ELSEVIER Materials Science and Engineering A217/218 (1996) 89-93

MATERIALS SCIENCE 8r

ENClWEERlNG

A

Computer simulation of crystal surface smoothing by accelerated cluster ion impacts

Z. Insepov”, I. Yamada Ion Beam Engbtee&g Experimental Laboratory, Kyoto Uniueuity Salcyo, Kyoto 606-01, Japan

Abstract

Gas cluster ions accelerated to high kinetic energies can be used successfully for surface modification. The most impressive result of cluster ion irradiation appears to be a surface smoothing effect: a rough surface containing valleys and hills of average heights of the order of 100 8, becomes almost flat with the residual roughness reduced by a factor of 10. The Langevin dynamics based on the Kardar-Parisi-Zhang equation, combined with a Monte-Carlo procedure for crater formation, was used for simulation of the surface modification at cluster ion impacts. We found that for a crater size of the order of 20 A, significant smoothing occurs after irradiation by approximately lo3 cluster impacts; this was confirmed by experiment at dose of lOI ions cmm2. The rate of the smoothing process depends on the value of surface diffusion coefficients, and can be accelerated significantly if the lateral sputtering phenomenon is taken into account.

Keylror&: Computer simulation; Crystal surface smoothing; Cluster ion impact

1. Introduction

Materials with high quality surfaces are needed and applied widely in advanced technologies. Examples in- clude smooth surfaces required for quantum well struc- tures, surfaces with changed electrical and optical properties, and surfaces with increased hardness and wear resistance in optoelectronic and microelectronic applications [l]. The most recent application of smooth surfaces appears to be the thin magnetoresistant layers in new data storage devices.

Cluster ion irradiation of solid surfaces has become a unique method for surface modification, distinguished from other techniques by its ability to deliver a high total energy, determined by the cluster size and acceler- ation voltage, together with soft impact on the surface. The latter feature of cluster impact is explained by the sharing of the total cluster energy between the con- stituent cluster and collisional surface atoms on impact. As a consequence of the dual nature of cluster energy, new physical effects occur at cluster impact on a solid surface. The most interesting effect of cluster ion irrad-

* Corresponding author. Phone: + 81 75 753 4987; Fax: + 81 75 751 6774; E-mail: insepov@kuee-u.ac.jp.

0921-5093/96/$15.00 0 1996 - Elsevier Science S.A. All rights reserved PII SO92i-5093(96)10322-l

iation on a solid substrate appears to be the surface smoothing effect. As was established experimentally in Ref. [2], the surface roughness of various substrate materials measured by atomic force microscopy has been reduced considerably after irradiation with CO, cluster ions accelerated to 10 kV. These results have been obtained for Pt, Cu, poly-Si, SiOZ, S&N, Glms and glass substrates.

The molecular dynamics (MD) calculations of cluster impact on a solid surface have revealed that a hot and highly compressed region with a transient temperature of up to 10’ K and pressure up to 1 Mbar arises in a short time interval which probably leads to the genera- tion of strong shock waves [3-51. These shock waves may penetrate to much deeper distances than the clus- ter itself, Reflection of these shock waves off open surfaces and defects, as well as their superposition, can lead to amorphization of the substrate material. MD calculations revealed the lateral sputtering effect, when most of the ejected surface atoms acquire momentums with a lateral orientation, which allows them to diffuse much more widely, noticeably smoothing rough sur- faces [3].

MD simulations of cluster-surface impacts account for many of the new phenomena except for this surface smoothing. This is because the smoothing effect re- quires a very long time interval compared with typical

90 2. fizsepozt, I. Yatnada / MuteTials Science and Etzgitzewitzg A217/218 (1996) 89-93

MD calculation times for single cluster impacts. The MD technique can provide data for many cluster im- pacts, however it is limited to the study of small surface areas with typical size of the order of 100 x 100 A’ [4,6]. The computational cell size for this new surface smoothing phenomenon should be at least of the order of 1000 x 1000 A’, which imposes extreme require- ments for hardware.

In Ref. [7], the authors considered that the smoothing and corrugation of a surface profile is induced by tensile or compressive stresses which act along the surface plane. Based on MD simulations the authors have shown that surface step free energies are essential for surface mor- phologies. These results were obtained for an Si(100) surface where the surface structure was complicated by the existence of two types of step [8]. We believe that surface transformations produced by cluster irradiation differ from the subject discussed in Ref. [7] because of their non-equilibrium origin. Here we study a rough surface deposited by CVD technique at conditions far from equilibrium.

