voltammetric and amperometric analyses of electrochemical ...€¦ · the cv- and ps-based...

Journal ofElectroanalytical

Chemistry

Journal of Electroanalytical Chemistry 568 (2004) 121–133

www.elsevier.com/locate/jelechem

Voltammetric and amperometric analyses ofelectrochemical nucleation: electrodeposition of copper on nickel

and tantalum

Samuel B. Emery, Jennifer L. Hubbley, Dipankar Roy *

Department of Physics, Clarkson University, P.O. Box 5820, Potsdam, NY 13699-5820, USA

Received 17 August 2003; accepted 15 January 2004

Available online 20 March 2004

Abstract

We present theoretical and experimental results demonstrating how the techniques of cyclic voltammetry (CV) and potential step

(PS) amperometry can be combined for quantitative analysis of electrochemical nucleation reactions. We have integrated two ex-

isting technique-specific (PS or CV) theoretical models of 3-D nucleation in a single framework of the general nucleation rate law.

This framework provides a phenomenological basis for combining CV and PS for nucleation studies. We report two experimental

systems, involving electrodeposition of Cu2þ on Ni and Ta, that exhibit nucleation behaviors predicted from these theoretical

considerations. Deposition and stripping of Cu2þ are found to be reversible at the Ni surface, and irreversible at the (naturally

oxidized) Ta surface. For both the Ni/Cu2þ and Ta/Cu2þ systems, distinct features of 3-D nucleation are detected in CV. These

features are investigated further through detailed examination of PS-induced current transients. The common links between the

nucleation currents observed in the CV and PS experiments are discussed in detail.

� 2004 Elsevier B.V. All rights reserved.

Keywords: Copper; Current transients; Cyclic voltammetry; Nickel; Nucleation; Tantalum

1. Introduction

Electrochemical nucleation is a widely studied subject

in several areas of material fabrication where the

technique of electrodeposition is used [1–6]. The most

frequently employed technique for studying electro-

chemical nucleation is the potential step (PS) method,

also referred to as chronoamperometry [7]. Dependingon the experimental system, however, sometimes this PS

technique can be associated with two types of experi-

mental difficulties. First, all PS-induced current tran-

sients contain a component of double layer charging

that dominates the initial part of the recorded data [8,9].

The double layer current depends on the effective time

constant of the experimental cell, and this time constant

is sensitive to the voltage dependent surface coverage ofthe electrodeposited species [8]. Consequently, often it

* Corresponding author. Tel.: +315-268-6676; fax: +315-268-6610.

E-mail address: [email protected] (D. Roy).

0022-0728/$ - see front matter � 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.jelechem.2004.01.012

becomes difficult to separate the double layer and nu-

cleation currents from the amperometric data. The sec-

ond set of complications in PS measurements of fast

nucleation processes can arise from instrumental limi-

tations. If the data-sampling rate is slower than the rate

of current variations, the measured current transients

can be severely distorted; this can lead to incorrect

(smaller than actual) values for the nucleation rate and/or active site density. In an earlier work, we have dem-

onstrated the expected consequences of this instrumen-

tal artifact [8]. Due to the aforementioned reasons, it is

useful to employ an auxiliary experimental technique

with PS experiments that can independently verify the

presence of nucleation. Scanning probe microscopic

methods are sometimes used for this purpose [9–12].

These techniques can provide important morphologicaldetails of the electrode surface, but are not generally

designed to detect surface kinetics. In our present paper,

we use the simple in situ electrochemical method of cy-

clic voltammetry (CV) as an accompanying technique of

mail to: [email protected]

122 S.B. Emery et al. / Journal of Electroanalytical Chemistry 568 (2004) 121–133

PS amperometry to probe nucleation kinetics in elec-

trodeposition.

To combine CV with PS for nucleation studies, it is

necessary to link the theoretical considerations of nu-

cleation effects in the two techniques properly. In thepresent work, we establish this necessary link between

the CV- and PS-based nucleation mechanisms [7,13–15]

by treating both these mechanisms as special cases of a

general formulation based on the nucleation rate law.

We focus here on 3-D nucleation, and present experi-

mental results for two electrodeposition systems in this

category. The two systems considered here, involving

electrodeposition of Cu2þ on polycrystalline Ni and Ta,have not been previously studied in detail in the context

of electrochemical nucleation. The selection of these

systems for our present study is based on considerations

of their applications in electrocatalysis [16,17] and ma-

terial synthesis [18–20].

2. Theoretical considerations

2.1. General form of faradaic nucleation current density

We consider the cathodic electrodeposition reaction,

Ozeþ + ze� !Rad. Here, Ozeþ is the oxidized cation of

charge +zjej in the solution, e� is the electronic charge,

and Rad is the (reduced) electrodeposited species, ad-

sorbed on the substrate electrode. Such a reaction canlead to direct deposition of Rad without the formation of a

critical nucleus, or can lead to nucleation, resulting in

localized growth of the depositedmaterial.We denote the

faradaic current densities for direct deposition (DD) and

nucleation and growth (NG) as i(DD) and i(NG), re-

spectively. According to the general rate law of nucle-

ation, the latter current density has the form [15,21–25]

iðNG; tÞ ¼Z t

0

Inðt � sÞAðsÞds; ð1Þ

where t denotes time; Inðt � sÞ is the current contributionper growth site; s is the induction time; AðsÞ is the rate ofappearance of nuclei. In the absence of nucleation rate

dispersion [27], the expression for AðsÞ takes the familiar

simple form [26]

AðsÞ ¼ ðdN=dsÞ ¼ N0kN expð�kNsÞ; ð2Þwhere N is the time dependent surface density of nu-

cleation sites; N0 and kN are the saturation density of

active sites and the nucleation rate constant, respec-

tively. In most systems, N0 and kN vary with changes in

the electrode potential [21]. Two special cases, corre-

sponding to instantaneous and progressive nucleation,are obtained from Eq. (1) for large and small values of

kN, respectively.Restricting our discussion to the case of 3-D nucle-

ation, and using the standard model of hemispherical

growth [23], the general form of In can be written as [26]:

Inðt � sÞ ¼ zFqMðdV =dtÞ, with V ¼ ð2=3ÞpR3. Here, qMis the molar density of the electrodeposited species; Vand R are the time dependent volume and radius of the

nucleus, respectively. According to this description

Inðt � sÞ ¼ ½zF qM�Snðt � sÞkRðtÞ; ð3Þwhere kRðtÞ is the average rate of growth of nuclei;

Sðt � sÞ is the surface area of an individual growthcenter at time t; Sðt � sÞ ¼ 2p½Rðt � sÞ�2. Following

previous authors [15], we have assumed kRðtÞ to be in-

dependent of s, that is kRðt0Þ ¼ ½dRðt0Þ=dt� � ½dRðtÞ=dt� ¼ kRðtÞ, where t0 ¼ ðt � sÞ. Both Rðt � sÞ and kRðtÞdepend on the nature of the voltage perturbation (CV or

PS) used to activate electrodeposition. The specific

forms of Rðt � sÞ and kRðtÞ for CV and PS measure-

ments are discussed next.

