Scaling of roughness in silver electrodeposition

Article abstract of DOI:10.1149/1.1567267

The electrodeposition of silver from thiosulfate solutions and its surface roughness are studied using scaling methods. Although silver electrodeposition from photographic fixing baths containing thiosulfate has been done successfully for many years, the vast majority of information about this process remains empirical. A comparison is made between plating silver from ammonium- and sodium-thiosulfate-containing solutions. Atomic force microscopy is used to study surface roughness, which is then analyzed by scaling methods. Silver electrodeposition from sodium-thiosulfate-containing solutions was found to be smoother than from ammonium-thiosulfate-containing solutions. The obtained scaling exponents, found after correction for local effects, depend strongly on the nature of the electrolyte; the growth exponents β are 0.13 and 0.71 for sodium and ammonium thiosulfate solutions, respectively. Local effects are observed only for the sodium but not for the ammonium thiosulfate solution.

Full text of DOI:10.1149/1.1567267

Journal of The Electrochemical Society, 150 ͑6͒ C375-C380 ͑2003͒
C375
0013-4651/2003/150͑6͒/C375/6/$7.00 © The Electrochemical Society, Inc.
Scaling of Roughness in Silver Electrodeposition
a,b
a, ,z
David G. Foster,a,c, Yonathan Shapir, and Jacob Jorne
´
*
*
b
aDepartment of Chemical Engineering and Department of Physics and Astronomy,
University of Rochester, Rochester, New York 14627-0166, USA
cEastman Kodak Company, Rochester, New York 14650-1824, USA
The electrodeposition of silver from thiosulfate solutions and its surface roughness are studied using scaling methods. Although
silver electrodeposition from photographic fixing baths containing thiosulfate has been done successfully for many years, the vast
majority of information about this process remains empirical. A comparison is made between plating silver from ammonium- and
sodium-thiosulfate-containing solutions. Atomic force microscopy is used to study surface roughness, which is then analyzed by
scaling methods. Silver electrodeposition from sodium-thiosulfate-containing solutions was found to be smoother than from
ammonium-thiosulfate-containing solutions. The obtained scaling exponents, found after correction for local effects, depend
strongly on the nature of the electrolyte; the growth exponents ␤ are 0.13 and 0.71 for sodium and ammonium thiosulfate
solutions, respectively. Local effects are observed only for the sodium but not for the ammonium thiosulfate solution.
© 2003 The Electrochemical Society. ͓DOI: 10.1149/1.1567267͔ All rights reserved.
Manuscript submitted November 15, 2001; revised manuscript received October 29, 2002. Available electronically April 10, 2003.
The goal of this work is to further the electrochemical and mor-
phological understanding of silver electrodeposition from thiosulfate
solutions. The recovery of silver from photographic fixing solutions
is a well-established practice in the photographic industry. A com-
prehensive description of the mechanism of electrodeposition is
complicated by the large number of variables that affect the process,
including surface and local morphology, solution-surface interac-
tions, solution chemistry, and transport mechanisms. In recent years,
ammonium thiosulfate has been considered to replace sodium thio-
sulfate for environmental reasons.
This work represents the first attempt to obtain quantitative in-
sight into silver electrodeposition that can be directly compared with
other electrodeposited surfaces using scaling analysis. Scaling
analysis of silver electrodeposited onto vapor-deposited silver sub-
strates was done to gain a better understanding of the differences in
plating from sodium and ammonium thiosulfate, in the presence of
strong silver ion complexing agents. Empirical observations of sil-
ver plated from sodium and ammonium thiosulfate solutions indi-
cate that the electrodeposits obtained from sodium thiosulfate solu-
tion are macroscopically smoother than those obtained from the
ammonium-thiosulfate-containing solution. Atomic force micros-
copy ͑AFM͒ images of the surface topography were analyzed using
scaling methods to gain insight into the differences in morphology
and surface roughening.
x, y. The value of ␴ depends on the extent of the surface examined.
