Sputtering of ice by low-energy ions

vailable online at www.sciencedirect.com Surface Science 602 (2008) 56 6 www.elsevier.com/locate/susc Sputtering of ice by low-energy ions M. Famá *, J. Shi, R.. aragiola Laboratory for tomic and Surface Physics, University of Virginia, harlottesville, V 22904, US Received 7 ugust 2007; accepted for publication October 2007 vailable online 5 October 2007 bstract We measured the total sputtering yield Y of amorphous water ice at 80 K for 0.35 4 kev He and r ions. We found that Y depends linearly on the elastic stopping cross section at low energies as predicted by the standard linear cascade theory of sputtering. s the energy increases, a quadratic dependence with the electronic stopping cross section arises due to cooperative effects between excitations produced by the projectile. We also studied how sputtering depends on the projectile incidence angle and found that Y follows a cos f (h) dependence with f =.45 ± 0.05 for 2 kev He + and f =.78 ± 0.08 for 2 kev r +. Measurements of Y for 2 kev ions vs. ice temperature between 30 and 40 K show the same temperature dependence as that reported previously for high-energy ions. We introduce a general formula to calculate Y below 00 kev once the ice temperature, projectile type, energy and angle of incidence are known. This formula can be used for modeling the production of extended neutral atmospheres around astrophysical icy bodies subject to ion bombardment. Ó 2007 Elsevier.V. ll rights reserved. Keywords: Ion bombardment; Stopping power; Sputtering; Water; Ice. Introduction * orresponding author. Tel.: + 434 9822335; fax: + 434 924353. E-mail address: maf7e@virginia.edu (M. Famá). The erosion or sputtering of water ice by energetic particles is an important process in the outer solar system, where icy bodies are constantly exposed to magnetospheric ions, the solar wind and cosmic rays. Sputtering, together with sublimation, is responsible for the production of tenuous, extended neutral atmospheres of water molecules ejected from icy satellites and ice grains embedded in planetary magnetospheres [,2]. Such atmospheres have been detected around icy satellites of Jupiter [3] and Saturn [4]. Modeling the production of tenuous atmospheres requires accurate laboratory data for sputtering yields of ice at ion energies and ice temperatures relevant to those astrophysical environments. The ejection of surface molecules by sputtering is characterized by the yield Y, or number of molecules ejected per incident ion. Sputtering occurs by either direct momentum transfer by the projectile to a target atom (elastic) or due to long lived repulsive electronic excitations which lead to atomic or molecular motion (electronic) [5,6]. While elastic sputtering is well understood and described by the standard linear cascade theory [7] (see review books [8,9]) electronic sputtering is still a subject of discussion due to the lack of identification of the repulsive electronic states. Electronic sputtering of ice was discovered three decades ago by rown et al. [0], who found that Y of water ice bombarded by MeV protons was orders of magnitude higher than predicted by the linear cascade theory, and was proportional to the square of the electronic energy deposition near the surface. Sputtering of water ice has been extensively studied since this pioneering work, and the extant literature is consistent with the total electronic sputtering yield Y being proportional to S 2 e [], where S e =de/ndx is the electronic stopping cross section, de/ dx is the projectile energy loss per unit path length and N is the target number density. The quadratic dependence has been thought to signal that sputtering is dominated by the interaction of pairs of excitations, such as the 0039-6028/$ - see front matter Ó 2007 Elsevier.V. ll rights reserved. doi:0.06/j.susc.2007.0.002

M. Famá et al. / Surface Science 602 (2008) 56 6 57 screened oulomb repulsion of ionized molecules. n alternative of historical interest is the suggestion that the quadratic behavior is caused by thermal spikes [2], temporary hot regions caused by the energy deposition of the projectile, from which evaporation can transiently occur. This has been disproved by detailed molecular dynamic simulations which, instead, support the view that the sputtering yield is quadratic in the repulsive energy deposited per unit path length near the surface [3]. eviations from the S 2 e at low ion velocities have been attributed to different projectile charge states and synergism between electronic and elastic collision processes, among others []. Recently, we proposed that the electronic sputtering yield at low velocities is indeed dominated by (screened) oulomb repulsion, but enhanced by the additional ionization produced close to the surface by electron capture by the projectile ion [4]. In contrast with the numerous studies of electronic sputtering of ice (a guide to the literature can be found in Ref. []), elastic sputtering by very low-energy ions (from hundreds evs