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Nuclear Instruments and Methods in Physics Research B 242 (2006) 498–502

NIMBBeam Interactions

withMaterials &Atoms

Surface erosion by highly-charged ions

Z. Insepov a,*, J.P. Allain a, A. Hassanein a, M. Terasawa b

a Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439, USAb Laboratory of Advanced Science and Technology for Industry (LASTI), 3-1-2, Koto, Kamigori-cho, Ako-gun, Hyogo 678-1205, Japan

Available online 16 September 2005

Abstract

Interaction of single- and highly-charged ions (HCI) with solid surfaces is a key factor for the development of extreme ultra-violetlithography (EUVL) source devices. To understand the mechanisms of surface erosion by ion bombardment, molecular dynamics(MD) simulation models of hollow atom formation, charge neutralization, electric field screening, surface sputtering and crater forma-tion were developed. These models were applied to studies of erosion of Au, W and Si surfaces irradiated by singly-charged Xe+ ions.Surface erosion of a Si(100) surface by low energy HCI bombardment has been modeled by studying interactions of slow Xeq+ ions.Further development and application of the MD methods to erosion of conductive surfaces by HCIs is analysed. The sputtering yieldof insulators and semiconductors by HCI impacts significantly increases with the charge state of the ion and leads to surface rougheningvia crater formation for higher charge states. This phenomenon has been studied based on the mechanisms of ‘‘Coulomb explosion’’ and‘‘thermal spike’’. The calculated sputtering yields of various surfaces bombarded by low energy single-charged Xe+ ions and highly-charged Xeq+ ions are compared with available experimental data.� 2005 Elsevier B.V. All rights reserved.

PACS: 32.80.Rm; 68.49.Sf; 79.20.�m; 96.35.Gt; 81.16.Nd

Keywords: Highly-charged ions; Sputtering; Craters; Extreme ultra-violet lithography

1. Introduction

An emerging EUV-lithography technology based on gas-discharge produced plasma (GDPP) and laser producedplasma (LPP) needs highly stable and durable surfaces ofcondenser optics and surfaces facing the plasma.

Erosion of reflecting metal and silicon surfaces by thehighly-charged Xe10+ ions (HCI) that are generated ingas discharge or laser plasmas impedes the developmentof future EUV-lithography sources. Mitigation of thiseffect needs materials of high stability and toughness andthat is essential [1,2].

As HCIs possess very high potential energies character-ized by their high charge states, their kinetic energy is oftenmuch less important. At an impact on a target surface, anHCI transfers its potential energy into electronic degrees of

0168-583X/$ - see front matter � 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.nimb.2005.08.061

* Corresponding author. Tel.: +1 630 252 5049; fax: +1 630 252 3250.E-mail address: insepov@anl.gov (Z. Insepov).

freedom thus leading to a high-density ionization of localtarget atoms on the surface. A mechanism for the energytransfer of such an electronic excitation into atomic motionhas been discussed based on the ‘‘Coulomb explosion’’ or‘‘thermal spike’’ models [3,4].

In the bombardment of slow HCIs into solids, the sput-tering yield of secondary ions increases significantly withthe charge state of the ions for insulator materials likeSiO2, LiF and UO2 [5–9]. Similar phenomena have alsobeen observed for electrically conductive materials like C,Al, Si, Ni, Cu and others [10]. A crater formation isreported on mica surface bombarded with Xe44+ ions [11].

A widely used model to study the relaxation (neutraliza-tion) of HCI approaching a metal or semiconductor sur-face gives the following scenario [12]. The strongCoulomb field of HCI can pull the electrons from the solidsurface. The electrons are then captured into Rydbergstates of the ion by the mechanism of resonant capture.Thus, a super-excited state – the so-called hollow atom

Fig. 1. Schematic of a HA formation. The potential function of a highly-charged ion, with the charge of +q, is shown as a solid curve. The totalenergy of HCI is roughly equal to the total ionization energy: Epi = qIXe.HA depicts the potential function of a hollow atom. Resonant neutral-ization of HCI occurs if it approaches to the surface closer than x0. Eq isthe potential energy stored in the charged surface area after the formationof a HA. DE is an energy spent for ionization of Nq surface Si atoms.

