FABRICATION OF CU NANOWIRE AT THE INTENDED POSITION
BY UTILIZING STRESS MIGRATION
F. Yamaya, N. Settsu and M. Saka
Department of Nanomechanics, Graduate School of Engineering, Tohoku University
Aoba 6-6-01, Aramaki, Aoba-ku, Sendai 980-8579, Japan
[email protected] (M.Saka)
ABSTRACT
Stress migration (SM) is a phenomenon that the atoms diffuse from the region of lower stress towards the region of higher
stress. In the present research, fabrication of Cu nanowire at the intended position by controlling the direction of atomic flux
caused by SM is studied. First, the position whereat the Cu atoms are accumulated is found in the hydrostatic stress
distribution by finite element analysis. Then the Cu atoms are experimentally accumulated at the intended position on the basis
of the present analysis, and the Cu nanowire is fabricated there.
Introduction
In recent years, it has become important to develop the processes for production of nanomaterials, which have the potential of
being utilized in many fields. The top-down approach is well-known as a technique of producing the fine materials. However, it
becomes more difficult to fabricate the nanomaterials by the top-down approach, such as the conventional deposition,
photolithography and etching, because of the limitations of the exposure wavelength and precision of etching. On the other
hand, the bottom-up technologies are the methods for constructing nanomaterials from individual atoms and molecules [1, 2].
Although the bottom-up technologies allow us to fabricate the nanomaterials, they still have a problem of their inefficiency.
Therefore, current researchers have paid attention to produce the nanomaterials efficiently with the bottom-up technology.
As the bottom-up technology, a technique based on a phenomenon caused by electromigration (EM) has been proposed to
fabricate metallic nanowires. EM is a phenomenon of atomic diffusion due to current density as the driving force. On the other
hand, a foundation of fabricating metallic nanowires by utilizing effective collection of the atoms caused by SM, which is a
phenomenon of atomic diffusion due to the gradient of hydrostatic stress as the driving force, has been proposed. Fabrication
of the Al nanowire has been achieved by controlling the accumulation of atoms diffused by EM [3, 4]. Moreover, the Cu
nanowire, which has superior electrical characteristic than Al, has been fabricated by utilizing SM [5]. Although the Al nanowire
was successfully formed at, intended, anode end of Al line by utilizing EM [4], it has not been achieved to fabricate the metallic
nanowire at an intended position by utilizing SM. It is expected that the metallic nanowires will be effectively used as excellent
new materials, and controlling the sites whereat such nanowires form will give us the potential of using the nanowires in many
fields.
In the present paper, the technique of fabricating the Cu nanowire at the intended position by utilizing SM is studied. For
establishing this technique, it is required to control the direction of atomic diffusion and the accumulation of the diffused Cu
atoms. The hydrostatic stress distribution is induced in the sample of Cu thin film covered with a Ta film as a passivation layer
by heating. First, the stress distribution in the sample is analyzed by finite element method (FEM) and the position whereat the
diffused Cu atoms accumulate is determined. Then the Cu nanowire is practically fabricated at the intended position, based on
the result of FE analysis.
Theoretical background
The atomic flux caused by stress migration Js can be described as the following equation [6, 7]:
Js =
 Q − Ωσ
CΩ
D 0 exp  −
k BT
k BT


∇σ

(1)
where
C = atomic concentration
Ω = atomic volume
kB = Boltzmann’s constant
T = absolute temperature
D0 = self diffusion coefficient
Q = activation energy
σ = hydrostatic stress
Let σx, σy and σz be the normal components of stress in orthogonal Cartesian coordinates system (x, y, z). The driving force for
atomic diffusion is given by ∇σ, where σ = (σx + σy + σz) / 3. If we consider a material part with a distribution of compressive
stress as shown in Figure 1, then atoms diffuse from the position A with more-negative stress (higher compressive stress) σA
towards the position B with less-negative stress (lower compressive stress) σB. Therefore, the hillocks are formed at the
position B due to the local accumulation of diffused atoms [8]. In the present research, Cu thin films were subjected to thermal
stress when the sample was heated due to the mismatch of the thermal expansion coefficients of each component of the
sample. According to this thermal stress, the hydrostatic stress distributions as shown in Figure 1 were generated in the Cu
thin films.
