Crater formation by single ions, cluster ions and ion “showers”

Flyura Djurabekovaa,∗, Juha Samelaa, Helga Timkoa,b, Kai Nordlunda, Sergio Calatronib, Mauro Taborellib, WalterWuenschb

aHelsinki Institute of Physics and Department of Physics, P.O. Box 43, FI-00014 University of Helsinki, FinlandbCERN, Geneve 23, CH-1211, Switzerland

Abstract

The various craters formed by giant objects, macroscopic collisions and nanoscale impacts exhibit an intriguing re-semblance in shapes. At the same time, the arc plasma built up in the presence of sufficiently high electric fieldsat close look causes very similar damage on the surfaces. Although the plasma-wall interaction is far from a singleheavy ion impact over dense metal surfaces or the one of a cluster ion, the craters seen on metal surfaces after a plasmadischarge make it possible to link this event to the known mechanisms of the crater formations. During the plasmadischarge in a high electric field the surface is subject to high fluxes (∼ 1025 cm−2 s−1) of ions with roughly equalenergies typically of the order of a few keV. To simulate such a process it is possible to use a cloud of ions of the sameenergy. In the present work we follow the effect of such a flux of ions impinging the surface in the “shower” man-ner, to find the transition between the different mechanisms of crater formation. We also introduce the “shower”-likeregime of ion bombardment (underdense cloud of ions) as a subsequent regime between the single ion impact (a rare“shower”) and cluster ions (densely packed cloud).

Keywords:Molecular dynamics simulation, craters, plasma wall interactionPACS: 52.80.Mg,52.80.Vp,79.20.Rf,61.80.Jh

1. Introduction

That huge craters modify faces of planets is part ofcommon knowledge since the ancient times. Althoughthey seem to be well investigated, the link between theshape of the damage and the impact energy as well asthe nature of the projectiles (as single piece, extensivefront of material or “staccato” mode of several pieces)still rises scientific interest. The similarity of cratershapes caused by giant asteroids and meteorites, bombs,explosives, gun bullets, and the microcraters seen onsolid surfaces exposed to cluster ion irradiation isvery well know. In addition, the similarity of scalingof crater volume in large metal clusters impacts andmeteorite impacts has been clearly established [1]. Theapplication of a very high electric field does also causea damage in the shape of craters, seen on the surfacesof metal parts after a plasma discharge (Fig. 1). Thisevokes the idea of a possible combination of the crater

∗Corresponding author.Email address: flyura.djurabekova@helsinki.fi (Flyura

Djurabekova)

formation mechanisms by the different kinds of impactsto derive a common law to enable the prediction of thecrater shapes and the size of damage from a certain ionimpact.

The shapes of the craters obtained from single ionand cluster ion impacts have been intensively studiedover the last decades [2, 3, 4, 5, 6, 1, 7]. However, thesestudies have always excluded the third possibility ofan impact, namely the “staccato” mode, or “shower”of ions, in which instead of being packed in a singlecluster, scattered ions are carrying the energy towardsthe surface, each behaving as a single ion, but withminutely small delay between the impacts. MD simu-lations of such ion “showers” give results very close tothe experimentally observed ones [8], which stronglysuggests that the side craters are formed by the “ionshower”. Although mostly this damage comprises alarge area of a solidified metal liquid, the craters seenaside from the main spot resemble greatly the cratersfrom ion and cluster ion impacts (Fig. 1).

Preprint submitted to To be submitted for publication in IBMM 2010 October 9, 2014

2 µm20µm

Figure 1: Experimental craters on a Cu surface caused by the plasmaformed in the high electric field (E0 ≈ 400 MeV

m ). The inset in the rightbottom corner shows the overall view of the entire damaged area.

Is it the same phenomenon that is observed dur-ing the plasma discharge and single ion/cluster ionimpacts? Can common features be found betweenthe three cases? In the present paper we consider thesurface damage evolution during impacts in 3 differentregimes: (i) from a single ion, (ii) ion “shower”, and(iii) a cluster ion. All three regimes are considered untilthe formation of a crater on the surface. By the ion“shower” we understand a regime of ion impacts withthe ultra high fluxes, observed when a plasma is formedin sufficiently high electric fields.