For example, if the length scale used for the calculation of the rms
height is chosen small enough to fall on top of an individual nucleus
of growth, the value of ␴ will be much smaller than a value calcu-
lated for a larger surface region that includes a number of nuclei. If
the length scale is small enough, placing it in two different areas of
the surface, vastly different ␴ values can be observed. Measuring on
the top of an individual nucleus, or on the side of a sharp peak gives
very different results. Inherent in this analysis is the fact that as the
length scale used to calculate ␴ increases, the value of ␴ also in-
creases up to a certain magnitude and then levels off, unchanging as
the analysis region is taken larger and larger. This saturation of ␴ is
a characteristic of the system being studied. This scaling behavior
provides considerable insight into the operative microscopic mecha-
nism of electrodeposit growth.
The scaling behavior of ␴ is considered below. If the growing
surface is such that H(r) is indistinguishable from ␬ H(␬r) for
Ј
␬
Þ ␬, then the surface is said to be self-affine. Self-affine objects
Ј
change morphology when a scale change is made in all directions. If
a scale change is made that is different for each direction, then
self-affine surfaces do not change morphology. For self-affine sur-
faces, additional information can be extracted for the way in which
␴ scales with length. The rms of self-affine surfaces scales as11
␴ L,t͒ ϭ L␣ f t/L␣/␤
͒
͓2͔
͑
͑
Theory
where ␣ and ␤ are defined as the static and dynamic scaling expo-
nents, respectively. The exponents ␣ and ␤ are also known as the
roughness and growth exponents, respectively. The growth exponent
characterizes the time-dependent dynamics of the roughening sur-
face, and the roughness exponent characterizes the roughness of the
saturated interface.11 The function f(t/L␣/␤) is defined so that ␴ϰL␣
for t/L␣/␤ ӷ 1, and ␴ ϰ t␤ for t/L␣/␤ Ӷ 1. Self-affine surfaces are
also characterized by a limiting value, denoted as ␰L , which is the
limiting value of ␴ for large analysis regions. The characteristic
length, above which the rms height of the surface does not change,
is known as the critical scaling length, Lc . For a self-affine surface,
a plot of ␴ vs. L on a log-log scale yields a straight line with slope
Scaling methods have been used to identify the dominant growth
processes during deposition and etching of vapor-deposited
surfaces.1 These methods have been used to study copper elec-
trodeposition on gold in the presence of thiurea and benzotriazole,2
copper deposition,3 dissolution,4 copper deposition with additives,5
and local effects in copper deposition.6 Silver electrodeposition has
been extensively studied,7 as well as underpotential silver
deposition,8,9 and roughness of silver electrodeposition from silver
nitrate in water dioxane solutions.10 It has been shown that the na-
ture of the electrolyte affects the structure of underdeposited silver.
As yet, scaling analysis has not been applied to silver.9
The quantitative measure of surface roughness is obtained from
the standard deviation of the perpendicular surface variation, ␴, also
known as the root mean square ͑rms͒ height of the surface
Ͻ
Ͻ
1 for L р Lc . The roughness exponent, ␣, will be equal
0
␣
to 1 for a self-similar surface.
Huo and Schwartzacher6 have recently shown that for copper
electrodeposition, an extra scaling exponent is required to character-
ize the time evolution of the local roughness
2
␴ ϭ ͱ
H x,y͒ Ϫ H x,y͒
͓1͔
͓
͑
͓
͑
͔͔
͗
͗
͘
͘
where H(x,y) represents the height of the surface relative to the
arbitrary plane, generally taken as the average value at the ordinates
␣/␤
␴ L,t͒ ϭ L␣t␤ f t/L
͒
͓3͔
loc
͑
͑
The influence of local effects on the growth exponent ␤ is applied
here by calculating ␤loc at a length scale well below the correlation
length. This is done by selecting a length scale ͑e.g., Lϭ1,000 nm)
* Electrochemical Society Active Member.
z E-mail: jorne@che.rochester.edu
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C376
Journal of The Electrochemical Society, 150 ͑6͒ C375-C380 ͑2003͒
plating solution containing 0.5 M of ammonium or sodium sulfate
Table I. Comparison of scaling parameters for silver elec-
was used so that the thiosulfate solutions would not dissolve the
silver off the vapor-deposited silver substrate at open circuit at the
start of the experiment. All chemicals and silver wire were obtained
from Aldrich in the highest purity available and were used without
further purification. Millipore-Q water was used as the solvent in all
experiments.
trodeposition from ammonium and sodium thiosulfate solutions
to theoretical models.
