. and Meth. in Phys. Res. B 193 (2002) 240–247
Fig. 7. Calculated ratio enm for electronic sputtering under Aun impacts.
around E > 4 MeV/at (see Fig. 11 of Ref. [14]), where the electronic energy losses exceed the nuclear ones, albeit the yield still cannot be attributed fully to the electronic sputtering. The calculation predicts such a trend for electronic sputtering (Fig. 7). The experiment shows a linear increase of Yn with n (see Fig. 14 of Ref. [14]) in contrast to the Yn / n3 or Yn / n2 enhancement at lower projectile energies, where electronic sputtering is inferior to the nuclear one. The deviation is caused by the sweeping-out-electrons effect which predicts for electronic sputtering Yn / nb with b < 1. Around E ¼ 4 MeV/at, b ¼ 0:6, while for electron emission yield under Aun [1], which is linear with ðdE=dxÞe , b ¼ 0:26. The final trend of Yn ðnÞ depends on the shares of electronic and nuclear sputtering in the total yield.
6. Conclusion The formalism used in the above calculations is rather simple and transparent. It consists in the summation a geometrical progression with a factor, containing only the ratio re =prn2 or dn ðdE=dxÞe . That leaves very little, if any, space for fitting, because the value of the fraction is based mostly on the information, taken from the same experiment. Nevertheless it gives both the right sequence for Rn and its dependence on n, as well as the de-
pendence on E. The energy dependence of the sublinear effect always reflects the energy dependence of the electron removing collisions, as well as the dispersion of cluster atom trajectories. The contribution of these two factors is different in different phenomena. In electron emission, coming from a thin surface layer, there is no sufficient increase in rn along the trajectory and Rn ðEÞ is determined by the energy dependence of re ðEÞ or ðdE=dxÞe . By contrast, in the charge state formation, the energy loss in thin films is negligible, so the dependence Rn ðsÞ would come from rn ðsÞ. The trajectory straggling was important also in luminescence under hydrogen cluster impacts. The effect of sweeping out electrons is not just a vicinage-parameter effect, but a deeply dynamic collision process. It is obvious that no projectile could sweep out all the target electrons, and there is no shortage of electrons in the solid. The idea behind the original calculation was that the crosssection of single ionization in Eqs. (1) and (2) is the largest one to produce secondary electrons. The next one, the cross-section of the second ionization of an atom, that has already lost one electron in a binary collision with a front running cluster atom, is much smaller because the second ionization potential is larger. That was the meaning of the mechanism: the remaining ions are much harder to be ionized, so they do not contribute anymore to the electron emission. Of course this was just the first approximation. The next one was to take into account the increase of the ionization potential of the trek due to its charging by the front running atoms. One has, of course, to take into account the ionization (stripping) and charging of the projectile cluster itself. This is important in the case of electron emission under large biomolecule impacts and is the essence of the projectile ion charge calculation. Actually the collision is symmetrical: both the projectile and the target atoms do form, what in molecular orbital theory is called, a quasimolecule. In this temporal flying-by object the ionization state of the target atom affects the probability of electron emission in the same way as the ionization state of the projectile. One would say that there is an analogy between the secondary emission phenomena described
E. Parilis / Nucl. Instr. and Meth. in Phys. Res. B 193 (2002) 240–247
