surface processing with ionized cluster beams: computer simulation

Surface processing with ionized cluster beams: computersimulation

Z. Insepov *, I. Yamada

Ion Beam Engineering Experimental Laboratory, Kyoto University, Yoshida-Honmachi, Sakyo-ko, Kyoto 606-8501, Japan

Abstract

Molecular Dynamics (MD) and Monte Carlo (MC) models of energetic gas cluster irradiation of a solid surface have

been developed to investigate the phenomena of crater formation, sputtering, surface treatment, and the material

hardness evaluation by irradiation with cluster ions. Theoretical estimation of crater dimensions formed with Ar gas

cluster ion irradiation of di�erent substrates, based on hydrodynamics and MD simulation, are presented. The atomic

scale shock waves arising from cluster impact were obtained by calculating the pressure, temperature and mass-velocity

of the target atoms. The crater depth is given as a unique 1/3 dependence on the cluster energy and on the cold material

Brinell hardness number (BHN). A new ``true material hardness'' scale which can be very useful for example for thin

®lm coatings deposited on a soft substrate, is de®ned. This ®nding could be used as a new technique for measuring of a

material hardness. Evolution of surface morphology under cluster ion irradiation was described by the surface relax-

ation equation which contains a term of crater formation at cluster impact. The formation of ripples on a surface

irradiated with oblique cluster ion beams was predicted. MD and MC models of Decaborane ion (B10H14) implantation

into Si and the following rapid thermal annealing (RTA) have been developed. Ó 1999 Published by Elsevier Science

B.V. All rights reserved.

PACS: 36.40; 07.05.T; 79.20.A; 68.35.G

Keywords: Cluster; Ion; Crater; Ripple; Implantation

1. Introduction

Clusters, or assemblies of atoms, are aggregateswhich can consist of many weakly bound atoms ormolecules. Beams of large clusters can be gener-ated in supersonic expansions of gas into vacuumthrough a nozzle. The cluster beams can be used

for the bombardment of a target placed in thesame vacuum chamber. The unique feature ofcluster ion beams has already been used for surfacesmoothing, shallow implantation, thin ®lm for-mation [1±9].

2. Crater formation

Single energetic gas cluster ion impacts formcraters on a solid surface. The phenomenon of

Nuclear Instruments and Methods in Physics Research B 153 (1999) 199±208

www.elsevier.nl/locate/nimb

* Corresponding author. Tel.: +81-75-753-5956; fax: +81-75-

751-6774; e-mail: [email protected]

0168-583X/99/$ ± see front matter Ó 1999 Published by Elsevier Science B.V. All rights reserved.

PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 0 0 4 7 - 6

crater formation is well known in so-called hy-personic velocity (or hypervelocity) impacts ofmacroscopic bodies on a solid surface. These ve-locities are in the range of vp/c� 1±10, where vp

and c are the projectile velocity and the soundvelocity in a target, respectively. Crater formationat hypervelocity impacts of macroscopic projec-tiles on metal surfaces was studied in Refs. [10±12].Merkle and J�ager [13] observed crater formationby TEM on Au foils due to 10±500 keV irradiationby Bi and Bi2 ions.

At a high velocity impact a hemispherical craterwas obtained on metal surfaces [10±12]. The craterdepth could be well ®tted with the empirical for-mula (in CGS units in original):

hd� 12� 10ÿ9�E=B�

2p=d

� �1=3

; �1�

here h is the crater depth and d is the projectilediameter, in cm, E is the projectile energy in erg, Bis the BHN in kg/m2. The parameter 1/3 is slightlyreduced to 0.29 at velocities higher than 10 km/s[10]. The linear correlation between the projectileenergy per crater volume and BHN was obtainedfor the variety of metals which includes lead, alu-minium, copper, bronze, brass, steel, and titanium.The projectile masses were ranging from 10-11 to 10gm (which is 12 orders of magnitude), and theirvelocities up to 15 km/s [11].