2.2. Nucleation current density in cyclic voltammetry

The faradaic current density for direct cathodic

electrodeposition by CV without nucleation has the

form [28,29]

iCVðDD; tÞ ¼ zFk0Cð0; tÞ exp½�BfEðtÞ � E00g�: ð4ÞHere, the distance perpendicular to the electrode surface

is chosen along the x direction, and Cð0; tÞ is the con-

centration of Ozþ at x ¼ 0 on the solution side of the

electrode interface; k0 is the reaction rate constant;

B ¼ ðazF =RT Þ. F , a, R, T , and E00 represent the Faraday

constant, the charge transfer coefficient, the gas con-stant, the ambient temperature and the formal (thresh-

old) potential for electrodeposition, respectively. EðtÞ isvaried in CV as EðtÞ ¼ Ei � f ðtÞ, starting from an initial

voltage Ei. The voltage scan parameter f ðtÞ is defined as

f ðtÞ ¼ vt for 06 t6 T0, and as f ðtÞ ¼ vð2T0 � tÞ for

T0 6 t6 2T0 [15]; v is the voltage scan speed; 2T0 is the

period of a full voltage cycle of CV. In the presence of 3-

D nucleation in CV, ICVn ðt � sÞ ¼ ½SCVn ðt � sÞ�

½iCVðDD; tÞ�, or by using Eq. (4)

ICVn ðt � sÞ ¼ ðzF qMÞ½SCVn ðt � sÞ�aðtÞ exp½bðtÞ�; ð5Þ

where aðtÞ ¼ a0Cð0; tÞ, bðtÞ ¼ Bf ðtÞ, and a0 ¼ ðk0=qMÞexp½�BðEi � E00Þ�. By comparing Eqs. (3) and (5), one

obtains the CV-induced growth rate kCVR of individualnucleation sites

kCVR ðtÞ � kCVR ðEÞ ¼ a0Cð0; tÞ exp½bðtÞ�: ð6ÞThe corresponding expression of the nucleation/

growth current iðNG; tÞ from Eq. (1) is written as

iCVðNG; tÞ � iCVðNG;EÞ

¼ ðzF qMÞkCVR ðE; tÞZ t

0

SCVn ðE; t � sÞAðsÞds:

ð7ÞThe radius, RCVðt � sÞ of an individual growth site

can be determined by integrating Eq. (6)

S.B. Emery et al. / Journal of Electroanalytical Chemistry 568 (2004) 121–133 123

RCVðtÞ ¼ a0

Z t�s

0

Cð0; tÞ exp½bðtÞ�dt: ð8Þ

Numerical evaluation of Eq. (8), is rather complicated

due the voltage dependent as well as diffusion controlled

term Cð0; tÞ [28,29], and will not be considered in the

present work. In the following discussion, we examinethe main implications of Eq. (7).

In the absence of nucleation, iCVðDD;EÞ, exhibits a

peak as E is scanned cathodically (06 t6 T0) through

the region of electrodeposition [29]. In the reverse (an-

odic) voltage scan (T0 6 t6 2T0), this current becomes

positive, usually shows an anodic stripping peak, and

then approaches its initial pre-scan value (at Ei), without

crossing over the current of the cathodic half-cycle. Ifthe variations of the double layer charging current is

small compared to those of iCVðDD;EÞ (which usually is

the case in CV), the resulting voltammogram follows the

behavior of the faradaic current [28]. A large number of

systems involving foreign metal deposition on metals are

characterized by this type of simple ‘‘uncrossed’’ vol-

tammogram [30]. However, as noted by Fletcher et al.

[13–15], this simple situation is likely to change in thepresence of 3-D nucleation. Depending on the values of

B, v, Cð0; tÞ and E00 in Eq. (7), the current density

iCVðNG; tÞ during the positive half-cycle can cross over

the corresponding current of the cathodic half-cycle.

This effect occurs as a result of the current density

iCVðNG; tÞ going through a maximum in the positive

scan during T0 6 t6 2T0. It is the resulting ‘‘crossed

voltammogram’’, that carries the signature feature ofnucleation in CV [15].

The variations of iCVðNG; tÞ in Eq. (7) and hence, the

criteria for the observation of a crossed voltammogram

of nucleation are determined by the relative values of a,z, v, E00, T0, D, and Cb (bulk concentration of Ozeþ).Nevertheless, it is also possible in some cases, that just

one or two of these parameters (irrespective of the val-

ues of the rest) would dictate a sufficient condition forthe occurrence of a crossed voltammogram of nucle-

ation. Let us show that such a condition in fact exists

provided (i) kCVR does not depend strongly on E, and (ii)

the electrodeposition reaction is predominantly charge

transfer limited, with Cð0; tÞ � Cb at all times during the

CV experiment. According to Fletcher et al., the suffi-

cient condition for the occurrence of a crossed voltam-

mogram in the description of Eq. (7) (i.e., the conditionfor a maximum in iCVðNG; tÞ during T0 6 t6 2T0) is

written as [15]

2 kCVR ðT0Þ� �2

PZ T0

0

kCVR ðtÞdt� �

d

dtkCVR ðtÞdt

� ��T0þdt

; ð9Þ

where dt � 0. In the charge transfer limited case, Eq. (6)

is simplified as kCVR ðtÞ ¼ a0Cb exp½bðtÞ�, and using this

last expression, the left hand side of Eq. (9) is calculated

to be ða0CbÞ2 exp½2BvT0�. The first and second terms on

the right hand side of Eq. (9) are evaluated as

½a0Cb=Bv� exp½BvT0 � 1�, and as a0CbB expðBvT0Þ, re-

spectively. Incorporating these results in Eq. (9), one has

2 expð2BvT0ÞP expð2BvT0Þ � expðBvT0Þ: ð10ÞThe sufficient condition for a crossed voltammogram, as

expressed in Eq. (10), is valid regardless of the values of

B, v and T0, as long as active electrodeposition ismaintained by satisfying the requirement jEðT0Þj > jE00j.The conditions for a crossed voltammogram in the dif-

fusion limited case are more complex and depend on

several experimental parameters.