Growth
exponent
␤
Roughness Growth exponent ␤
exponent
corrected for local
effects
Solution
␣
An AFM flow cell ͑Digital Instruments͒ was used as the reaction
vessel for all experiments. A silver wire reference electrode was
placed in the inlet port, the counter electrode was a silver wire
placed in the outlet port, and a vapor-deposited silver substrate
served as the working electrode. A silver wire was connected to the
0.30 cm2 working electrode with silver epoxy ͑Chomerics, Woburn,
MA͒. The anode, cathode, and reference electrodes were connected
to an EG&G PAR model 273A potentiostat controlled by an IBM
386 computer using EG&G model 270/259 software. The cell was
cleaned prior to each experiment by soaking in concentrated sulfuric
acid and rinsing in Millipore-Q water.
Experimental
results
Ammonium thiosulfate
Sodium thiosulfate
Continuum
0.71 Ϯ 0.1
0.13 Ϯ 0.08
0.71 Ϯ 0.05 0.62 Ϯ 0.05
0.88 Ϯ 0.05 0.36 Ϯ 0.03
models
Surface diffusion11
Surface diffusion
and step growth11
KPZ equation11,19,20
Ballistic11,21,22
0.25
0.20
1.0
0.67
0.25
0.23
0.39
0.3
Deposition times were used so as to pass 0.20, 0.25, 0.30, 0.35,
0.40, and 0.45 coulomb ͑C͒ of charge per cm2. The corresponding
low thickness of the deposits was such that crystallization was mini-
mized. A constant current density of 0.8 mA/cm2 was used to ensure
that the current distribution was fairly uniform, as confirmed by the
uniform deposit thickness at various locations along the electrode.
This low current density was chosen so as to prevent depletion of
silver ions at the interface during electrodeposition. Flow analysis in
the AFM cell has indicated that the flow at the center of the substrate
was uniform.15 Consequently imaging of substrates for this work
was done in the center between the inlet and outlet ports. The vol-
ume of the AFM flow cell is very small, below 0.5 mL. To maintain
silver concentration in the bulk solution of the cell, the plating so-
lution was delivered to the cell at a very low flow rate, on the order
of 1 mL/min. This flow rate was enough to prevent depletion of
silver ions, as monitored by the cathode potential, which remained
constant throughout the experiments.
and log-plotting the roughness rms vs. time. The obtained ␤loc is
then subtracted from the experimental ␤ to obtain the universal ␤.
Various models have been used to describe surface growth. Scal-
ing parameters calculated from experimental data are commonly
compared to results of continuum growth models to gain insight on
surface growth. This is done even though the strict theoretical limi-
tations required by continuum growth models are seldom entirely
satisfied by actual experimental results. One commonly used model
to describe surface growth is the Kardar, Parisis, and Zhang ͑KPZ͒
equation.11,17 The KPZ equation is given by
ץh r,t͒
␭
͑
2
ϭ
ٌ2h ϩ
ٌh͒ ϩ ␩ r,t͒
͓4͔
v
͑
͑
ץt
2
where is the surface tension and ٌ2h describes the relaxation of
v
the interface caused by surface tension. The (ٌh)2 term reflects the
presence of lateral growth and ␩(r,t) is a noise term. The basic
nature of the equation is that the growth rate at any point depends on
the local surface geometry and stochastic noise.12 The KPZ equation
has been found to predict parameters that are close to experimentally
Vapor-deposited silver substrates were prepared at room tem-
perature at a pressure of 1.5 ϫ 10Ϫ5 Torr and an evaporation rate of
15.0 Å/s on 0.15 cm thick quartz. The resulting silver surface had a
thickness of 2.0 ␮m. Each substrate was 1 ϫ 1 cm and all the sub-
strates used in the experiments were made at the same time to insure
uniformity from experiment to experiment.
observed results.13 The precise physical interpretation of the KPZ
equation is still a topic of discussion, but is generally accepted to
apply to cases where the dominant surface relaxation mechanism is
not surface diffusion, as the equation does not conserve particle
numbers.14 The equation does take into account smoothing pro-
cesses on surfaces as the result of the filling in of recesses and the
erosion of asperities.11
A comparison between theoretical and experimentally obtained
exponents provides a valuable perspective on surface growth. Table
I gives the accepted roughness and growth exponents for the KPZ
model, surface diffusion, and surface diffusion with step growth
models. Huo and Schwarzacher6 attempted to explain anomalous
scaling of the surface width during copper electrodeposition by in-
troducing a local growth exponent ␤loc , which was found to become
significant when the rate approached the diffusion-limiting current
in the electrolyte. The current data was obtained at a current density
͑0.8 mA/cm2͒ well below the diffusion-limiting current.