above. Actually it is not an analogy, it is the same event: a group of fast atoms is passing through a solid experiencing collisions with target atoms. If one collects the electrons, knocked out from the target atoms and stripped from the projectiles, it is the electron emission with sublinear cluster effect. If one follows the stripped projectile atoms, it is the reduction in the charge state of the cluster atoms, because fewer electrons were removed. If one looks at the ionization of the target atoms it is the photon emission or any other of electronic energy loss effects, like electronic sputtering with a yield per atom that would decrease with the number of cluster constituents. What other phenomena should we expect to be affected by the mechanism of sweeping-outelectrons? Probably everything that is connected to the electronic stopping, for instance, creation of radiation defects, colors centers, electron–hole pairs, and induced conductivity, electronic desorption and the electronic sputtering, including the desorption of large biomolecules under cluster and molecular bombardment. An interesting sublinear effect in the emission of Si2þ ions under Aum cluster impacts was reported at the ICACS-19 by Belykh [15]. The creation of doubly charged ions, like the electron emission [16], is a binary collision ionization phenomenon that should be strongly affected by the sweeping-out-electrons effect. The same mechanism could explain the pulse height defect in a surface barrier detector under MeV cluster impacts, which is due to a reduction in the electron–hole pair creation. An estimate of the contribution into the pulse height defect, caused by sweeping-out-electrons, gives a correct dependence on both n and E. The main goal of this paper was to attract attention to a peculiar and yet neither well studied, nor fully understood effect, which has been ob-
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served in too many phenomena to be regarded as just an occasional event. References [1] K. Baudin, A. Brunelle, S. Della-Negra, J. Depauw, Y. Le Beyec, E. Parilis, Nucl. Instr. and Meth. B 117 (1996) 47. [2] E.S. Parilis, L.M. Kishinevsky, N.Yu. Turaev, B.E. Baklitzky, F.F. Umarov, V.Kh. Verleger, S.L. Nizhnaya, I.S. Bitensky, Atomic Collisions on Solid Surfaces, NorthHolland, Amsterdam, London, New York, Tokyo, 1993. [3] A. Billebaud, D. Dauvergne, M. Fallavier, R. Kirsh, J.-C. Poizat, J. Remillieux, J.-P. Tomas, H. Rothard, Nucl. Instr. and Meth. B 112 (1996) 79; A. Billebaud, D. Dauvergne, M. Fallavier, R. Kirsh, J.-C. Poizat, J. Remillieux, J.-P. Tomas, H. Rothard, Radiat. Eff. Defect. Sol. 126 (1993) 373. [4] Y. Susuki, Z. Phys. D 42 (1997) 293. [5] S.M. Ritzau, R.A. Baragiola, Phys. Rev. B 58 (1998) 2529. [6] E. Veje, Nucl. Instr. and Meth. 194 (1982) 433. [7] A.M. Borisov, E.S. Mashkova, E.S. Parilis, Vacuum, to be published. [8] A. Brunelle, P. Chaurand, S. Della-Negra, Y. Le Beyec, E. Parilis, Rapid Commun. Mass Spectrom. 11 (1997) 353. [9] K. Baudin, E.S. Parilis, J.F. Blankenship, M.J. Van Stipdonk, E.A. Schweikert, Nucl. Instr. and Meth. B 134 (1998) 352. [10] K. Koch, W. Tuszynski, Ch. Tomaschko, H. Voit, Nucl. Instr. and Meth. B 146 (1998) 198. [11] A. Brunelle, S. Della-Negra, J. Depauw, D. Jacquet, Y. Le Beyec, M. Pautrat, Phys. Rev. A 59 (1999) 4456. [12] E. Parilis, Charge State of Carbon Atoms Passing Through Thin Foils, Report to IPN, Orsay, 1998. [13] E. Parilis, Comments on Atomic and Molecular Physics (2001). [14] A. Brunelle, S. Della-Negra, J. Depauw, D. Jacquet, Y. Le Beyec, M. Pautrat, K. Baudin, H.H. Andersen, Phys.Rev. A 63 (2001) 022902. [15] S.F. Belykh, A.V. Samartzev, V.V. Palitsin, A. Adriaens, F. Adams, in: 19th International Conference on Atomic Collisions in Solids, Paris, 2001, Abstracts, p. 221. [16] M. Fallavier, R. Kirsch, J.C. Poizat, J. Remillieux, J.P. Thomas, Nucl. Instr. and Meth. B 164–165 (2000) 920.