The depth of a crater which is formed at clusterion bombardment of a solid surface can be roughlyestimated from the mass, momentum and energyconservation laws assuming that the impact gen-erates shock wave [14]:

E0 � Ei � Ehyd; �2a�

Ei � 1

2P HV ; �2b�

P H � Pc � Pth: �2c�Here E0 is the total cluster ion energy, Ei and Ehyd

are, respectively, the internal energy of a com-pressed area and the energy of a radial hydrody-namic motion of the compressed materialencompassed by shock compression, as a whole.P H is the HugoniotÕs pressure, V is the crater vol-

ume, Pc and Pth are the cold (elastic) and thermal(temperature depending) pressure components,respectively.

For weak shock waves, with PH well below104 MPa, the two parts of the energy on theright side of Eq.(2a) have the same values, andPth in Eq. (2c) can always be neglected in com-parison with Pc. For example, at compression of30% of the initial volume the total pressure be-hind the shock wave for Pb has the followingcomponents: Pc� 21.6 GPa and Pth� 3.35 GPa[14]. According to this estimation, the internalthermal energy of the compressed material en-tering Ei can also be neglected, in comparisonwith the compression internal energy of coldmaterial. While the radius of the hemisphericalshock front is increasing in time, the mass ofcompressed target material increases propor-tional to cube of radius, which eventually re-duces its energy. The radius at which the shockwave stops could be estimated by equating theHugoniotÕs pressure, PH, to the BHN of thesurface material. That gives the BHN value forthe cold pressure from Eqs. (2a,2b), taking intoaccount the condition Ein�Ehyd.

According to the formulas (2), the crater vol-ume Vcr should be proportional to the total clusterenergy E0 and the crater depth- to the 1/3 power ofenergy: h�E

1=30 , as it was previously obtained for

hypervelocity macroscopic body impacts on solid(preferentially metal) surfaces:

h � �E0=B�1=3: �3�

This relation will not be valid for the pressuresabove �104 MPa because the Eqs. (2a)±(2c) arenot valid above this pressure [14], a case which israre for the cluster ion impacts with cluster ener-gies below 200 keV. The last statement could easilybe obtained if we roughly estimate the maximalattainable pressure from the energy conservationlaw as: Pmax < E0/Vcr, and use the crater radius�100 �A from experiment [18,19].

We use the Hybrid MD (HMD) model whichwe have proposed in our earlier papers for Sitarget sputtering [15,16]. In this paper, Cu targethas been represented by a cylindrical fragment ofan fcc structure of 105 Cu atoms embedded into

200 Z. Insepov, I. Yamada / Nucl. Instr. and Meth. in Phys. Res. B 153 (1999) 199±208

the rest of the target treated by continuum me-chanics and linear thermodynamics. In HMD[15,16], an MD system is embedded into a boun-dary set which correctly describes the energy andmomentum ¯ow from the MD system to the rest ofsystem, according to the elasticity and thermody-namics equations. The target was initially at roomtemperature. Ar cluster was prepared by cuttingout a sphere from the bulk solid and had no initialthermal motion: Tcl� 0 K.

The interactions between copper target atomswere modeled by embedded-atom-method (EAM),which is a many-body potential derived from asecond-momentum approximation of the tight-binding scheme [17]. Interactions between Arcluster atoms and Ar and Cu atoms were modeledwith a pair-additive Buckingham-type potential.

The craters in Fig. 1 were obtained by MD forArn (n� 236, 370) cluster impacts on a Cu (1 0 0)surface, for energies of 6.4 keV (a) and 10 keV (b).The parameters of the MD calculations are sum-marized in Table 1.

Fig. 2 shows the 1/3 power dependence of thecrater depth on the total cluster energy calculatedby MD for impacts of Arn (n� 236, 370, 490, and736), with energy of 6.4±20 keV. As can be seen,the 1/3 power law is the best ®t of these results.The crater depth was de®ned as a distance fromthe original surface to the bottom of the crater.Two other dependencies are plotted in this ®gure:the dotted line, with a� 1/2, and the dashed line,with a� 1/4.