1.1. Ion “shower” impact during plasma developmentIf an electric field between two plane electrodes

is gradually increased, the plasma starts building upinevitably, filling the gap between the electrodes andsubsequently damaging their surfaces. If the plasma isformed in the relatively low fields, the surface exhibitsno damage seen by a bare eye. This fact makes thepractical application of plasma in industry possible.The situation changes dramatically when the electrodesare operating in high and ultra high vacuum. Undersuch condition, the electric field can grow to the valueclose to the critical one, when the breakage of themetal surface is foreseen [9, 10]. Modern technologiesrequire an extensive insight into the ongoing processesduring this particular kind of plasma-wall interaction,when the ions escape plasma with the high fluxesand energies of the order of a few keV. The damagecaused by such a dense cloud of energetic ions can notbe neglected, since it may affect the performance ofsensitive parts of high-precision machinery. This is amajor problem at hand, for instance, in the acceleratingstructures of linear colliders of the next generation [11].

A high formation probability of tiny arcs, which deflectelectron and positron bunches and result in bunch loss,reduces the efficiency of the costly machine.

The study of the mechanisms which lead to thedamage clearly visible on the cathode surface willgive a valuable information, which can enable the highlevel prediction of surface damage as well as a partialsuppression of the probability of arcs in the structures.

Our previous studies of the formation of a 1D plasma,using the same condition as in experiments carried out atCERN [12], showed that the huge fluxes of plasma ionsare accelerated towards the surface through the plasmasheath formed near the cathode. The energies of theions are distributed between 0 and a few keV (depend-ing on the voltage applied to the electrodes, and the dis-tance between them) with a clear peak close to the max-imum energy defined by the applied voltage. The sim-plified approach to the simulation of plasma formationprovided us with values of the ion current close to thoseobserved in the experiment[12]. In fact, these fluxes areof the order of 1025 cm−2s−1 and the peak of the en-ergy distribution appears at ∼ 8 keV. Moreover, beforethe plasma is built up, the surface is exposed to impactsof single ions accelerated towards the surface with themaximum energy. Thus, during the process of plasmaformation, the surface is subject to a gradual increase ofthe rate of ion impacts, from a single ion till the denseion “shower” when the plasma can sustain the densitiesof a dynamic equilibrium.

Such a combination of ion impacts of many differentkinds makes evident the complexity of a plasma-wallinteraction, when the plasma is maintained in a suf-ficiently high electric field. A valuable insight canbe obtained from a scaling law which can enable theprediction of a transition between the different regimes(mechanisms) of crater formation. Previously we haveintensively studied the Au cluster ion impacts for such ascaling law [1]. Hence our aim in the present work is tobroaden the scope of the studied impacts by includingthe case of dense ion cloud (“shower”).

Some details of the simulation of Cu surface damageby the ions from self-plasma built-up in the presence ofsufficiently high electric field can be found in [8]. Forthe current article, we carried out a new set of simula-tions of Au projectiles to be consistent with the singleions and Au cluster ion impacts investigations. The re-sults are combined with the previous conclusions.

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2. Method

To simulate the interaction within the Au samplewe used the MD/MC CEM potential, which includes ahigh-energy repulsive part [13]. This potential was cho-sen since it has been previously found to describe thesputtering yields of Au quantitatively correct over 3 or-ders of magnitude in energy [14].

The principles of the Au cluster ion simulations weredescribed in detail in [1]. To simulate the ion “shower”impact we used the following model. We created a set ofsimulations with variable flux where only one parame-ter of the projectile(s) was varied, as follows. We beganwith a normal 8 nm diameter Au nanocrystal. We thenstarted scaling its z size up with factors of f = 1 (orig-inal nanocrystal), 3, 10, 100, 1000 and 10000. Afterthe elongation, the positions of atoms in the z directionwere fluctuated randomly between -1/4 and +1/4 of theenhanced lattice constant. Thus the higher-elongationcases corresponded to the arc plasma “ion shower”. Wedid not consider explicitly “shower” ions ionically in-teracting between each other. In fact, the elongation off = 10000 corresponded to a typical arc plasma fluxφ = 1.3 × 1025cm−2s−1 [8, 12]. We note that the in-termediate fluxes (∼ 1027 − 1028) are used only to findthe transition between the “shower” and cluster impactsand do not correspond to any likely experimental con-dition. After creation, a kinetic energy of 500 eV wasgiven to all atoms in the cluster or ion shower towardsthe surface.

To contain the energy of the projectile, we used sim-ulations cells of 32 million atoms (a cube with 82 nmside length) , and cooled down the system towards 0 Kat 2 – 5 nm thick regions at the side and bottom bound-aries. The atoms in the bottom unit cell layer of thebox were held fixed. The simulations were ran until allatoms in the projectile had hit the simulation cell, andany overheated or densified regions of the cell had re-laxed to normal temperatures and densities. The sim-ulations were carried out using the classical MD codeparcas on 128 – 1024 processors [15].