Sweeping-out-electrons effect under impact of large molecules and clusters E. Parilis
*
California Institute of Technology, 200-36, Pasadena, CA 91125, USA
Abstract This paper presents a review of one of the most intriguing effects of non-additivity under impacts of polyatomic molecules and clusters, observed up to now only in a variety of electronic energy loss phenomena: electron emission, luminescence, projectile charge state formation, electron–hole pairs generation and the high-energy part of sputtering under cluster impacts. The sublinear effects consist in decreasing yields per atom with increasing number of cluster constituents. The reduction is caused by the mechanism of sweeping-out-electrons that removes some electrons from the cluster trek in binary collisions between the front running cluster atoms and the target atoms, leaving fewer available for the tailing ones. In addition to the pioneering experimental studies performed at IPN, Orsay, these and similar effects were observed in many laboratories and are thought to be the expressions of a general mechanism. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 79.20.Rf; 36.40.)c; 34.50.Dy
1. Introduction After decades of studying the secondary emission under ion bombardment, the time had came to investigate the same processes under impacts of molecules and clusters. The first question was: are all the effects additive? Is there a dependence of the secondary yields per atom on the number of atoms in a cluster impinging the solid surface at the same velocity? Along with the linear phenomena, a group of non-linear effects has been discovered. They consist in an enhancement, in some cases very drastic, of the yield per atom, with increasing number of atoms in the cluster. All of them are
*
Tel.: +1-562-634-7417. E-mail address: [email protected] (E. Parilis).
connected to the nuclear stopping and could be regarded as a natural result of the synergetic action of the cluster constituents. What was puzzling and intriguing and yet not completely explained was the existence of some non-additivity effects, in which the total yield is sublinear, i.e. it is less than proportional to the number of atoms in the cluster. The extent of reduction increased with the increasing number of cluster constituents. It looked like the atoms were mutually blocking or screening each other, diminishing the resulting effect. All the sublinear effects were observed only in the electronic stopping related phenomena. They were discovered in different laboratories, studying the secondary electron emission, luminescence, and projectile charge state formation after passing through thin films. Clusters and polyatomic molecules in wide
0168-583X/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 2 ) 0 0 7 5 6 - 5
E. Parilis / Nucl. Instr. and Meth. in Phys. Res. B 193 (2002) 240–247
range of energies, from a few keV/atom to 4 MeV/ atom, were used as projectiles. It was supposed that the sublinear reduction is due to a sweepingout-electrons effect, consisting in removing some electrons from the cluster trek in binary collisions between the front running cluster atoms and target atoms, leaving fewer available for the rear ones.
2. Secondary electron emission A sublinear effect in the secondary electron emission from CsI under impacts of gold clusters Aun has been observed experimentally by the group of Le Beyec at IPN, Orsay [1]. The effect manifests itself in a decrease of the electron yield per one cluster atom cn ðEÞ=n with increasing number of atoms in the cluster n. The ratio Rn ¼ cn ðEÞ=nc1 ðEÞ, being a measure of the effect, is less than 1 and decreases from 0.75 to 0.5 with n increasing from 2 to 4 and the projectile energy E increasing from 0.5 to 4 MeV/atom. The mechanism of sweeping-out-electrons was proposed to explain this effect. The electron emission yield under n-atom cluster impacts equals cn ¼
n X
Nk1 qre kw;
ð1Þ
k¼1
It was reasonable to take for rs the same crosssection as for ionization, rs ¼ re . Another possibility is to take the cross-section just proportional to the electronic energy losses re ¼ ke ðdE=dxÞe =q, where ke (ions/eV) is the efficiency of the electronic energy losses ðdE=dxÞe for internal ionization in solid. Then the ratio re =prn2 could be replaced by dn ðdE=dxÞe with dn ¼ ke =qprn2 The Eq. (2) gave a good agreement with the experimental data [1]. The decrease of Rn ðEÞ with the energy is due to the increase of re ðEÞ and ðdE=dxÞe in this energy region. That it is not always so, is shown by the experiments with hydrogen clusters. A similar non-linear effect in electron emission from carbon films under hydrogen cluster impacts has been observed at Lyons by Billebaud et al. [3] (Fig. 1). They used cluster beams Hn with n ¼ 1–13 and energy E ¼ 20–150 keV/proton. The ratio Rn ðEÞ < 1 was increasing slightly with the energy E. The same calculations using Eq. (2) show a good agreement between experimental and theoretical functions Rn ðnÞ and Rn ðEÞ (Fig. 2). The values of the parameters used were: N0 ¼ 1, 3 , k ¼ 30 A , w ¼ 0:5. In this case, in q ¼ 0:11 at/A accordance with Eq. (2), the Rn ðEÞ increases with E because both c1 ðEÞ and ðdE=dxÞe decrease in the given energy region. The same group studying
where (N q)k1 is the number of available electrons after passage of (k 1)th projectile atom through the cross-section prn2 (where rn is the radius of the n-atom cluster); q is the atomic density of the solid; k is the secondary electron path length, w is the electron escape probability; re is the binary atom– atom or ion–atom collision ionization cross-section. It could be taken from the same experimental data as re ¼ c1 =kwN0 q or calculated from the theory [2]. The numbers of available electrons decrease in a geometrical progression ðN qÞk ¼ ðN qÞk1 (1 rs =prn2 ), depending on rs , the cross-section of electron sweeping out from the volume by one projectile atom. By summation the geometrical progression one gets Rn ¼ cn =nc1 n ¼ 1 1 rs =prn2 = nrs =prn2 :
ð2Þ
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Fig. 1. Scheme of hydrogen cluster impact on carbon.