2.3. Nucleation current density in potential step amper-

ometry

Several authors have discussed various theoretical

aspects of this particular case [2,24,31–33]. Nevertheless,

a number of different models of PS-induced nucleation,

varying both in treatments and notations, are found in

the literature [21]. Here we briefly summarize certain

main equations of potentiostatic nucleation by using the

theoretical approach (general rate law) considered in

Eqs. (1)–(3). This will allow us to note the parallel fea-tures of potentiodynamic and potentiostatic nucleation

processes in a common theoretical framework. If 3-D

nucleation is activated by a cathodic PS from Ei > E00 toE < E00 at t ¼ 0, the current contribution of each growth

site is expressed as [15,23]

IPSn ðt0Þ ¼ zFD½SPSn ðt0Þ� oCðr; t0Þ

or

� �r¼R

; ð11Þ

where r denotes the radial coordinate for hemisphericaldiffusion; t0 ¼ ðt � sÞ; Cðr; t0Þ is the concentration profile

of the electroactive cation Ozþ at time t � s and at a

distance r away from the nucleus-center. Assuming that

Rðt0Þ � ðpDt0Þ1=2, it is possible [23] to write

½oCðr; t0Þ=orÞ�r¼R � ½Cb=Rðt0Þ�. Using this last expression

in Eq. (11), and comparing the resulting expression with

Eq. (3), we get the rate constant kPSR of hemispherical

growth in PS amperometry

kPSR ðtÞ ¼ dRðtÞdt

� �PS¼ DCb

qM

� �1

RPSðtÞ : ð12Þ

Integration of Eq. (12) gives the radius of a PS-deposited

hemispherical island

RPSðt � sÞ ¼ ½ð2DCb=qMÞðt � sÞ�1=2: ð13ÞThe formula for RPSðtÞ is found by replacing ðt � sÞ witht in Eq. (13): RPSðtÞ ¼ ½ð2DCb=qMÞt�

1=2. Incorporation of

this formula in Eq. (12) gives

kPSR ðtÞ ¼ ðDCb=2qMÞ1=2t�1=2: ð14Þ

By using Eqs. (13) and (14) in the general nucleation

expressions of Eqs. (1)–(3), and accounting for overlap

of diffusion zones according to Avrami’s theorem


(discussed in the Appendix A), we get the expression for

diffusion controlled nucleation current density as de-

fined in Scharifker and Mostany’s [33] model

iPSðNG; tÞ ¼ a0ffiffit

p 1½ � exp f � b kNtð � 1þ exp ð � kNtÞÞg�;

ð15Þwhere

a0 ¼ c=ðpkdDÞ ¼ zFCbðD=pÞ1=2;

c ¼ ðpzF Þ½q�1=2M ð2DCbÞ3=2�;

b ¼ ½ðpkdDN0Þ=kN�;

kd is a dimensionless parameter, kd ¼ ð8pCb=qMÞ1=2

. Thecommonly known special cases of instantaneous nucle-

ation (IN) and progressive nucleation (PN) follow from

Eq. (15) for large and small values, of kN, respectively.Denoting the current for these two cases as iPSðIN; tÞand iPSðPN; tÞ, one writes

iPSðIN; tÞ ¼ ða0=ffiffit

pÞ 1½ � exp ð � bItÞ�; ð16Þ

iPSðPN; tÞ ¼ ða0=ffiffit

pÞ 1�

� exp� bPt

2�; ð17Þ

where bI ¼ bkN, and bP ¼ bk2N=2. In Appendix A of this

report, we have summarized certain implications of Eqs.

(15)–(17) that can be noted from the general consider-

ations of Eqs. (1)–(3), and are relevant in the context of

our present work.

In the formulation of Eq. (15), the expansion of the

diffusion layer is assumed to be independent of the nu-cleation rate constant [21,22]. Any possibility of partial

charge transfer in the electrodeposition reaction is also

neglected here. Furthermore, Eq. (15) assumes that the

diffusion and growth processes are not affected by any

complex effects of surface blocking by products of side

reactions. This last effect, in particular, is often associ-

ated with certain metal electrodes (including Ni and Ta)

that are likely to contain native oxides [34]. These oxidesare likely to be spatially inhomogeneous across the

electrode surface and thus, may change the nucleation

efficiency of an oxide-free uniform surface. Here, we

account for the above-mentioned factors in a strictly

phenomenological way, by introducing a time indepen-

dent dimensionless current-scaling factor H. In other

words, we replace a0 in Eqs. (16) and (17) with a new

parameter a0H. In this simplistic approach, we have twofitting parameters, H and N0 to test for IN by using Eq.

(16), or H and N0kN to test for PN by using Eq. (17).

3. Experimental

The instruments and experimental procedures used in

this work are discussed elsewhere in detail [34–37]. Inbrief, the Ni and Ta working electrodes, both 6.5 mm

diameter polycrystalline cylinders (mounted in Teflon

holders) were polished down in several steps, with 1, 0.3,

0.1 and 0.05 lm alumina abrasives. Electrolytes of 0.1 M

NaNO3 + y mM Cu(NO3)2 (y ¼ 0 or 0.6) were prepared

with triply distilled water and ultrapure chemicals, and

were purged with ultra high pure Ar before each ex-periment. All experiments were performed at room

temperature. The three-electrode experimental cell used

a Pt counter electrode and a saturated calomel electrode

(SCE). The cell was controlled by a high-resolution fast

(1 MHz) potentiostat [8] interfaced with a computer via

a 16-bit data acquisition card from National Instru-

ments. Data acquisition and processing were performed

using LabVIEWTM-based programs developed by ourgroup. Experimental data for CV (at 10–100 mV s�1)

were typically collected at the rate of 20–100 data points

s�1. An adequate rate of data acquisition [8], typically at

1000 points s�1, was used for PS measurements. PS data

were collected both in the absence and in the presence of

Cu2þ, with all other experimental parameters main-

tained at their respective values in the two cases. The

difference of these two current transients, that is thebackground-corrected electrodeposition current was

compared with calculated nucleation models.

4. Results and discussion

4.1. Electrodeposition of Cu on Ni by cyclic voltammetry

Fig. 1(A) shows cyclic voltammograms for Ni in

Cu2þ-containing (solid line plot a) and ‘‘blank’’ (dashed

line plot b) electrolytes. The voltage is scanned at 10 mV

s�1 between 0:9 and �0:4 V. The cathodic current in the

forward cycle (0:9 ! �0:4 V) represents deposition of

Cu2þ on Ni, and the anodic peak in the reverse cycle

represents stripping of this deposited Cu. The single

deposition (as well as stripping) feature indicates thatseparate 2-D (underpotential deposition, or upd) and 3-

D (bulk) deposition processes are not operative here

[30]. Using a previously reported potentiostatic method

[34,35,38], we have confirmed that Cu2þ deposition on

Ni under the conditions of our present experiment oc-

curs predominantly in a 3-D mode. The main striking

feature of the voltammogram (a) in Fig. 1(A) is that the

plot during the anodic part of the cycle crosses over theplot of the cathodic cycle. Such a ‘‘crossed’’ voltam-

mogram is not an usual feature of direct deposition, but

as explained in the context of Eq. (9), is indeed expected

in the presence of 3-D nucleation [13–15]. Numerous

examples of such crossed voltammograms are also

found in the published literature on electrodeposition

[1,39–51]. However the origin of these relatively unusual

voltammograms is rarely discussed [13–15,39,47–49].In view of the above discussion, Fig. 1(A) shows ev-

idence for 3-D nucleation of electrodeposited Cu on Ni.

