Manipulation and Joule heat welding of Ag
nanowires prepared by atomic migration
Hironori Tohmyoh* and Satoru Fukui
Department of Nanomechanics, Tohoku University, Aoba 6-6-01, Aramaki, Aobaku, Sendai 980-8579, Japan
*Corresponding author, e-mail: tohmyoh@ism.mech.tohoku.ac.jp
A: Fabrication of Ag nanowires
The driving force for atomic diffusion in stress-induced migration is the gradient of the
hydrostatic stress, . The atomic flux due to the stress-induced migration can be described by
(Herring 1950; Korhonen et al. 1993),

JS 
 Q  
CD0
exp 
kBT
kBT


  ,

(A1)
where C is the atomic concentration,  is the atomic volume, kB is Boltzmann's constant, T is the
absolute temperature, D0 is the self-diffusion coefficient and Q is the activation energy. According
to Eq. (A1), the atoms move from positions with high compressive stress toward ones with lower
compressive stress. Moreover at higher temperatures, the mobility of the atoms is enhanced.
In the present SiO2/Ag/Ti/SiO2/Si system, uniform hydrostatic stress is generated in the layers
on a macroscopic level due to the thermal expansion mismatch between each layer, provided that
the multi-layered sample is heated. However, uniform hydrostatic stress never brings about stressinduced migration. Stress-induced migration in the Ag film in the present system arose due to the
anisotropy of the polycrystalline Ag grains. When a polycrystalline metallic film with anisotropic
grains is subjected to a uniform compressive stress, a microscopic stress field appears due to the
stress concentration at the grain boundaries brought about by the material and geometrical
singularities. The microscopic stress field induces a stress migration field.
In the present Ag samples, the Ag atoms diffuse via the interface between the Ag and the SiO 2
due to stress-induced migration, and the diffused atoms accumulate at interfacial sites. Due to the
lack of atoms around the SiO2/Ag interface, a perpendicular stress gradient appears in the Ag film
and this contributes to further atomic diffusion towards the SiO2/Ag interface.
Here the SiO2 layer plays an important role in the formation of the Ag NWs. It has been found
that Ag NWs are formed provided that there is a suitable balance between the interfacial pressure
at the SiO2/Ag interface and the resistance of the SiO2 layer to atoms being discharged via the
weak spot (Tohmyoh et al. 2010). Because the number of atoms accumulated at the interface is
governed by the temperature and it is closely related with the interfacial pressure, there is an
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optimum temperature at which a significant amount of Ag NWs are formed. In the present
samples, the optimum temperature was 300oC in the examined temperature range of 200 to 350oC,
see also the reference (Tohmyoh et al. 2010).
B: Derivation of U
We consider the electro-thermal problem (Tohmyoh 2009), where the current I flows through
a thin wire of length l and cross sectional area A (Figure A1). As an ideal case, we consider that no
heat transfer from the surface of the wire to the ambient occurs and the temperature at both ends of
the wire is constant at T0. In this case, the temperature takes its maximum value at the middle of
the wire and the value in the steady state is given by
2
T1 
1  l 
 I   T0 ,
8 K  A 
(A2)
where K is the heat conductivity, and  the electrical conductivity. In a realistic situation, the
thermal boundary conditions, and consequently the heat transfer properties of the wire system, are
different to the ideal case. To calibrate the difference in thermal boundary conditions between the
actual and ideal conditions, the function f is introduced, and the parameter U, given by Eq. (1), is
defined as the product of f and the term I (l / A) [= u0] which appears in Eq. (A2) (Tohmyoh 2009).
The parameter U has been verified as being effective in describing the conditions for the
successful welding of ultrathin Pt wires in air (Tohmyoh 2009; Fukui and Tohmyoh 2011) and in
vacuum (Tohmyoh and Fukui 2009). Here u0 /  corresponds to the voltage between the ends of
the wire system. Moreover, the temperature at the middle of an actual wire system can be
described in terms of U as
T
Fig. A1
1
U 2  T0 .
8K
(A3)
Electro-thermal problem (a) in the ideal case and (b) in a realistic case. In the ideal case,
no heat transfer from the wire surface to the ambient occurs and the temperature at both ends of
the wire is constant at room temperature. On the other hand, in a realistic case, the temperature at
both ends of the wire becomes greater than room temperature under a current supply.
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References
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Phys 50:057201
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Korhonen MA, Borgesen P, Tu KN, Li C-Y (1993) Stress evolution due to electromigration in
confined metal lines. J Appl Phys 73:3790-3799
Tohmyoh H (2009) A governing parameter for the melting phenomenon at nanocontacts by Joule
heating and its application to joining together two thin metallic wires. J Appl Phys 105:014907
Tohmyoh H, Fukui S (2009) Self-completed Joule heat welding of ultrathin Pt wires. Phys Rev B
80:155403
Tohmyoh H, Yasuda M, Saka M (2010) Controlling Ag whisker growth using very thin metallic
films. Scr Mater 63:289-292
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