Brief Report
Molecular Dynamics Simulation Study on the Melting of Ultra-thin
Copper Nanowires
Jeong Won Kang* and Ho Jung Hwang
Semiconductor Process and Device Laboratory, Department of Electronic Engineering,
Chung-Ang University, 221 HukSuk-Dong, DongJak-Ku, Seoul 156-756, Korea
ABSTRACT
We have investigated the melting behavior of ultra-thin copper nanowires using classical
molecular dynamics simulations. The caloric curves of cylindrical multi-shell copper nanowires
showed an insight into the specific phase transition. The melting temperature of copper nanowires
is linearly proportional with the number of atoms per layer. When nanowires have almost the same
number of atoms per layer regardless of the initial structures, the melting temperatures of
nanowires are much the same.
PACS Numbers: 61.46.+w, 61.82.Rx, 62.25.+g
*E-mail: [email protected]
Tel: 82-2-820-5296
Fax: 82-2-825-1584
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In studies of nanoelectronic-device fabrications, metallic nanowires (NWs) have been
extensively investigated over the past decade [1-25]. The structure of ultra-thin metallic NWs has
been investigated using molecular dynamics (MD) simulations [2-15,20-25]. Previous works have
shown that ultra-thin Cu NWs obtained from atomistic simulations under various conditions can
have several structures such as face-centred-cubic (fcc) structure [24], pentagonal multi-shell
(PMS)-type [24,25], and cylindrical multi-shell (CMS)-type [22-25], etc.
Melting behavior of NWs have been investigated using the MD simulations for NWs of Au
[9] and Pb [15]. All nanowires have molten below the bulk melting temperature [9,15]. Copper is
an important engineering material, so in this investigation we present a specific phase transition
and the melting behavior of ultra-thin Cu NWs using MD simulations.
We have performed several MD runs at different temperatures and for different radii and
structures of wires. We used twelve NWs with fcc, PMS-type, and CMS-type, as shown in Table 1.
This MD simulation used the same MD methods as our previous works [20-25,27-32] with time
step of 10-15 s.
The periodic boundary condition (pbc) was applied along the axes of NWs. The
lengths of supercells for Cu NWs with {100}, {110}, and {111} are 36.150, 61.343, and 41.738 Å,
respectively. The lengths of supercells of Cu NWs with PMS-type and CMS-type structures are
2
63.284 and 66.512 Å, respectively. The initial structures were first relaxed by the MD steps of 200
000 at 300 K using NWs with the ideal atomic positions. Each system was then heated by the MD
runs of 10 000 time steps (10 ps) with a temperature step of 1 K from 300 K.
We monitored the
internal energy as a function of temperature. Interaction between Cu atoms was described by a
well-fitted potential function of the second moment approximation of the tight-binding (SMA-TB)
scheme [26], which has been used in our previous works [20-25, 27-32].
Figure 1 shows the caloric curves for some of ultra-thin Cu NWs in Table 1. In the caloric
curves, we can identify four regions, labeled as A, B, C, and D in Fig. 1. In region A, the ultra-thin
nanowire is solid, and the slope corresponds to the Gulong-Petit specific heat. In the region B, the
caloric curve exhibits an upward curvature where the specific heat pronouncedly increases by the
beginning of melting. In the region C, the ultra-thin nanowire is melting state, and the slope is the
same with that in the region A.
In the region D, the ultra-thin nanowire is broken and then a
spherical cluster is formed. Since the pbc were applied to the supercells for the MD simulations, a
spherical cluster in the region D is shown. The slope in the region D is the same with that in the
region A and C. When the number of atoms per layer (N) for NWs is below 16, regions B and C are
not shown. Since N of NW is very small, as soon as temperature reaches the melting point of NW,
NW is broken and then spherical cluster is formed. In NWs with N above 18, all specific regions,
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such as A, B, C, and D regions, appear. However, in the cases including some structural
transformations, such as fcc to CMS-type and PMS-type to CMS-type, the slope of caloric curve is
slightly greater than the normal slope before the region B. These phenomena are shown in ultrathin Cu NWs with initially FCC and PMS-type structures. All transformed NWs don’t have CMStype structure. However, most of them have the structures mixed by fcc or CMS-type. Cu NWs
with the mixed-structures were shown in previous work [24].
