Sputtering by cluster ions

493

Nuclear Instruments and Methods in Physics Research B33 (1988) 493-496 North-Holland, Amsterdam

SPUTlXRING

BY CLUSTER

IONS

Y. YAMAMURA Okayama

Uniuersity of Science, Ridai-cho, Okayama

700, Japan

Using the Monte Carlo simulation code DYACAT, the sputtering by cluster ions (more than 100 atoms) has been investigated. In the DYACAT program which is based on the binary collision approximation, trajectories of ions and recoil atoms are followed dynamically. In order to simulate the nonlinear cascade development, three types of collision events are taken into account, i.e., between two moving particles, between a moving atom and a target atom and between a moving particle and an interstitial. The time-dependent material change is also followed. The energetic cluster ions, 100 eV/atom (Ar), (n being 10 to 200) have been bombarded on a carbon target. It is found that the energy spectra of slowing down ions which are spread until 200 eV is much different from those of a monatomic ion. Although the incident energy is in the near-threshold region, nonlinearity in sputtering is clear for large n.

1. Introduction

2. Model of DYACAT program

Investigation of the effects of impact of cluster ions containing more than 40 molecules on thin carbon shows the production of craters and holes visible to transmission electron microscope (TEM) [1,2]. Cluster impact processes have some practical interest because they have the potential of depositing a large amount of translational energy in very thin surface layers with very efficient sputtering of the surface [3,4]. The collision processes and sputtering phenomena associated with cluster impact cannot be described within the linear collision cascade theory [5]. About five years ago, Yamamura [6] developed the time-dependent Monte Carlo simulation program in order to know the surface roughness due to ion-bombardment and the non-linear sputtering. Recently, this cascade model has been successfully applied to relativistic nuclear collisions, in order to explain the forward suppression of low-energy protons in Ne + U collisions and the pion multiplicity in Ar + KC1 central collisions [7,8]. Another powerful method to investigate the dynamical cascade development in solids due to the ion bombardment is molecular dynamics [9,10] in which coupled Newtonian equations are numerically solved step by step. Molecular dynamics is time-consuming if the incident energy is high and the number of associated particles is large. On the other hand, it can predict the simultaneous collision of slow atoms and simulate the collective motions of dense collision cascades. Up to now, radiation damage and sputtering due to cluster-ion bombardment have not been investigated systematically from the theoretical point of view [1,2]. In this paper, we refine the previous time-dependent Monte Carlo simulation code in order to simulate the cascade development due to cluster-ion bombardment.

The DYACAT program was developed for the DYnamical simulation of Atomic Collisions in Amorphous Targets within the framework of the binary collision approximation, and it is in a sense the ACAT [ll] in the dynamical mode. The DYACAT program is a nonlinear Monte Carlo simulations code in which we can treat three types of collisions; 1) the collision between two moving particles, 2) the collision of a moving particle with a target atom at rest, and 3) the collision of a moving particle with an interstitial. The kinetics of the latter two collisions are special cases of the two moving-particle encounter [12,13]. Then, let us consider the kinetics of a two moving particles collision of masses M, and M2. As a result of the collision, the velocities of both particles change in direction and in magnitude. We denote their velocity vectors before collision by u1 and ua, respectively, and after a collision by u;, and u;. According to the elementary theory of binary collision [12,13], the velocity vectors after collision are given as

0168-583X/88/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

MA + MPZ v’=

*‘=

M,+M, MA + M,+M,

M2 + M,+MZ

44202

V’,

MI

-

qTxf3

where V’ = u; -u; is the relative velocity after the collision which is represented in terms of the scattering angle in the center-of-mass system 0 and the absolute value of the relative velocity V as V’ = V(e,

sin 0 + ep cos 0).

(3)

The unit vectors ep and eA are the direction of a projectile Ml and the direction perpendicular to ea, respectively. VII. SPUTTERING/SIMS

494

Y. Yamamura / Sputtering by cluster ions

The collision partner of a slowing down particle is selected among the many candidates, which are moving atoms, interstitial atoms and virgin target atoms. At each collision event, we calculate the distances in time between the moving atom and many candidates, and pick up a real collision partner which has the minimum distance in time.