to few kevs) has been barely studied, in spite of its importance to understand the interaction of solar wind ions and cold plasmas with comets, icy ring particles and satellites. ar-nun et al. [5] performed experiments using 0.5 6 kev H þ 2 and neon ions and a quadrupole mass spectrometer to measure the flux of the ejected species during bombardment. This method, based on the measurement of the partial pressure of water in vacuum conditions and the relation of the vapor pressure of ice vs. temperature, may not be reliable in terms of absolute values for the sputtering yield. They found that the sputtering yield of water molecules ejected intact does not depend on the ice temperature between 30 and 40 K. They indicate that the main contribution to the total sputtering yield is due to radiolytic production of O 2 and H 2. However, the molecular oxygen synthesized in ice by ion bombardment contributes less than 0% to the total yield for temperatures below 00 K [6,7]. hristiansen et al. [8] measured the sputtering yield of H 2 O, O 2 and N 2 O at 78 K under 2 6 kev r +, Ne +,N + and He + bombardment at 45 incident angle from the total ion fluence needed to remove a film of known thickness. They found that the linear cascade theory agrees with the experimental results only for ice water. On the other hand, Haring et al. [9] found that water molecules sputtered from ice by 6 kev ions have energies much lower than predicted by the linear cascade theory, although still much higher than thermal. They explained this difference as resulting from a lower (by a factor of 2 3) effective surface-binding energy. However, this was not reconciled with the fact that yields agree with theory using normal binding energies. Here we present an experimental study of the total sputtering yield of water ice at 80 K by low-energy ions (0.35 4 kev) of significantly different masses, He and r. The yields are obtained from the change in mass of the ice films during irradiation with a known fluence. Together with previous published data at higher energies, our results show the transition from elastic to electronic sputtering of water ice for both ions. We also measured the angular and temperature dependences of the sputtering yield. We used these results to introduce a simplified model containing the main physical features of the process, which reproduces the available experimental data from several laboratories with surprising accuracy. We give an empirical formula that can be used to model the production of sputtered tenuous H 2 O atmospheres around icy bodies embedded in magnetospheres of the outer solar system. 2. Experimental The measurements were done in an ultra-high vacuum chamber (base pressure 3 0 0 Torr), equipped with a 6 MHz gold-coated quartz-crystal microbalance (QM) with a sensitivity of 0.05 ML [20] ( ML corresponds to a single, closely packed layer of molecules 0 5 molecules/cm 2 ). The microbalance is mounted at the tip of a LHe-cooled rotary manipulator. The water films were vapor deposited onto the microbalance at 80 K with a deposition rate of 0.4 ML/s by dosing pure H 2 O gas through a microcapillary array and at normal incidence. The mass per unit area of the condensed films was determined by measuring the shift in the resonance frequency of the quartz-crystal during deposition. Within these conditions, films densities are likely >0.9 g/cm 3, implying an upper limit for porosity of 4% [2]. Electrostatic charging effects may be present on insulators under particle bombardment; in particular, water ice can be charged up to several hundreds volts before dielectric breakdown occurs, depending on film thickness and projectile range [22]. For this reason, we used two different film thicknesses (00 and 3000 ML) for r + to test the influence of charging effects upon the total sputtering yield. The ion beam is produced with a differentially-pumped electron impact ionization gun (Nonsequitur 40) and scanned uniformly over the area of the quartz-crystal. The films were irradiated at fluxes between 0 and 0 2 ions cm 2 s. The total sputtering yield is obtained converting the mass loss given by the microbalance to number of water molecules and dividing it by the number of incident particles. The sputtering yield measured by the crystal microbalance Y m was corrected for the mass due to implanted projectiles using the equation: Y = Y m + n m /m 2 ; where m and m 2 are the masses of the projectile and a water molecule and n the projectile trapping probability. For large fluences, trapping may be neglected (n = 0) and the total sputtering yield is given directly by the frequency change of the crystal. For small fluences we assume that all projectiles are retained (n = ), since reflection coefficients are very low; thus Y = Y m + m /m 2.We did not measure n ; therefore we use an average value for n = /2, which means that the error bars in the figures include both the experimental uncertainties and the small constant term /2m /m 2. The sputtering yields were insensitive to ion beam current.