Z. Insepov et al. / Nucl. Instr. and Meth. in Phys. Res. B 242 (2006) 498–502 499

(HA) is formed which evolves further by emitting electronsand/or photons via the Auger process.

The total number of electrons pulled out of the solid sur-face can be greater than the initial charge of the ion and iscontrolled by the total energy conservation law. If the pro-cess of HCI relaxation is fast enough, a highly chargedzone is formed in close proximity or �below� the fallingion. Strong repulsive interaction between the newly formedions belonging to the target produces the so-called ‘‘Cou-lomb explosion’’ effect, which, in turn, leads to formationof a nanocrater on the surface and an enhancement insputtering.

Chen and Gillaspy [13] investigated the Coulomb explo-sion of Si(111) surface by using MD simulation method.Singly-charged Si ions up to 360 were embedded in a hemi-spherical region in the simulated block of solid surface. Thechoice of ion�s number was rather arbitrary. It was basedon experimental observations [14,15].

It is known that an HCI is neutralized very rapidly(<10 fs) in a solid [16]. Therefore, the electronic potentialenergy of HCI (the energy needed to strip the atomic elec-trons to the charge state q+ of the HCI) is released verynear the surface. The higher the charge of the ion, the moreeffect it produces on the surface during bombardment.

In the present work, we study surface sputtering causedby single low energy Xe+ ions and Coulomb-explosioninduced sputtering by Xeq+ ion bombardment on Si,assuming that the total potential energy of incident Xeq+

ion can be consumed to produce singly-charged Si+ ionsin the Si target. Finally the sputtering yields as a functionof the potential energy of Xeq+ are studied.

2. Computational model

The potential energy of Xeq+ (q 6 54) is calculated by amulti-configuration Dirac–Fock method [10]. Formationof the HA was modeled by switching the interaction poten-tial of Xe ion with the surface atoms. The dynamics of HAformation was studied via visualization of the events byrecording movies at various energies and charge states q.

The ions are embedded into a surface as an initial con-dition, resulting in fast charge neutralization, electric fieldscreening and following Coulomb explosion. Differentscreening models were studied and compared with themodels existing in the literature. The characteristic chargeneutralization time was approximated by the Maxwellrelaxation time which gives sn � 1 ps for Si. Therefore,charge neutralization in Si could be neglected because thistime is much longer than the interaction time. However,these times are much shorter for conductive targets. Forexample, tungsten has the time of 0.1 fs, copper and gold0.02 fs. Therefore, any atomistic simulation model ofHCI interaction with conductive targets should treat thecharge neutralization dynamically, e.g. by simultaneouslysolving the Poisson equation for the electrons in the target.

The dynamics of particle ejection (sputtering) from thesurface and crater formation on the surface were simulated.

Time and angular dependencies of the sputtering yield forthe secondary ions and neutral material atoms are studied.

The surface was represented by a large cylindrical slabof particles that were initially placed in the nodes of thelattice inside the sample. The particles initially inside thehemisphere with its equator lying on the upper plane ofthe sample were considered to be ions bearing the charge+e each. The number of the Si+ is computed by the MDmethod so that the total potential energy of Si+ ions (Eq)embedded in a hemispherical region should be equal tothe potential energy of the incident Xeq+ (Epi).

There are two important physical effects that were takeninto account: charge neutralization and electric field screen-ing. The classical over-the-barrier (COB) model [12,17] iswidely used to estimate the distance where the firstresonant charge transfer can take place. For a flat metalsurface, the characteristic distance is approximately in theorder of 20 A. The capture takes place into the electronicshell of the projectile with high principal quantum num-bers. The lifetime of HA is much greater than the interac-tion time: sI � 10�13 s [18].