Following Fletcher et al., here we will use the term

Fig. 1. Cyclic voltammograms for electrodeposition of Cu2þ on Ni in

0.1 M NaNO3 + 0.6 mM Cu(NO3)2, recorded with different negative

limits, En, of the voltage scan. The applied voltage E is cycled at 10 mV

s�1 in the range, 0.9! En !0.9 V. En ¼ �0:40 V (solid line (a) in A),

�0:36 V (solid line (a) in B), �0:32 V (dashed line (b) in B), �0:28 V

(solid line (a ) in C), �0:24 V (dashed line (b) in the inset of panel C).

The arrows indicate directions of voltage scans. The dashed line in A

shows the double layer charging current for En ¼ �0:40 V in the Cu2þ-free solution. When En becomes more negative than �0:30 V, the

current (only in the presence of Cu2þ) during the anodic (increasing

voltage) cycle intersects and crosses over the current of the cathodic

(decreasing voltage) cycle.


‘‘crossover voltage’’ (denoted as Ec) to refer to the point

in CV where the currents of the forward and reverse

cycles intersect. Both kCVR and SCVn in the expression of

ICVn are complicated functions of E and t. Thus kCVR , as

well as SCVn has two separate origins of its time depen-

dence; one is from voltage effects coming through the

time dependence of EðtÞ in CV, and the other is asso-ciated with cumulative effects of aging of the nucleation

centers. In the present work, we do not attempt any

rigorous calculation of Eq. (7) to resolve these detailed

interfering effects of E and t. Instead, we examine the

overall features of the experimental data, using the

general considerations of Eqs. (5)–(8).

To locate the cathodic voltage threshold for electro-

deposition and nucleation, we perform a series of CVexperiments, where we keep the positive limits of all

voltage cycles fixed at 0.9 V, and change the corre-

sponding negative limits En in successive cycles. The

results of these experiments are shown in Fig. 1(B) and

(C), where En ¼ �0:36, �0:32, �0:28 and �0:24 V, for

(a) in B, (b) in B, (a) in C and (b) in C, respectively. The

deposition and stripping features become smaller as En

is made less negative (in panel B), eventually disap-pearing as En turns less negative than �0:30 V (in panel

C). In the plots of panel C, the voltammograms for the

Cu2þ-containing solution do not exhibit any intersecting

features of nucleation, and become very similar to the

voltammograms (like plot (b) in A) of the Cu2þ-freesolution. The last observation indicates that the processof electrodeposition itself stops at voltages less negative

than �0:30 V.

If the nucleation reaction is reversible and charge

transfer limited throughout the entire voltage range of

CV, the cross-over potential Ec should not vary with

variations in En. On the other hand, if the deposition

reaction becomes diffusion limited at large negative

values of En, then Ec shifts in the opposite direction ofany shifts in En [15]. The results of Fig. 1 indicate a

similar situation, suggesting the presence of diffusion

limited mass transfer. Ec in Fig. 1 shifts against the shifts

in En, having the values of �0:13, �0:11 and �0:09 V for

En at �0:32, �0:36 and �0:40 V, respectively. We note

in the present context that in some earlier reported ex-

periments, crossed voltammograms with more than one

crossover points have been observed [1,39,41,43–45]. Aswe will show in Section 4.3, the Ta/Cu2þ system also

falls in this latter category. In the description of Eq. (7)

such nucleation systems can be characterized in terms of

multiple current maxima in the anodic half-cycle.

In a separate set of experiments (results not shown

here), we tested if nucleation of electrodeposited Cu on

Ni depended on the voltage scan speed v. Variation of vbetween 5 and 50 mV s�1 always yielded crossed vol-tammograms, indicating the presence of nucleation in all

these scans. For vP 100 mV s�1, the voltages changed

too fast to support electrodeposition. Based on these

results, and those of Fig. 1, we conclude that under the

experimental conditions of our present study, nucleation

of Cu on Ni is active as long as deposition of Cu2þ is

active. Because deposition of Cu2þ is a precondition for

nucleation of Cu on the electrode surface, features ofnucleation are observed only under conditions that al-

low for measurable electrodeposition.

4.2. Electrodeposition of Cu on Ni by potential steps

Let us now verify the findings of the CV experiments

of Fig. 1 by using an independent set of PS measure-

ments. We initially hold the Ni sample in a Cu2þ-con-taining solution at 0.3 V, where deposition of Cu2þ is

absent. Subsequently, we step E to a cathodic value in

the active region of electrodeposition, and after a certain

time, we apply an anodic stripping scan at 10 mV s�1,

increasing up to 0.9 V, to remove the PS-deposited Cu.

The current transients observed in these experiments can

be described as iPS ¼ iPSðNGÞ þ iPSb , where iPSb is the

background current, consisting of the nonfaradaicdouble layer charging current as well as any other far-

adaic currents due to cathodic side reactions. We repeat

each step experiment in both Cu2þ-free ðCb ¼ 0Þ and

Fig. 3. Comparison of experimental (points) and calculated (solid lines)

potentiostatic current transients due to electrodeposition of Cu2þ on

Ni at different step voltages, (A) �0:32 V, (B) �0:34 V and (C) �0:36

V. The dotted line curves in A, B and C are results of subtracting

current transients recorded in the absence of Cu2þ from corresponding

transients collected in the presence of 0.6 mM Cu2þ in the electrolyte.


Cu2þ-containing ðCb 6¼ 0Þ solutions, measuring the

electrode currents iPSðCb ¼ 0Þ and iPSðCb 6¼ 0Þ in the

two cases, respectively. The actual nucleation/deposition

current density is obtained as a function of step voltage

by writing

iPSðNG;EÞ ¼ iPSðCb 6¼ 0Þ � iPSðCb ¼ 0Þ: ð18ÞFig. 2 shows illustrative experimental data for

iPSðCb ¼ 0Þ (in panels A, B and C) and iPSðCb 6¼ 0Þ (in

panels D, E and F). The potential steps are applied at

t ¼ 0 from 0.3 to �0:28 V (A and D), �0:34 V (B and E),and �0:40 V (C and F). The inset of each panel shows

the first 0.02 s of the current transient in that panel. The

detailed variations between the two sets of graphs in

the two columns of Fig. 2 are detected after subtracting

the current densities in the left column from their

counterparts in the right column according to Eq. (18).

Typical background-subtracted experimental current

densities, iPSðPN;EÞ are shown by the dashed lines inFig. 3.

In the CV data of Fig. 1, we have seen evidence for

nucleation under diffusion control. Therefore, it is now

necessary to test if the PS data of Fig. 3 also agree with

the description of diffusion controlled nucleation. Using

both Eqs. (16) and (17) as trials, we find that Eq. (16) for

diffusion limited instantaneous nucleation shows good

agreement with the experimental data. The solid lines inFig. 3 represent iPSðINÞ, calculated from Eq. (16) using

two voltage dependent fitting parameters, N0 and H.