The aim of this work is to develop a simple numerical model of solid surface modification by cluster irradiation based on a phenomenological Langevin dynamics equa- tion of motion in the form of the Kardar-Parisi-Zhang (KPZ) equation [9]:

ah (r, t) - = vV2h + (42)(vh)2 + ?y(r,t)

at

This equation was used quite successfully to describe a wide variety of growth models including ballistic aggregation, vapor deposition, and the morphology of growing surfaces or interfaces [lo-121. This equation represents the non-linear dynamics of growing surface profiles in terms of the coarse-grained interface heights h(r,t) in a d-dimensional space where I’ is the radius-vec- tor in a (d- l)-dimensional plane at time t, and accu- rately describes the behavior in later stages or scaling properties of a growing interface. The first term describes the surface relaxation driven by diffusion processes, the coefficient v is the surface tension. The non-linear second term corrects the velocity of the growing height, and the last term represents a Gaussian white noise with time average

where hi is the height of the ith column, L is the length of the computational cell, and It,, is the mean surface height

h,, = s

(Ijl(I’J)) = 0

(q(r,t)q(r’,t’)) = 2G6(e - r’)s(t - t’)

The crater geometry was obtained in our previous paper [3], and was introduced using a Monte-Carlo procedure [ 161: (1) select a random position for cluster impact; (2) form a crater with a volume that corresponds to the

given cluster size and energy; (3) select a position on the surface for redeposition; (4) calculate the change in potential energy dU; (5) if dU is negative, accept a new position; {6) otherwise, select a uniformly distributed random

number CE [Oo, 11; where G is the amplitude of the noise which can be (7) if exp(dU/k,T) cc, do not accept a new position; identified with the equilibrium evaporation rate multi- (8) simulate another jump of the redepositing particle, plied by the surface temperature [13]. i.e. start from (3).

2. The model

The typical irradiation parameters used for surface

smoothing are as follows: doses are in the range 10’2-10’5 ions cmm2 average cluster sizes are of the order of 10” atoms, iota1 cluster energies are approxi- mately 20-200 keV. A single hill having a typical area of order 10G-107 A2 was placed in the center of the computational cell. The average cluster dose was of the order of lo”-lo5 clusters per hill. We assumed also that clusters hit the surface with a normal direc- tion at a random position, Displacements of surface particles after the cluster impact were modeled in ac- cordance with the probability obtained from our MD simulation of single cluster ion impact on a flat sur- face [3,14]. To obtain the result of many cluster im- pacts, we assumed that a given amount of surface material is sputtered independently for each cluster impact.

We added the pinning forces in order to favor in- teger values of heights, in units of the layer space parameter c, according to Ref. [13]:

Vpin = V&in ( 1

2nho c

The stochastic term in the KPZ equation was modified according to a crater formation procedure which reflects the cluster impact of a given energy and cluster size. We defme the surface roughness from the variance:

“’

To understand better the effect of the geometry of surface atoms ejected by cluster impact, we modeled different occurrences for the redeposition event. Particles can be reflected from the first position and redeposited at another position. Thus, we have taken

Z. Insepov, I. Yamnda / Materials Scieme and Engineering A2171218 j1996) 89-93 91

k-i- , 4 1 J

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0 200 400 600 800 1000

X Axis,[a.u.] DOSE, 10qo clusters/cm2

Fig. 1. (a) Dose dependence of the surface profile, and (b) dose dependence of the surface roughness after cluster ion irradiation of a one-dimensional surface.

into consideration a lateral sputtering effect. The shape of the rim around the crater was chosen depending on the local hill slope.

Periodic boundary conditions were used in two direc- tions along the x and y axes.

Eq. (1) contains the model parameter v which can be considered as the surface diffusion coefficient [15]. Choice of this parameter allows us to model different substrate materials.

3. Results and discussion

The non-linear differential Eq. (1) was transformed to the difference equation and computed numerically. We used dimensionless units for the length and time variables. The parameters in Eq. (1) were v = 10V4 cm* s - ’ [17] and To = 300 K. We supposed in this work that sputtered surface atoms diffuse with the maximal diffusion coefficient. The calculations were performed for the cell sizes L2 = 625, 2601, 10000 and 40000 atomic positions.