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Fig. 2. Sublinear effect in electron emission under Hn impacts on carbon. Solid lines – calculation, points – experiment [3].
electron emission from C under Aun impacts observed a decrease in R3 from 0.85 to 0.77 with E increasing from 150 to 500 keV/at and a decrease from R3 ¼ 0:85 to R9 ¼ 0:65 at E ¼ 150 keV/at [16]. Susuki [4] of Osaka Kyoiku University studied the vicinage effect (the influence of the neighboring cluster atoms) in secondary electron emission from a (0 0 1) SnTe surface induced by hydrogen clusters H2 and H3 and found the ratios Rn to decrease from R2 ¼ 0:95 to 0.85 and from R3 ¼ 0:9 to 0.8 with the energy increase from 7 to 12 keV/amu. Both values of Rn and their energy dependence are in a good agreement with a calculation using Eq. (2). Ritzau and Baragiola [5] of the University of Virginia found a molecular effect in secondary electron emission in the backward direction from carbon foils under 0.5–50 keV/amu H2 , CO, N2 and O2 ion bombardment. In a study by Veje [6] a similar effect has been observed for electron emission induced by HeH compared to the sum of electron yields for H and He at the same velocity (Fig. 3). Recently Borisov and Mashkova [7] of Moscow University observed a molecular effect in the electron emission from graphite, chromium and gold under N2 with the energy 15–34 keV. The ratios R2 , they found, fit Eq. (2). A sublinear effect in kinetic electron emission from CsI under impacts of very slow (the velocity v ¼ 5 105 –7 106 cm/s) and large (the mass
Fig. 3. Molecular effect in electron emission under HeH impacts [6].
M ¼ 1182–66 430 amu) biomolecules has been reported by the Orsay group [8]. The electron yield for biomolecules of the same velocity was found to be roughly proportional to M 0:69 which means a lack of additivity in electron emission by projectile atoms. The data on electron yield by single atoms were not available. Given that the bioorganic molecules have very close elemental composition, one can take the mass of the biomolecule LHRH (M ¼ 1182 amu) as unity, n ¼ 1. Then for INSULIN (M ¼ 5733 amu) n 5, for TRYPSIN (M ¼ 23 296 amu) n 20 and for ALBUMIN (M ¼ 66 430 amu) n 56, approximately (Fig. 4). One can calculate from the experimental data the ratios Rn ¼ cn =nc1 with c1 being the electron emission yield for LHRH. The ratios were equal to Rn ¼ 0:25–0:75 and decreased with both n and v increasing. This is a typical sublinear effect described very well by the same equations. The simple rule M 0:69 that would give cn / n0:69 and Rn / n0:31 does not reflect in full the mass dependence of the electron emission (Fig. 5).
3. Luminescence under molecular ion bombardment As both luminescence under ion bombardment and ion induced electron emission are due solely to electron energy deposition, one should expect a similar sublinear effect in light emission from solids under cluster impacts. Indeed a group of Texas
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Fig. 4. Scheme of electron ejection from CsI under impact of biomolecules. r5 and r20 are the cluster radii. A typical chain structure of the biomolecules is shown in the window.
out-electrons, and the same formalism was applied to calculate it [9]. The formula for the reduction factor Rnm , has been generalized for heteroatomic clusters containing n atoms of type a and m atoms of type b, n Rnm ðv; xÞ ¼ 1 1 dnm ð dE=dxÞa ð1 dnm ðdE=dxÞb Þm = ndnm ð dE=dxÞa þ mdnm ð dE=dxÞb ; ð3Þ
Fig. 5. Sublinear effect in kinetic electron emission from CsI under impacts of large (M ¼ 1182–66 430 amu) biomolecules [8]. The mass of LHRH is taken as 1. The horizontal lines represent the M 0:69 rule.