Fig. 3 shows the experimental 1/3 dependencebetween the crater diameters and accelerationvoltage and traces (craters) observed by a scanningtunnelling microscope (STM) on Au ®lms depos-ited on mica bombarded by 20±150 keV Ar3000

cluster ions [18,19]. Fig. 4 shows a linear depen-dence between the full crater depths and diametersobtained by MD in this paper. The full craterdepth was de®ned as a distance between the top ofthe rim and the bottom of the crater. The circles inthis ®gure are calculations for a small target of77 000 Cu atoms, and the square for a larger targetmodel of 10 5000 Cu atoms. This ®gure shows thatthe crater diameter could be measured by STMinstead of the crater depth, at least for the lowenergy region.

Fig. 5 shows double-logarithmic straight linedependence between the crater depth, h, and theBrinell hardness number, BHN, where the totalenergy of cluster ion E0 is given as a parameter.The main reason of this ®gure is to show howEq. (3) works. By using our MD data for lowerenergies and Eq. (3), the crater depths forhigher cluster energies could be obtained, whichare extremely di�cult to calculate but easy tomeasure experimentally. This idea was ®rstproposed in Refs.[20,21]. The calibration of thelines was made for Cu as target material, forwhich there are available data for the BHN andcrater sizes. The circle corresponds to the craterdepth of 7 �A obtained by the MD for 10 keVcluster impact. The lines were calculated ac-cording to Eq. (3) for 50, 90, and 150 keV of

Fig. 1. Side view of the craters formed on a Cu(1 0 0) surface

calculated by MD for Ar236 cluster ion impacts with energy of

6.4 keV after 17 ps (a), and for Ar370 10 keV impact (b) after 10

ps from the beginning of an impact. Hemispherical craters are

formed.

Z. Insepov, I. Yamada / Nucl. Instr. and Meth. in Phys. Res. B 153 (1999) 199±208 201

total cluster energy. If the experimental craterdepth of 22 �A for 150 keV cluster impact onAu [18] is used, the line for 150 keV from Fig.5 gives a predicted hardness value of 0.25 GPAwhich agrees with the experimental BHN of 0.3,with the error bar from 0.24 to 0.5 [22]. Thegood agreement obtained in Fig. 5 shows thatthe correlation between crater depth, clusterenergy, and Brinell hardness number given byEq. (3) is quite reliable and, therefore, it couldbe used for prediction of crater depths and

BHN for new materials including hard thin®lms [20,21].

The crater volume itself depends on the mate-rial surface properties, such as sound velocity,compressibility, and density. It also depends on thecluster properties, such as cluster diameter, type ofcluster atoms, etc. Therefore, hardening of thematerial due to plastic deformation (work hard-ening) should lead to a di�erent crater volume. Ash�Bÿ1=3, we can use this to calibrate variousmaterials by the crater depth, and in this way tode®ne a new ``true material hardness'' scale. Thisscale can be very useful for thin ®lm coatings de-posited on a soft substrate.

Fig. 2. Crater depths (de®ned from the original surface) cal-

culated by MD for Arn (n� 236, 370, 490, 736) cluster ion

impacts with energies of 6.4±20 keV on a Cu(1 0 0) surface

(circles). the straight line corresponds to the E1=3 power law.

For comparison, the power law dependencies with the expo-

nents a� 1/2 (dotted line) and 1/4 (dashed line) are also added.

Fig. 3. STM measurements of crater diameters for Ar3000

cluster ion impacts, with total energies of 20±150 keV, on a Au

(1 1 1) thin ®lm surface deposited on mica.

Table 1

Parameters used in the MD simulations

Cluster energy,

E0 (keV)

Cluster size, Ncl Energy per

cluster atom,

E0/Ncl (eV)

Number of

target atoms

Diameter and

height of MD

target (�A)

Computation

time (ps)

6.4 236 27 77000 130 and 76 17

10 370 27 77000 130 and 76 10

13.3 490 27 77000 130 and 76 10

20 736 27 105000 150 and 76 10


3. Sputtering yield

The sputtering yield Y (atoms/ion) is de®ned asa number of target atoms removed from the sur-face with one cluster impact. We have obtainedthis value as a long-time limit of a function y(t),which represents the total number of atoms thatcrossed a certain control plane at a height zcut

above the surface, with zcut taken as a parameterwhich is varied between 0 and 40 �A. The numberof atoms crossing the zcut plane increases with thetime elapsed from the beginning of impact, andthen saturates at a value corresponding to thesputtering yield [23].

