Stress Effect on the Reaction Kinetics of Metal/Silicon
systems
計畫編號：甲-91-E-FA04-1-4
執行期限：94 年 4 月 1 日至 95 年 3 月 31 日
主持人：C.J. Tsai
計畫參與人員：Y.C. Chu, and L.H. Wu
Department of Materials Science and Engineering, National Tsing Hua University,
Hsinchu, Taiwan, ROC
Ⅰ. Abstract
stability of phase3,4, the nucleation site of
epitaxial growth5,6, and even the property of
The stress-field distribution of the
periodic nano-scale-pattern NiSi2 templates,
fabricated using polystyrene nanosphere
lithography, has been simulated using finite
element method in our previous experiments.
From the results of simulation, controllable
nano-scale stress field is formed clearly on
the surface of Si substrate. In this experiment,
we show that this stress which induced by the
lattice mismatch between NiSi2 and Si
device7. In our previous experiments, we
have observed that a tensile stress obviously
enhances the mobility of Si during the
annealing process in the TiN/Ti/Si system.
Here, another effect of stress: stress-induced
shape transition of epitaxial NiSi2 clusters on
Si substrate, is shown and explained by the
results of strain energy simulated by finite
element method.
NiSi2 is easy to form epitaxial structures
substrate will influence the shape of NiSi2
clusters as the clusters grow. By calculating
the total strain energy of different aspect ratio
of NiSi2 clusters, long thin structure is found
to allow better stress relaxation but has larger
NiSi2 surface and NiSi2/Si interface. Because
the volume-to-area ratio increase as the
volume of NiSi2 clusters increase, NiSi2
clusters form a special stable shape on the
balance between strain energy and interface
with Si because the lattice mismatch between
one another is only 0.46 ％ (at room
energy for different volume. For this reason,
NiSi2 cluster will grow in a square shape at
first and transform to a shape with high
aspect ratios at larger sizes.
polystyrene nanosphere lithography in our
pervious experiments. The stress field of
these structures has also been simulated using
finite element method. From the results of
simulation, the NiSi2 can induce a stress
distribution in the Si substrate due to the
lattice mismatch between the NiSi2 and Si
substrate. These structures with periodic
stress distribution on substrate surface are
temperature). The normal shapes of NiSi2
epitaxial cluster are facet bar structures with
{111}-oriented interfaces with Si and
<110>-oriented edges on the surface of Si
substrate. Large-area periodic nano–scale
-pattern NiSi2 templates have been
successfully fabricated using a convenient
and simple nano-lithography method:
Ⅱ. Introduction
Stress is found to influence the rate of
chemical reaction1,2, the formation and
1
useful for experiment studies or device
on Si substrate. During the simulation
applications.
Tersoff and Tromp have use a simple
geometry to derive an approximation for the
strain energy of a dislocation-free islands and
proposed that a strain-induce shape transition
may occur from square to rectangular as the
islands grow8. Brongersma etc. have also
seen this phenomenon in the growth of CoSi2
clusters on Si substrate9. In opposition to the
approximation calculation Tersoff and
Fig. 1. The 3-D structures used to simulate the strain
energy of the NiSi2 cluster.
Tromp use, more accurate solutions to the
strain energy in the epitaxial structures are
simulated using finite element method with a
3-D structure. The more exactly relation
process, the cubic symmetry of mechanical
property for Si substrate and NiSi2 are taken
into account. The volumes of the Si
substrates in all cases are fixed and large
enough to stabilize the solutions of
simulation.
In order to fix the volume of NiSi2
clusters, a cluster with unit length in all (110)
edges is selected as the reference structure.
between stable shape, strain energy, surface
energy, and interface energy of the epitaxial
structures is obtain in this experiment.
There are two parts in the analysis of the
relation between strain energy and aspect
ratios of NiSi2 clusters. First, we fix the
volume and simulate the strain energy of
different aspect ratios NiSi2 clusters. The
surface and interface areas of different aspect
ratios NiSi2 clusters are calculated to
compare with the strain energy. A most
stable shape will be obtained if the surface
and interface energy of the NiSi2 are known
in this volume. Second, we calculate the
evolution of total energy change for different
aspect ratios of NiSi2 clusters as the volume
We change the length of short edges in Fig. 1
from nine-tenth to two-tenth of the unit
length and use the volume of reference
structure to calculate the lengths the long
edges need to have. NiSi2 clusters with nine
different aspect ratios range from 1 for the
reference structure to about 84 for the
structure with two-tenth short edge length are
obtained.
Fig. 2 (a) shows the relation between the
of the clusters grow. A shape transition can
be observed clearly in this process.
strain energy and the aspect ratios of the
NiSi2 clusters. It can see clearly that the
relaxation of the lattice-mismatch-induce
stress is strongly dependent on the geometry
of the NiSi2. As the aspect ratio of NiSi2
cluster increase form 1 to about 10, the strain
energy decrease rapidly. As the aspect rations
increase more, the strain energy decrease
Ⅲ. Results and Discussion
An example of the 3-D structures we
used to simulate the strain energy in this
experiment is shown in Fig. 1. These
structures mimic the real NiSi2 clusters grow
more slowly. Fig 2 (b) is the evolution of the
2
and interface energy as the aspect ratios of
NiSi2/Si Interface Area / Volume of NiSi 2
NiSi2 surface and the NiSi2/Si interface areas
Strain Energy
1.0
0.9
0.8
0.7
0.6
0
(a)
20
40
60
Aspect Ratio
80
100
10
structure with 3/10 short edge length
structure with 5/10 short edge length
structure with 7/10 short edge length
structure with 9/10 short edge length
9
8
7
6
5
4
3
2
1
0
20
40
(a)
60
80
100
Volume of NiSi2
120
140
7
6
NiSi2/Si interface
NiSi2 surface
6
5
2.4
4
3
2
2.2
2.0
3
2
1.8
1.6
1.4
1.2
1
1
(b)
4
Aspect Ratio
Aspect Ratio
Area
5
1.0
0.8
0
20
40
60
Aspect Ratio
80
100
0
(b)
Fig. 2 (a) The relation between the strain energy and
0
100
0
200
2
4
300
Volume
6
8
10
Volume
400
12
500
14
600
Fig. 3 (a) The evolution of volume-to–area ratios as
the aspect ratios of the NiSi2 clusters. All of the strain
the volume of NiSi2 growth for different aspect ratios
energy are normalized to the strain energy of reference
structures. (b) The stable shapes for different volume
structure. (b) The relation between the area of NiSi2/Si
of epitaxial structure. The inset shows the evolution of
interface, NiSi2 surface, and the aspect ratios of the
shape when the volume of cluster is small.