A&M University observed a reduction, with n and E increasing, in the number of photons per atom emitted from CsI bombarded with polyatomic þ þ þ projectiles Hþ n , (NaF)n N ðn ¼ 1; 2Þ, Na , Cs2 I þ and Cs at impact energy E ¼ 5–30 keV. The effect has been attributed to the mechanism of sweeping-
2 with dnm ¼ ke =qprnm , where rnm is the cluster radius, and ke (ions/eV) is the efficiency of the electronic energy losses ðdE=dxÞe for internal ionization and creation of electron–hole pairs in the solid. The formula has been refined by taking into account that the energy to be spent to remove an electron increases by a factor 1 þ dnm ðdE=dxÞe due to charging the volume with every single atom passing through it. Unlike electrons, that can escape the solid only from a thin layer, the photons come out from the depth, and the luminescence yield should be integrated along the path. For Hn , the lightest among the projectiles, the lateral straggling of the trajectory had to be taken into account. This formula could be applied also to the electron
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emission under heteroatomic clusters of the type used in [5,6]. The calculated ratio Rnm < 1 decreases with the number of atoms in the cluster and projectile energy in a good agreement with the experiment. In the same year Koch, Tuszynski, Tomaschko and Voit in Oldenburg and Erlangen [10] have studied the photon emission under 1 MeV carbon cluster Cn ðn ¼ 2–10) impacts. They found that the luminescence exhibits a very strong sublinear effect ranging from Rn ¼ 0:9–0.6 for CsI to Rn ¼ 0:5–0.2 for POPOP.
4. Charge state of cluster atoms passing through thin foils The most recent manifestation of the sweepingout-electrons mechanism was found by the same group of IPN, Orsay, having studied the charge state of fast atoms passing through solids [11]. They have observed the mean charge state qn of carbon atoms, passing through a thin carbon foil ) with energy 1, 2 and 4 MeV/at, (s ¼ 100–2000 A in clusters Cn (n ¼ 3, 5, 8 and 10), being smaller than the mean charge q1 of a single carbon atom C1 passing through the same foils with the same velocity. The curves Rn ðsÞ < 1, show an explicit decrease with n and increase with the increasing path in the solid s, approaching Rn ¼ 1 at large s, or a decrease with the exit energy E, which was calculated using the SRIM code. It means that the closer are the clusters to the point of entrance into the solid, the larger is the vicinage effect of diminishing the charge state. The curve for q1 ðsÞ, which is the equilibrium charge qe ðEÞ of a single carbon atom, formed in competing electron capture and loss collisions, can be obtained from the same experiment. It is very important that the experimental value qe ðsÞ proved to be proportional to the electronic energy loss ðdE=dxÞe and to follow its trend in all three explored energy ranges: qe ðsÞ ¼ kðdE=dxÞe , for energy with k 1 ¼ 66:67, 58.3 and 45.5 eV/A regions 1, 2 and 4 MeV/at respectively, that reflects some differences in the mechanisms of electron stripping around the maximum of ðdE=dxÞe .
