Surface growth of Ni thin films electrodeposited on Ni(100) surfaces

Article abstract of DOI:10.1149/1.1539499

Surface growth of Ni thin films electrodeposited on Ni(100) substrates has been investigated using atomic force microscopy. In the early stage of growth, islands nucleated on the Ni(100) substrates, which appear to be rectangular in cross section, grow laterally in the same crystallographic orientation. Growth surfaces display a normal scaling behavior characterized by the linear surface diffusion universality class. Along the time evolution, instability in growth occurs and a transition from two- to three-dimensional growth is observed. In this stage, surface growth obeys anomalous scaling characterized by local roughness exponent ζ_loc = 1.0, global scaling exponent ζ = 2.1, and dynamic exponent z = 1.0.

Full text of DOI:10.1149/1.1539499

Journal of The Electrochemical Society, 150 ͑3͒ C99-C103 ͑2003͒
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0013-4651/2003/150͑3͒/C99/5/$7.00 © The Electrochemical Society, Inc.
Surface Growth of Ni Thin Films Electrodeposited on Ni„100…
Surfaces
,z
*
M. Saitou, K. Hamaguchi, and W. Oshikawa
Department of Mechanical Systems Engineering, University of the Ryukyus, Okinawa 903-0213, Japan
Surface growth of Ni thin films electrodeposited on Ni͑100͒ substrates has been investigated using atomic force microscopy. In the
early stage of growth, islands nucleated on the Ni͑100͒ substrates, which appear to be rectangular in cross section, grow laterally
in the same crystallographic orientation. Growth surfaces display a normal scaling behavior characterized by the linear surface
diffusion universality class. Along the time evolution, instability in growth occurs and a transition from two- to three-dimensional
growth is observed. In this stage, surface growth obeys anomalous scaling characterized by a local roughness exponent ␨
loc
ϭ 1.0, global scaling exponent ␨ ϭ 2.1, and dynamic exponent z ϭ 1.0.
© 2003 The Electrochemical Society. ͓DOI: 10.1149/1.1539499͔ All rights reserved.
Manuscript submitted April 15, 2002; revised manuscript received August 22, 2002. Available electronically January 23, 2003.
␰ ϳ t1/z and z ϭ ␣/␤ do not hold. Hence, the anomalous scaling
Kinetic surface roughening has been a study of great interest for
the past decade due to a good example of statistical scale
invariance.1 Studies on growing surfaces have revealed the presence
of scaling exponents that determine universality classes. An inter-
face width2 W(L,t) is usually related to the scaling exponents,
which is defined as the root-mean-square ͑rms͒ of the fluctuations of
the surface height h(r,t)
system has two roughness exponents: the local roughness ␨ inde-
loc
pendent of experimental conditions, and global roughness exponent
␨ dependent on experimental conditions. In this paper, the anoma-
lous scaling behavior in electrodeposition on single-crystal Ni sub-
strates is presented.
Epitaxial growth in electrodeposition has been attempted for
metal/metal systems.11-13 Coadsorbates that usually exist in electro-
chemical environments affect growth modes classified as Frank-van
der Merve growth or layer-by-layer growth ͑two-dimensional
growth͒, Stranski-Krastanov growth ͑a transition from two- to three-
dimensional growth͒, and Volmer-Weber growth ͑three-dimensional
growth͒. Some kinds of coadsorbates are known to promote two-
dimensional growth.14,15 However, electrochemical processes have
not yet produced epitaxial films thick enough for technological use.
Theoretical models predict a critical two-dimensional island size16
beyond which three-dimensional growth occurs. The transition is
thought to correspond to a significant increase in the surface rough-
ness, which is observed as a change from smooth surfaces to rough
surfaces. In this study, the surface images measured by atom force
microscopy ͑AFM͒ indicate the presence of the transition.
The data presented here indicate: ͑i͒ in the early stage of growth,
the surface roughness exhibits the normal scaling behavior of the
linear surface diffusion model, and ͑ii͒ as time proceeds, a transition
from two- to three-dimensional growth is observed, which is char-
acterized by anomalous scaling.
2
1/2
¯
W L,t͒ ϭ h r,t͒ Ϫ h
͓ ͑
͓1͔
͑
͔
͘
͗
¯
where ͗ . . . ͘ indicates an average over a system size L and h indi-
cates an average of h(r,t). The interface width has been recognized
to obey the Family-Vicsek function3
W L,t͒ ϭ t␣/z f L/t1/z
͒
͓2͔
͑
͑
which behaves as
u␣
for u Ӷ 1
const for u ӷ 1
f u͒ ϭ
͑
͓3͔
ͭ
where ␣ is the roughness exponent that describes the spatial scaling
behavior and z is the dynamic exponent. The growth exponent ␤ is
given by ␤ ϭ ␣/z, which represents the time-dependent dynamics
of the surface roughness. These exponents ␣, ␤, and z determine the
universality class to which a system belongs. The exponent ␣ is
usually calculated from the height-height correlation function2 de-
fined by
Experimental
Single-crystal Ni disks of 12 mm diam and 1 mm thick were
prepared for cathode electrodes, which have ͑100͒ crystallographic
surfaces within an accuracy of 2°. The single-crystal Ni disks were
polished using three kinds of pastes including diamond powders of
5, 1, and 0.1 ␮m diam, and finally lapped with a solution of 0.05 ␮m
colloidal silica in diameter. The surfaces appear to be mirror-like
and have the rms roughness of 1.2 nm for a widow size of 2 ␮m.
Then the single-crystal Ni disks were electrochemically etched in a
H2SO4-C3H5(OH)3 ͑glycerin͒-H2O solution. As pointed out in Ref.
11, nickel oxides will be left on the etched surfaces. In our prelimi-
nary experiments, as surface growth on ͑100͒ surfaces that were
polished mechanically did not display two-dimensional growth,
͑100͒ surfaces etched electrochemically after mechanical polishing
were chosen for this study. Figure 1 shows AFM images of the
single-crystal Ni disk before and after electrochemical etching. The
vertical scale is magnified by a factor of 18 in order to enhance
viewing. It can be seen from Fig. 1b that the etched Ni surface has
no flaws made mechanically during polishing. The single-crystal Ni
disk and carbon plate for anode electrodes cleaned by a wet process
were located parallel in a still bath containing ͑g/L͒: nickel sulfa-
mate, 600; nickel chloride, 5; and boric acid, 40. The bath was
maintained at pH 4 and a temperature of 323 K. A direct current was
applied between the two electrodes. The direct current density in
2
G r,t͒ ϭ h r,t͒ Ϫ h 0,t͒
͓ ͑
ϰ r2␣
͘
͓4͔
͑
͑
͔
͗
However, recently it has been found that surface roughening in
some theoretical models4-7 and thin-film surfaces in growth8-10 de-
viate from the Family-Vicsek function. Therefore an anomalous
scaling function related to a local interface width has been proposed
to describe the anomalous scaling behavior. The local interface
width4 w(l,t) is defined by
t␤
l
for lz Ӷ t Ӷ Lz
for t Ӷ lz
␨
loc
*
w l,t͒ ϭ
͑
͓5͔
ͭ
␨/z
t
*
where ␤ ϭ (␨ Ϫ ␨loc)/z is an anomalous growth exponent and l is
a window size. The local interface width w(l,t) is calculated over a
window size l less than the system size L. Equation 5 indicates the
presence of a crossover time for the time regime for 0 Ӷ t Ӷ Lz
and the same form as the Family-Vicsek function for the time re-
gime t Ӷ lz. In the case of anomalous scaling, the correlation length
* Electrochemical Society Active Member.
z E-mail: saitou@tec.u-ryukyu.ac.jp
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C100
Journal of The Electrochemical Society, 150 ͑3͒ C99-C103 ͑2003͒
Figure 1. AFM images of the single-crystal Ni͑100͒ surfaces: ͑a͒ mechanically polished and ͑b͒ electrochemically etched surface after mechanical polishing.
The vertical scale of each image with a resolution of 512 ϫ 512 pixels was magnified by a factor of 18 in order to enhance viewing.
electrodeposition was 0.1 mA/cm2, at which the growth rate is about
0.2 ML ͑monolayers͒/s. Only one current density is chosen in this
study according to the scaling hypothesis in modern statistical
mechanics,17,18 which requires that the scaling exponents and the
relationships between them are insensitive to specific systems and
experimental conditions. Nickel thin films were electrodeposited on
the indium tin oxide ͑ITO͒ glass of 1 ϫ 1 cm2. The system size L in
this experiment is 1 cm. The nickel thin films were grown for the
growth time ranging from 500 to 80,000 s. The nickel deposits were
Results and Discussion
Discussion of AFM images.—Figure 2 shows typical AFM im-
ages of nickel electrodeposits grown for different times. In the early
stage of growth, many islands which appear to be rectangular in
cross section grow laterally with time and coalesce into large sizes
͑Fig. 2a-c͒. In addition, the islands grow not in the random crystal-
lographic direction but uniformly in the same one. The surface mor-
phology remains surprisingly flat and appears to evolve obeying the
two-dimensional growth mode. A line scan of Fig. 2b appears in Fig.
3a and clearly shows the existence of flat surfaces of the islands. The
height h in Fig. 3a corresponds to 10 ML. But in the later growth
time regime, the lateral growth rate of the islands decreases and the
surfaces become rough ͑Fig. 2d-f͒. A line scan of Fig. 2e is shown in
Fig. 3b that indicates that the heights of the islands increase rapidly.
Figure 4 shows a plot of the average diameter of the islands vs. time.
It can be seen that the diameter appears to saturate with time.
scanned in air with AFM that has
a resolution of 512
ϫ 512 pixels. The AFM images with different scan regions of
1000 ϫ 1000, 2000 ϫ 2000, and 5000 ϫ 5000 nm2 were used for
the calculations of the scaling exponents.
Determination of Local Exponents ␨
local
In this study, the local roughness exponent ␨ is determined by
loc
two methods: the Hurst rescaled range ͑R/S͒ analysis19 and the Fou-
rier transformation method.20 The formula for the calculation of the
Scaling analysis.—For a finite window size l, the local width is
expected to scale as w(l,t) ϳ t␤. Figure 5 shows plots of w(l,t) vs.
l in a log • log scale for l ϭ 1000 and 5000 nm. In our experiment,
along the time evolution, we find that the exponent ␤ takes up to
three different values. At the early time, we measure ␤ ϭ 0.25
Ϯ 0.07, which is close to that of the linear surface diffusion model
for MBE21,22 described by
exponent ␨ in the R/S analysis is as follows: An arbitrary radius
loc
on the AFM images is represented by rk
␨
k
loc
R k,t͒/S k,t͒ ϰ r
͓6͔
͓7͔
͑
͑
where
ץh r,t͒/ץt ϭ ϪKٌ4h r,t͒ ϩ ␩
͓10͔
R k,t͒ ϭ max X i,t͒ Ϫ min X i,t͒
͑
͓
͑
͔
͓
͑
͔
͑
͑
0рiрk
0рiрk
k
1/2
where ␩ denotes the random fluctuation in deposition and K is a
constant. The mean roughness exponent, ␣ ϭ 0.96 Ϯ 0.05 is deter-
mined as shown in Fig. 6. In this time regime, the surface morphol-
ogy remains flat and obeys the two-dimensional growth mode.
In the further time regimes, instability in growth takes place,
which corresponds to a greater increase in the slopes of islands and
is associated with a transition from two-dimensional to three-
dimensional growth. This instability is reflected in the very large
values of ␤ ϭ 2.1 Ϯ 0.1 and 1.1 Ϯ 0.2, which belong to no univer-
sality classes for normal scaling and indicate anomalous values by
far greater than 1/2. In addition, this may correspond to the presence
of a critical island diameter16 for the transition from two- to three-
dimensional growth. Islands comprise many atomic layers and a
layer nucleates on the top of the island at the critical island diameter.
Owing to the diameter of the islands beyond the critical size that is
an order of (4a2D/F)1/6 where a is the lattice constant, D is the
surface diffusion coefficient of adatoms, and F is the incident atom
flux, this transition, i.e., an abrupt increase in the local interface
width takes place as shown in Fig. 5. Hence we can divide the
experimental time into two time regimes: the early stage of growth
S k,t͒ ϭ kϪ1
h r ,t͒ Ϫ h r,t͒ ͒
͑ ͑
2
͑
͑
͗
͘
ͫ
ͬ
i
i
͚
iϭ1
k
X k,t͒ ϭ
h r ,t͒ Ϫ h r,t͒
͓ ͑ ͔
͘
k
͑
͑
͗
i
͚
iϭ1
First we calculate X(k,t) within a radius rk on the AFM image.
Next, we find the maximum and minimum change of X(k,t) and
normalize R(k,t) by the standard deviation S(k,t).
The Fourier transformation method is to determine the local
roughness exponent ␨ from the power spectrum. The power spec-
loc
trum of H(f,t) that is the Fourier transform of h(r,t) is given by
2
͉
H f,t͒
͑
͉
ϰ fϪ␥
͓8͔
where f is the frequency and ␥ is a constant value. The local rough-
ness exponent is expressed by the slope ␥
␨
ϭ
␥ Ϫ 2͒/2
͓9͔
͑
loc
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Journal of The Electrochemical Society, 150 ͑3͒ C99-C103 ͑2003͒
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Figure 2. AFM images of Ni thin-film surfaces grown on the Ni͑100͒ substrates for different growth times: ͑a͒ 4500, ͑b͒ 6000, ͑c͒ 8000, ͑d͒ 16,000, ͑e͒ 32,000,
and ͑f͒ 60,000 s. The vertical scales of ͑a-d͒ and ͑e,f͒ images were magnified by a factor of 18 and 5, respectively, in order to enhance viewing.
in which surface growth obeys normal scaling characterized by the
linear growth model universality class, and the later stage of growth
in which the surface morphology is expected to obey the anomalous
scaling function in Eq. 5.
80,000 s becomes 0.99 Ϯ 0.05. In Fig. 7b, the slope of ␥ best fitted
to the data yields 3.92, which gives a value of ␨ ϭ 0.96. In a
loc
similar fashion, the average value of ␨ for the nickel films grown
loc
for 10,000-80,000 s using the Fourier transform method becomes
1.0 Ϯ 0.08, which is independent of the window length l. Now, it is
concluded that the local roughness ␨loc obtained from the two meth-
ods is 1.0. In the case of normal scaling, the roughness exponent ␣
is equal to the local roughness ␨loc . In this study the roughness
exponent ␣ for 500-10,000 s becomes 0.96 Ϯ 0.05. The values of
the slopes in Fig. 5 and 7 yield the global roughness exponent ␨ of
2.1 and the dynamical exponent z of 1.0. Thus we can determine the
In the later time regime, the local roughness exponent ␨ is
loc
determined by the Hurst rescaled range ͑R/S͒ analysis and the Fou-
rier transformation method. Figure 7a and b shows typical log-log
2
plots of R(k,t)/S(k,t) vs. rk and
͉
H(f,t)
͉
vs. the frequency f. The
AFM image of 2000 ϫ 2000 nm2 electrodeposited for 25,000 s was
used for the calculations in Fig. 7. The slope of the best straight-
fitted line to the data in Fig. 7a gives the local roughness exponent
␨
ϭ 1.0. The average ␨ for the nickel films grown for 10,000-
loc
loc
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Journal of The Electrochemical Society, 150 ͑3͒ C99-C103 ͑2003͒
Figure 3. One-dimensional line scans from AFM images of Fig. 2b and e;
t ϭ (a) 6000 and ͑b͒ 32,000 s.
universality class of the anomalous scaling characterized by ␨
loc
Figure 5. Log-log plots of local width w(l,t) vs. time t for the different
window sizes: ͑a͒ l ϭ 1000 and ͑b͒ 5000 nm. The slopes take up to three
different values. The straight lines are plotted as a guide for the eye.
ϭ 1.0, ␨ ϭ 2.1, and z ϭ 1.0
Conclusions
Ni thin films were grown by electrodeposition on Ni͑100͒ sub-
strates at a very low current density. In the early stage of growth,
islands nucleated on the Ni͑100͒ surface, which appears to be rect-
angular in cross section, grows laterally in the same crystallographic
orientation, and displays normal scaling that belongs to the linear
diffusion growth universality class. Along the time evolution, insta-
bility in growth takes place and a transition from two to three-
Figure 6. Hurst plot for the AFM image of 2000 ϫ 2000 nm2 electrodepos-
ited for 3500 s. The solid straight line best fitted to the data indicates a slope
of 0.97.
Figure 4. Time evolution of the average diameter of islands.
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Journal of The Electrochemical Society, 150 ͑3͒ C99-C103 ͑2003͒
Acknowledgments
C103
This work was supported by Grant-in-Aid for Scientific Research
͑C͒, no. 13650029, by the Ministry of Education, Science, and Cul-
ture of Japan.
The University of the Ryukyus assisted in meeting the publication costs of
this article.
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