www.elsevier.com/locate/nimb

Nuclear Instruments and Methods in Physics Research B 258 (2007) 172–177

NIMBBeam Interactions

with Materials & Atoms

Surface erosion and modification by ions studiedby computer simulation

Z. Insepov a,*, J. Norem a, D.R. Swenson b, A. Hassanein a, M. Terasawa c

a Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439, USAb Epion Corporation, 37 Manning Road, Billerica, MA 01821, USA

c University of Hyogo, 3-2-1 Kouto, Kamigori-cho, Ako-gun, Hyogo, 678-1205, Japan

Available online 29 December 2006

Abstract

Surface erosion problems common in the development of TeV accelerators and of the extreme ultra-violet lithography (EUVL)devices have been reviewed. The gas cluster ion beam (GCIB) surface smoothing technique can mitigate them. It has recently been real-ized that GCIB can also be used to determine the basic mechanisms of the Q-slope that is yet another serious problem for the high-gra-dient linacs. Mechanisms of surface erosion by GCIB and highly-charged ions (HCI) bombardments were studied by using computersimulation. Sputtering, crater formation and surface modification models were developed. Various mechanisms of the ion energy transferinto the solid target, such as shock wave generation, hollow atom formation, Coulomb explosion, charge screening and neutralizationwere analyzed.� 2006 Elsevier B.V. All rights reserved.

PACS: 71.15.Pd; 34.50.Fa; 61.80.Az; 61.90.Jh; 79.20.Rf; 62.50.+p

Keywords: Molecular dynamics; Gas cluster ion beam; Highly-charged ion; Electronic excitation; Coulomb explosion; Sputtering; Shock wave; Craterformation

1. Introduction

Interactions of gas cluster ion beams (GCIB) andhighly-charged ions (HCI) with solid surfaces have funda-mental and practical interests in such areas as nuclearfuels [1], TeV accelerators [2], and extreme ultra-violetlithography (EUVL) source devices [3], HCI drivenSIMS for surface analysis [4], protein desorption byHCI impacts [5].

Mitigation of high voltage rf breakdowns and Q-slopeis a major concern in development of higher-field RF cav-ities for next generation accelerators [3]. When the electricfield in an rf linac accelerator increases to 25–30 MV/m, asignificant decrease of the quality factor Q0 has beenobserved by many groups (FNAL, CEA, JLab, DESY

0168-583X/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.nimb.2006.12.117

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

and KEK). A general belief attributes the Q-slope to thefollowing items: a residual surface resistance (BCS-surfaceresistance), the Kapitza impedance (KI) of the interfacebetween the metal and gasses, the niobium oxide forma-tion and degradation during baking, and to the Nb grainboundary features.

GCIB and HCI are the energetic sources that are capa-ble of nanoscale surface erosion and modification. Surfacetreatment by GCIB method has recently been proposed asa new way to significantly reduce the surface roughness andthe dark current from the rf-cavity surfaces and enablingoperation at higher acceleration gradients [6]. In additionto the suppression of the dark current, GCIB might alsobe an important treatment for mitigation of the Q-slopein superconducting cavities.

In this paper, various ion energy transfer mechanismsfrom GCIB and HCIs into the solid target were studiedby computer simulation.

Z. Insepov et al. / Nucl. Instr. and Meth. in Phys. Res. B 258 (2007) 172–177 173

2. Simulation models

2.1. Electronic processes

As an HCI ion approaches a metal or semiconductorsurface, the strong Coulomb field of HCI can pull the elec-trons from the solid surface into the Rydberg states of theion [7]. Thus, the hollow atom (HA) is formed whichevolves further by emitting electrons and/or photons viathe Auger processes. The potential energy of Xeq+

(q 6 54) is calculated by a multi-configuration Dirac–Fockmethod [8]. The total energy of HCI is roughly equal to thetotal ionization energy: Epi = q � IXe, where q is the chargestate. The classical over-the-barrier (COB) model [7,9] iswidely used to estimate the distance where the first reso-nant charge transfer can take place. This model estimatesthe distance above the surface where HCI is neutralized:x0 � 20 A. The life time of HA is much greater than theinteraction time: sI � 10�13 s [10].

Another physical effects that should be taken intoaccount is electric field screening. We used the screeninglength for the Coulomb forces between the ions to be 5 Awhich is of the order of the Si lattice parameter. A detailedanalysis of the previous work on screening processes hasbeen given in [11,12].

Electrons are pulled out of the solid surface and a highly-charged zone is formed in close proximity or ‘below’ thefalling ion. Strong repulsive interaction between the newlyformed ions belonging to the target produces the so-called‘‘Coulomb explosion’’ effect, which, in turn, leads to forma-tion of a nanocrater on the surface and an enhancement insputtering. An excessive charge inserted into a plasmawhich will be neutralized within a characteristic time calledthe Maxwell relaxation time. This time could be obtained bya solution of the static Maxwell equations: Nq(t) =N(0)exp(�t/s), where s = ee0/r. Here, Nq(t) is the totalnumber of charges at a time t. e and e0 – are the electricalpermittivities of a material and vacuum, respectively, andr is the electrical conductivity. The formula for Nq was firstproposed by Bringa and Johnson in [11,12], without refer-ring it to the Maxwell relaxation time. It allows one to findthe neutralization times from the fundamental materialproperties. Table 1 shows the neutralization times calcu-lated by the above equation for various materials.

Table 1Neutralization times of various materials obtained from the Maxwellrelaxation formula given in the text

Materials Conductivity, (X * m)�1 Neutralization time, s (fs)

Au 4.55 · 107 0.02W 1.89 · 107 0.1Si 100 103

LiF 10�4 109

GaAsa 2.8 · 10�6 1010�11

a Although GaAs is a semiconductor, its intrinsic carrier density at300 K is very low: ni = 2 · 107 cm�3. Therefore, the conductivity of pureGaAs is extremely small.

2.2. Surface erosion

Molecular dynamics (MD) models were developed forvarious materials that included Si, Al, Cu, Ni, W andNb. The Stillinger–Weber and Born–Mayer potential func-tions were used for Si [13,14], and a Finnis–Sinclair poten-tials for bcc tungsten and niobium [15]. The surface slabwas bombarded by gas clusters and HCIs. The size of theclusters was varied between 13–1055 atoms/molecules andthe HCI types were Xeq+ (q = 8–44). The dynamics of par-ticle ejection (sputtering) from the surface and crater for-mation on the surface were simulated.

The particles representing the charged zone on the sur-face were placed inside the hemisphere with its equatorlying on the upper plane of the sample. The number ofthe ions Nq is computed by the MD method so that thetotal potential energy of ions (Eq) embedded in a hemi-spherical region plus the ionization energy of Nq ionsshould be equal to the potential energy of the incidentXeq+ (Epi). In addition, a disk shaped ionized substrate vol-ume was also employed, for comparison with the hemi-spherical volume shape.

The sputtering yields as a function of the potentialenergy of Xeq+ were studied. 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 cuttoff distance for the interaction potential.The atoms crossing the plane placed at zcut, will leave thesolid.

2.3. Mesoscale surface modification equations

A mixed continuum–discrete model will be used for sur-face modification in which each HCI or GCIB impactinstantly creates a hemi-spherical symmetrical crater anda rim around it. The crater volume and the volume of therim parameters of the model depending on the impactenergy. The total number of atoms leaving surface is higherthan the number of redepositing atoms, therefore the sur-face height is decreasing with time. The mesoscale surfacedynamics equation represents the nonlinear dynamics ofgrowing surface profiles in terms of the coarse-grainedinterface heights h(r,t) in a d-dimensional space where r isthe radius-vector in a (d � 1)-dimensional plane at time t,and accurately describes behavior in later-stages, or scalingproperties, of a growing interface and can be found else-where [6].

3. Simulation results

3.1. Sputtering yield

The calculated and experimental results [8] for thesputtering yield shown in Fig. 1 were obtained for ahighly-charged Xeq+ ion, with a kinetic energy of 1 keV,

Fig. 1. Comparison of calculated sputtering yield for Si surface withexperimental data available for various materials: CsI, LiF, SiO2 andGaAs [8,18]. The dashes are linear fits to the data points and MD data.The solid line is drawn according to a simple shock wave theory model[19].

Fig. 2(a) The radial kinetic energy of the target atoms on time and radialdistance from the collision spot on the top of the Si target.

Fig. 2(b) The tangential kinetic energy of the target atoms on time andradial distance from the collision spot on the top of the Si target.

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bombarding a Si (100) surface. Although the recentlydeveloped microbalance technique [17] allows one to mea-sure the frequency shift and calibrate the experimentaldevice against the absolute surface erosion characteristics,there are still no available experimental data for the sput-tering yields of Si surfaces induced by Xeq+ HCIs. The cal-culated data were also compared to the experimentalsputtering yields obtained for LiF, SiO2 and GaAs in[8,18]. This comparison shown a good agreement of the cal-culated data with the measurements of the yield from Siand are in the same order of magnitude as the yields ofall semiconducting materials. There are clearly seen twocharacteristic energy intervals where the sputtering yieldshave a linear power-law dependence (above 0.1 keV forSi), and a constant (below that threshold value). Thethreshold energy for these two energy regions are almostthe same for CsI, SiO2, LiF and Si. However, the thresholdis much bigger for GaAs. One reason for such behaviorcould be a very low intrinsic density (ni = 2 · 106 cm�3)of the carriers in GaAs at room temperature. The solid linein Fig. 1 is drawn according to a simple shock wave theorymodel [19] which predicts a linear dependence of the sput-tering yield on the total Coulomb energy.

3.2. Shock waves and crater formation by HCI collision

Shock wave generation was studied for a Xe44+ HCIimpact on a Si (100) surface. Figs. 2(a), 2(b) show the depen-dence of the radial Fig. 2(a) and tangential Fig. 2(b) kineticenergies on time and radial distance from the collision spoton the top of the Si target. These figures reveal two differentshock waves, with the velocities of 18.3 and 19 km/s for theforward and rare-facted waves, respectively. After a fewhundreds of fs, the forward wave decays and propagateswith a slow wave velocity, of 8.6 km/s, which we shouldrelate to a longitudinal acoustic wave. The tangential wavesmoving forward have the same velocities Fig. 2(b).

Velocity distribution of the ejected atoms reveals themechanism of sputtering – the shock wave mechanismgives a v�3 dependence at higher velocities which can beobtained from the shock wave theory [16,19].

3.3. Crater formation by GCIB

Fig. 3 shows two crater shapes that were obtained byour MD simulations. Fig. 3(a) shows the crater formedby an accelerated Ar429 cluster with the kinetic energy of125 eV/atom. We assumed multiple charges per clusterwhich makes the total cluster energy a few times higherthan that of a single charge in the same acceleration voltage[20]. Fig. 3(b) shows a much shallower crater formed by an(O2)429 cluster that was having energy of 50 eV/molecule(or 100 eV/atom). The simulated shapes and sizes of thecraters have been scaled up to larger cluster sizes typicalfor experiments and then were employed in a mesoscalesimulation of the surface morphology.

Fig. 3. Two crater shapes obtained by our molecular dynamics simula-tions. Fig. 4(a) shows the crater formed by Ar429 cluster with the kineticenergy of 125 eV/atom. Fig. 4(b) shows a much shallower crater formedby an (O2)429 cluster that was having energy of 50 eV/molecule (or 100 eV/atom). Fig. 4. The results of a mesoscale simulation for the Nb surface

smoothening irradiated by O2 molecular cluster ion beam at a maximumdose of 1013 ions/cm2. The cluster energy was 30 keV and the cluster sizewas of about 3000 oxygen molecules in a cluster. The surface containedtwo types of tips: narrow and tall and wide and short.

1 These experimental results were provided by Sinclair and his group atCornell University.

Z. Insepov et al. / Nucl. Instr. and Meth. in Phys. Res. B 258 (2007) 172–177 175

A preliminary analysis based on the local atomic stresses[21] and on the slip vector calculation [22] showed thatboth the GCIB and HCI craters strongly emit dislocationloops and stacking faults that are located near the surfaceand are stable for the whole period of simulation which was75 ps. The maximum calculated shear stress for the tung-sten target was well above the lattice strength and the tung-sten bulk modulus [23]. Such extended defects can easily bethe driving force for the surface hillocks observed on thetop of conductive surface irradiated by HCI and by high-energy heavy ions [24–26].

3.4. Surface smoothing by GCIB

We modeled surface modification of a Nb surface con-taining two types of surface tips, with greatly different sizes:one of the tips was a narrow and tall hill, with the diameterof a few nm, and the second tip was modeled with a wideand short hill having a typical area of a many tens ofnm. Both these tips had equal volumes and shown inFig. 4. The total modeled area was in the order of 106–107 A2, and this area was irradiated by up to 1000 largeoxygen 30 keV clusters bombarded randomly the wholesimulation cell. The cluster dose was in the order of103–104 cluster/cell. Fig. 5 demonstrates the results of oursimulations for the Nb surface smoothening. The simula-

tion showed that the narrower hill is removed by an irradi-ation dose that five times lower than the blunt hill. Thenarrower hills have a higher chemical potential than thosewith a larger diameter. Therefore, the surface treatment bychemically inactive GCIB should remove narrow hills fas-ter than the bigger ones.

4. Experimental

As an illustration of the simulation results, Fig. 5 showsthe results of the first high voltage test of a GCIB treatedelectrode [20].1 The field emission of a 150-mm diameterstainless steel electrode was measured as a function of thegap field. This electrode was treated using a sequence ofhigh and then low energy Ar, for smoothing followed byhigh and then low energy O2 to improve the oxide charac-teristics. Fig. 5 shows a comparison of this electrode to atypical non-processed electrode. In spite of the fact that

Fig. 5. Field emission measurement for unprocessed (squares) and GCIBprocessed (circles) photocathodes [20].

176 Z. Insepov et al. / Nucl. Instr. and Meth. in Phys. Res. B 258 (2007) 172–177

the initial mechanical polish was inferior on the GCIBprocessed electrode, the processing caused a reduction ofsix2 orders of magnitude of the field emission. Recent mea-surements have shown a ‘‘dramatic reduction’’ in the num-ber of field emitters of Nb SRF cavity material and will bepublished elsewhere [27].

Experimental data on Q-slope includes: (1) changes inthe Q(E) slope with baking, (2) stability of Q(E) with expo-sure to air, (3) dependence on density of surface impurities(Nb on Cu, ‘‘single’’ crystal, etc.), (4) even heating of cav-ities with high Q-slope losses, (5) surface roughness and, ofcourse, (6) a discontinuous change in the Q at high fields.There have been a number of mechanisms proposed toaccount for this phenomenon. Visentin [28] has recentlyreviewed the models under active consideration. Theseinclude: (1) Magnetic field enhancements due to surfaceirregularities, (2) interface tunnel exchange, where the elec-trons are affected by the presence of states in the surface,(3) thermal feedback, magnetic field dependence of theenergy gap, (4) grain boundary effects and a variety ofother models.

5. Summary

Various mechanisms of surface erosion by HCI ionbombardment were studied by molecular dynamics (MD)method: surface erosion, shock wave generation, crater for-mation and sputtering of Si (100) surfaces irradiated byhighly charges slow Xeq+ ions. The calculated sputteringyields of various surfaces bombarded by highly-chargedXeq+ ions were compared with experiments.

2 Another test made several months later showed seven orders ofmagnitude drop.

We did a preliminary analysis of the stresses and dislo-cation emission from the impacts of HCI and acceleratedclusters.

Gas cluster ion beams surface modification method havebeen proposed for controlling and studying the microstruc-ture of Nb surfaces in ways which are relevant to supercon-ducting rf systems. The existing surface smootheningmethods were analyzed and the results of the smoothingexperiments show the reducing of the dark current by a fac-tor of 106. Q-Slope models were discussed and a new mit-igation method was proposed.

Acknowledgements

This work was supported in part by Contract DE-FG02-04ER83944 with Epion Co. and in part by the USDepartment of Energy under Contract W-31-109-Eng-38.

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