One can introduce a variable rðsÞ ¼ ðdE=dxÞe = ðJ qÞ ¼ qe ðsÞ=ðJ qkÞ, which has a meaning of the cross-section of producing one positive charge, and J is the mean energy needed for this. It could be estimated as J ¼ 2Ri Vi =qe þ Ee qe where Vi are the carbon ionization potentials: V1 ¼ 10:6 eV; V2 ¼ 26:05 eV and V3 ¼ 50:4 eV, the factor 2 reflects the symmetry of the C–C collisions, and Ee ¼ 5–10 eV is the average energy of the stripped electrons. For J ¼ 64:96 eV which is compara2 , a value that is ble with k 1 one gets r ¼ 25:6 A reasonable for the region of maximum stripping and ionization. To verify the applicability of the mechanism, one has to calculate the total charge Qn ¼ nqn of a n-atom carbon cluster, where qn is the equilibrium charge of one atom, passing through the solid within a cluster. The foil thickness was much larger than the charge equilibrium path, s se , so qn depended only on the exit energy E. Each of the front running cluster atoms, forming its charge in binary collision with target atoms, increases the ionization energy of the cluster, that equals Vn ¼ V þ Qn e2 =rn , by a factor 1 þ rðsÞ=prn2 ¼ 1 þ dn 1 ðdE=dxÞe , where dn ¼ ðprn2 J qÞ and V is the ionization energy of one atom. In the mean time the number of target atoms available for stripping collisions with the same cross section is reduced by 1 dn ðdE=dxÞe . The total charge Qn is a sum of a geometrical progression with the factor (1 dn ðdE=dxÞe )/(1 þ dn ðdE=dxÞe ) and the ratio Rn equals Rn ¼ qn =q1 ¼ Qn =ðnq1 Þ n ¼ 1 1 dn ð dE=dxÞe = 1 þ dn ð dE=dxÞe ð4Þ = 2ndn ð dE=dxÞe = 1 þ dn ð dE=dxÞe : The Eq. (4) gives an increase of Rn with increasing path s, caused both by decreasing ðdE=dxÞe and by increasing separation of the cluster atoms rn due to Coulomb repulsion. The corresponding differential equation, Md 2 rn =dt2 ¼ ðn 1Þq2 e2 =ern2 ;
ð5Þ
connects the radial acceleration with the electrical force, acting on each carbon atom with charge q from the rest of the cluster atoms (n 1), charged q each, e is the dielectric constant, which takes ac-
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count of the Coulomb force screening. The charge qðv; sÞ of a single carbon atom C1 is a variable depending on the velocity v and distance s, qðv; sÞ ¼ qe ðvÞ½1 expð s=s0 Þ ;
ð6Þ
where qe ðvÞ is the equilibrium charge of C1 in carbon. The equilibrium charge path length pa. rameter s0 is known to equal approximately 20 A As the calculations show, the separation rn ðsÞ does not depend very much on s0 , because in the experiments in hand the thickness of the foils and the total path were much larger s s0 . We can take qðvÞ ¼ qe ðvÞ depending only on the exit velocity v or exit energy E ¼ Mv2 =2. With t ¼ s=v the differential equation for radial motion in s is d2 rn =ds2 ¼ ðn 1Þq2e e2 =2Eern2
ð7Þ
with the initial conditions rn ¼ rno and drn =ds ¼ 0 at s ¼ 0, where rno is the radius of the carbon cluster. The radius of the group of carbon atoms after passing the charge equilibrium distance s0 , where q ¼ qe is close to rno . As the carbon cluster size and shape are unknown, it is natural to assume that rno ¼ 1=3 ð3n=4pqÞ , i.e. rno / n1=3 . Here q is the atomic 3 , the initial density of carbon. With q ¼ 0:1 at/A ; radii of the clusters are: r3o ¼ 1:92 A; r5o ¼ 2:28 A r8o ¼ 2:67 A; r10o ¼ 2:88 A. It is well understood that this formula cannot be used for fullerenes or ring-shaped molecules. If the radii rno are known, they can be used in the formulae above. Resolving the differential equation (7) one gets the functions Rn ðsÞ for different n. The dielectric constant for carbon with the density 2.2 g/cm3 for the frequency m ¼ v=s ¼ 1013 1014 s1 is equal to e ¼ 1:67. The result of the calculation [12,13] is shown in Fig. 6, where the calculated curves Rn ðsÞ are compared to the experimental ones. It is seen, that the sequence of the curves, their mutual distance and the general trend with s agree well with the experiment.
