Study of Cluster-size Effect on Damage Formation
Takaaki Aoki1,2), Toshio Seki1,2), Atsuko Nakai1),
Jiro Matsuo1) and Gikan Takaoka1)
1) Ion Beam Engineering Experimental Laboratory, Kyoto University
2) Collaborative Research Center for Cluster Ion Beam Process Technology
Abstract. Computer simulation and experiments were performed in order to understand the effect of cluster size on
damage formation. Results of molecular dynamics simulations of cluster impact on solid targets derived the model
function, which explains the relationship among cluster size, incident energy and number of displacements. On the other
hand, time of flight mass measurement system was installed a cluster irradiation system, so that cluster ion beam which
cluster size distribution is well known can be irradiated on the target. The damage properties under various cluster
irradiation conditions were examined using RBS. The results from computer simulations and experiments showed good
agreements with each other, which suggests that irradiation damage by cluster ion beam can be controlled by selecting
cluster size distribution and incident energy.
INTRODUCTION
COMPUTER SIMULATION
The impact process of cluster, an aggregation of
several tens to thousands of atoms, is very different
from that of monomer ions. The difference is due to
that, in the collisional process of cluster and surface,
large number of interactions occur between cluster and
surface atoms within very narrow region (~100nm
square) and within very short time (~several ps). This
high-density collisional process causes ‘non-linear
effect’, which cannot be explained by the simple
summation of independent event by monomer ion
impact. Various applications are expected by utilizing
the non-linear effect of cluster ion impact [1-3]. The
non-linear effect depends on various parameters of
cluster ion irradiation, such like the atomic species,
incident energy and cluster size. In order introduce the
cluster ion beam process to industrial applications, it is
important to clarify the relationship between the nonlinear effect and the irradiation condition of cluster ion.
In this work, both computer simulations and
experiments were performed in order to examine the
cluster size effect on the damage formation and discuss
the efficiency of the development of size control
technique for cluster ion beam.
Molecular dynamics (MD) simulation is one of the
powerful methods to understand the collisional process
of cluster on solid surface. Cluster size dependence on
damage formation was studied by MD simulations [4].
Figure 1 shows the MD snapshots of Ar clusters with
various sizes impacting on Si(001) surface. Each
cluster has same total incident energy of 20keV; in
other words, has different energy per atom. Black and
gray circles indicate Ar and Si atom, respectively, and
displaced Si atoms are indicated as white circles.
Figure 1 suggests that, as the amount and structure of
damage is strongly depends on cluster size. When
cluster size is in a range from several hundreds to
several thousands, large number of Si atoms are
displaced spherically and a crater-like damage remains
on the surface after the re-evaporation of incident Ar
atoms. This crater-like damage is confirmed by in-situ
STM observation of Si surface bombarded with Ar
cluster ions [5]. When cluster size is as small as 20,
crater-like damage is not formed but dense damaged
region remains in the surface, which shows deeper
depth profile than that by Ar200 and Ar2000. On the
other hand, when the cluster size as large as 20000,
and incident energy is as low as 1eV/atom, as shown
in Fig. 1, the cluster does not penetrate the surface but
CP680, Application of Accelerators in Research and Industry: 17th Int'l. Conference, edited by J. L. Duggan and I. L. Morgan
© 2003 American Institute of Physics 0-7354-0149-7/03/$20.00
741
Dt ( N , Et ) = A1 ( N α Et − T1 N α +τ +1 ) ,
(1)
where
T1 = 10.38[eV], τ = −0.25
A1 = 0.076[atoms/eV], α = 0.26
.
(2)
The parameters T1 and A1 indicate the threshold
energy to cause damage and yield of damage
formation for Ar monomer, respectively. This formula
represents the characteristics of damage formation
depending on cluster size. At the Et of 20keV for
example, Dt reaches maximum at the cluster size of
several thousands and gives 0 at the size of several
tens of thousands. Eq. (1) gives the cluster sizes
where a cluster causes no displacement (N0) or
maximum number of displacements (Nm). These
characteristic cluster sizes are given by,
1
break-up on the surface. During this collisional process,
some surface atoms are displaced, but the displaced
length is small, so that, these displacements recover
and no damage remains on the surface within several
pico-seconds after the impact.