These two parameters will be further discussed in the

context of Fig. 9. Here, we note that the agreement

between experimental and calculated current transients

Fig. 2. Potentiostatic current transients in the first 0.5 s following

variable voltage steps applied to a Ni electrode in 0.1 M NaNO3 (A–C,

double layer charging) and in 0.1 M NaNO3 +0.6 mM Cu(NO3)2 (D–

F, double layer charging in the presence of Cu2þ deposition). Each plot

contains 1000 data points s�1. The inset in each panel shows a close-up

view of the first 0.02 s following the voltage step. The steps are applied

from an initial voltage of 0.30 to �0:28 V (in A and D), �0:34 V (in B

and E), �0:40 V (in C and F).

for Cu2þ deposition on Ni is quite reasonable in the

entire range (�0:28 to �0:40 V) of step voltages we

explored. This confirms the predictions of the CV results

of Fig. 1 about the diffusion controlled characteristics of

electrodeposited Cu on Ni. A comparison of the overallcurrents in Figs. 1 and 3 shows that the PS currents are

considerably larger than the CV currents. This is not

surprising, because the magnitude of iðNGÞ is governedprimarily by the two parameters RCVðt � sÞ and kRðtÞ,and as noted in Eqs. (6), (8), (13) and (14), these

parameters can be very different for CV and PS

measurements.

4.3. Electrodeposition of Cu on Ta by cyclic voltammetry

Cyclic voltammograms for Ta in 0.1 M NaNO3 +0.6

mM Cu(NO3)2, collected with different negative scan-

limits En are shown in Fig. 4 by the plots in B and C, and

by plot (a) in A. The experimental parameters are noted

in the figure caption. The featureless plot (b) in panel A

is a voltammogram collected in 0.1 M NaNO3. All othervoltammograms recorded at less negative values of En

(not shown here) in the Cu2þ-free ‘‘blank’’ electrolyte

are similarly featureless. As in the case of Cu2þ depo-

sition on Ni in Fig. 1, the crossed voltammograms for

Cu2þ deposition on Ta in Fig. 4 also exhibit signature

features of nucleation. If En is less negative than �0:25 V(for example, for plot (b) in panel C), the voltammo-

gram is no longer crossed, and appears like those re-

Fig. 4. Cyclic voltammograms for electrodeposition of Cu2þ on Ta in

0.1 M NaNO3 + 0.6 mM Cu(NO3)2, where the negative limit of the

cycle is varied in successive scans. The applied voltage is scanned at 10

mV s�1 in the range, 0:3 ! En ! 0:3 V. En ¼ �0:60 V (solid line (a) in

A), �0:50 V (solid line (a) in B), �0:40 V (dotted line (b) in B), �0:20 V

(solid line (a) in C) and �0:10 V (inset plot (b) in panel C). The arrows

indicate directions of voltage scans. The dashed line (a) in panel A

shows the double layer charging current, for En ¼�0:60 V in 0.1 M

NaNO3. When En becomes more negative than �0:25 V, the current

(only in the presence of Cu2þ) during the anodic half-cycle crosses overthe current of the cathodic half-cycle.


corded in the blank electrolyte. This suggests that elec-

trodeposition of Cu2þ on Ta starts near �0:25 V, andthat nucleation occurs as long as this deposition reaction

is operative. This threshold voltage for deposition of

Cu2þ on Ta is noticeably close to the corresponding

deposition voltage of �0:30 V observed for the Ni/Cu2þ

system in Fig. 1. This observation is consistent with the

work function considerations for electrodeposition [52].

The work functions of Ni and Ta are similar, 4.5 eV [53]

and 4.2 eV [54], respectively. Therefore the depositionvoltages for Cu (work function of 4.4 eV [55]) are likely

to be similar in the cases of Ni and Ta substrates.

In the nucleation voltammograms for Ni, we ob-

served a single crossover point. However, in the case of

Ta in Fig. 4, depending on the negative voltage limit of

voltage CV, we sometimes (as in A) observe two such

points. Another major difference between the nucleation

voltammograms for Ni and Ta is that for Ni, a clear Cu-stripping peak is observed in the anodic scan, whereas

for Ta, no such stripping peaks are observed. This im-

plies that unlike the case of Ni, Cu2þ on Ta is deposited

irreversibly. Nevertheless, as for Ni, Ec for Ta depends

on En. The primary crossover point (where the current is

close to zero) occurs at �0:02, 0:00, and 0:02 V, for En at

�0:40, �0:50 and �0:60 V, respectively.

The observed differences between the substrate be-

havior of Ni and Ta are probably associated with dif-

ferent amounts of native oxide-contents of the two

electrodes. Unlike single crystal noble metals [10,56],

both the polycrystalline Ni [57,58] and the Ta [59]electrodes used here contain native oxides at their sur-

faces. However, the Ta surface is likely to contain more

native oxides (predominantly Ta2O5) than the Ni (NiO)

surface [59–61]. The native (�30–50 �A thick) film of

Ta2O5 on Ta is a semiconductor, and is responsible for

the so-called ‘‘valve effect’’ (or ‘‘diode effect’’) that

causes the resistance against anodic reactions (such as

Cu-stripping in the present experiment) to be muchlarger than the resistance against cathodic reactions

(such as Cu2þ deposition in the present work) [62]. Ir-

reversible electrodeposition of Cu2þ on Ta, as observed

in Fig. 4 is most likely a consequence of this valve effect.

The lattice constants of Ni (3.52 �A) and Ta (3.30 �A) are

comparable in their un-oxidized states [63], but the rel-

atively more oxidized Ta surface should be rougher

[62,65,66]. It is possible that through interactions, theoxide species of Ta act to induce irreversible lattice in-

corporation or alloying of the deposited Cu (atomic

diameter 2.56 �A [63]) on Ta. A similar case of surface

alloy formation during electrodeposition of Cu on

polycrystalline Pt has been reported [64]. It is also pos-

sible that irreversible lattice incorporation of Cu con-

tributes to the occurrence of double cross-over points

observed in CV of the Ta/Cu2þ system.To further explore the role of Ta-oxides in nucleation

of electrodeposited Cu, we perform a series of CV

measurements where the Ta substrate is intentionally

oxidized under voltage control. We use four successive

cycles of the voltage sequence, 0:3 V ! 1:4 V !�0:6 V ! 0:3 V, where the thickness of the surface

Ta2O5 film grows in successive voltage cycles. An anodic

charge of 1 mC cm�2 corresponds to an additionalgrowth of Ta2O5 by �5 �A [62,66]. The results for the

first three cycles are shown in Fig. 5(A). The dashed and

solid line plots (a) and (b) represent E and iCV as func-

tions of time, respectively. Unlike the CV cycles of

Fig. 4, the Ta surface in Fig. 5 is first scanned in the

anodic direction, introducing irreversible electro-oxida-

tion before the first activation of the Cu2þ deposition

reaction. The first (left-most in Fig. 5(A)) anodic currentpeak corresponds to this oxidation reaction [62,66]

2Taþ 5H2O ¼ Ta2O5 þ 10Hþ þ 10e� ð19Þ

The faradaic steps of Eq. (19) involve charge transport

through the oxide film according to a ‘‘high-field’’

mechanism discussed previously [66]. The relatively

small cathodic current features observed in the�0:3 ! �0:6 V region of each cycle in A represent

electrodeposition of Cu2þ. A magnified view of these

cathodic features is presented in Fig. 5(B). The magni-

fied cathodic currents for voltage cycles 1–4 are plotted

Fig. 5. Panel A shows a time versus voltage plot (graph (a)) and an

unfolded voltammogram (time vs current plot (b)) for electrodeposit-

ion of Cu2þ on Ta in the presence of voltage activated oxidation of Ta.