Our MD simulation of HA formation is based on theCOB model [12]. We assumed that the processes of chargecapture from the surface and electric field screening insidethe target are much faster than those that lead to surfacesputtering and crater formation (a similar approach is usedin [13]).

Fig. 1 shows a physical model of HA formation. Thepotential function of a highly-charged ion is shown as asolid curve HCI; and the total energy of HCI is roughlyequal to the total ionization energy: Epi = q * IXe, whereq is the charge state. HA depicts the potential function ofa hollow atom. Resonant neutralization of HCI occurs ata distance x0 where two potential curves cross each other.The energy balance gives the following relation betweenthe Epi and Eq: Epi = Eq + Nq · ISi + Ese + Eph, where Nq

Fig. 3. Comparison of the calculated sputtering yields of a W(100)surface irradiated with Xe+ ions, with energies of 50–10,000 eV, calculatedin this paper (open circles), with the experimental data [23,25–27].

1 [10] contains the experimental sputtering yield data for Xeq+ on manymaterials in arbitrary units.

Fig. 2. Comparison of the sputtering yields of a Au(100) surfaceirradiated with Xe+ ions, with energies of 50–10,000 eV, calculated inthis paper (open circles), with experimental data [23,24].

500 Z. Insepov et al. / Nucl. Instr. and Meth. in Phys. Res. B 242 (2006) 498–502

and ISi are the number of Si+ ions created during the HAformation and the ionization energy of a Si atom; Ese

and Eph are the energies spent for generation of secondaryelectrons and photons, respectively.

When an HCI approaches the surface, bulk electronswill be polarized and build up an induced charge density.This image charge is located inside the solid at the samedistance from the surface as the ion but with an oppositesign and the interaction between the HCI and its image willaccelerate the ion towards the surface. The Si+ ions createdin the surface layers interact with the neutral Si atoms via apolarization potential for which a simple function waschosen to be �R�4 at long distances and a constant, atshorter distances.

The kinetics and dynamics of a HA formation above thesurface is not well understood. One of the purposes of thispaper is to simulate the HA formation and to find the char-acteristic times of HA interaction with the surfaces.

The dynamics of a slow Xeq+ HCI impact on a Si(100)surface is analysed with a hybrid MD model [19]. Realisticinteraction potentials are used for the interactions betweendifferent kinds of particles. Xe+ ion interacts with the sur-face via a Buckingham potential [19], the EAM-potentialswere used to describe interactions between Au [20] andW [21] atoms and the Stillinger–Weber three-body poten-tial – for the interactions between two and three Si atoms[22].

The boundary conditions were used [17], where a newhybrid molecular dynamics method was proposed. Localtarget temperatures were obtained using the equipartitiontheory by deducting atomic kinetic energies from the aver-age kinetic energy for the given spherical layer and localpressures were calculated from the virial formula.

Sputtering is a process of surface erosion by ion impacts.The sputtering yield Y is defined as a number of targetatoms removed from the surface with one singly- orhighly-charged ion impact. We have obtained this valueas a long-time limit of a function y(t) which representsthe total number of atoms that crossed a certain controlplane at a height zcut above the surface, with zcut taken asa parameter. The value of zcut = 2Rcut was chosen, whereRcut is the cutt-off distance for the interaction potential.The atoms crossing the plane placed at zcut, will leave thesolid.

The MD model was verified against existing experimen-tal data of sputtering by single charge Xe+ ion bombard-ment of Au, W and Si surfaces. These include candidatematerials for EUVL optical surfaces.

3. Sputtering yields

Singly-charged Xe+ ions generated by gas-dischargeplasma usually have translational energies well below1 keV and one of the engineering challenges is to mitigatethe surface erosion caused by such ions and to make theirsputtering yields as small as possible. Experimental dataare available for the sputtering yields of Xe+ on various

target materials including Au, W, Si [23–27]. As there areno experimental data for the sputtering yields by Xeq+ onthese materials,1 our MD model has been verified by com-paring the calculated yields for single Xe+ ion interactionswith those targets.