Sputtering yields were derived from the satu-ration values of function y(t). They are shown inFig. 6 as ®lled circles for cluster energies of 6.2,10, 13.2, and 20 keV, and Ar cluster sizes of 236,370, 490, and 736 atoms in a cluster, respec-tively. The ®gure shows that the MD results arereasonably close to the experimental data [24].Fitting the MD and the experimental resultswith the formula Y�E a gives a value of thenonlinearity parameter a� 1.4. This result isclose to that attributed to the shock-wave

mechanism [26]. The thermal spike model [27],gives a larger exponent than that obtained in thepresent paper.

4. Ripple formation by cluster ion beams

A ®nite-di�erence model for modi®cation ofan initially ¯at surface by oblique cluster beamswas developed in Ref.[25]. The shape of a craterand of a rim was de®ned by a local surface slopeof the impact area with size of Lx ´ Ly . The re-laxation of the surface after creation of a craterwas modeled with a continuum surface dynamicsequation containing a viscous ¯ow term, a sur-face tension term, and a surface di�usion term[25,29±31]. We have used two models with twodi�erent scales for the plane surface. With ModelI for the smaller scale features a crater with a

Fig. 5. The BHN data (in GPa), are correlated with the crater

depth. The total cluster energy is given as a parameter. The

calibration of the lines was made for Cu as target material.

Circle corresponds to the crater depth of 7 �A obtained by the

MD for 10 keV cluster impact. Lines are calculated according

to formula (3). Square is the BHN predicted by the present

method for the Au crater depth of 22 �A measured for 150 keV

cluster impact on Au [18,19]. The error bar on the right side

scale shows experimental Au hardness data BHN� 0.24±0.5

GPa [22].

Fig. 4. MD calculation of a diameter-(full) crater depth de-

pendence. Here, the full crater depth was de®ned from the top

of the rim to the bottom of the crater. Energies and cluster sizes

are the same as in Figs. 1,2.


diameter of 100 �A, typical for a 20 keV Ar3000

cluster ion impact in experiment [19], was rep-resented by about 50 mesh nodes. A Model IIfor the larger scale has a coarse grained meshwith a crater reproduced by one mesh cell. Thepositions of the craters were randomly distrib-uted over an area of about 103±104 mesh nodes.This area represents a surface area of 103 ´ 103

�A2 for Model I, and 104 ´ 104 �A2 for Model II.All cluster impacts occur at 60° o�-normal inci-dence angle to the horizontal plane. When theabsolute value of a local surface slope was lessthan 45°, we simulated an oblique impact. Cra-ters were not created when a local surface anglewas larger than this limit. The length of theejection was also chosen depending on the localangle in a simple Gaussian form: L(u)�Lav exp{ÿ(u/u0)2}, where Lav is the average range ofejection, and u is the local surface angle. Thetypical irradiation parameters used for rippleformation are Lav� 100 �A, cluster ion doses arein the range of 1012±1015 ion/cm2. They corres-

pond to 103±104 clusters impacts on a simulationarea. The cluster beam was directed along the x-axis and periodical boundary conditions wereused in the beam direction. Fig. 7(a) shows theresult of simulation for a dose of 1015 ion/cm2