NiSi2 clusters. All of these areas are normalized to the
NiSi2 surface area of the reference structure.
structures change, we can speculate that
when an epitaxial system with small strain
energy or larger interfacial energy, it will
tend to form lower aspect ratios structures to
reduce the total energy. Oppositely, a higher
as the aspect ratios of NiSi2 clusters increase.
A continuously increase of the NiSi2 surface
and the NiSi2/Si interface areas is shown
even the aspect ratios of NiSi2 clusters are
large than 80. The stable shape of NiSi2
cluster at this volume is the structure with the
lowest total energy: strain energy adds the
surface and interface energy. If the surface
and interface energy of NiSi2 are known and
take into account, the stable shape will be
obtained.
According to evolution of strain, surface,
aspect ratio structure will form in an epitaxial
system with larger strain energy or lower
interfacial energy. Besides, epitaxial clusters
with aspect ration lager than 100 are difficult
to obtain because the strain energy decrease
little but the surface and interface areas still
increase when the aspect ratios of structures
are large.
During the growth of NiSi2 clusters, the
3
volume and area of them will growth with
different rates. Fig. 3 (a) is the evolution of
volume-to–area ratios as the volume of NiSi2
growth for different aspect ratios NiSi2
clusters (surface areas have the same
tendency as interface area and are not shown
in the figure). The higher aspect ratios
structures have larger areas at the same
volume, but no matter what structures the
NiSi2 clusters are, the volume-to-area ratios
are lower when the sizes of clusters are
Fig. 4 The SEM image of the NiSi2 clusters growth on
Si (001) substrate.
smaller and increase as the clusters growth. It
implies that the stable structures of epitaxial
clusters will change during the growth
process. Here we arbitrarily give a value to
volume of NiSi2 clusters have been seen in
experiments and are shown in Fig. 4. Squarer
shapes for smaller NiSi2 clusters and long
thin structures for larger clusters are shown
in the SEM image and this result is in
coincidence with our speculation.
the interface and surface energy of NiSi2
clusters and investigate the evolution of
shape transition of NiSi2. The results are
shown in Fig. 3 (b). We can see clearly that
the stable shapes of epitaxial structures are
squarer in the beginning and then elongate as
Ⅳ. Conclusions
the clusters grow. The reason for the shape
transition is because a squarer shape will
reduce the interface energy more than the
increase of strain energy increase as the
volume-to-area ratio is small at the beginning.
After the clusters become larger, high aspect
ratios structures can relax more strain energy
expense a lesser increase in the surface and
interface energy due to the larger
volume-to-area ratios. The aspect rations of
We calculate the strain energy for
different aspect ratios NiSi2 epitaxial
structures using finite element method with a
3-D structure in this experiment. A
stress-induced shape transition in the growth
of NiSi2 clusters is anticipated and evidenced.
The understanding of the factors which
influence the stable shapes of epitaxial
clusters is useful to control the geometries of
nano-structures.
structures do not increase without limit as
show in Fig. 3. As the volume of the NiSi2
clusters increase to a critic size, the aspect
rations of structure are difficult to increase
more. It is because the further elongation of
shape does not efficiently relax the strain
energy but raises the surface and interface
energy as shown in Fig. 2.
The different aspect ratios for different
Ⅴ. Reference
[1] J. Tersoff, Yuhai Tu, and G. Grinstein,
Appl. Phys. Lett, 73, 2328 (1998).
[2] K. S. Kim, J. A. Hurtado, and H. Tan,
Phys. Rev. Lett, 83, 3872 (1999).
[3] E. M. Schaller, B. I. Boyanov, S. English,
and R. J. Nemanich, J. Appl. Phys. 85,
3614 (1999).
4
[4] S. L. Cheng, H. M. Lo, L. W. Cheng, and
L.J. Chen, Thin Solid Films, 424, 33
(2003).
[5] S. Y. Shiryaev, F. Jensen, J. L. Hansen,1
J. W. Petersen, and A. N. Larsen, Phys.
Rev. Lett, 78, 503 (1997).
[6] G. Jin, J. L. Liu, S. G. Thomas, Y. H. Luo,
and K. L. Wang. Appl. Phys. Lett. 75,
2752 (1999).
[7] A. K. Fung, L. Cong, J. D. Albrecht, M. I.
Nathan, P. P. Ruden, and H. Shtrikman, J.
Appl. Phys. 81, 502 (1997).
[8] J. Tersoff and R. M. Tromp, Phys. Rev.
Lett, 70, 2782 (1993).
[9] S. H. Brongersma, M. R. Castell, D. D.
Perovic, and M. Zinke-Allmang, Phys.
Rev. Lett, 80, 3795 (1998).
5