 α
Et
Nm = 
α
τ
1
T1
+
+

Cluster Size to Cause (No / Max.) Damage
Number of Total Displaced Atoms (Dt)
Et=10keV
Et=20keV
Et=50keV
Model Curves
20000
10000
1
10
100
1000
10000
(3)
1
 τ +1
 = 0.146 N 0

(4)
Figure 3 shows the N0 and Nm for various total
incident energy of cluster ion. It is supposed that
various characteristic irradiation effects can be realized
by selecting cluster size and incident energy.
40000
0
,
and
Figure 2 shows the cluster size dependence of
number of displacements at the total incident energy of
10, 20 and 50keV. From the simulation data, the model
curve is proposed to describe the number of
displacements (Dt) as a function of cluster size (N) and
total incident energy (Et) as follows,
30000
1.33
τ +1
N 0 =  Et  =  Et 
 T1 
 T1 
Figure 1: MD snapshots of Ar cluster with various sizes
(total energy 20keV, 16ps after impact).
100000
100000
10000
No Damage Region
1000
100
10
N0 (No Damage)
Nm (Max. Damage)
1
10
100
1k
10k
100k
Total Incident Energy (Et) [eV]
Cluster Size (N)
Figure 2: Cluster size dependence of total number of
displacements by Ar clusters with total acceleration
energies of 10, 20 and 50keV. The dashed lines are
model functions given by eq. (1).
Figure 3: Total energy dependence of the cluster size to
no displacement (thick line) and maximum number of
displacements (dashed line).
742
Magnet
Ionizer
1.0
Target
monomer
0.8
Faraday
cup
Chop
0.7
Filament
Extraction
Electrode
Accel.
Electrode
pulse generator
gate
Intensity
Skimmer
Inlet Pressure:6233Torr
Accel. Voltage: 20kV
Ve:50V Ie:50mA
Ve:100V Ie:100mA
Ve:300V Ie:300mA
0.9
Nozzle
Ar Gas
current-voltage
amplifier
oscilloscope
TOF system
Figure 4: Schematic diagram of cluster size measurement
and irradiation system.
0.6
0.5
0.4
0.3
0.2
0.1
0.0
EXPERIMENTAL STUDY OF CLUSTER
SIZE DISTRIBUTION AND DAMAGE
CHARACTERISTICS
0
10000
20000
30000
40000
Cluster Size (atoms)
Figure 5: Cluster size distribution measured by TOF at
various ionization voltage (Ve) and current (Ie).
Figure 4 shows a schematic diagram of cluster ion
beam irradiation and size measurement system [6].
Gas cluster is generated by inletting source gas
through a laval nozzle at high pressure. Because of
rapid compression and expansion of source gas, the
source gas is cooled down and atoms are condensed to
make clusters. Neutral cluster beam is induced to
ionization chamber through a skimmer and is ionized
by electron bombardment. An ionized cluster is
accelerated and irradiated on a target. A magnetic
mass filter is equipped to avoid monomer and small
cluster ion to be irradiated on the target. In order to
measure the size distribution in the cluster beam, the
time of flight (TOF) mass measurement system can be
installed as shown in figure 4. Figure 5 shows the size
distribution of cluster size at various ionization
voltages and current. The previous work reported that
[7], the higher inlet gas pressure contributes the
generation of large size clusters. In this study, large
cluster with the size of 15000 for mean size was
obtained, which is larger cluster size than that
previously reported. Figure 5 also indicates that, as the
ionization voltage and current increase, the cluster size
distribution decreases. At 300V and 300mA of
ionization voltage and current, the mean cluster size is
reduced to 2500. It is considered that, the high-energy
electron bombardment with larger current induces
multiple ionization or thermal excitation of cluster,
which results in the corruption of large cluster.