with Model I (Lx� 75, Ly � 25). Light areas inthis Figure correspond to surface heights abovethe average level and dark areas are below theaverage. One can see the formation of a ripplestructure with the wavelength k of about 300 �A.The relaxation of the surface in this Figure wasmodeled within a viscous ¯ow model [32,33]which is suitable for Si or SiO2 surfaces with alow surface di�usion. Fig. 7(b) shows the resultobtained with Model II for the isotropic surfacedi�usion: Dx�Dy , where Da is the di�usivityalong the a-axis (a� x, y). The patterns in this®gure resemble ripples with k� 250 �A, but theyare divided by lower level spaces. This result istypical for the modeling of a metal surface withisotropic surface di�usion such as a Cu(1 0 0)surface. This picture agrees well with the exper-imental results of cluster ion irradiation of aCu(1 0 0) surface with 20 keV Ar3000 cluster ionbeams [18,19]. The situation was changed dras-tically when we used an anisotropic surface dif-fusion. When Dx was set to 10 ´ Dy , it showedthat wide ripples were formed with k� 500 �A.Fig. 7(c) shows the opposite case with Dx�Dy/100. A well de®ned ripple structure was obtainedin this case. We see that this last modeling resultagrees qualitatively with the experimental obser-vation of ripple formation on a Ag (1 1 0) sur-face [34]. Fig. 7(d) shows a result for theformation of a dot-structure with a wavelengthof 300 �A, found when beam current was in-creased to 3 ´ 1015 ions/cm2. The dot-structureformation could be explained as follows, ripplestructures found in simulation and in experimentare travelling along the beam direction [35].Mathematically this movement is described bythe viscous ¯ow term in the surface dynamicsequation. As periodic boundary conditions(PBC) were not used in this paper in the y-axisdirection, the surface waves could have beenre¯ected from the walls in this direction. Theinterference of the viscous waves may lead to theformation of standing waves in this case.

Fig. 6. Calculated and experimental sputtering yields as a

function of cluster energy. The line 1 represents ®tting of the

MD data by a dependence: Y�E1:4. Experimental data [24]:

open circles- Ar/Cu, squares- Ar/Ag, triangle- Ar/Au. Our MD

results-®lled circles. The inset in this ®gure shows angular dis-

tribution of the sputtered atoms 10.3 ps after the Ar736, 20 keV,

cluster impact, obtained in the MD, (dashed line) in compari-

son with the experimental data [24] shown by circles.


5. Shallow decaborane implantation and RTA

Decaborane implantation into Si at roomtemperature and the subsequent rapid thermalannealing (RTA) process at a much higher tem-perature was simulated in a low ion energy im-plantation region. As RTA is usually applied for10 s, a time scale which is too long for a MDmethod, a method combining MD with Met-ropolis Monte Carlo (MMC) is developed inRefs.[36,37]. The proposed method could easilyextend simulation time up to �1 ms, which is longenough for ®nding parameters of dopant di�usion.

The atomic positions at monomer ion andDecaborane implantation were obtained by theMD simulation at room temperature. The De-caborane molecule was modeled with a B10 clusterbombarding a Si substrate. The basic cell size for

the MD simulation was determined from thecluster energy between 2±5 keV and experimentaldose of 1013 ion/cm2 [9]. A cubic slab consisting ofabout 105 Si atoms was used for one Decaboraneion impact or for 10 implanted B� ions. The PBCwere used in x and y directions, and Langevinforces were applied to 4 atomic layers, in order tokeep the system at a desired temperature. Atoms inthe two bottom atomic layers were ®xed. The ZBLpotential at short distances combined with theStillinger±Weber potential at equilibrium distanceswere used to evaluate interactions between twoand three Si atoms, as usual [38]. Interaction be-tween B and Si atoms was modeled via the ZBLscreened Coulomb potential at short distances,r < r1� 0.52 �A, and with a Morse-type potential atlong distances, r > r2� 0.86 �A. The binding energyof B in the Si lattice was used as an adjustable

Fig. 7. The results of surface dynamics simulation of 103±104 oblique cluster impacts for two discrete models with cell size of 75 ´ 25:

(a) on an insulating surface; (b) on an isotropic metal surface. (c) Simulation of a surface with anisotropic di�usion: the di�usion

coe�cient in perpendicular direction is much higher than along the beam direction. (d) A dot-structure found at a higher ion beam

current and at a dose of 3 ´ 1015 ions/cm2.


parameter with values between 0 to 1.5 eV. Inter-action between two B dopants was modeled withan (exp-6)-type potential, with the depth of 0.2 eV,req� 1.5 �A.