Fig. 1 shows the dose dependence of the surface profile and surface roughness for a one-dimensional (Id) surface. The initial profile is depicted as a thin solid line, the dotted line corresponds to 100 cluster impacts on the surface, and the thick solid line repre- sents the result of 1000 cluster impacts. In this figure, the linear size of the hill was 400 A. For one cluster impact this gives a dose of 10” ions cm -2, and a dose of 10’” ions cm - 2 for 1000 cluster impacts in the same area. As seen in Fig. I, the surface roughness is de- creased five-fold after 1000 cluster impacts, and remains constant if the irradiation dose is increased further. Here, we used a simple definition of roughness of hlax - ftTlin)/~nlax. The one-dimensional model, of

course, suffers from an insufficiently high atomic mobil- ity, but it includes all the necessary mechanisms, such as crater formation, melting and diffusion, and there- fore it is useful for gaining qualitative understanding of the cluster irradiation processes.

Fig. 2 shows the sequential results of 100 cluster impacts on a 2d surface containing 625 atomic posi- tions for 5, 10, 50 and 100 cluster impacts respectively. The size of the area corresponds to 80 x 80 A2 in this

a) D=5c1/L2 b) D=lO

c) D=50 d) D=lOO

Yhk Y&s

Fig. 2. Dose dependence of the surface profile for a small computa- tional cell of size L = 25 (80 I%), the dose D = 100 clusters per area corresponds to 1.5 x 1OT4 ions cm-‘.

92 Z. Insepov, I. Yamada / Materials Scieme and Engineering A21 7/218 (1996) 89-93

0.12 , -4 0 20 40 60 80 100 120

CLUSTER DOSE, cl / L*

Fig. 3. Dose dependences of the surface roughness for different values of the parameters in Eq. (i). When no diffusion is allowed (v = h = O), the roughness increases.

case. The diameter of the crater was chosen to be 20 is which corresponds to the impact of 3000 Ar atoms on the Si surface [3,4]. One cluster impact corresponds to a cluster ion dose of 1.5 x lOI ions cmw2. Eq. (1) was used without pinning forces to obl;ain these results. This model describes the physics of surface smoothing much better than the Id model. It shows the smoothing process with an increase in dose, as well as an increase in roughness if the irradiation dose continues to in- crease, which agrees with the experimental observation PI.

Fig. 3 depicts a comparison of surface roughness for different values of parameters of Eq. (1) for the surface containing 2601 atomic positions. As is seen, the sur- face roughness increases when su.rface diffusion is not allowed (v = 3\ = 0), and its rate depends on the value of diffusion coefficient. If one uses a typical surface diffusion coefficient of the order of 10 - Is cm2 s-l for Si adatoms on an Si surface at room temperature [17], no modification can be achieved.

We supposed that modification of the Si surface with cluster irradiation would be possible if laterally sput- tered substrate atoms were overhit as a result of their significant momentum along the surface, and the fact that they are highly non-equilibrated with the surface. Obviously, this is a new mechanism of surface modifica- tion which does not need as much energy as conven- tional surface melting,

Fig. 4 shows the dose dependence of the surface profile for the case when Eq. (1) includes the pinning forces. These forces are necessary to stabilize a rough surface in the case when no irradiation is applied to the surface. The size of hill was 160 x 160 A’. The dose

a) D=100cl/L2 b) D=200

c) D=300 d) D = 400

50 0

'&is '4%/s

Fig. 4. Dose dependence of the surface profile for a surface with L= 50 (160 A). The dose D =400 corresponds to 1.5 x 1Oz4 ions crnm2.

D = 400 clusters per surface area corresponds to 1.5 x 1014 clusters cm-*.

Fig. 5 represents the results of surface roughness calculations for the case when no pinning forces are included in Eq. (l), for two cell sizes L = 100 and L = 200 corresponding to 320 x 320 A’ and 740 x 740 A” respectively. Both results show almost the same rate of decreasing roughness for cluster ion doses up to 1.5 x lOI ions cm-*.

0.25 . Circles -L = 100 Solid line and squares - I, = 200

0 100 200 300 400 DOSE, ions / L2

Fig. 5. Dose dependence of the surface roughness for L = 100 (320 A) and L = 200 (640 A).

Z. Insepov, I. Yamada / Materials Science a& Engineering A217/218 (1996) 89-93 93

4. Summary

A new simple numerical model for surface smoothing by accelerated cluster impacts based on the Kardar- Parisi-Zhang equation was developed. The craters formed after cluster impact on a substrate surface were modeled using the Monte-Carlo technique. The proba- bilities of sputtering were extracted from previous MD calculations of cluster-surface impacts,

The calculations were performed for cell sizes L2 = 625, 2601, 10 000 and 40 000 atomic positions. If no lateral diffusion was included in the equation of mo- tion, the surface roughness increased after irradiation with cluster impacts. A significant smoothing effect was obtained for all cell sizes owing to enhancement of the surface diffusion coefficient after cluster bombardment.

The shape of the rim around the crater affects the surface roughness very little.

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