58 M. Famá et al. / Surface Science 602 (2008) 56 6 3. Results and discussion 3.. Temperature dependence Fig. shows the normalized total sputtering yield of ice for He + and r + vs. ice temperature between 30 and 40 K. ata from the compilation of aragiola et al. [] at 30 kev (mostly electronic processes) and from the present measurements at 2 kev (elastic collisions) indicate that the sputtering yield has a universal behavior as a function of the ice temperature, irrespective of the excitation mechanism. The data was fitted with the expression Y =Y 0 ¼ þ Y =Y 0 e Ea=kT, where k is oltzmann s constant, Y /Y 0 = 220 and E a = 0.06 ev. These values are similar to those found in Ref. []. The temperature dependence is thought to originate in the formation and consequent behavior of radicals and molecular products (H 2,O 2 ) during irradiation [6,7,23], but a detailed description is lacking. 3.2. ngular dependence Fig. 2 shows measurements of the normalized sputtering yield of ice at 80 K irradiated by 2 kev He + and 2 kev r +, as a function of the projectile incidence angle h. The results were fitted to a cos f (h) dependence with f =.45 ± 0.05 for He + and f =.78 ± 0.08 for r +. There is only one previous experimental report of the angular dependence of the sputtering yield of water ice, and it corresponds to the electronic regime (00 kev protons) [24]. There, the authors Normalized Sputtering Yield 2.6 2.4 2.2 2.0.8.6.4.2.0 0.8 r + (2 kev) He + (2 kev) r + (30 kev) He + (30 kev) 0 20 40 60 80 00 20 40 60 Ice Temperature (K) Fig.. Normalized sputtering yield of ice for He + and r + at normal incidence versus temperature. This work: d and m 2 kev r + and He +, respectively. aragiola et al. []: s and n, 30 kev r + and He +, respectively. The solid line is a fit to the expression Y =Y 0 ¼ þðy =Y 0 Þe Ea=kT, with Y /Y 0 = 220 and E a = 0.06 ev. Y(θ) / Y(θ = 0) 3.5 3.0 2.5 2.0.5.0 0 0 20 30 40 50 60 ngle (deg) state that Y(h) also follows a cos f (h) distribution with f =.29 ± 0.02 (.32 ± 0.05) at 20 (00) K. nother study of electronic sputtering, but for solid oxygen irradiated with 2 MeV He +, reports f.6 [25]. The factor f > is caused by the near-surface variation in the energy density along the incident direction [24,26]. For electronic sputtering this is in part due to the forward directedness of the fast secondary electrons produced by the projectile, that relocate the electronic energy deposited near the surface into the bulk of the ice and to the near-surface variation in the S e due to changes in the incident ions charge state. The effect of the secondary electrons should disappear at low projectile velocities, since most of the secondary electrons cannot produce further ionizations. For elastic collisions, the standard linear cascade theory also predicts a cos f (h) dependence for the sputtering yield, where f depends on the spatial shape of the distribution of deposited energy and is nearly independent of the projectile energy. Results of f for metals irradiated by noble-gas ions at low energies were found to be between and 2 [27] but they may not be strictly comparable since water ice is a molecular solid with strong internal bonds and weak intermolecular bonds. 3.3. Energy dependence He r Fig. 2. Normalized sputtering yield as a function of the incidence angle of 2 kev He + and r + ions. The lines are fits to Y(h)/Y(0) = cos f (h) with f =.45 for He + and.78 for r +. Figs. 3 and 4 show measurements of the total sputtering yields of ice at 80 K irradiated by 0.35 4 kev He + and r +, together with previous results of hristiansen et al. at 78 K [8] at 45 incidence (the data were multiplied by cos(45).78, see Section 3.2), aragiola et al. at 60 K [] (as shown before, in the Section 3., the total sputtering yield of ice is nearly constant for temperatures <00 K), rown et al. at 60 K [28] and Rocard et al. at 60 K [29]. For r + we used two very different ice film thicknesses (00 and 3000 ML) to test any dependence with Y, but for both cases the sputtering yields follow the same projectile energy dependence, within errors.