Hydrostatic stress σ
Tensile
0
A
B
σB
Position
r
Direction of the atomic diffusion
σA
Compressive
Figure 1. Phenomenon of stress migration
Conditions for numerical analysis
MSC.Marc was used to perform the numerical simulation by FEM. The physical model of the analysis was developed as
follows. The Cu thin film of 10 µm in width, 100 µm in length and 85 nm in thickness was joined onto the 60 nm of Ta layer.
Then the 125 nm Ta film was joined onto this structure as a passivation layer. The Si plate covered with 300 nm of SiO2 was
100µ
µm
10µ
µm
10µ
µm
Table 1. Material properties
10µ
µm
10µ
µm
Cu
10µ
µm
Ta
125nm
85nm
60nm
300nm
10µ
µm
Ta
Cu
Ta
SiO2
Si
Figure 2. The schematic illustration of the
physical model
Material
Young's
Poisson's
modulus
ratio
(GPa)
Thermal
expansion
coefficient
-6
-1
×10 (K )
Cu
110
0.34
16.2
Ta
186
0.34
6.6
SiO22
180
0.28
4.15
Si
163
0.28
4.15
used as a substrate. The schematic illustration of the physical model is shown in Figure 2, and the mechanical properties of
each material are shown in Table 1. A three-dimensional quarter model was created as shown in Figure 3(a) because of the
symmetry of the physical model and the manner of heating. The macrograph of the end of the Cu thin film and the top surface
of the Cu thin film of the physical model are shown in Figures 3(b) and (c), respectively. The boundaries between the Cu thin
film and Ta film are modeled with fine meshes because the hydrostatic stress concentrates in those sites. The initial
temperature of the physical model was set to be 293 K. As a thermal boundary condition, the temperature at the bottom
surface of the Si substrate was raised to 613 K. The temperature in the model was uniform because the thickness was
extremely thin. Therefore, the other surfaces were assumed to be thermally insulated. For the planes of symmetry, the normal
displacement for each of the planes was restrained. The analysis for obtaining steady-state thermal stress was carried out
under these conditions.
y
z
Cu
Ta
(a) Quarter model
y
x
SiO2
50µ
µm
Si
5µ
µm
x
(b) Local view
(c) The top surface of the Cu thin film
Figure 3. Model for numerical analysis
Results of numerical analysis and discussions
The hydrostatic stress distribution in the Cu thin film was evaluated. Here, it is well-known that the Cu atoms can easily diffuse
on the surface than via the grain boundaries [9]. Therefore, the atomic diffusion on the surfaces, especially the top surface, of
y
50µ
µm
5µ
µm
x
(a) Overall view
(MPa)
-376.1
-411.4
-382.0
-417.3
-387.9
-423.2
-393.8
-429.1
-399.7
-435.0
-405.6
-927.7
(b) The range of the hydrostatic stress
1µ
µm
(c) The end of the Cu thin film
Figure 4. The hydrostatic stress distribution at the top surface of the Cu film by analysis
the Cu thin film may be dominant to the accumulation of Cu atoms. The hydrostatic stress distribution generated on the top
surface of the Cu thin film and the range of the hydrostatic stress are shown in Figures 4(a) and (b), respectively. From the
result of the analysis, lower compressive stress distribution along the line at a distance of approximately 0.5 µm from the
boundary between the Cu thin film and Ta film was confirmed. Moreover, the hydrostatic stress distribution at the end of the
Cu thin film is shown in Figure 4(c). The lowest compressive stress was generated at the neighborhood of the corner.