Figs. 2–4 show the results for the sputtering yields ofAu(100) (Fig. 2), W(100) (Fig. 3) and a Si(111) (Fig. 4)surfaces irradiated with Xe+ ions, with energies of50–10,000 eV, calculated in this paper (open circles). Thecalculated data were compared with available experimentalresults [23–27]. The comparison with the experiment showsthat the MD method gives good results for the intermediateenergy region.

The calculated yields for an ideal crystalline Si(111)surface shown in Fig. 4 are systematically higher than theexperimental data [23]. The deviation of our results fromthe experiment could be explained by the fact that the Sisurface in experiment [23] was polycrystalline and rough,which could significantly decrease the sputtering yield.

Fig. 4. Comparison of the calculated sputtering yields of an ideal Si(111)surface irradiated with slow Xe+ ions, with energies of 50–10,000 eV,calculated in this paper (open circles), with the experimental data obtainedfor a rough polycrystalline surface [23].

Z. Insepov et al. / Nucl. Instr. and Meth. in Phys. Res. B 242 (2006) 498–502 501

Moreover, the Si surfaces are easily oxidized, which againmakes the comparison difficult. For the energies below100 eV, where experimental data are insufficient and whereother computational tools (TRIM methods) become lessreliable, our MD results are the only predictions for thesputtering yields.

Strong dependence of the sputtering yield on the HCIspotential energy is found in MD study and this findingagrees with experiment. Fig. 5 shows the calculated andexperimental results [8] for the sputtering yield obtainedfor a highly-charged Xeq+ ion, with a kinetic energy of1 keV, bombarding a Si(100) surface. Although the

Fig. 5. Comparison of the slopes of calculated and experimental sputter-ing yields obtained for a highly-charged Xeq+ ion bombarding a Si(100)surface with a kinetic energy of 1 keV. Insert in this figure shows thedependence of the Xeq+ potential energy on the charge state calculated in[10].

recently developed microbalance technique [28] allowsone to measure the frequency shift and calibrate the exper-imental device against the absolute surface erosion charac-teristics, there are still no available experimental data forthe sputtering yields of Si surfaces induced by Xeq+ HCIs.All existing experimental data on the system Xeq+/Si aregiven in arbitrary units [10]. Therefore, Fig. 5 comparesthe slope of our calculated sputtering yields data to thatof the experimental yields of Si surfaces bombarded withXeq+ HCIs [10]. The insert in Fig. 5 shows the dependenceof the potential energy of Xeq+ HCIs on the charge state qcalculated in [10].

Fig. 5 shows two sets of calculated sputtering yield data:one for a semi-spherical charged area and the other for adisk-shaped area filled with Si+ ions. This figure shows thata hemi-spherical shape of the charged area gives excellentagreement for the experimental slope. The slope of the cal-culated yields is much smaller, if the charged area is chosenas a disk.

4. Summary

Interaction characteristics of single Xe+ and highly-charged Xeq+ ions with condenser optics and plasma facingsolid surfaces are key factors for the development of ex-treme ultra-violet lithography that promises higher bitcapacity and work frequency for future nanoelectronicdevices.

Mechanisms of surface erosion by ion bombardmentwere studied by molecular dynamics (MD) simulationmodels of hollow atom formation, charge neutralization,electric field screening, surface sputtering and crater forma-tion were developed. These models were applied to studiesof erosion of Au, W and Si surfaces irradiated by singlecharge Xe+ ions.

Surface erosion of a Si(100) surface by low energy HCIbombardments has been modeled by studying interactionsof slow Xeq+ ions. Further development of MD simula-tions and application of them to erosion of conductivesurfaces by HCIs is discussed.

The calculated sputtering yields of various surfacesbombarded by low energy single-charged Xe+ ions andhighly-charged Xeq+ ions are compared with availableexperiments.

Acknowledgement

This work is partially supported by Intel and Interna-tional Sematech Corporation.

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