053106-3
Görlich, Schmitz, and Tu
Appl. Phys. Lett. 86, 053106 ͑2005͒
the grain boundary and the solid/liquid interfaces ͑see Fig. 5͒
according to
GB
cos
=
,
͑1͒
2
2 ·LS
where ⌽ is the wetting angle, GB the grain boundary energy,
and LS the interface energy between scallop and melt. Ob-
viously LS for Sn is higher than LS for SnPb, since ⌽ is
significantly larger for the binary reaction. Indeed the higher
interface energy for the binary system has to be expected
because of the higher melting point of pure Sn in comparison
to the eutectic SnPb alloy. ͑ii͒ GB transport of Cu must be
taken into account when the kinetics is discussed quantita-
FIG. 5. Schematic of the solid/liquid interreaction zone.
scallop size, it is suggested that the observed wetting angle is
an equilibrium feature at the reaction temperature instead of
being formed at quenching. In consequence, those channels
must be interpreted as ordinary grain boundaries separating
two grains of Cu Sn . Potentially, the much thicker molten
tively. Probably, this is the rate controlling step. The use of
8
6
5
the triple product D=s␦D does not change the principle
GB
channels postulated in previous work are an artifact of the
etching needed to obtain sufficient contrast for SEM.
Between the scallops and the Cu substrate a polycrystal-
of Gusak’s model. Regarding the conservation of mass, we
find again a cube root kinetics
line Cu Sn layer has formed, 300 nm in thickness ͓Fig. 4͑c͔͒.
2
2D⌬c
R2
3
cidV = c dR = Jdt =
dt,
͑2͒
͑3͒
In contrast to previous SEM work and its interpretation by
Gusak’s model, this layer seems to form just at the beginning
of the reaction, as we can detect it in TEM micrographs after
only 10 s annealing with a thickness of already 115 nm. The
i
3
⌬
c 2
c 1
3
⇒
R = kt with kª9D
,
dense Cu Sn layer consists of a row of columnar grown
i
3
grains. However, with its high density of grain boundaries it
is probably not the rate limiting factor for the Cu supply to
the reactive solid/liquid interface.
where c , V, J, and ⌬cϷ0.01 are the mole fraction of Cu in
i
Cu Sn , the scallop volume per unit area, the total Cu cur-
6
5
rent, and the concentration variation across the Cu Sn layer,
6
5
We cannot observe any correlation between the scallop
structure and the grain boundary structure of the underlying
Cu substrate. Thus, grain boundaries of Cu can be excluded
as preferential nucleation sites. During the reaction, the sub-
strate develops a certain waviness in correspondence to the
scallop structure. The onset of this process is already noticed
in the presented pictures ͓Fig. 4͑d͔͒. This confirms that Cu is
predominantly transported along the Cu Sn grain bound-
−19
3
respectively. From Fig. 2 we find k=1.5ϫ10 m /s, which
requires a grain boundary diffusion of DGB=5ϫ10 m /s,
−10
2
close to values for bulk melts. However, considering that the
9
−13
2
bulk diffusion of Cu Sn amounts already to 10 m /s at
6
5
5
13 K , such a value of grain boundary diffusion seems to be
in the possible range. This all the more as recent diffusion
10
studies by Herth et al. have demonstrated that wetted grain
6
5
boundaries, although structurally different from liquid chan-
nels, may have a diffusivity near to that of the bulk melt.
The insight by TEM indicates a potential lever to reduce
aries. The outflow of Cu cannot be compensated by volume
diffusion inside the Cu substrate or by diffusion along the
interfaces to the Cu Sn layer. In consequence the region
3
the growth rate of the intermetallic. Sputtering a Cu Sn5
6
close to the Cu Sn GBs shifts into the Cu substrate. Also the
6
5
layer as “under bulb” metallization on Cu substrates, anneal-
ing it to obtain a coarse grained microstructure and selecting
ripening process can be observed in Fig. 4͑d͒. Due to the
Gibbs–Thomson effect a small scallop has already shrunk to
a thin disk. In the SEM these leftovers of a former scallop
may be overlooked, as they are destroyed during the prepa-
ration, and erroneously a broad channel is indicated. The
observed characteristics of the reaction zone are summarized
in the schematics of Fig. 5.
a solder distinguished by a high interfacial energy to Cu Sn5
6
might be a promising strategy to reduce the scallop length
and the transport rate of Cu.
1
K. N. Tu and K. Zeng, Mater. Sci. Eng., R. 34, 1 ͑2001͒.
2
H. K. Kim, H. K. Liou, and K. N. Tu, Appl. Phys. Lett. 66, 2337 ͑1995͒.
3
We proved the same features at the ternary Cu/SnPb sys-
H. K. Kim and K. N. Tu, Phys. Rev. B 53, 16027 ͑1996͒.
4
K. N. Tu, T. Y. Lee, J. W. Jang, L. Li, D. R. Frear, K. Zeng, and J. K.
tem. Again after 10 s, a fine-grained Cu Sn layer appears in
3
Kivilahti, J. Appl. Phys. 89, 4843 ͑2001͒.
a thickness of about 60 nm. Also in this case the channels
between the scallops turn out to be grain boundaries. Only
the wetting angle ⌽ at the grain boundaries is significantly
smaller, so that the scallops are elongated normal to the in-
terface.
The presented TEM observations have two important
consequences: ͑i͒ The shape of the scallops is controlled by
the equilibrium of the tensions at the triple junction between
5
A. M. Gusak and K. N. Tu, Phys. Rev. B 66, 115403 ͑2002͒.
6
V. V. Slezov, Theory of Diffusion Decomposition of Solid Solution ͑Har-
wood Academic, Dordrecht, 1995͒.
7
C. Wagner, Z. Elektrochem. 65, 581 ͑1961͒; 65, 485 ͑1961͒.
8
I. Kaur, Fundamentals of Grain and Interphase Boundary Diffusion, 1989.
9
H. Mehrer, Landoldt-Börnstein, Diffusion in Solid Metals and Alloys
0͑
Springer Berlin, 1990͒.
1
S. Herth, F. Ye, M. Eggersmann, O. Gutfleisch, and R. Würschum, Phys.
Rev. Lett. 92, 095901 ͑2004͒.
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