Prior work by Schmidt et al.2 with copper electrodeposition from
copper sulfate was done in situ where copper was plated on gold
substrates, imaged with the AFM, and then continued to be plated
and imaged. Due to the slow capturing speed of the AFM scanning
mechanism, this method does not allow for real time data acquisi-
tion. Unfortunately, thiosulfate is such a good silver solvent that the
plating solution used here could dissolve the substrate, making the
use of in situ methods impossible. As a result, the experiments were
carried out such that each experiment used a total of six substrates,
one for each level of silver plate. After electrodeposition, the sur-
faces were carefully and thoroughly washed and dried and were
individually imaged using the AFM. It was expected that the oxida-
tion of the surface due to exposure to air did not alter the surface
morphology and roughness. Imaging with the AFM was done in
contact mode, using gold-coated Si3N4 cantilevers from Digital In-
struments.
Experimental
The silver plating solutions were prepared by dissolving silver
bromide into solutions containing sulfite and thiosulfate, because
silver bromide is not soluble in water and must be complexed with
thiosulfate. The ammonium thiosulfate plating solution contained
0.10 M of silver bromide, 0.20 M ammonium sulfite, and 0.25 M
ammonium thiosulfate. The natural pH of this solution is between
6.8 and 7.2 and was not changed. The sodium thiosulfate plating
solution contained 0.10 M of silver bromide, 0.20 M sodium sulfite,
and 0.25 M sodium thiosulfate. In both solutions this represents a
ratio of 2.5 moles of thiosulfate for every 1 mole of silver. A pre-
Results and Discussion
Silver electrodeposition on evaporated silver surfaces from am-
monium and sodium thiosulfate solutions was studied by galvano-
statically depositing various amounts of silver and then imaging
these surfaces using AFM. It was essential that the original substrate
be as flat as possible so that this initial surface will have as little
influence as possible on the electrodeposited surface characteristics.
The rms of the original substrates was on the order of a few nano-
meters.
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Journal of The Electrochemical Society, 150 ͑6͒ C375-C380 ͑2003͒
Silver electrodeposition from ammonium thiosulfate solu-
C377
tion.—Figure 1 contains 15 ϫ 15 ␮m AFM images of silver elec-
trodeposited from ammonium thiosulfate solution. During the initial
stages of electrodeposition, small nuclei are formed on the surface.
These nuclei continue to grow by incorporation of adatoms diffusing
toward them. Substantially fewer growth sites are observed, suggest-
ing that smaller sites have combined to form larger growths. The
number of growth sites significantly decreases when going from
0.20 to 0.45 C/cm2 of charge passed, and these growth sites are seen
to be taller and more lateral growth appears on the surface. As the
amount of silver plating increases, the surface roughness increases
and the sites become larger, probably due to the mechanism of
Schwoebel barriers.
Analysis of the images for roughness was done using the AFM
software.16 Each image was analyzed at different length scales, the
largest being 15 ϫ 15 ␮m, from which the rms height of the surface
was found as a function of length scale. Especially for small length
scales, up to 40 sites were measured and averaged. It was observed
that increasing the number of sites beyond 40 did not affect the rms
height results. Plots of the rms height vs. the length scale are in-
cluded in Fig. 2. Each data point in the figure represents a different
roughness measurement. For each surface the rms height increases
with length and then levels off, so that the rms height does not
change as the length scale is further increased. Each level of charge
used is represented in the figure with a different symbol.
The saturation rms height was determined by averaging the last
few data points in the saturation region. Figure 3 presents a loga-
rithmic plot of the saturation rms height vs. the deposition time for
the ammonium, as well as for the sodium thiosulfate systems. The
slope of the resultant straight line is ␤, the growth exponent, which
gives the time dependence of the total interface width. A linear
regression analysis of the data was done to determine the slope,
␤ϭ0.71. These results, as well as the results with the sodium sys-
tem, are included in Table I. This ␤ is significantly higher than the ␤
associated with any of the continuum model values included in
Table I, and probably associated with the large and rapid surface
growth of a few selected points. The local growth exponent ␤locϭ0
was calculated according to Eq. 3 and hence the universal growth
exponent remains ␤ ϭ 0.71.