M. Famá et al. / Surface Science 602 (2008) 56 6 59 Y ¼ KF ðe; h; xþ ðþ Sputtering Yield (molecules/ion) Sputtering Yield (molecules/ion) 0 00 0 4. Model He + 0. 0 00 Energy (kev) Fig. 3. Sputtering yield of ice versus He + energy. This work: d (50 ML) at 80 K. hristiansen et al. [8]: h at 78 K (the data were multiplied by cos(45 ).45, see text). aragiola et al. []: s at 60 K. rown et al. [28]: n at 60 K. Rocard et al. [29]:, at 60 K. The dotted line is proportional to the elastic stopping cross section, whereas the dash-dotted line is proportional to the square of the electronic stopping cross section. The solid line represents the sum for both contributions (see text in Section 4). r + 0. 0 00 Energy (kev) Fig. 4. Sputtering yield of ice versus r + energy. This work: d (3000 ML) and m (00 ML) at 80 K. hristiansen et al. [8]: h at 78 K (the data were multiplied by cos(45 ).78, see text). aragiola et al. []: s 60 K. The dotted line is proportional to the elastic stopping cross section, whereas the dash-dotted line is proportional to the square of the electronic stopping cross section. The solid line represents the sum for both contributions (see text in Section 4). 4.. Elastic sputtering ccording to the standard linear collision cascade theory [7], the elastic sputtering yield for atomic targets can be expressed as, where E is the projectile energy, h is the angle of incidence of the projectile to the surface, F (E,h,x) is the distribution of deposited energy over depth x, andk depends only on target parameters such as the surface-binding energy U 0 and the molecular density N. necessary condition for the yield to be proportional to the deposited energy at the surface is that E U 0. This condition is satisfied in our case since U 0 = 0.45 ev for water and E was at least 350 ev. For sputtering at perpendicular incidence Eq. () may be simplified into, Y ¼ 3 as n ð2þ 4p 2 0 U 0 where S n is the nuclear-stopping cross section, a is an energy-independent function of the ratio between the mass of the target m 2 and of the projectile m [30], and 0 is the constant of the differential cross section dr for elastic scattering in the binary collision approximation, i.e., dr = 0 dt/t, with T the energy of the recoil [7]. Since the molecular dissociation energy of water is much larger than U 0, we take m 2 to be the mass of H 2 O. To evaluate S n, we followed the formalism from Ref. [3] using the ZL Universal Potential (see ppendix for a full description). For the particular case of water as a target, we evaluate S n for a compound constituted of 2/3 atomic hydrogen and /3 atomic oxygen. n alternative, used by hrisey et al. [32], is to multiply Eq. (2) by a factor of /3 converting the molecular S n into an averaged atomic value. In Figs. 3 and 4 we plot the elastic component of the sputtering yield according to Eq. (2) where we used a = 0.54 for He and a = 0.26 for r from Ref. [30], and 0 =.3 Å 2. learly, at very low energies, the sputtering yield of water ice can be explained by the elastic collision theory for sputtering, but as the energy increases the electronic processes become dominant. The application of S n in Eq. (2) is not necessarily straightforward since the molecular solids contain internal chemical structure which can absorb some of the elastic energy transferred to the molecule into internal inelastic energy rather than transforming it into collision cascades. For instance, the internal O H binding in water can absorb up to 5.2 ev before dissociation, an order of magnitude larger than U 0. However, results from a classical dynamical simulation of the bombardment of ice by 23, 59 and 5 ev O + [33], can be fitted with Eq. (2) using values for S n following Eqs. (.) (.3) in the ppendix and a = 0.32 in agreement the value adequate for monoatomic solids [30]. We should also mention that for the fitting we do not consider the effect of reflected projectiles (they contribute only partially to the S n ) since an estimation using the TRIM code [3] gives us 5% for 0.35 kev He + and <0.% for 0.35 kev r +. 4.2. Electronic sputtering We also included in Figs. 3 and 4 curves proportional to S 2 e to fit the experimental data at higher energies.