Figure 2 shows the snapshots of C34 NW for temperatures and would be mish helpful to
understand the melting behavior of NWs. Figure 2(a) shows that the structure of the solid region, A,
at 450 K maintains the initial structure. However, at 580 K, the melting temperature of C34 NW, the
structure is deformed as shown in Fig. 2(b). At 700 K, C34 NW is in the melting state, the structure
is similar to an amorphous state as shown in Fig. 2(c). Figure 2(d) shows the structure just before
the breaking of NW at 800 K. As the temperature reaches near the breaking point of NW, the neck
of NW becomes more and more narrow and finally is broken as the fuse by the heat burns out. As
mentioned above, Fig. 2(e) shows a spherical cluster formed after the breaking of NW. The
spherical cluster is induced by the pbc applied to the supercell.
Figure 2 shows the melting temperature (TMnw) of NWs as a function of the number of atoms
4
per layer (N).
In Fig. 2, TMnw is linearly proportional with N, TMnw= 4.5 N + 420. When NWs have
almost the same N regardless of the initial structure, the melting temperatures of NWs are much
the same in height. This implies that TMnw is related to more the initial diameter than the initial
structure.
This brief report showed the specific states achieved by the temperature elevation from the
caloric curves. The melting temperatures of ultra-thin Cu nanowires are much lower than the bulk
melting temperature, and are linearly proportional with the number of atoms per layer. When the
number of atoms per layer of nanowires is below 16, a nanowire is broken as soon as the
temperature reaches the melting point of the nanowire. In cases including the structural
transformations of nanowires, the slope of caloric curves of the nanowire is slightly greater than
normal slope. The caloric curves of cylindrical multi-shell Cu nanowires with above four shells
give an insight into a specific phase transition, solid to melting. From the result that cylindrical
multi-shell Cu nanowires maintain their structures at below the melting temperature, we can expect
to apply to Cu nanowires to nanoelectronic devices.
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[20] J. W. Kang and H. J. Hwang, J. Korean Phys. Soc. 38 695 (2001).
[21] J. W. Kang and H. J. Hwang, Nanotechnology 12, 295 (2001).
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[24] H. J. Hwang and J. W. Kang, unpublished (Preprint: cond-mat/0202032),
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7
Table
Table I. Several ultra-thin Cu nanowires simulated in the work.
Structure
Atoms/layer
Cross-section shape
N18{100}
{100}
18
Octagon
N50{100}
{100}
50
Octagon
N18{110}
{110}
18
Hexagon
N54{110}
{110}
54
Hexagon
N13{111}
{111}
13
Hexagon
N49{111}
{111}
49
Hexagon
P6
PMS-type 5-1
6
Pentagon
P16
PMS-type 10-5-1
16
Pentagon
P51
PMS-type 20-15-10-5-1
51
Pentagon
C7
CMS-type 6-1
C18
C34
7
Circle
CMS-type 11-6-1
18
Circle
CMS-type 16-11-6-1
34
Circle
8
Figure Captions
Figure 1. The caloic curves, i. e. energy per atom as a function of temperature for some nanowires
in Table. I
Figure 2. Snapshots of C34 nanowire for the temperature. (a) 450 K. (b) 580 K. (c) 700 K. (d) 800
K. (e) 850 K.
Figure 3. The melting temperature of naowires (TMnw) in Table. I as a function of the number of
atom per layer (N).
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FIGURES
-2.7
-2.8
P6
Energy (eV/atom)
C7
-2.9
N13{111}
D
-3.0
C
P16
-3.1
-3.2
-3.3
B
C18
N18{100}
A
C34
N50{100}
N49{111}
N54{110}
300
400
500
600
700
Temperature (K)
Figure 1. (color)
10
800
900
1000
(a)
(b)
(c)
Figure 2.
11
(d)
(e)
Melting temperature of Cu nanowire (TMnw , K)
700
PMS-type
CMS-type
{100}
{110}
{111}
600
500
400
TMnw = 4.5ٛN + 420
300
0
10
20
30
40
Number of atom per layer (N)
Figure 3.
12
50