17
2
Number of Displacements [atoms/cm ]
1.0x10
16
8.0x10
16
6.0x10
16
4.0x10
Ve:50V Ie:50mA
Ve:100V Ie:100mA
Ve:300V Ie:300mA
16
2.0x10
0.0
background
0
5
10
15
20
Accel. Voltage [kV]
Figure 6: Incident energy dependence of number of
displacements at various cluster size distributions. Each
line style corresponds to similar style shown in Fig. 5.
ions/cm2, which is enough large to accumulate damage
and to form well-amorphousized layer on nondamaged region in a substrate. In figure 6, the style of
each line corresponds to the size distribution with
similar style shown in figure 5. As shown in figure 6,
damage formation by cluster ion depends on the
cluster size distribution. When cluster size increases,
the total number of displacements decreases and the
threshold energy to cause damage increases. This
tendency agrees with the results by MD simulations
where cluster size is larger than several thousands. The
correspondence of some typical irradiation conditions
to the damage-formation model predicted by MD
simulation (given by figure 3) is shown in figure 7. In
figure 7, the range of cluster size at each condition is
Cluster ion beams with above-mentioned size
distribution were radiated on Si substrates and number
of displacements was measured using Rutherford
backscattering spectrometry (RBS). Figure 6 shows
the incident energy dependence of the number of
displacements at various cluster size distributions. For
each irradiation condition, the ion dose was 1.0×1015
743
100000
no-Damaged
increases and reaches the size where no displacement
is generated (N0).
(2)
(3)
(1)
Cluster Size
10000
As for experiments, the time of fight system was
installed the cluster irradiation system in order to
measure the precise cluster size distribution during
irradiation process. It was found that the cluster size
distribution was changed with the change of ionization
condition. Ar cluster ion beams with various size
distributions were irradiated on Si target and induced
damages were measured with RBS. It was found that
the amount of damage is different depending on cluster
size distribution. As the mean cluster size increases,
the number of displacements decreases. Through these
experiments, no damage irradiation can be achieved
with several irradiation conditions. These no-damage
irradiation conditions agreed with the predictions by
MD simulations. These results conclude that cluster
size technique is important and useful to realize
various irradiation processes using cluster ion beam.
(4)
1000
Damaged
100
100
1k
10k
100k
Total Incident Energy (Et) [eV]
Figure 7: Correspondence of experimental and simulation
results from the viewpoint of size distribution and damage
formation.
indicated by the length of the bar. The irradiation
conditions shown in figure 7 are,
ACKNOWLEDGEMENT
(1) Ve: 300V, Ie: 300mA, Va: 1keV
This work is supported by New Energy and
Industrial Technology Development Organization in
Japan.
(2) Ve: 50V, Ie: 50mA, Va: 5keV
(3) Ve: 100V, Ie: 100mA, Va: 10keV
(4) Ve: 300V, Ie: 300mA, Va: 20keV
where Ve, Ie and Va are ionization voltage,
ionization current and acceleration voltage,
respectively. For each irradiation condition, the cluster
size distribution and the number of displacements can
be referred in figure 5 and 6, respectively. The results
from RBS measurements shown in figure 6, it is found
that the condition (1) and (2) does not cause damage
but (3) and (4) causes damage. These results show
good agreement with that by MD simulation.
REFERENCES
[1] I. Yamada, J. Matsuo, Z. Insepov, T. Aoki, T. Seki and N.
Toyoda, Nucl. Instr. and Meth., B 164-165 (2000) 944.
[2] I. Yamada, T. Kitagawa, J. Matsuo and A. Kirkpatrick,
Mass and charge transport in inorganic materials:
fundamentals to devices, part B (Advances in science
and technology 29), (2000) pp. 957,
[3] J. Matsuo, H. Katsumata, E. Minami and I. Yamada,
Nucl. Instr. and Meth., B 161-163 (2000) 952.
SUMMARY
[4] T. Aoki, J. Matsuo and G. Takaoka, Nucl. Instr. and
Meth., accepted.
Cluster size effect on damage formation was
studied by both simulation and experimental method.
Molecular dynamics simulations of Ar cluster impact
on Si substrate leaded the model function to describe
the number of displacements depending on cluster size
and incident energy. The model function revealed that
when total incident energy is constant, the number of
displacements increases with increasing cluster size,
but there is specific number (Nm) to cause maximum
number of displacements. If the cluster size is larger
than Nm, the damage is reduced as the cluster size
[5] T. Seki, J. Matsuo, G. H. Takaoka and I. Yamada, Proc.
of 16th international conference on the application of
accelerators in research and industry, (AIP Conference
Proceedings Vol. 576, 2001) 1003.
[6] T. Seki, in this issue.
[7] N. Toyoda, M. Saito, N. Hagiwara, J. Matsuo and I.
Yamada, Proc. of 12th Ion Implantation Technology,
(1998) 1234.
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