Therefore, it can easily be predicted that the Cu atoms mainly diffuse towards the neighborhood of the corner and accumulate
there.
Sample preparation
The sample having the same structure as shown in Figure 2 was used in the present experiment. The sample was developed
as follows. A SiO2 layer of 300 nm in thickness was deposited on a Si [100] substrate (thickness: 0.28 mm, diameter: 50.8 mm).
A Ta layer of 60 nm in thickness, which works as a barrier layer to prevent the diffusion of Cu atoms into the SiO2 layer and as
an adhesion layer for the Cu film, was deposited on the SiO2 layer by sputtering. Cu film of 85 nm in thickness was then
–3
deposited on the Ta layer by an electron beam evaporation technique under a vacuum of 1.1 × 10 Pa. The Cu film was
formed into the thin films of 10 µm in width and 100 µm in length, through the lift-off process by photolithography. Finally, a Ta
film of 125 nm in thickness which works as a passivation layer was deposited on those structures by sputtering. Figure 5
shows the micrographs of the sample, obtained by a field emission scanning electron microscope (FE-SEM).
Cu thin film covered with the Ta layer
5µ
µm
30µ
µm
(a) Top view
(b) The end of the Cu thin film
Figure 5. The micrographs of the sample
Experiment
The experimental apparatus is shown in Figure 6. The temperature of the samples was raised to 613 K by the ceramic heater
positioned beneath the samples. The temperature of the sample was monitored by a thermocouple, and was kept at a
constant value by a controller. The experiment was conducted under the atmospheric condition for up to 10 h after starting the
heating. After this heating process, the sample was observed by using FE-SEM.
Optical
microscope
Ceramic
heater
Sample
Figure 6. Experimental apparatus
Experimental results and discussions
As a result of the heating, some hillocks were confirmed by FE-SEM observation at the corner of the Cu thin film as shown in
Figure 7(a). The formation of the hillocks was never observed in places other than the corner. Therefore, a large amount of Cu
atom was collected at the intended position on the basis of the result of the present analysis. Moreover, the Cu nanowire of 20
nm in diameter and 3 µm in length was successfully fabricated from the surface of hillock at the intended position as shown in
Figure 7(b).
1µ
µm
5µ
µm
(a) Hillocks at the corner (intended position)
(b) Cu nanowire generated from the hillock
Figure 7. FE-SEM observation of hillocks and nanowire
Considering the generating manner of the hillocks on the top surface of the Ta layer, the Cu atoms diffused by the stress
migration may pass through the Ta layer around the corner of the Cu thin film. By comparing the diameter of the Cu atom and
the interatomic distance of Ta, the former is smaller than the latter. This difference in each size supports the assumption
mentioned above. Moreover, it is well-known that thin wirelike crystals called whiskers are generated spontaneously as a result
of a compressive stress release phenomenon in the case of Sn [10], in addition, such stress release may occur at the weak
spots in the oxide layer [11]. In this study, according to Ellingham straight-line plots [12], it is clear that the surface oxide layer
presents on the Cu hillocks. If the compressive stress inside the hillocks attains a critical value, then accumulated atoms start
to be discharged towards the outside. Thus, the Cu nanowire was formed on the surface of the hillock.
Conclusions
A technique of fabricating Cu nanowire at the intended position by utilizing stress migration was reported. The hydrostatic
stress distribution at the top surface of the Cu thin film was obtained by FE analysis. Thus, the position whereat the diffused
Cu atoms were accumulated by stress migration was determined. On the basis of the result of the present analysis, the Cu
atoms diffused by stress migration were practically accumulated at the intended position and hillocks were formed due to the
local accumulation of Cu atoms there. Then, the Cu nanowire of 20 nm in diameter and 3 µm in length was successfully
fabricated on the surface of hillock.
Acknowledgments
This work was supported by Grant-in-Aid for Scientific Research (S) 18106003. A part of this work was performed at the
Micro/Nano-Machining Research and Education Center of Tohoku University.
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