The kinetics of copper island growth on ruthenium oxide in perchlorate solution

Article abstract of DOI:10.1016/j.electacta.2010.07.034

The nucleation potential for the deposition of copper on ruthenium oxide is very small and hence island growth can occur in the kinetic regime. Previously, we have reported on island growth in sulfate solution where anion adsorption results in the formation of hexagonal, disk-shaped islands. Here we report on island growth in perchlorate solution, in the absence of specific anion adsorption. All islands have a 〈1 1 1〉 surface orientation dictated by the amorphous substrate. The islands are hemispherical in shape and island growth follows power law kinetics in both lateral and vertical directions with exponents 0.50 and 0.26, respectively. From analysis of the time-dependent extended area using Avrami analysis, analysis of the near-neighbor distribution, and the correlation between the island size and the spatial distribution, we conclude that island growth is controlled by surface diffusion-mediated lateral growth.

Full text of DOI:10.1016/j.electacta.2010.07.034

Electrochimica Acta 55 (2010) 8416–8421
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Electrochimica Acta
journal homepage: www.elsevier.com/locate/electacta
The kinetics of copper island growth on ruthenium oxide in perchlorate solution
∗
Lian Guo, Alexander Thompson, Peter C. Searson
Department of Materials Science and Engineering, Johns Hopkins University, Baltimore, MD 21218, United States
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 28 May 2010
Received in revised form 14 July 2010
Accepted 14 July 2010
Available online 21 July 2010
The nucleation potential for the deposition of copper on ruthenium oxide is very small and hence island
growth can occur in the kinetic regime. Previously, we have reported on island growth in sulfate solution
where anion adsorption results in the formation of hexagonal, disk-shaped islands. Here we report on
island growth in perchlorate solution, in the absence of specific anion adsorption. All islands have a
ꢀ
1 1 1ꢁ surface orientation dictated by the amorphous substrate. The islands are hemispherical in shape
and island growth follows power law kinetics in both lateral and vertical directions with exponents
.50 and 0.26, respectively. From analysis of the time-dependent extended area using Avrami analysis,
Keywords:
Electrodeposition
Island growth
Nucleation and growth
Copper deposition
0
analysis of the near-neighbor distribution, and the correlation between the island size and the spatial
distribution, we conclude that island growth is controlled by surface diffusion-mediated lateral growth.
© 2010 Elsevier Ltd. All rights reserved.
1
. Introduction
The electrochemical deposition of metals onto foreign sub-
rate anions do not adsorb onto copper [15,16] this system provides
an opportunity to study island growth kinetics in the absence of
anion adsorption. The key features of island growth in perchlorate
solution are: (1) the formation of hemispherical islands in contrast
to the hexagonal disk-shaped islands formed in sulfate solution,
and (2) the island density increases linearly with time up to island
coalescence (about 2000 s), following the kinetics for progressive
nucleation; in contrast the island density in sulfate solution sat-
urated within the first 20 s, following instantaneous nucleation
kinetics.
strates in the overpotential regime usually occurs through
Volmer–Weber growth, resulting in the formation of three-
dimensional (3D) islands [1]. The kinetics of island growth is
strongly influenced by the nucleation overpotential: the potential
corresponding to the onset of nucleation of metal M on substrate
+
S, referenced to the equilibrium potential for the M /M couple
[
2]. In the absence of underpotential deposition, the nucleation
overpotential is usually several hundred millivolts so that after
nucleation island growth is in the mixed diffusion/kinetic control
regime [3–10].
In previous work we have reported on the growth of cop-
per islands on amorphous ruthenium oxide in sulfate solution
The island growth kinetics were determined by analyzing the
projected area and height of all islands at different deposition times
using a method that we have developed previously [12]. The evo-
lution of island size L and height h with time follow power law
a
b
behavior according to L ∝ t and h ∝ t where the exponents a and b
describe the time dependence of the island dimensions. The growth
exponent can be used to extract information on the mechanism of
island growth. For example, a growth exponent of 1.0 is charac-
teristic of direct metal ion reduction at the surface of the island
[1]. However, in the kinetic regime other growth mechanisms can
result in other growth exponents. Here we show that the lateral and
vertical growth exponents are 0.50 and 0.26, respectively. Analy-
sis of the island dimensions, the distribution of nearest-neighbor
distances, and the correlation between island sizes and the local
environment, indicate that island growth is controlled by surface
diffusion-mediated lateral growth.