The static scaling or roughness exponent, ␣, is determined by
linear regression analysis of the slope of the log-log plot of rms
height vs. length scale, in the region below the rms height saturation.
An average was calculated for each of the six levels of charge
passed ␣ ϭ 0.62 Ϯ 0.05. This ␣ corresponds best to that of surface
diffusion and step growth (␣ ϭ 0.67) in Table I, indicating that
silver electrodeposition from ammonium thiosulfate solution is a
self-affine surface dominated by surface growth mechanism. Kah-
anda et al.12 observed similar behavior for copper electrodeposition,
where the value of ␣ agreed well with a continuum model, but the
value of ␤ was significantly higher than predicted by any of the
continuum models.
Silver electrodeposition from sodium thiosulfate solu-
tion.—Figure 4 contains 15 ϫ 15 ␮m AFM images of silver elec-
trodeposited from sodium thiosulfate solution after the passage of
0.20, 0.25, 0.30, 0.35, 0.40, and 0.45 C/cm2 of charge. Progressing
from 0.20 to 0.45 C/cm2, the number of nucleation sites decreases
with increasing charge passed, and there are fewer, wider, and
higher peaks present on the surface.
Plots of the rms height variation with length scale are included in
Fig. 5. Each data point represents an individual roughness measure-
ment. As was found with the ammonium thiosulfate system, the rms
height increases with increasing measurement length scale for each
of the surfaces and then levels off to the saturation rms height. The
saturation rms height for each level of charge passed are plotted vs.
deposition time in Fig. 3 for the sodium thiosulfate system. A linear
regression of the data was done to determine the slope for this sys-
tem, ␤ ϭ 0.88. This value is included in Table I along with results
Figure 1. Silver electrodeposits from ammonium thiosulfate solution at ͑a,
top left͒ 0.20, ͑b, bottom left͒ 0.30, ͑c, top right͒ 0.45 Vertical scale: 1,
␮m/div; horizontal scale: 5 ␮m/div.
from the ammonium thiosulfate system. The value for ␤ is relatively
large, larger than any of the continuum models, and represents sur-
face growth of a few selected points that rapidly increase the rough-
ness of the surface. The local growth exponent ␤loc ϭ 0.75 was
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C378
Journal of The Electrochemical Society, 150 ͑6͒ C375-C380 ͑2003͒
Figure 2. Roughness rms vs. length scale for silver electrodeposition from
ammonium thiosulfate solution with coverage of 0.20 to 0.45C.
calculated according to Eq. 3 and hence the universal growth expo-
nent becomes ␤ ϭ 0.88 Ϫ 0.75 ϭ 0.13.
The static scaling or roughness exponent, ␣, is determined by
linear regression analysis of the slope of the log-log plot of rms
height vs. length scale, below saturation. The average calculated
␣ ϭ 0.36 Ϯ 0.03. This level of ␣ corresponds best to the KPZ
model.17,18 This agreement suggests that for the sodium thiosulfate
Figure 4. Silver electrodeposits from sodium thiosulfate solution at ͑a͒ 0.20,
͑b͒ 0.35, ͑c͒ 0.45 C. Vertical scale: 1 ␮m/div; horizontal scale: 5 ␮m/div.
system, the smoothing of self-affine surface is not dominated by
surface-diffusion processes, but rather by the erosion of asperities
and filling in of surface recesses.11
Figure 3. Saturation roughness rms vs. deposition time for silver elec-
trodeposition form ammonium and sodium thiosulfate solutions.
Comparison of results from ammonium and sodium systems.—A
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Journal of The Electrochemical Society, 150 ͑6͒ C375-C380 ͑2003͒
C379
thiosulfate system corresponds closely with what would be predicted
by the KPZ equation.
Exchange current density results23 indicate that sodium ions slow
down the kinetics as indicated by the lower value of the exchange
current density for the sodium thiosulfate system. This lower value
of i0 would result in a larger surface overpotential, which contrib-
utes to a smoother deposit from the sodium thiosulfate system.
Incorporating the rms height at a particular point of deposition,
e.g., the saturation rms height of the system after the passage of 0.35
C of charge, shows that the level of roughness in the ammonium
system was 44% greater in magnitude than in the sodium system.