3. Results and discussions In order to investigate the nonlinear collision cascades due to cluster ion bombardment, the DYACAT program was applied to the (Ar): + C combination, where n is the number of atoms in a cluster ion, and the Moliere potential is used as the interatomic potential. In the DYACAT code we have two options for simulating the collision cascade, i.e., nonlinear simulation which is denoted by NON-LNR in the figures

20 KEV

(AR)200

-C

(TIME = 0.20

PSEC)

LINEAR

Table 1 Sputtering yields Y, projected ranges R, and particle reflection coefficients RN of DYACAT simulations under various conditions. Model

E,

Y

n

Linear

u, w2

1 1

Nonlinear

US

10 20 50 100 200

Q/2

10 20 50 100 200

<10-s x10-3

ZOKEV

1.36 2.04

0.260 0.280

0.01 0.04 0.09 0.11 0.12

1.96 2.31 3.33 4.39 6.08

0.054 0.044 0.043 0.039 0.036

0.02 0.06 0.14 0.17 0.17

2.56 3.20 4.73 6.26 8.57

0.043 0.040 0.038 0.033 0.032

(AR1200

-:

t = 0.2 ps where a target at

R,

and linear simulation denoted by LNR in the figures. In the case of the linear simulation any change in the crystal is ignored, and the collision events between two moving particles and between a moving atom and an interstitial are excluded. In fig. 1, comparison between linear and nonlinear cascade developments is shown at t = 0.2 ps, where the 100 eV/atom (Ar), cluster ion bombards the carbon

-->

C

AR . . . LNR

---- : -: --&a- :

Fig. 1. Comparison of cascade development at between linear and nonlinear DYACAT simulations, 100 eV/atom (Ar)aaa cluster ion bombards a carbon normal incidence.

\R *p (A)

(atoms/ion)

(ev)

C . . . LNR AR . . . NON-LNR c . . . NON-LNR

I

TIHE

IPSECI

Fig. 2. The time-dependent particle ejections for 100 eV/atom (Ar),, on carbon, where Eb = U,/2.

Y. Yamamura

ZOKEV ENERGY EB

10-l

=

[RRlzoo SPECTRUM

US/2

--> OF

/ Sputtering

C

ARGON

INON-LNR)

0

100 ENERGY

200 IEVI

Fig. 3. The time-dependent Ar energy spectrum at an early stage for 100 eV/atom (Ar) 2oo+ C, where E, = U,/2.

target normally, and the bulk binding energy E, is assumed to be US/2 (US being the sublimation energy). In the nonlinear simulation, when an upper part of the

495

by cluster ions

cluster ions come to the surface, most target atoms near the surface are in motion due to collisions by foregoing atoms in the lower part of a cluster ion, and the tailing atoms in an upper part of a cluster can enter deeply with less energy loss. As a result, the nonlinear simulation gives a greater projected range than the linear simulation (see table 1). The surface binding energy plays a role for cascade developments in solids and associated sputtering phenomena. In the DYACAT code the surface binding energy is numerically determined for each outgoing atom considering the surrounding surface atoms near it. In other words, we employ a damage-dependent surface binding energy [14]. In table 1 we show the molecular effect for several bombardment conditions, where the sputtering yield Y and the particle reflection coefficient RN are normalized as Ycluster/n and RN,c,,,ter/n, respectively. The theoretical threshold energy of an Ar+ ion on C is about 60 eV [HI, and 100 eV Ar bombardment is in the near-threshold region. The ACAT sputtering yield of a 100 eV Ar+ ion on C is about 0.0015. Then, the molecular enhancement ratio of a 100 eV/atom (Ar) 2a,, cluster ion on carbon is about 80. Fig. 2 shows the time-dependent sputtering yield for (Ar),, + C, where E, = Us, and the time-dependent reflection is also plotted against time. The difference between the nonlinear and the linear treatments is very

3.0

1

1

I

2.5 10’

20

2.0

kk,

ZOKEV

(AR1200

--->

C

j

(AR) OF

2o0

-C

SURFACE

DENSITY

1.0

loo ENERGY

KEV

TIME-DEPENDENCE

I .5

0.5

SPECTRUM

1.5 TIME

10-l

-: -: __*_ ____

=

: :

0.15 AR c RR C

PSEC :::

k/d

. . . . . .

NON-LNR NON-LNR

1 .o

‘!

1

*

0.5

t z?