60 M. Famá et al. / Surface Science 602 (2008) 56 6 Experimental Sputtering Yield (molecules/ion) 00 0 E E 0 00 alculated Sputtering Yield (molecules/ion) ergy, temperature and angle of incidence. Our results show a clear transition from elastic to electronic sputtering regimes for both projectiles. t very low energies the sputtering yield is proportional to the S n in agreement with the standard linear cascade theory. s the energy increases, and electronic processes become important, the sputtering yield can be fitted to a S 2 e dependence. We observe a temperature dependence of the sputtering yield that is the same for elastic and electronic processes, likely attributed to thermally activated processes leading to O 2 and H 2 production. Finally, we introduced a generalized formula to calculate the total sputtering yield of water ice relevant for the astrophysical icy bodies in the outer solar system. This formula is valid for ice temperatures up to 40 K, ion energies from few hundreds of ev up to energies below the maximum in S e, and it has only been tested with H +,He +, N +,O +,Ne +, and r + projectiles. Fig. 5. Experimental vs. calculated sputtering yield of ice. () hristiansen et al. [8]: Z = 2, 7, 0, and 8, E = 2 6 kev, T =78K,h =45 ; () aragiola et al. []: Z = 2, 8, and 8, E = 0 50 kev, T =60K,h =0 ; () present measurements: Z = 2 and 8, E = 0.35 4 kev, T = 30 40 K, h = 0 60 ; () rown et al. [28]: Z = and 2, E = 5 50 kev, T =60K, h =0 ; (E) Rocard et al. [29]: Z =2,E = 5 25 kev, T =60K,h =0. Experimental results for S e of He + and r + in water at low energies do not exist. Therefore, to evaluate S e, we used the effective-charge theory by Yarlagadda et al. [34] for S e (Z ) as a function of the projectile atomic number Z, normalized to extrapolated experimental S e values for protons in ice [35], and assumed a linear dependence of S e with projectile velocity at low energies (see the ppendix for a full description). Within the precision of our measurements and those in previously published reports we could fit a complete analytical expression for the total sputtering yield of water ice valid for temperatures up to 40 K and projectile energies below the maximum in S e, and incidence angle h (see ppendix for a full description), Y H2 OðE; m ; Z ; h; T Þ¼ 3 U 0 4p 2 0 as n þ gs 2 e þ Y e Ea=kT cos f ðhþ Y 0 where g is an oscillatory function of the atomic number of the projectile (see ppendix) needed because the effectivecharge theory of stopping [34] does not include the known shell effects that produce Z oscillations. In Fig. 5. we compare the validity of Eq. (3) with more than seventy experimental data points from several authors, including different temperatures, incidence angles, energies and projectile type (Z =, 2, 7, 8, 0, and 8), finding an excellent match. 5. onclusions We have measured the sputtering yield of water ice for low-energy He + and r + as a function of the projectile en- ð3þ cknowledgements We thank R.E. Johnson for useful discussions. This material is based upon work supported by the National Science Foundation under Grant No. 0506565. ppendix. Elastic stopping In units of ev/ (0 5 atoms/cm 2 ) the nuclear-stopping cross section S n can be expressed [3], S n ¼ 8:462Z Z 2 m S red ðeþ ðm þ m 2 ÞðZ 0:23 þ Z 0:23 2 Þ ð:þ where Z and Z 2 are the atomic numbers of the projectile and the target atoms and e is the reduced energy expressed in terms of the projectile energy E (kev units) as, e ¼ 32:53m 2 E Z Z 2 ðm þ m 2 ÞðZ 0:23 þ Z 0:23 2 Þ ð:2þ The reduced nuclear-stopping S red (e), valid for e < 30, is fitted to an analytical expression, as shown in Ref. [3]: S red ðeþ ¼ Function a lnð þ :383eÞ 2ðe þ 0:032e 0:2226 þ 0:9593e 0:5 Þ ð:3þ a can be interpolated from experimental sputtering yields from Ref. [30] and fitted by a double exponential function. Particularly for water (m 2 = 8) we found, a ¼ 0:25574 þ :25338 expð 0:8697m Þþ0:3793 expð 0:0508m Þ ð:4þ