Panel B shows a close-up view of the cathodic current peaks observed

in plot (b) of panel A. Results are shown for the first three successive

voltage cycles of four cycles recorded in the range,

0:3 ! 1:4 ! �0:6 ! 0:3 V, at 10 mV s�1 in 0.1 M NaNO3 + 0.6 mM

Cu(NO3)2. The main anodic current peak observed during the initial

part (0:3 ! 1:4 V) of the first cycle corresponds to irreversible electro-

oxidation of Ta. The cathodic current peaks in panel B represent ir-

reversible electrodeposition of Cu2þ on the oxidized Ta surface.


in the form of conventional folded voltammograms in

panels A–D of Fig. 6. The cathodic currents for Cu2þ

deposition on the electrochemically oxidized Ta in Fig. 6

are considerably smaller than those observed in Fig. 4

where the Ta electrode is covered by a thinner film ofnative oxides. In the first three of the four cycles con-

sidered in Fig. 6, the Ta2O5 layers of the Ta electrode are

thin enough to permit cathodic electrodeposition of

Fig. 6. Test for nucleation effects using voltage vs current plots (folded

voltammograms) of selected sections of the current data shown in Fig.

5. The voltage region between 0.40 and �0:60 V of the first, second,

third and fourth voltage cycles are shown in panels A, B, C and D of

Fig. 6, respectively. The arrows indicate directions of voltage scans.

Crossed voltammograms, indicating nucleation of electrodeposited Cu

on Ta are observed during the first three cycles (A–C). This feature of

nucleation is absent in the voltammogram of the fourth cycle where the

electrodeposition reaction is completely blocked by thick Ta2O5 films.

Cu2þ, although anodic stripping of Cu is completely

blocked in these cycles. Here, the primary cross-over

point exhibits a weak shift, passing through the values,

�0:15, �0:16 and �0:18 V, for the first, second and third

cycles, respectively. In view of the discussion of Fig. 4,the direction of these shifts implies that the effects of

increasing the oxide-content of the Ta surface is essen-

tially equivalent to making En less negative. Less nega-

tive En implies slowing down of the electrodeposition

reaction with lower driving potentials. Therefore, the

thicker the surface oxide layer, the weaker is the rate of

Cu2þ deposition. This scenario is consistent with the

aforementioned valve effect that leads to inhibition ofCu2þ deposition by Ta oxides. During the fourth cycle in

Fig. 6(D), the Ta2O5 layer of the electrode becomes too

thick to allow any Cu2þ deposition, and the crossover

feature of nucleation disappears from the voltammo-

gram. This implies that the electrodeposition reaction

itself ceases on a heavily oxidized Ta surface.

4.4. Electrodeposition of Cu on Ta by potential steps

Fig. 7 shows typical potentiostat current transients

for Ta collected at different step voltages in the absence

(left column) and in the presence (right column) of 0.6

Fig. 7. Potentiostatic current transients in the first 0.5 s following

variable voltage steps applied to a Ta electrode in 0.1 M NaNO3 (A–D,

double layer charging) and in 0.1 M NaNO3 + 0.6 mM Cu(NO3)2 (E–

H, double layer charging in the presence of Cu2þ deposition). The inset

of each panel shows a close-up view of the first 0.02 s following the

voltage step. The steps are applied from an initial voltage of 0.30 to

�0:20 V (A and E), �0:30 V (B and F), �0:40 V (C and G), and �0:50

V (D and H).


mM Cu2þ in 0.1 M NaNO3. The initial pre-step voltage

is 0.3 V in all cases, and the different step voltages are

noted in the figure caption. Typical background sub-

tracted experimental current transients for electrode-

position of Cu2þ on Ta (Ta2O5) are shown with thedotted lines, labeled (a), in Fig. 8. The magnitudes of

these Cu2þ deposition currents are significantly smaller

than the corresponding currents observed in Fig. 3 for

the Ni electrode. This implies that kPSR ðtÞ and SPSn in the

expression of iPS for the oxide-coated Ta are smaller

than their respective values in the case of the compara-

tively oxide-free Ni. At step voltages P�0.2 V, the iPS

data for Ta exhibit shapes very similar to those observedin the case of the Ni electrode. Fig. 8(A) is an example of

this simple case. At more negative step voltages, how-

ever, the time dependent behavior of iPS for Ta deviates

from that of iPS for Ni. Examples of this latter case are

shown in Fig. 8(B)–(D), where the current recovers from

its initial spike, and then exhibits a secondary, slowly

varying broad feature. These latter current transients are

typical of systems where multiple faradaic reactions,including different nucleation processes operate

[9,10,48,67].

It is expected that the native oxides of the Ta elec-

trode play a crucial role in the manifestation of different

nucleation mechanisms observed in Fig. 8. However,

Fig. 8. Comparison of experimental (graphs (a), indicated by points)

and calculated (solid lines) potentiostatic current transients due to

electrodeposition of Cu2þ on Ta at different step voltages, (A) �0:20 V,

(B) �0:30 V, (C) �0:40 V and (D) �0:50 V. The dotted curves are

obtained by subtracting current transients recorded in Cu2þ-free so-

lutions (like those in the left panels of Fig. 7) from corresponding

current transients recorded in Cu2þ-containing solutions (like those in

the right panels of Fig. 7). The calculated plots, labeled as (b), are

obtained from Eq. (16). These plots match the entire experimental

current transient in A, and the earliest short segments, 06 t6 t1, ofdata in B–D. The end of this segment, t1, is indicated by the left vertical

arrow pointing on the time axis. The calculated plots (b) are obtained

from Eqs. (20)–(22), and match the segments of the experimental

current transients starting at the time t2. In B, t1 � t2 ¼ 0:055 s; in C

and D, t2 is indicated by the right vertical arrow on the time axis. In C,

t1 ¼ 0:078 s and t2 ¼ 1:205 s. In D, t1 ¼ 0:061 s and t2 ¼ 1:124 s.

considering the complex nature of the nucleation pro-

cesses operating in such a case, it is unlikely that these

effects can be adequately described in terms of the cur-

rently available simple nucleation models for flat, oxide-

free electrodes [21,68]. In the following, we examine ifthe main features of the experimental data in Fig. 8 can

be explained, at least qualitatively, by using the standard

existing models of potentiostatic nucleation.