1.5

g

1.0

D # 3

0.5

2

1.0

z

0.5

I 1

4

1.5

1

1.5

I I

I

I

I

1.0 ‘1

0.5

1 .o 0.5 40 0

100 ENERGY

Fig. 4. The time-dependent

200 IEVI

energy spectra of Ar and C at (Ar)200 +C, where the nonlinear and linear treatments are compared.

t = 0.15 ps for 100 eV/atom

t I

LI

0.0

PSEC

0.20

PSEC

0.10

PSEC

0.05

PSEC

l----I 1

I.5

0.50

t--J

I

+

-

I

I

I

20

0

20

RADIUS

40

(A)

Fig. 5. The time-dependence of the surface density at different times for 100 eV/atom (Ar),, bombardment on carbon target, where E, = L&/2, and the density is normalized density before bombardment.

by the normal

VII. SPUTTERING/SIMS

Y. Yamamura / Sputtering by cluster ions

496

20

KEV

(AR1200

-

This peak moves until 20 A at t = 1 ps, reflects at some deeper layer, and comes near the surface like a wave [16,17].

C

2

4. Conclusion In order to investigate the time-dependent collision cascade due to cluster ions, we have developed the nonlinear Monte Carlo simulation code DYACAT which includes collisions between two moving atoms. Several nonlinear effects are observed: The cluster enhancement ratio of the sputtering yield for 100 eV/atom (Ar),, -t C is about 80, the energy spectrum of moving atoms at the early stages is spread by about 200 eV which is larger than the incident energy, and a crater whose size is larger than that of a cluster ion is formed. 1 0 0

10

20 DEPTH

30

40

SO

(A)

Fig. 6. The time-dependence of the bulk density at various + C, where E, = U,/2, and the times for 100 eV/atom (Ar),, density is normalized by the normal density before bombardment.

In the case of the linear simulation, the target material is assumed to be unchanged during cluster ion bombardment. Then, the particle reflection is equal to that from the virgin material surface. The time-dependent energy spectra for 100 eV/atom on C are shown in figs. 3 and 4. Fig. 3 shows the (Ar) 2m nonlinear results of energy spectra of Ar atoms in the early stage of slowing down process. It is very interesting that we have many argon atoms with energies more than 100 eV. In fig. 4 we compare the energy spectra of the nonlinear simulation with those of the linear simulation at t = 0.15 ps. The difference between the two calculational methods is both large and instructive. The time-dependences of surface density and bulk density are drawn in figs. 5 and 6, where the surface density means that of the first two layers. From fig. 5 it is clear that the cluster ion (Ar),, makes a crater with a diameter of more than 10 A, and we know form fig. 6 that the depth of a crater is larger than 5 A. This crater size is larger than that of the cluster ion [I]. In fig. 4 we can observe the high density peak which moves inward, large.

This work was supported by the Special Project Research on Ion Interactions with Solids from the Japanese Ministry of Education, Science and Culture.

References [l] M.W. Matthew, R.J. Beuhler, M. Ledbetter and L. Friedman, Nucl. Instr. and Meth. B14 (1986) 448. [2] R. Beuhler and L. Friedman, Chem. Rev. 86 (1986) 521. j3] T. Takagi, Thin Solid Film 92 (1982) 1. (41 I. Yamada and T. Takagi, Thin Solid Films 80 (1981) 105. 1.51 P. Sigmund, Phys. Rev. 184 (1969) 383. [6] Y. Yamamura, Nucl. Instr. and Meth. 194 (1982) 515. [7] Y. Kitazoe, M. Sano, Y. Yamamura, H. Furutani and K. Yamamoto, Phys. Rev. C29 (1984) 828. [S] Y. Kit-, M. Gyulassy, P. Daneilewicz, H. Toki, Y. Yamamura, and M. Sane, Phys. Rev. Lett. B138 (1984) 854. [9] J.B. Bibson, A.N. Goland, M. Milgram and G.H. Vineyard, Phys. Rev. 120 (1960) 1229. [lo] M.M. Jakas and D.E. Harrison, Nucl. Instr. and Meth. B14 (1986) S3S. [ll] Y. Yamamura and Y. Misuno, IPPJ-AM-40, Institute of Plasma Physics, Nagoya University (1985). [12] R.K.B. Helbing, J. Chem. Phys. 48 (1968) 472. [13) M. Gryzinski, Phys. Rev. 138 (1965) 305. [14] D.A. Thompson, J. Appl. Phys. 52 (1981) 982. [lS] Y. Yamamura and J. Bohdansky, Vacuum 35 (1985) 561. [16] Y. Yamamura and Y. Kitazoe, Radiat. Eff. 39 (1978) 251. [17] Y. Kitazoe and Y. Yamamura, Surf. Sci. 111 (1981) 381.