M. Famá et al. / Surface Science 602 (2008) 56 6 6 Electronic stopping For projectile energies up to 50 kev/amu, we found the electronic stopping cross section expressed in units of ev/ (0 5 atoms/cm 2 ) to be, S e ¼ 225ðE=m Þ =2 ðe=m Þ 3=2 þ 500 Z2 Factor g e 0:2ðE=m Þ =2 Z 2=3 e 0:2ðE=m Þ =2! 2 ð:5þ The variable g in Eq. (3) gives the proportionality between electronic sputtering and S 2 e =U 0. The following empirical fit includes a sin 2 term to take into account oscillations in S e with Z since they are not included in the effective-charge theory [34], g ¼ 0:0002223 þ 0:003326 sin 2 ð2:72923ðz Þ 0:382 Þ ev Å 4 ð:6þ ngular dependence exponent f The exponent f in the angular dependence term has been approximated by fitting the few existing experimental data as f ¼ :3 þ ln m ð:7þ 0 References [] R.E. Johnson, Energetic harged-particle Interactions with tmospheres and Surfaces, Springer-Verlag, New York, 990. [2] M. Shi, R.. aragiola,.e. Grosjean, R.E. Johnson, S. Jurac, J. Schou, J. Geophys. Res. 00 (995) 26387. [3] R.E. Johnson, R.W. arlson, J.F. ooper,. Paranicas, M.H. Moore, M.. Wong, in: F. agenal, T.E. owling, W.. Mc Kinnon (Eds.), Jupiter: The Planet, Satellites and Magnetosphere, ambridge University Press, 2007, p. 485. [4] S. Jurac, R.E. Johnson, J.. Richardson,. Paranicas, Planet. Space Sci. 49 (200) 39. [5] R.E. Johnson, J. Schou, in: P. Sigmund (Ed.), Fundamental Processes in Sputtering of toms and Molecules (SPUT92), Mat-fys. Medd. 43 (993), p. 422 and 459. [6] R.. aragiola, Philos. Trans. Roy. Soc. 362 (2004) 29. [7] P. Sigmund, Phys. Rev. 84 (969) 383. [8] R. ehrisch (Ed.), Sputtering by Particle ombardment I, Springer- Verlag, erlin, 98. [9] R. ehrisch, W. Eckstein (Eds.), Sputtering by Particle ombardment: Experiments and omputer alculations from Threshold to MeV Energies, Springer, erlin, 2007. [0] W.L. rown, L.J. Lanzerotti, J.M. Poate, W.M. ugustyniak, Phys. Rev. Lett. 40 (978) 027. [] R.. aragiola, R.. Vidal, W. Svendsen, J. Schou, M. Shi,.. ahr,.l. tteberry, Nucl. Instrum. Meth. Phys. Res. 209 (2003) 294. [2] R.E. Johnson, W.L. rown, Nucl. Instrum. Meth. 98 (982) 03. [3] E.M. ringa, R.E. Johnson, Phys. Rev. Lett. 88 (2002) 6550. [4] M. Famá,.. Teolis,.. ahr, R.. aragiola, Phys. Rev. 75 (2007) 000(R). [5]. ar-nun, G. Herman, M.L. Rappaport, Yu. Mekler, Surf. Sci. 50 (985) 43. [6] R.. aragiola,.l. tteberry,.. ukes, M. Famá,.. Teolis, Nucl. Instrum. Meth. 93 (2002) 720. [7].. Teolis, R.. Vidal, J. Shi, R.. aragiola, Phys. Rev. 72 (2005) 245422-. [8] J.W. hristiansen,. elli arpini, I.S.T. Tsong, Nucl. Instrum. Meth. Phys. Res. 5 (986) 28. [9] R.. Haring, R. Pedrys,.J. Oostra,. Haring,.E. de Vries, Nucl. Instrum. Meth. Phys. Res. 5 (984) 483. [20] N.J. Sack, R.. aragiola, Phys. Rev. 48 (993) 9973. [2] M.S. Westley, G.. aratta, R.. aragiola, J. hem. Phys. 08 (998) 332. [22] J. Shi, M. Famá,.. Teolis, R.. aragiola, in press. [23].. ahr, M. Famá, R.. Vidal, R.. aragiola, J. Geophys. Res. 06 (200) 33285. [24] R.. Vidal,.. Teolis, R.. aragiola, Surf. Sci. 588 (2005). [25] K.M. Gibbs, W.L. rown, R.E. Johnson, Phys. Rev. 38 (988) 00. [26] R.E. Johnson,. Sundqvist, P. Håkansson,. Hedin, M. Salehpour, G. Såve, Surf. Sci. 79 (987) 87. [27]. Oliva-Florio, R.. aragiola, M.M. Jakas, E.V. lonso, J. Ferrón, Phys. Rev. 35 (987) 298. [28] W.L. rown, W.M. ugustyniak, E. rody,. ooper, L.J. Lanzerotti,. Ramirez, R. Evatt, R.E. Johnson, Nucl. Instrum. Meth. Phys. Res. 70 (980) 32. [29] F. Rocard, J. énit, J.P. ibring,. Ledu, R. Meunier, Radiat. Eff. 99 (986) 97. [30] H.H. ndersen, H.L. ay, in: R. ehrisch (Ed.), Sputtering by Particle ombardment I, Springer-Verlag, erlin, 98 (hapter 4). [3] J.F. Ziegler, J.P. iersack, U. Littmar, in: J.F. Ziegler (Ed.), The Stopping and Range of Ions in Solids, Pergamon Press, New York, 985. [32].. hrisey, J.W. oring, J.. Phipps, R.E. Johnson, W.L. rown, Nucl. Instrum. Meth. Phys. Res. 3 (986) 360. [33].W. renner,.j. Garrison, Phys. Rev. 34 (986) 5782. [34].S. Yarlagadda, J.E. Robinson, W. randt, Phys. Rev. 7 (978) 3473. [35] P. auer, W. Käferböck, V. Nečas, Nucl. Instrum. Meth. Phys. Res. 93 (994) 32.