In MD simulation, all B and Si atomic posi-tions and velocities were calculated as output data.The Decaborane implantation results were com-pared with simulation of B� ion implantation,with the same dose and same energy per atom. Alarge amorphized pocket is obtained directly underthe surface. The area heavily disordered with De-caborane implantation has an rdf which contains aglass peak at P 3 �A. The same simulation of B�

implantation has shown that there are almost noamorphized areas in the Si substrate.

The atomic positions obtained with the MDwere transferred into a MC code for which theMetropolis MC (MMC) algorithm was used[39,40]. In the MMC method, every atomic posi-tion of the studying system is displaced withinsome small increment. This increment can be ob-tained from the virial expression for a given tem-perature Tref which varies between 100 and 2000K. In the MMC method, the time variable isusually measured in MC steps per atom, sMC, andan additional e�ort should be made to obtain thereal time variable [41]. Using the standard Ar-renius logarithmic representation {log D vs. 1/T},the real time variable tR could be obtained. Thedi�usion constant Di (i�B, Si) can be calculateddirectly from the mean-square displacement of a Bor Si particle. The B and Si di�usion constants canbe calculated from the slopes of these displace-ments.

A typical evolution of B trajectories during theMC simulation shows that the displacements inxy-plane and in z-direction are almost the same.This is a pure geometric e�ect caused by a non-uniform initial dopant distribution.

Fig. 8 shows the B and Si di�usion coe�cientsobtained for 2.5 and 5 keV implantation energymodeled by a small and a large target, respectively.Here curve 1 is the experimental B di�usion con-stant [42], curves 2 and 3- are the Si and B di�usioncoe�cients computed in this work. For the high-temperature region the obtained activation energyfor B is of about 3 eV, which is close to the ex-perimental value 3.4 eV. A signi®cant lowering of

the activation barrier could be seen for the low-temperature region where this value is less than�0.2 eV. This low energy activation process couldbe ascribed to the vacancy mechanism [43]. Thehigh-temperature part of the curve 2 was contin-ued to 1/T� 0, which gives a measure of the MCstep per atom in real time to be: tMC� 105/mSi. Thefrequency of Si thermal oscillations mSi can beroughly estimated to be in the interval 1013±1012

sÿ1. This estimation gives for the MC-time steptMC� 10ÿ8±10ÿ7 s which makes it possible tomodel the RTA process, with the duration of �10s. The Si di�usion constant shown in Fig. 8 wasfound similar to that of B, and it corresponds tothe di�usivity of disordered Si atoms. The Si dif-fusion constant for the well crystallized areas ismuch smaller than that of the disordered areas.

6. Summary

MD and MC models of gas cluster irradiationof a solid surface have been developed to study thephenomena of crater formation, sputtering, sur-face hardness evaluation, and surface treatment.

Fig. 8. Boron and silicon di�usion coe�cients obtained with

the MC simulation for 2.5 (modeled by a small target) and 5

keV (a large target) B10 implantation into Si: (1) experimental

data for B di�usivity [5], (2) the Si di�usion coe�cient obtained

in this simulation, open symbols, (3) the B di�usion coe�cient,

®lled symbols.


A 1/3 power law dependence of the crater depthon the cluster energy was obtained. A new hard-ness measurement technique is proposed based onthe use of large gas cluster beams for indentationinto surfaces. This method is based entirely on asurface e�ect which depends only on the surfacematerial and not on the substrate and thereforecould be particularly suitable for thin deposited®lms.

Discrete models for ripple formation on a sur-face irradiated by cluster ion impacts based on asurface dynamics equation with crater formationand di�erent mechanisms of surface relaxation:viscous ¯ow, surface tension, and surface di�usionwere developed.

MD and Metropolis MC models of Decabo-rane cluster ion implantation into Si substratewere developed which allow simulation of im-plantation and subsequent RTA processes.

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surface processing with ionized cluster beams: computer simulation

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