This parameter can be used to make further comparisons of surfaces,
especially when the differences are less obvious.
Different ␤loc are obtained for the sodium and ammonium thio-
sulfate systems, 0.75 and 0, respectively. The universal ␤, corrected
for local effect, are therefore 0.13 and 0.71, respectively. It is not
clear why the local effect, which depends on the proximity to the
diffusion-limiting current, is significant in the sodium thiosulfate
system and is insignificant in the ammonium thiosulfate system.
Ammonium ion is known to be a complexing agent for the silver
ion, however its complexing strength is weaker than that of the
thiosulfate ion. This might explain the difference in roughness and
roughness exponents, especially since the thiosulfate-complexed sil-
ver ion is negatively charged, while the ammonium-complexed sil-
ver is positively charged. Chen et al.9 also observed that, during
underpotential deposition of silver on gold, the structure of the Ag
monolayer depends on the nature of the electrolyte.
Figure 5. Roughness rms vs. length scale for silver electrodeposition from
sodium thiosulfate solution.
Discussion
The growth of silver surfaces by electrodeposition from the two
thiosulfate solutions cannot be explained in terms of the simplistic
models like equivalent weight, KPZ, or the molecular beam epitaxy
models of surface diffusion. Indeed, in none of the systems we
looked at, did both scaling exponents ␣ and ␤ simultaneously fit the
values of any of these models. Moreover, the widely different expo-
nents found for deposition from ammonium and sodium thiosulfate
solutions and from no thiosulfate at all, imply that the notion of
universality fails in these systems. The scaling exponents change
from system to system and thus do not fall into a few universal
classes. The reasons for that are not well understood but could origi-
nate from the following phenomena:
comparison of the AFM images for silver electrodeposition from
ammonium and sodium thiosulfate solution indicates some signifi-
cant differences. At each level of charge passed, the surfaces plated
from the ammonium thiosulfate solutions are rougher than those
plated from sodium thiosulfate solutions. There are more nucleation
sites on the initial surface plated from sodium thiosulfate than from
ammonium thiosulfate solution. The surface plated from sodium
thiosulfate has more nucleation sites, and they are noticeably smaller
in magnitude. This trend is maintained throughout the series of im-
ages.
Figure 3 is a plot of saturated rms height for both the ammonium
and sodium thiosulfate systems. The rms height is greater in mag-
nitude for the ammonium thiosulfate system at all deposition times.
The slope of the line through these points gives the growth expo-
nent, which is larger for the sodium thiosulfate system than for the
ammonium thiosulfate system. This suggests that the time-
dependent dynamics of the roughening process is greater for the
sodium than for the ammonium thiosulfate system, which indicates
that the surfaces plated from sodium thiosulfate are increasing in
roughness with time faster than those plated from ammonium thio-
sulfate. This does not mean to suggest that silver plated from the
sodium thiosulfate system is rougher, but rather that the increase
with time is faster in the sodium system. The growth exponents,
after being corrected for local effects, support this trend; the cor-
rected ␤ for the ammonium thiosulfate (␤ ϭ 0.71) is significantly
larger than that for the sodium thiosulfate-supported electrolyte
(␤ϭ0.13). The incorporation of the rms height at a common depo-
sition time helps to clarify that plating from the ammonium system
is significantly rougher. The larger ␤ for the sodium thiosulfate-
supported electrolyte appears to be due to local effects ͑diffusion-
limited current͒ as evident by the large ␤loc ϭ 0.75. Ammonium ion
is known to complex silver ion, although the complexation is
weaker than that of the anionic thiosulfate.
1. Nonlocal growth.—All the above theoretical models assume
that the growth rate at a point depends only on few lower derivatives
of the surface height at that point. However, the interaction between
the ion and the surface boundary extends to a finite range given by
the screening length. Thus, depending on the extent of the screening
length, the assumption of locality might not apply. If the length is
large, local tips will grow even faster, resulting in rougher surfaces
͑in the extreme case of large screening length, this effect gives rise
to diffusion-limited aggregation clusters which are full fractal and
not just self-affine͒.
2. Crystallization.—If the deposited metal crystallizes, then the
size of the microcrystals is another important length scale of the
system. In the present work, we extracted the exponents in the re-
gime in which the correlation length is larger than the microcrystal-
ite size. In this regime, the paradigm of an amorphous self-affine
surface may still apply, but with a local correction ͑due to the crystal
formation͒ just as we find for the sodium system.
3. Convection.—The motion of the ions toward the surface is
accompanied by a convective motion of the electrolyte. Near the
surface these convection flows have a component parallel to the
surface as well. The effect of the convective flow on the surface
morphology has not been elucidated yet, although we observed that
the flow affects the scaling exponents.23
Other phenomena may also contribute to the failing of universal-
ity in our systems. The surface diffusion of silver adatoms was mea-
sured by Porter and Robinson25 at the Ag͑111͒/water interface and
The value of the roughness exponent, ␣, is larger for the ammo-
nium thiosulfate system. This suggests that the growth process for
silver electrodeposition from the ammonium thiosulfate system is
more dominated by surface diffusion and step growth than plating
from the sodium thiosulfate system. The value of ␣ for the sodium
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C380
Journal of The Electrochemical Society, 150 ͑6͒ C375-C380 ͑2003͒
was found to be similar to that obtained in ultrahigh vacuum, indi-
cating little effect of the liquid water. The surface-diffusion length
was estimated at Ͼ40 ␮m. The observed exchange current at atomic
steps was found to be ten orders of magnitude higher than at the
planar surface,25 which might contribute to the disagreement among
scaling exponents and the lack of universality in the present work.
It is important to make it clear that the KPZ model and the
Schwoebel effect have no relation to each other. Indeed, the
Schwoebel effect is present only in crystalline growth. Its origin is
in the energy barrier for an adatom from one terrace to fall down the
stair to a lower terrace. Since no such barrier exists for an adatom of
the lower terrace to diffuse and stick to the step ͑and effectively
extending the upper terrace͒ the Schwoebel effect is responsible for
a bias in the diffusion from the lower terrace to the higher one. On
a coarse-grained scale this gives rise to an effective flux of adatoms
in the direction of elevating height.
The KPZ model describes a surface which grows locally in the
normal direction to itself. On a coarse-grained scale it gives rise to a
term proportional to the square of the local gradient, resulting in a
higher growth velocity for the surface segments with higher slopes.
Crystalline surfaces do not grow in the normal direction and thus are
not described by the KPZ model ͑note that in crystalline models
used in simulations, like the ballistic deposition and the Kim-
Kosterlitz models,26 the effect of lateral growth is achieved through
nonrealistic growth rules͒.
In the early stage of electrodeposition, competition between
nucleation and growth determines the granularity and roughness of
the surface.24 The forms of the growing crystals determine the struc-
ture and appearance of the deposit. The subsequent growth of crys-
talline faces depends on the orientation of the seed crystal. The
growing front in the case of silver can be one of the close-packed
faces of the single-crystal: octahedral ͑111͒, cubic ͑100͒, or rhom-
bododecahedral ͑110͒. The emergence points of the screw disloca-
tions emerge as growth pyramids. Quadrangular pyramids are ob-
tained from Ag͑100͒, whereas triangular pyramids are obtained from
Ag͑111͒. The slope of the growing pyramids depends on the current
density employed.24 Indeed, upon prolonged silver electrodeposi-
tion, especially subjected to periodic partial dissolution, crystalline
pyramids were observed.23
Comparison of the roughness exponent, ␣, for these two systems
suggests that the difference in roughness is due to the fact that the
ammonium system is surface-diffusion-limited while the sodium
thiosulfate system is dominated by the erosion of asperities and
filling in of surface recesses. This difference is determined by the
agreement of ␣ for the two systems with accepted continuum mod-
els. The values for ␤ obtained for silver electrodeposition in these
two systems do not correspond well to any of the continuum models.
This suggests that there are important factors involved in the elec-
trodeposition process that are not being taken into account in the
continuum models. The lower exchange current density, found for
plating from sodium thiosulfate, might contribute to this difference.
Acknowledgment
D.G.F. and J.J. gratefully acknowledge the support of Eastman
Kodak Company. The support of the Office of Naval Research
͑ONR N00014-00-10057͒ is gratefully acknowledged.
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Conclusions
Comparison of silver electrodeposition from sodium and ammo-
nium thiosulfate solutions after the passage of 0.20 to 0.45 C/cm2 of
charge shows that silver electrodeposition from ammonium thiosul-
fate solutions produced noticeably rougher surfaces than those
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