[
11,12]. In this system the nucleation potential is very close to the
2+
Cu /Cu equilibrium potential so that island growth is in the kinetic
regime. Specific adsorption of the sulfate anion on the (1 1 1) planes
[
13,14], combined with a (1 1 1) surface normal, results in suppres-
sion of vertical growth and leads to the formation of hexagonal
disk-shaped islands [11]. Combining scaling analysis of the island
dimensions with Avrami analysis, we showed that lateral growth is
initiated by attachment of adatoms to the island perimeter [12] and
then proceeds by direct electrochemical reduction of metal ions on
the island facets.
Here we report on the island growth kinetics for copper on
amorphous ruthenium oxide in perchlorate solution. Since perchlo-
2. Experimental
∗ Corresponding author.
E-mail addresses: lguo@jhu.edu (L. Guo), searson@jhu.edu (P.C. Searson).
Copper islands were deposited on polycrystalline ruthenium
with an amorphous native oxide about 2 nm in thickness [11,12].
0
013-4686/$ – see front matter © 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.electacta.2010.07.034

L. Guo et al. / Electrochimica Acta 55 (2010) 8416–8421
8417
Experiments were performed in a three-electrode cell with a cop-
per wire reference electrode and platinum mesh counter electrode.
2
The working electrode area was 0.31 cm . Nucleation and growth
are relatively slow in the near-equilibrium regime and hence a
Cu(II)/Cu reference electrode was used to avoid contamination
during the relatively long experiments. All experiments were per-
formed in solution containing 0.1 M Cu(ClO ) (99.999%, Alfa Aesar)
4
2
and 0.2 M HClO (99.9999%, Alfa Aesar) in 18 Mꢀ deionized water at
4
2+
an applied potential of −64 mV (vs. Cu /Cu) and at room temper-
◦
ature 23 C. Deposition experiments were performed at constant
potential to ensure a constant thermodynamic driving force and
to avoid complications due to the fact that the island density is
strongly dependent on potential.
The ruthenium substrate, which was prepared by physical vapor
deposition of ruthenium on single crystal silicon, is smooth with
rms roughness 1.8 A˚ over 2 ␮m × 2 ␮m area [11,12,17]. The ruthe-
nium has no in-plane ordering but has strong (0 0 2) texture with
an average grain size of 14 nm and a native oxide about 2 nm in
thickness [11].
Cu islands were examined by atomic force microscopy (Molecu-
lar Imaging Pico-Plus) and X-ray diffraction (Philips X’Pert 4-circle
system). In a typical experiment, after copper deposition the sam-
ple was rinsed in distilled water and at least four AFM images
(
50 ␮m × 50 ␮m) were obtained at random locations on the sam-
ple using a 70 ␮m scanner. From each of the four AFM images we
obtained the volume and projected area of every island. The aver-
age charge density associated with the islands was obtained from
the sum of the volume of each island using Faraday’s law.
Fig. 1. (a) AFM images (50 ␮m × 50 ␮m) of Cu islands electrodeposited from solu-
2+
tion containing 0.1 M Cu(ClO4)2 and 0.2 M HClO4 at −64 mV (vs. Cu /Cu) for 200,
5
00, 1000 and 2000 s. (b) AFM image (7 ␮m × 7 ␮m) of a hemispherical Cu island
formed at 500 s.
3
. Results and discussion
the current transients recorded at each deposition time. The excel-
lent agreement between the global charge density from the current
transient and the local charge density from the AFM images, shows
that the island distribution is uniform across the surface and that
the AFM images are representative of the whole electrode. The dis-
continuity at 1000 s corresponds to the onset of island coalescence.
A similar effect was seen for deposition of disk-shaped islands from
sulfate solution [12].
3
.1. Cu electrodeposition
The AFM images in Fig. 1a reveal the time evolution of island
growth during copper deposition on ruthenium oxide from per-
chlorate solution. The number density of copper islands increases
until island coalescence at 2000 s. This is in contrast to deposition
from sulfate solution under the same conditions, where the island
density saturates in the first 20 s, well before island coalescence
Fig. 4 shows the time dependence of the island density, up to
island coalescence at 2000 s. The island density N increases approx-
imately linearly with time according to progressive nucleation
kinetics (N(t) = knt) spanning the whole island growth regime with
[
12]. The series of images in Fig. 1 clearly shows the progression
from isolated island growth to island coalescence (about 2000 s).
Since there is no specific adsorption of the perchlorate anion on
copper, the islands are approximately hemispherical shape (Fig. 1b)
with an aspect ratio of about 0.5. At longer times, re-nucleation
results in polycrystalline islands with multiple grains. To investi-
gate the island growth kinetics, we focus on the first 2000 s.
A unique feature of copper deposition on ruthenium oxide is
that nucleation occurs at potentials very close to the equilibrium
potential, allowing the study of island growth under kinetic control.
Fig. 2 shows a typical current–time transient for copper deposition.
4
−2 −1
s . The final island density at
a nucleation rate kn = 1.0 × 10 cm
7
−2
coalescence is about 2 × 10 cm , which is five times larger than
the island density for Cu deposition from sulfate solution at the
After a short induction time t of about 5 s, copper nucleation leads
0
to a current peak after about 40 s, as shown in the inset in Fig. 2.
Subsequent island growth and continued nucleation result in an
increase in the current from about 400 s up to island coalescence
at about 2000 s, after which the current density is approximately
constant and determined by the vertical growth rate. The steady
−
2
state current density after island coalescence is about 3 mA cm
−
2
in perchlorate solution, larger than the 1 mA cm current density
in sulfate solution [12]. Since the islands do not contribute sig-
nificantly to the surface roughness (at maximum a factor of 2 for
close-packed hemispheres), the smaller current in sulfate solution
can be attributed to the specific adsorption of sulfate on the (1 1 1)
planes that suppresses the vertical growth rate.
Fig. 2. Current density vs. time for copper deposited from solution containing 0.1 M
2
+
Cu(ClO4)2 and 0.2 M HClO4 at −64 mV (vs. Cu /Cu). The inset shows the induction
time t0 from which nucleation occurs. Seven current–times curves gives t0 = 5 ± 1 s,
which is negligible compared to deposition times.
In Fig. 3 we compare the charge density derived from the AFM
images to the deposition charge density obtained by integration of

8
418
L. Guo et al. / Electrochimica Acta 55 (2010) 8416–8421
Fig. 3. Deposition charge density (dotted line) obtained from the integration of indi-
vidual current–time transients at 100, 200, 500, 1000, 2000 and 5000 s. (o) Charge
density obtained from analysis of AFM images at different deposition times. The
charge density was obtained from the volume of all islands in four 50 ␮m × 50 ␮m
AFM images using Faraday’s law.
same potential. This difference may be attributed to slower adatom
surface diffusion on the substrate, as discussed later.
The out-of-plane orientation of the copper islands was charac-
terized by X-ray diffraction. Up to island coalescence (about 2000 s),
only the Cu (1 1 1) peak is observed (Fig. 5a). The intensity of the
Cu (1 1 1) peak increases with time due to the increase in num-
ber and size of the islands. Cu (2 0 0) and Cu (2 2 0) peaks emerge
after island coalescence is complete at 2000 s. Fig. 5b shows the
time dependence of the intensity of the Cu (1 1 1) peak and the
deposition charge density. The Cu (1 1 1) peak is normalized by the
intensity of the Ru (0 0 2) peak to eliminate experimental varia-
tions between measurements. The intensity of the Cu (1 1 1) peak
increases linearly with time up to island coalescence at 2000 s. The
correlation with the deposition charge density up to 1000 s sug-
gests that deposition is dominated by the growth of (1 1 1) oriented
islands up to the onset of island coalescence (1000 s). After 1000 s,
the intensity of the Cu (1 1 1) peak does not increase as rapidly as
the deposition charge due to the contribution of islands with other
orientations.
Fig. 5. (a) X-ray diffraction patterns for copper deposited from solution containing
0.1 M Cu(ClO4)2 and 0.2 M HClO4 at −64 mV (vs. Cu2+/Cu) at different times. (b)
The intensity of the Cu (1 1 1) peak normalized to the Ru (0 0 2) peak (ꢁ) and the
deposition charge density (o) (see Fig. 3) vs. time. The Cu (1 1 1) diffraction intensity
has a linear dependence (dashed line) on time up to island coalescence at 2000 s.
(4) Island nucleation is linear with time (progressive nucleation)
up to island coalescence (2000 s).
3.2. Island growth kinetics
The results from analysis of the AFM images, X-ray diffraction,
and current–time curves can be summarized as follows: (1) island
nucleation and growth occurs at potentials very close to the Cu2 /Cu
equilibrium potential, allowing access to the kinetic deposition
regime. (2) The islands have a thermodynamically favorable close-
packed (1 1 1) basal plane, due to the amorphous ruthenium oxide
substrate. (3) The absence of selective anion adsorption in the per-
chlorate solution results in the formation of hemispherical islands.
The island growth kinetics are determined using scaling analysis
based on the evolution of island size and shape that we developed
previously [12]. In Fig. 6, each data point represents the volume
and corresponding projected area of an individual island, and the
different colors indicate islands grown at different times. At each
deposition time there is a broad distribution in both volume and
area due to the progressive nucleation mechanism and the ran-
dom distribution of nuclei (see below). The solid line represents
the isotropic growth of ideal hemispherical islands:
+
2
V =
√
A3/2
(1)
3
ꢂ
where V is the volume of the island, A is the projected area, and
the exponent m = 3/2 defines the slope in the double-logarithmic
plot. As the deposition time increases from 100 to 500 s, the island
dimensions at each time increase reflecting the overall growth.
m
The island dimensions follow the scaling relation V ∝ A with a
scaling exponent m = 1.26. The exponent is less than 3/2 indicat-
ing that the island aspect ratio decreases with time, i.e. the islands
become slightly flatter. After 1000 s, the smaller islands exhibit the
same scaling relation, however, the larger islands deviate from this
behavior (Fig. 6b). This effect is due to the transition from isolated
island growth to coupled island growth at the onset of island coa-
lescence. As we suggest below, this transition is due to the onset of
competition for adatoms on the surface.
Fig. 4. Number density of Cu islands deposited from solution containing 0.1 M
2+
Cu(ClO4)2 and 0.2 M HClO4 at −64 mV (vs. Cu /Cu) vs. the deposition time. The
dotted line is the linear least square fitting.

L. Guo et al. / Electrochimica Acta 55 (2010) 8416–8421
8419
but they determine the time evolution of the island aspect ratio for
power law growth kinetics.
Fig. 7 shows histograms of the projected area and volume of
individual islands at different times. At 100 s, islands are narrowly
dispersed with average dimensions A = 1.7 ␮m2 and V = 1.2 ␮m .
The island sizes increase dramatically at short times (100–200 s)
but then increase more slowly at longer times. The small decrease
after 500 s is due to the contribution of islands born at later times.
The size dispersion gradually increases with time due to progres-
sive nucleation, but remains approximately constant after 500 s.
For instantaneous nucleation, the growth exponents a and b
can be obtained from the time dependence of the average island
dimensions [12]. However, this is difficult for systems that exhibit
progressive nucleation due to the large dispersion in island size.
Instead, we use the Avrami theorem to obtain the values of the
growth exponents by analyzing the time dependence of the sur-
face coverage of all islands on the substrate. The actual transformed
area derived from the independent growth centers can be calcu-
lated from Kolmogorov–Johnson–Mehl–Avrami (KJMA) equation
3
[
18] that takes into account island overlap:
n
f = 1 − exp[−S(t)] = 1 − exp(−kt )
(5)
where f is the actual 2D coverage by the islands, S(t) is the extended
coverage, k is a rate constant, and the exponent n can vary from
1
to 4. From Fig. 8 we obtain an exponent n = 1.7, close to the
value of 2 for progressive nucleation and two-dimensional surface
diffusion-mediated lateral growth [19]. For surface diffusion-
mediated lateral growth a = 0.5, and from Equation 4 we obtain
b = 0.26 (recall m = 1.26). The deviation from n = 2 is attributed to
the slight time variation of the nucleation rate and the fact that the
island distribution does not exhibit complete spatial randomness,
as discussed later.
In our experiments the nucleation overpotential is very small
and hence we can nucleate and grow islands at an applied poten-
tial of −64 mV (vs. Cu2+/Cu) where deposition is kinetically limited.
Fig. 6. (a) Volume vs. projected area for Cu islands deposited from solution con-
2+
taining 0.1 M Cu(ClO4)2 and 0.2 M HClO4 at −64 mV (vs. Cu /Cu) after 100 s (o),
2
00 s (ꢁ), 500 s (ꢀ), and (b) 1000 s (ꢁ). In both figures, the solid line corresponds
to isotropic island growth (m = 3/2) and the dashed line represents a power law fit
to the data up to 500 s (m = 1.26). The numbers of islands at each deposition time
were: 151 (100 s), 262 (200 s), 363 (500 s), and 802 (1000 s).
From the scaling relation V ∝ Am it follows that growth can be
described by a power law in each dimension:
a
L ∝ t
h ∝ t
(2a)
(2b)
b
where L and h are the lateral and vertical dimensions, respectively,
while a and b are the corresponding growth exponents. Note that
the exponents a and b only describe the time dependence of the
island dimensions, they do not reflect the magnitude of L and h
which are largely determined by the pre-factor. The island size and
height are calculated from the volume and the projected area of the
individual islands measured by AFM:
1
/2
L = A
(3a)
V
h =
(3b)
A
m
From Eqs. (2a)–(2b) and (3a)–(3b) and the scaling relation V ∝ A
we have:
m = 1
+ b
(4)
2
a
From the experimentally determined exponent m = 1.26 we obtain
b/a = 0.52, illustrating that lateral growth has a stronger time
dependence (a > b).
The island aspect ratio ˛, which is the vertical dimension divided
by the lateral dimension (i.e. h/L), follows the scaling relation
Fig. 7. (a) Volume and (b) projected area histogram at different times for Cu islands
deposited from solution containing 0.1 M Cu(ClO4)2 and 0.2 M HClO4 at −64 mV (vs.
b−a
˛
∝ t . Since b − a < 1, the island aspect ratio decreases as depo-
sition time increases. As stated above, the growth exponents by
themselves do not indicate the island dimensions and growth rates,
2+
Cu /Cu). Their average values and standard deviations are listed accordingly. The
numbers of islands analyzed at each time are the same as in Fig. 6.

8
420
L. Guo et al. / Electrochimica Acta 55 (2010) 8416–8421
Fig. 8. Plot of −ln(1 − f) vs. ln t according to the Kolmogorov–Johnson–Mehl–Avrami
KJMA) equation. The data were obtained from analysis of AFM images of copper
deposition for 100–200 s from solution containing 0.1 M Cu(ClO4)2 and 0.2 M HClO4
(
2+
at −64 mV (vs. Cu /Cu). The fractional coverage f was obtained from analysis of all
islands in four randomly selected AFM images (50 ␮m × 50 ␮m). The Avrami expo-
nent equals 1.7, implying progressive nucleation followed by 2D diffusion-mediated
growth.
In the kinetic regime, the exponents for lateral and vertical growth
are dependent on the growth mechanism [2]. For direct attach-
ment of metal atoms to the surface of the island the lateral and
vertical growth exponents are 1.0. Other growth mechanisms are
also possible. For example, if lateral growth is controlled by surface
diffusion of adatoms on the substrate to the island perimeter, then
the lateral growth exponent a = 0.5 [2]. In this latter case, metal ion
reduction on the substrate is kinetically limited but lateral island
growth is controlled by adatom surface diffusion. We note that a
growth exponent of 0.5 is also obtained at high overpotentials when
bulk diffusion of metal ions to the growing islands is rate-limiting
1
/2
and r ∝ t
.
The vertical and lateral growth exponents for island growth in
perchlorate solution are both less than 1.0, indicating that island
growth is not controlled by direct attachment to the island sur-
face. The vertical growth exponent b = 0.26 is less than the exponent
for direct surface attachment (b = 1), and also less than the lateral
growth exponent a = 0.5. As described above, the lateral growth
exponent of 0.5 is consistent with rate-limiting attachment of
adatoms on the substrate to the island perimeter. The slow attach-
ment of adatoms at the island perimeter is followed by fast direct
attachment of atoms on sequentially higher steps and/or interlayer
Fig. 9. Nearest-neighbor distances distribution obtained from spatial point analysis
of 124 (100 s), 202 (200 s), 300 (500 s) and 696 (1000 s) islands at different times. The
dotted lines show the Poisson distribution, indicating complete spatial randomness.
thermore, the lower surface diffusion coefficient in perchlorate
solution is consistent with the larger island density.
3.3. Island distribution
(
downhill) transport contribute to both lateral and vertical growth
Fig. 9 shows histograms of island near-neighbor distances
(nnds) at different times, which can reveal the spatial pattern of
dispersed islands on an electrode. At short times, between 100
and 200 s, the spatial distributions are in good agreement with
the Poisson distribution, indicating complete spatial randomness
(CSR). Note that the observed cutoff at about 1.6 ␮m is due to the
finite size of the islands (the average diameter is 1.7 ± 0.5 ␮m at
100 s, see Fig. 7). At longer times, the deviation from CSR increases
and becomes quite significant at 1000 s. A statistical Z-test [22]
was conducted on the spatial point pattern analysis to test the
hypothesis of CSR. Results show that with a significance of 0.05 (i.e.
95% confidence limit) islands are randomly distributed at 100 and
200 s. Significant deviation from CSR after 500 s is consistent with
surface diffusion-mediated lateral island growth. The formation of
adatom depletion zones around the islands suppresses nucleation
in these regions and hence leads to deviation from CSR. This effect
has been observed computer simulations of progressive nucleation
under bulk diffusion control [23], where ion depletion around exist-
ing islands suppresses nucleation by depleting the surface adatom
concentration.
Guo, and Searson [2]. As described above, if the sow step in lateral
growth is the direct attachment of atoms to the facet intersecting
the substrate, then lateral growth is described by a = 1 (L ∝ t ).
1
The vertical growth exponent of 0.26 suggests that there is negli-
gible attachment on the top of the island and that vertical growth is
limited by sequential attachment of atoms on the sides of the island.
In contrast to the disk-shaped islands formed in sulfate solution, the
hemispherical islands seen here (Fig. 1) effectively have no top sur-
face to sustain vertical growth. The evolution of surface roughness
in this system has been reported elsewhere [20].
The surface diffusion coefficient D for Cu adatoms on the ruthe-
S
nium oxide substrate can be estimated from the average island
spacing and the cross-over time in island growth. At the cross-
7
−2
over time (t = 1000 s) the island density is 1.2 × 10 cm , leading
1/2
to a surface diffusion coefficient (x = (4Dt)
in two dimensions)
−
12
2
−1
D = 5 × 10
cm s . This is more than an order of magnitude
S
−10
2
−1
lower than the value of 2 × 10
cm s estimated in the same
way for deposition from sulfate solution under the same condi-
tions. This difference is consistent with the observation that anion
adsorption on a metal can enhance surface diffusion of metal
adatoms by decreasing the energy barriers for hopping [21]. Fur-
In 3D island growth, if the lateral growth of islands is limited
by the diffusion of adatoms on the substrate to the island perime-

L. Guo et al. / Electrochimica Acta 55 (2010) 8416–8421
8421
The growth of hemispherical islands in perchlorate solution fol-
lows power law kinetics in both lateral and vertical directions. At
shorter times, the lateral and vertical growth exponents are equal
to 0.50 and 0.26, respectively. Analysis of the island dimensions,
the distribution of nearest-neighbor distances, and the correlation
between island sizes and local environment, confirm that island
growth is controlled by surface diffusion-mediated lateral growth.
The smaller vertical growth exponent results in the gradual flatten-
ing of the hemispherical islands at longer times and suggests the
importance of interlayer transport on the island surface.
Acknowledgement
The authors gratefully acknowledge support for NSF (grant
number CHE-0905869).
Fig. 10. Correlation between island projected areas and their nearest-neighbor dis-
tances at different times 100 s (o), 200 s (ꢁ), 500 s (ꢀ), and 1000 s (ꢁ). The solid lines
are power law fits.
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We have reported on the electrochemical growth of Cu islands
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on ruthenium oxide in perchlorate solution. In contrast to our pre-
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two dramatic differences are observed. First, islands are hemispher-
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from the suppression of vertical growth by specific adsorption
of sulfate anions on Cu (1 1 1) planes of the disk-shaped islands.
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nucleation is complete within the first 20 s. Slower adatom sur-
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which is dictated by the amorphous substrate, independent of solu-
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