We used a number of simple trial models based on

commonly used formulas to examine the current tran-

sients of Fig. 8(B)–(D). We limited these trials to a

maximum number of three current-components to avoid

incorporation of too many unknown variables in ouranalysis. The model that seems to give reasonable results

is characterized by the following expression

iPS ¼ iPSðCb 6¼ 0Þ � iPSðCb ¼ 0Þ

¼ iPSðINÞ� �

06 t6 t1þ iPS0ðNGÞh i

tP t2þ iPSs� �

tP t3: ð20Þ

In this equation, we assume two types of nucleation

currents, including one due to simple diffusion con-trolled instantaneous nucleation, iPSðINÞ as expressed in

Eq. (16), and another one, iPS0ðNGÞ, due to a secondary

progressive nucleation mechanism. Following previous

authors [69], we also assume that a side reaction, re-

sulting in a steady state faradic current iPSs is activated by

the nucleation processes. In addition, iPSðINÞ is assumed

to be active during an initial post-step interval of length

t1. The currents iPS0ðNGÞ and iPSs are activated at times t2and t3 after the step, respectively. To choose an appro-

priate model for iPS0ðNGÞ, we note that Cu2þ deposition

on Ta is irreversible and most probably associated with

a 3-D progressive nucleation process involving lattice

incorporation. Armstrong et al. [70] have modeled this

effect in terms of overlapping right circular cones, grown

on a plane surface, and according to this model

iPS0 ¼ a0½1� expð�b0t3Þ�; ð21Þ

b0 ¼ ðpk2gN0kNÞ=ð3q2MÞ; ð22Þ

where a0 ¼ ZFk0g; kg and k0g are the rate constants for thevertical and lateral growth components of the conical

nucleus, respectively. To compare the above descriptionof Eqs. (20)–(22) with the experimental data, we take a

simple case by setting t2 ¼ t3 in Eq. (20), along with the

assumption that iPS0½ �t6 t2¼ iPSs

� �t6 t2

¼ 0. In this simple

description, the current in Eq. (20) is characterized by

three discrete time zones: (I) An early stage, 06 t6 t1,where iPSðINÞ 6¼ 0, but iPS0ðNGÞ ¼ iPSs ¼ 0. (II) An in-

termediate transition stage, t1 6 t6 t2, where all or se-

lective components of the three currents on the righthand side of Eq. (20) are nonzero. (III) A late stage,

tP t2, where iPSðNGÞ ¼ 0, but iPS0ðNGÞ þ iPSs 6¼ 0. The

side reaction (iPSs ) is considered only when lattice in-

corporation of Cu is active, and can be assumed to be a

Fig. 9. Voltage dependences of the active site density (N0, circles) and

the phenomenological current-scaling factor (H, triangles) for elec-

trodeposition of Cu2þ on Ni (panel A) and Ta (panel B). The lines

through the symbols indicate the general trends of the plots.


catalytic cathodic reaction [38] promoted by the nucle-

ation sites. Examples of iPSs include oxygen reduction,

hydrogen evolution, and/or the reduction reaction Cu2þ

+ e� ¼ Cuþ [37,38,69]. In our analysis, we will focus on

fitting the experimental data in regions I and III, andwill examine only qualitatively the length of the transi-

tion region II. Calculated results, based on the above

considerations are shown by the solid lines labeled (b)

and (c) in Fig. 8(B)–(D). The values of t1 and t2 obtainedfrom these calculations are indicated by the arrows in

the figure and are listed in the figure caption.

In Fig. 8(B), plot (b) shows the iPSðINÞ component of

iPS calculated from Eq. (16). This calculated plot onlymatches a short initial time segment (0 < t < t1) of theexperimental data. The remaining segments of the data

in Fig. 8(B) fit reasonably to plot (c), which represents

the calculated current components of the last two terms

of Eq. (20). Thus, the data in Fig. 8(B) can be described

only in terms of the currents of regions I and III (that is,

using t1 ¼ t2), and without incorporating the transition

region II. In Fig. 8(C) and (D), however, we find thatt1 6¼ t2, and that a finite transition region II exists in the

interval t2 � t1. Plots (b) in Fig. 8(C) and (D) represent

the iPSðINÞ component of iPS, and once again, this

component fits the data during the early stage t6 t1 of

current variations. Plots (c) in Fig. 8(C) and (D) repre-

sent the calculated current contributions of the last two

terms of Eq. (20). The lattice incorporation parameters

used for these calculations (all expressed in mol cm�2

s�1) are as follows: kg ¼ ð6:23� 10�7Þ=ffiffiffiffiffiffikN

pand k0g ¼

4:77� 10�11 in Fig. 8(B); kg ¼ (8.59�10�7Þ=ffiffiffiffiffiffikN

pand

k0g ¼ 9:84� 10�11 in Fig. 8(C); kg ¼ ð8:81� 10�7Þ=ffiffiffiffiffiffikN

p

and k0g ¼ 8:29� 10�11 in Fig. 8(D). In these calculations,

we also use iPSs ¼ 4, 23, and 45 lA cm�2 for Fig. 8(B)–

(D), respectively. The agreement between experimental

and calculated results in Fig. 8(A) and (B) is reasonable.

The surface processes associated with the relativelyhigher deposition potentials in Figs. 8(C) and (D) ap-

pear to be more complex than the simple three-current

model of Eq. (20). Nevertheless, the simple model helps

us to understand the general trends of the PS data.

4.5. Voltage dependences of N0 and H

In the PS analyses of Sections 4.2 and 4.4, we treatedN0 and H as adjustable variables, and used the previ-

ously reported parameters, qM ¼ 0:14 mol cm�3 [55],

and D ¼ 5:8� 10�6 cm2 s�1 [71]. Fig. 9 shows the

voltage dependent behavior of N0 (circles) and H (tri-

angles) for nucleation of Cu2þ on Ni (panel A) and Ta

(panel B). The lines through the symbols are provided to

guide the eye. The values of N0 for Ni and Ta exhibit

similar increasing trends with increasingly negativevoltages, and this effect has been reported in earlier

studies of Cu2þ electrodeposition on different types of

solid electrodes [9,31,33,48].

The phenomenological current-scaling parameter Hexhibits different voltage dependences for the Ni and Ta

electrodes. If the characteristic behavior of H is con-

trolled primarily by the presence of surface oxides, the

effects of voltage variations on H should indeed be dif-

ferent for Ni and Ta [72]. From Figs. 1 and 3, we knowthat effects of native surface oxides on nucleation are

relatively small in the Ni/Cu2þ system. Therefore, the

current scaling factor H for Ni in Fig. 9(A) is insensitive

to any voltage dependent variations in the nucleation

kinetics. On the other hand, according to the results of

Figs. 4, 6 and 8, we expect a measurable voltage de-

pendent interplay between the native surface oxides of

Ta and the nucleation kinetics of electrodeposited Cu onTa. We propose that this interplay is manifested in the

voltage dependent variations of H in Fig. 9(B).