5. Electronic sputtering The process of sweeping out electrons should affect also the electronic sputtering under highenergy cluster impacts. The number of ionized atoms Ni left after each consecutive cluster atom
Fig. 6. Charge state ratio qn =q1 versus foil thickness s. Points – experiment [11], dashed lines – calculation [12,13].
has passed the charged trek cylinder is diminished by a factor 1 ri =prn2 , where ri is the ionization cross-section and rn is the cluster radius. The yield Yn is known to be proportional to the square of the number of ionized atoms Yn / Ni2 and, therefore, to ½ðdE=dxÞe 2 . The corresponding ratio Rn ¼ Yn =nY1 n 2 ¼ 1 1 ri =prn2 = nri =prn2
ð8Þ
is <1 and should decrease with the projectile energy per atom E and the number of cluster constituents n. To describe the non-linearity one uses usually the ratio enm ¼ mYn =nYm ¼ Rn =Rm enn1
ðn > mÞ or
¼ ðn 1ÞYn =nYn1 ¼ Rn =Rn1
ðm ¼ n 1Þ: ð9Þ
According to the above enn1 < 1 and decreases with E, but increases with n. Indeed, in the experiments on sputtering by 102 –104 keV/at Aun clusters [14] it was observed, that the ratios enn1 (n ¼ 2–4) sharply decrease with E and could be projected both to cross the line enn1 ¼ 1 and to change to the opposite the sequence of the curves
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Fig. 7. Calculated ratio enm for electronic sputtering under Aun impacts.
around E > 4 MeV/at (see Fig. 11 of Ref. [14]), where the electronic energy losses exceed the nuclear ones, albeit the yield still cannot be attributed fully to the electronic sputtering. The calculation predicts such a trend for electronic sputtering (Fig. 7). The experiment shows a linear increase of Yn with n (see Fig. 14 of Ref. [14]) in contrast to the Yn / n3 or Yn / n2 enhancement at lower projectile energies, where electronic sputtering is inferior to the nuclear one. The deviation is caused by the sweeping-out-electrons effect which predicts for electronic sputtering Yn / nb with b < 1. Around E ¼ 4 MeV/at, b ¼ 0:6, while for electron emission yield under Aun [1], which is linear with ðdE=dxÞe , b ¼ 0:26. The final trend of Yn ðnÞ depends on the shares of electronic and nuclear sputtering in the total yield.
6. Conclusion The formalism used in the above calculations is rather simple and transparent. It consists in the summation a geometrical progression with a factor, containing only the ratio re =prn2 or dn ðdE=dxÞe . That leaves very little, if any, space for fitting, because the value of the fraction is based mostly on the information, taken from the same experiment. Nevertheless it gives both the right sequence for Rn and its dependence on n, as well as the de-
pendence on E. The energy dependence of the sublinear effect always reflects the energy dependence of the electron removing collisions, as well as the dispersion of cluster atom trajectories. The contribution of these two factors is different in different phenomena. In electron emission, coming from a thin surface layer, there is no sufficient increase in rn along the trajectory and Rn ðEÞ is determined by the energy dependence of re ðEÞ or ðdE=dxÞe . By contrast, in the charge state formation, the energy loss in thin films is negligible, so the dependence Rn ðsÞ would come from rn ðsÞ. The trajectory straggling was important also in luminescence under hydrogen cluster impacts. The effect of sweeping out electrons is not just a vicinage-parameter effect, but a deeply dynamic collision process. It is obvious that no projectile could sweep out all the target electrons, and there is no shortage of electrons in the solid. The idea behind the original calculation was that the crosssection of single ionization in Eqs. (1) and (2) is the largest one to produce secondary electrons. The next one, the cross-section of the second ionization of an atom, that has already lost one electron in a binary collision with a front running cluster atom, is much smaller because the second ionization potential is larger. That was the meaning of the mechanism: the remaining ions are much harder to be ionized, so they do not contribute anymore to the electron emission. Of course this was just the first approximation. The next one was to take into account the increase of the ionization potential of the trek due to its charging by the front running atoms. One has, of course, to take into account the ionization (stripping) and charging of the projectile cluster itself. This is important in the case of electron emission under large biomolecule impacts and is the essence of the projectile ion charge calculation. Actually the collision is symmetrical: both the projectile and the target atoms do form, what in molecular orbital theory is called, a quasimolecule. In this temporal flying-by object the ionization state of the target atom affects the probability of electron emission in the same way as the ionization state of the projectile. One would say that there is an analogy between the secondary emission phenomena described
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above. Actually it is not an analogy, it is the same event: a group of fast atoms is passing through a solid experiencing collisions with target atoms. If one collects the electrons, knocked out from the target atoms and stripped from the projectiles, it is the electron emission with sublinear cluster effect. If one follows the stripped projectile atoms, it is the reduction in the charge state of the cluster atoms, because fewer electrons were removed. If one looks at the ionization of the target atoms it is the photon emission or any other of electronic energy loss effects, like electronic sputtering with a yield per atom that would decrease with the number of cluster constituents. What other phenomena should we expect to be affected by the mechanism of sweeping-outelectrons? Probably everything that is connected to the electronic stopping, for instance, creation of radiation defects, colors centers, electron–hole pairs, and induced conductivity, electronic desorption and the electronic sputtering, including the desorption of large biomolecules under cluster and molecular bombardment. An interesting sublinear effect in the emission of Si2þ ions under Aum cluster impacts was reported at the ICACS-19 by Belykh [15]. The creation of doubly charged ions, like the electron emission [16], is a binary collision ionization phenomenon that should be strongly affected by the sweeping-out-electrons effect. The same mechanism could explain the pulse height defect in a surface barrier detector under MeV cluster impacts, which is due to a reduction in the electron–hole pair creation. An estimate of the contribution into the pulse height defect, caused by sweeping-out-electrons, gives a correct dependence on both n and E. The main goal of this paper was to attract attention to a peculiar and yet neither well studied, nor fully understood effect, which has been ob-
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served in too many phenomena to be regarded as just an occasional event. References [1] K. Baudin, A. Brunelle, S. Della-Negra, J. Depauw, Y. Le Beyec, E. Parilis, Nucl. Instr. and Meth. B 117 (1996) 47. [2] E.S. Parilis, L.M. Kishinevsky, N.Yu. Turaev, B.E. Baklitzky, F.F. Umarov, V.Kh. Verleger, S.L. Nizhnaya, I.S. Bitensky, Atomic Collisions on Solid Surfaces, NorthHolland, Amsterdam, London, New York, Tokyo, 1993. [3] A. Billebaud, D. Dauvergne, M. Fallavier, R. Kirsh, J.-C. Poizat, J. Remillieux, J.-P. Tomas, H. Rothard, Nucl. Instr. and Meth. B 112 (1996) 79; A. Billebaud, D. Dauvergne, M. Fallavier, R. Kirsh, J.-C. Poizat, J. Remillieux, J.-P. Tomas, H. Rothard, Radiat. Eff. Defect. Sol. 126 (1993) 373. [4] Y. Susuki, Z. Phys. D 42 (1997) 293. [5] S.M. Ritzau, R.A. Baragiola, Phys. Rev. B 58 (1998) 2529. [6] E. Veje, Nucl. Instr. and Meth. 194 (1982) 433. [7] A.M. Borisov, E.S. Mashkova, E.S. Parilis, Vacuum, to be published. [8] A. Brunelle, P. Chaurand, S. Della-Negra, Y. Le Beyec, E. Parilis, Rapid Commun. Mass Spectrom. 11 (1997) 353. [9] K. Baudin, E.S. Parilis, J.F. Blankenship, M.J. Van Stipdonk, E.A. Schweikert, Nucl. Instr. and Meth. B 134 (1998) 352. [10] K. Koch, W. Tuszynski, Ch. Tomaschko, H. Voit, Nucl. Instr. and Meth. B 146 (1998) 198. [11] A. Brunelle, S. Della-Negra, J. Depauw, D. Jacquet, Y. Le Beyec, M. Pautrat, Phys. Rev. A 59 (1999) 4456. [12] E. Parilis, Charge State of Carbon Atoms Passing Through Thin Foils, Report to IPN, Orsay, 1998. [13] E. Parilis, Comments on Atomic and Molecular Physics (2001). [14] A. Brunelle, S. Della-Negra, J. Depauw, D. Jacquet, Y. Le Beyec, M. Pautrat, K. Baudin, H.H. Andersen, Phys.Rev. A 63 (2001) 022902. [15] S.F. Belykh, A.V. Samartzev, V.V. Palitsin, A. Adriaens, F. Adams, in: 19th International Conference on Atomic Collisions in Solids, Paris, 2001, Abstracts, p. 221. [16] M. Fallavier, R. Kirsch, J.C. Poizat, J. Remillieux, J.P. Thomas, Nucl. Instr. and Meth. B 164–165 (2000) 920.