3. Results and discussion

The simulation technique allowed us to investigatethe effect of the flux on the mechanism of the crater for-mation. The flux has been changed by increasing theaverage distance between atoms, thus we could coverall the possible fluxes from the compact cluster to thecloud representing a realistic plasma flux using the sameamount of ions, and hence, fixed fluence.

50 nm

Figure 2: Snapshots of the evolution of the crater formed by the cloudobtained as an Au cluster underdensified by a factor of 100. The lastimage to the right shows a clear overdensified front, which is observeddespite the fact that the impact is not by a condensed cluster of ions(simultaneous impact of all ions).

Fig. 2 depicts a typical shape evolution of a craterformed by a 100 times underdensified cluster (φ =

1.3 × 1028cm−2s−1). The decrease of the flux leads tothe transition in the mechanism of crater formation. Infact, we observed the explosion on the Au surface whichwas subject to a cluster impact with an energy of 500eV. Here we follow our definition of explosive crateringon the atomic level introduced in [1], namely, that theimpact causes on the surface the well defined continu-ous overdensified front. Fig. 3 shows the results for thedifferent cloud impacts (different fluxes) as distributionof the local densities around all atoms below the 8 nmradius diameter projectile impact area. This was ana-lyzed by finding all neighbours within 3.1 Å from atomsin this region (including the atoms from the projectile),then calculating the inverse of the average bond lengthsto these atoms and scaling this to a relative density, suchthat the equilibrium bond length leads to a relative den-sity of 1.0. The data is taken at the time in each differ-ent simulation when the number of atoms with a densityhigher than 1.8 times the normal one was the maximum.

Fig. 3 clearly shows the that explosive mechanismcan be expected at fairly high fluxes (φ = 1.3 ×1028cm−2s−1), at least at the explored impact energy. Al-though a single Au ion can form a crater on Au surface,this can happen only at the impact energy of about 5 keVand higher [16]. The 500 eV Au single ions form a lin-ear atomic cascade, which due to the high flux overlapand form a crater according to the thermal spike mech-anism. Only if the density of the cloud grows to a suf-ficient value, the overlap of the cascades becomes moreintense and the mechanism of crater formation under-goes a transition to the regime of an explosion.

In Fig. 4 we show the number of atoms whichhave overdensified neighbourhood versus ion flux, inthe range between the arc plasma fluxes and the caseof a cloud condensed back into a cluster. This figurethus provides a clear evidence of the presence of a tran-

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= 1.3 1029 ions/(cm2s) (nanocluster)= 0.4 1028 ions/(cm2s)= 1.3 1028 ions/(cm2s)= 1.3 1027 ions/(cm2s)= 1.3 1026 ions/(cm2s)= 1.3 1025 ions/(cm2s) (plasma flux)

500 eV

Figure 3: Density distribution in the crater region overdensified by theion clouds with different fluxes. The second peak which correspondsto the continuous overdensified front is seen at the fluxes ≥ 1.3 ×1028cm−2 s−1. The times used are 0.5 ps, 1 ps, 0.75 ps, 5 ps, 40 ps and20 ps, in order of decreasing flux.

sition between a thermal spike and an explosion mech-anism of crater formation. The effect of the energy ofbombarding ions requires further investigation to derivea common scaling law for the damage prediction.

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Figure 4: Transition from a thermal spike mechanism seen at the arcplasma fluxes to an explosive mechanism at the cluster ion impact.The energy of the impacting atoms is in all the cases 500 eV/atom.

4. Conclusions

In the present paper we show that the irradiation of asurface with the high fluxes can lead to the similar dam-age as that which is observed at the cluster ion bom-bardment. In spite of the fact that the ion “showers” area combination of single ion impacts, which do not dam-age the surface significantly, the combined effect leadsto the overlapping of the single atomic cascade, result-ing in intensive thermal spikes, which form a crater on

the surface. The increase of the ion flux leads to thetransition of the mechanism of crater formation as thedensity of the overlapped cascades grows significantlyleading to the explosion effect. Further investigations ofthe effect of the energy of the ions are required to derivea general law for the prediction of surface damage dueto the ion impacts in the different regimes.

Acknowledgements

This work was performed within the Finnish Cen-tre of Excellence in Computational Molecular Science(CMS), financed by The Academy of Finland and theUniversity of Helsinki, and also financed by Academyprojects OPNA and CONADEP. Grants of computertime from the Center for Scientific Computing in Espoo,Finland, are gratefully acknowledged. We also thankthe Australian Synchrotron Research Program, fundedby the Commonwealth of Australia, and the AustralianResearch Council for support.[1] J. Samela and K. Nordlund, Phys. Rev. Lett. 101 (2008)

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