5. Conclusions

We have combined cyclic voltammetry and potential

step amperometry to study nucleation of electrodepos-ited Cu on Ni and Ta in neutral aqueous electrolytes.

Both the Ni/Cu2þ and Ta/Cu2þ systems exhibit charac-

teristic crossed voltammograms of 3-D nucleation. The

deposited Cu can be reversibly removed from the Ni

surface by applying an anodic stripping voltage scan. On

the other hand, once deposited, the Cu on Ta cannot be

removed by a similar anodic scan; instead, when taken

to large anodic voltages (�1.4 V), the Ta surface be-comes further oxidized and less efficient as a substrate

for Cu2þ deposition. This indicates an active role of the

valve effect of Ta2O5 in electrodeposition of Cu2þ on Ta.


All potentiostatic current transients for Cu2þ deposition

on Ni are satisfactorily explained from simple consid-

erations of diffusion controlled 3-D instantaneous nu-

cleation. The Ta electrode follows this particular pattern

at weak (less cathodic) activation voltages (�0:10 to�0:20 V) for Cu2þ deposition, and only for short (<0.1

s) initial post-step intervals when activation voltages are

more cathodic ( < �0:30 V). The current transients for

Ta, recorded with step voltages < �0:30 V show a sec-

ondary feature at longer times, and this feature can be

associated with lattice incorporation of the nucleating

species. For the purpose of data analysis here, we have

combined the technique-specific descriptions of nucle-ation in a single phenomenological framework. This

framework can be further developed for detailed multi-

technique investigation [34,73] of electrochemical

nucleation.

Acknowledgements

This work was supported in part by the New York

State Office of Science, Technology and Academic Re-

search (NYSTAR). The authors thank K.A. Assiong-

bon, A.K. Hall, J.E. Garland, C.M. Pettit and M.J.

Walters for both technical assistance and useful discus-

sions. S.B.E and J.L.H. gratefully acknowledge their

undergraduate summer research scholarships from the

McNair Scholars Program.

Appendix A. Potential step amperometry in the frame-

work of the nucleation rate-law

In the absence of nucleation rate dispersion, the

simple nucleation rate-law is written as

N ¼ N0½1� expð�kNtÞ�: ðA:1ÞIf we replace t in Eq. (A.1) by s, and subsequently dif-

ferentiate the resulting expression with respect to s, weobtain Eq. (2). Eq. (1) gives the nucleation current

density from all nucleation sites per unit electrode area,

as dictated by Eq. (A.1). For instantaneous nucleation,

kN is taken to be very large, so that N � N0 in Eq. (A.1).

Traditionally, progressive nucleation has been defined as

a special case of Eq. (A.1), where dN=dt is a constant.To obtain this special case, one assumes that within the

relevant time scale of nucleation, kN is small enough to

meet the condition,

expð�kNtÞ � 1� kNt: ðA:2ÞIn this case, N ¼ N0kNt, and dN=dt satisfies the steady

state requirement for progressive nucleation, dN=dt ¼kN.

The general form of the PS-induced nucleation

current is obtained by combining Eqs. (1)–(3) with

Eqs. (13) and (14); this leads to the expression,

iPSðN ; tÞ ¼ cJðtÞt�1=2, with

JðtÞ ¼Z t

0

ðt � sÞAðsÞds

¼ ðN0=kNÞ½kNt � 1þ expð�kNtÞ�; ðA:3Þ

and c is defined in the context of Eq. (15). To evaluate

the integral in the first line of Eq. (A.3), we have used

AðsÞ from Eq. (2). The variable JðtÞ is proportional to

the extended (non-overlapping) surface coverage hex of

diffusion zones. As shown by Sluyters–Rehbach et al.

[23] (Eqs. (16)–(20)),

hexðtÞ ¼ ½pkdD�JðtÞ; ðA:4Þwhere kd is defined in the context of Eq. (15). According

to Eqs. (A.3) and (A.4),

iPSðN ; tÞ ¼ cJðtÞt1=2

� cpkdDt1=2

� �hexðtÞ

¼ cN0

kNt1=2

� �½kNt � 1þ expð�kNtÞ�: ðA:5Þ

In Scharifker and Mostany’s [33] model, Eq. (A.5) is

further generalized by accounting for overlap of diffu-

sion zones. This is done by replacing hex in the first line

of Eq. (A.5) by the actual coverage term, ha, where ha isdefined according to Avrami’s theorem [25],

ha ¼ ½1� expð�hexÞ�. Thus, the PS-induced nucleation

current including overlap of diffusion zones is written as

iPSðN ; tÞ ¼ chapkdDt1=2

; ðA:6Þ

where according to Eq. (A.4), haðtÞ ¼ 1� exp � pkdDð Þ½JðtÞ�. Eq. (15) is obtained by combining Eq. (A.5) and

this haðtÞ.In the limit of large kN, where expð�kNtÞ � 0 and

kNt � 1, Eq. (15) takes the form of Eq. (16). To obtain

Eq. (17) in the small-kN limit of Eq. (15), it is necessary

to consider the series expansion of expð�kNtÞ, keepingterms up to the second order in kNt,

expð�kNtÞ � 1� kNt þ ðkNtÞ2=2: ðA:7Þ

Using Eq. (A.7) in Eq. (15), we get Eq. (17). We note

here that, the ‘‘small-kN’’ limit usually considered for

defining progressive nucleation (a constant value of

dN=dt) in the description of Eq. (A.7) involves the ap-proximation in Eq. (A.2), where the expansion of

expð�kNtÞ is terminated at the first order term of kNt. On

the other hand, derivation of Eq. (A.7) and hence, that

of Eq. (17) requires the second order term in kNt. It ispossible that this apparent inconsistency between the

two approximations used in Eqs. (A.2) and (A.7) can be

resolved through further generalization of the nucle-

ation rate law [27]. We also note here that the analysis ofthe experimental data in the present work does not re-

quire direct use of either Eq. (A.2) or Eq. (A.7). If we use


Eq. (A.7), but ignore overlap of diffusion zones

(ha ¼ hex), Eq. (15) simplifies to the expression,

iPSðNG; tÞ ¼ ðcN0kN=2Þt3=2, which is close to the pro-

gressive nucleation current calculated in Ref. [32]. In the

absence of nucleation, Eq. (15) takes the simple form ofthe Cottrell equation, representing PS-induced direct

electrodeposition, iPSðDD; tÞ ¼ a0t�1=2.

References

[1] K. M�arquez, G. Staikov, J.W. Schultze, Electrochim. Acta 48

(2003) 875.

[2] W. Schindler, P. Hugelmann, M. Hugelmann, F.X. K€artner, J.

Electroanal. Chem. 522 (2002) 49.

[3] A. