Surface modi®cation with ionised cluster beams: Modelling

Z. Insepov *, I. Yamada

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

Abstract

Impacts of accelerated cluster ions which consist of hundreds of atoms on a solid surface have shown new surface

smoothing and roughening e�ects. Hybrid Molecular Dynamics (MD) and a two-dimensional MD method were used to

simulate rapid collision processes at the target impact zone and the subsequent thermalization. Gas clusters impacting

on metal and semiconductor target surfaces have been considered to study the ripple formation under irradiation with

oblique cluster beams. The dynamics of surface modi®cation is simulated by using a discrete model which contains

crater formation and surface relaxation. The continuum description of a surface relaxation is based on a dynamics

equation for surface heights containing viscous ¯ow, surface tension, surface di�usion, and crater formation terms.

Comparison of the results of the simulation with experimental data shows qualitative agreement. Ó 1999 Elsevier

Science B.V. All rights reserved.

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

Keywords: Cluster; Ion; Crater; Ripple; Viscous; Di�usion

1. Introduction

Materials of high surface quality are neededand applied widely in advanced technologies. Ex-amples include the smooth surfaces required forquantum well structures in optoelectronic andmicroelectronics applications [1,2]. Correspondingsurface irradiation e�ects have recently attractedmuch attention in experiments, theory and atom-istic simulations [3±12].

Metal surfaces have a high surface mobility ofadatoms and this feature has a strong in¯uence for

surface modi®cation processes caused by ionbombardment [4±7]. Ripple formation on ion im-planted Si was experimentally observed [8], and onamorphous SiO2 and crystalline Ge (001) surfacesfor low (below 1 keV) energy ions heavy (Xe) andlight (H, He) ions [9,10]. Ripple formation wasfurther observed on an amorphous Fe40Ni40B20

®lm surface [11], and ion induced stresses andsubsequent viscous ¯ow of SiO2 surfaces weremeasured directly in Ref. [12]. A two-dimensional(2D) macroscopic ripple formation theory wasproposed in Ref. [13]. According to this, a uniformion irradiation of a rough surface increases surfaceroughness because trough atoms gain a higherenergy than the atoms of the crests. This idea wasused to develop a scaling theory of ripple forma-

Nuclear Instruments and Methods in Physics Research B 148 (1999) 121±125

* Corresponding author. Tel.: (075)753-5956; fax: (075)751-

6774; e-mail: insepov@kuee.kyoto-u.ac.jp

0168-583X/98/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved.

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

tion in Ref. [14]. Monte Carlo computer modelsfor ripple formation in ion beam sputtering wererecently developed in Ref. [15].

The large gas cluster ion irradiation of a surfaceis subjected to di�erent mechanisms compared tosingle ion impact. The cluster itself does not pen-etrate into the substrate on impact. The model ofsurface instability [14] may not be valid for thesurface processes activated by cluster ion irradia-tion. Experimental studies of surface modi®cationwith cluster ion beams clearly show that a veryhigh smoothing rate of rough substrate surfaceswith normal cluster beams could be achieved[2,16]. Surfaces may roughen under oblique clusterimpacts resulting in a ripple structure. An AFMstudy of a Cu (100) surface irradiated with large20 keV Ar�3000 cluster ions with dose of 5 ´1015

ions/cm2 at 60° o�-normal incidence angle showsthe formation of ripples with an average wave-length of 300 �A [16,17].

The result of simulation of a large Ar-clusterimpact on a Cu surface is presented in this paper.The results of a 2D MD simulation of a roughsurface erosion with cluster impacts were com-pared with the predictions of Ref. [13]. A numer-ical model of ripple formation on a surface underoblique cluster ion beam irradiation is presented.

2. Molecular dynamics of cluster irradiation on a

surface

The result of a long simulation of a craterformed by a spherical Arn (n�750) cluster withtotal energy of 20 keV bombarding a Cu(100)surface of 105 Cu atoms interacting via EAM-po-tential is given in Fig. 1. The real time in this ®gurecorresponds to 20 ps after the beginning of theimpact. Such a long simulation was not feasiblewith the conventional MD method due to the re-¯ection of compression and temperature wavesfrom the boundaries of the computational cell.The hybrid MD method described in our previouspaper [20] was used here to eliminate the e�ect ofthe re¯ection and to obtain the crater shape after along time. A hemispherical crater is formed at 20keV Ar736 impact. A rim around the crater isformed due to the plastic ¯ow of the crater mate-

rial. We have simulated impacts of Ar clusters with6, 10, 13, and 20 keV total energy. A linear cor-relation between crater dimensions was obtained,e.g. between crater diameter and crater depth.

In contrast to normal incidence, the material ofa crater ¯ips over the crater edge in a down-streambeam direction, and forms an extended bump foran oblique impact. The existence of the two cratertypes on a solid surfaces irradiated with normaland oblique cluster beam orientations, are wellcon®rmed experimentally by AFM studies [18,19].

If a surface containing small irregularities isirradiated with an energetic uniform single ionbeam, the negative curvature of troughs gives ahigher sputter probability [13]. For the positivelocal curvature, this model gives a lower sputterprobability.

We have studied these two situations within a2D MD model of cluster impact and have com-pared the results with the predictions [13]. A singlehill having a cosine-shape with a size in the orderof 103 �A was placed in the center of the compu-tational cell. A 2D Ar349 cluster (a 3D cluster withthe same radius would consist of 4500 Ar atoms)with energy of 50±100 eV/atom was directed to-ward the hill in di�erent positions: a) a centralimpact into the hill's peak, b) a side impact close tothe center of the hill. We have calculated thenormal velocities along the z-axis of all surfaceatoms during the time instant of about 10 ps until

Fig. 1. Molecular Dynamics simulation of a 20 keV Ar736

cluster normal impact on a Cu(100) ¯at surface. The crater has

a hemispherical shape with a symmetrical rim around the cra-

ter.

122 Z. Insepov, I. Yamada / Nucl. Instr. and Meth. in Phys. Res. B 148 (1999) 121±125

the impact energy is dissipated into the bulk. Atypical ion ¯ux for the ion beam experiments, ofthe order of 1011±1012 ions/cm2 s, was also mod-elled. Fig. 2 shows the results of our simulationsfor 100 eV/atom central and side impacts on arough hcp-surface with the atomic parameters forSi. As one can see from this ®gure, a central clusterimpact leads to sputtering of a large number ofatoms from the body of the hill. Only some ma-terial from it would ®ll up the troughs. Side clusterimpacts can more e�ciently ®ll up the troughs.

Cluster impacts generate high temperature andhigh pressure areas which may completely destroy asigni®cant part of a single hill (for central impact)with a size less than 103 �A. The remainder of the hillbecomes heavily damaged, showing sliding planes,amorphization, void and vacancy formation. Thus,the result of a gas cluster irradiation of a roughsurface, obtained with the MD simulations, iscompletely di�erent from that of a single ion im-pact. Therefore, the surface instability analysismade in [13,14] is not valid for the cluster irradia-tion case. In the following, we will analyse the in-stability of a ¯at surface by using a surfacedynamics equation where a crater formation pro-cedure was introduced with a Monte Carlo method.

3. Discrete modelling of ripple formation with

cluster irradiation

A ®nite-di�erence model for modi®cation of aninitially ¯at surface with area of Lx ´Ly was de-veloped. The shapes of craters and their rims werede®ned by a local surface slope of the impact area.The relaxation of the surface after creation of acrater was modelled with a continuum surfacedynamics equation containing a viscous ¯ow term,a surface tension term, and a surface di�usion term[3,9,14,18,19]. We have used two models with twodi�erent scales for the plane surface. With Model Ifor the smaller scale features, a crater with a di-ameter of 100 �A, typical for a 20 keV Ar3000 clusterion impact in experiments [16,17], which was rep-resented by about 50 mesh nodes. Model II for thelarger scale has a coarse grained mesh with a craterreproduced by one mesh cell. The positions of thecraters were randomly distributed over an area ofabout 103±104 mesh nodes. This area represents asurface area of 103 ´ 103 �A2 for Model I, and104 ´104 �A2 for Model II. All cluster impacts areassumed to occur at 60° o�-normal incidence. Ifthe absolute value of a local surface slope was lessthan 45°, we have simulated an oblique impact.

Fig. 2. Molecular Dynamics simulation of cluster impacts on a rough Si surface containing a single hill with a diameter of 600 �A. Ar349

cluster, with energy of 100 eV/atom, hits the hill at di�erent positions: (a) central impact into the hill's mount; (b) a side cluster impact.

Z. Insepov, I. Yamada / Nucl. Instr. and Meth. in Phys. Res. B 148 (1999) 121±125 123

Craters were not created when a local surface anglewas larger than this limit. The length of the ejectionwas also chosen depending on the local angle in asimple Gaussian form: L(u)�Lav ´exp{(u/u0)2},where Lav is the average range of ejection, u is thelocal surface angle. The typical irradiation pa-rameters used for ripple formation are as follows:Lav� 100 �A, cluster ion doses are in the range of1012±1015 ion/cm2 which correspond to 103±104

clusters impacts on a simulation area. The clusterbeam was directed along the x-axis and periodicalboundary conditions were used in the beam direc-

tion. Fig. 3(a) shows the result of simulation for adose of 1015 ion/cm2 with Model I (Lx� 75,Ly � 25). Light areas in this ®gure indicate surfaceheights above the average level and dark areas arebelow the average. One can see the formation of aripple structure with a wavelength k of about 200±400 �A depending on the cluster energy. The relax-ation of the surface in this ®gure was modelledwithin a viscous ¯ow model [9,10] which is suitablefor Si or SiO2 surfaces, with a low surface di�usion.Fig. 3(b) shows the result obtained with Model IIfor the isotropic surface di�usion: Dx�Dy , where

Fig. 3. 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.

124 Z. Insepov, I. Yamada / Nucl. Instr. and Meth. in Phys. Res. B 148 (1999) 121±125

Da is the di�usivity along the a-axis (a� x, y). Thepatterns in this ®gure resemble ripples with k�250�A but they are divided by lower level spaces. Thisresult is typical for the modelling of a metal surfacewith isotropic surface di�usion such as a Cu(100)surface. This picture agrees well with the experi-mental results of cluster ion irradiation of aCu(100) surface with 20 keV Ar3000 cluster ionbeams [16,17]. The situation is changed drasticallyif we use an anisotropic surface di�usion. If Dx hasbeen set to 10´Dy , it shows that wide ripples areformed with k�500 �A. Fig. 3(c) shows the oppositecase with Dx�Dy /100. A well-de®ned ripplestructure was obtained in this case. We see that thislast modelling result agrees qualitatively with theexperimental observation of ripple formation on aAg (11 0) surface [7].

4. Summary

A Hybrid Molecular Dynamics was used tosimulate crater formation on a ¯at Cu(100) surfacewith 6±20 keV Arn (n� 200±800) cluster bom-bardment with normal incidence. A rim formedaround the crater shows a crystalline structure forenergies 6±10 keV and an amorphized structure forhigher energies.

2D MD simulations of the irradiation withlarge Ar clusters at an energy of 50±100 eV/atomon a rough Si surface containing mounts andtroughs, show that the predictions of a surfaceinstability theory for single ion bombardment [13]is not valid in the case of cluster ion beams.

Discrete models were developed for ripple for-mation on a surface irradiated by cluster ion im-pacts, based on a surface dynamics equation withdi�erent mechanisms of surface modi®cation, i.e.viscous ¯ow, surface tension, crater formation andsurface di�usion.

Within these models the e�ect of di�usion ani-sotropy was shown to be very important for sur-face ripple formation. Good qualitative agreementwith experimental results was obtained for rippleformation on an anisotropic metal surface. Insu-lating surfaces can be modeled with a high viscous¯ow and without surface di�usion. A ripple

wavelength of about 200±400 �A was obtained forinsulating surfaces which is very close to the ex-perimental value of 260 �A measured for a SiO2

surface.

Acknowledgements

The authors wish to thank A.J. Perry for hishelp in the preparation of this paper.

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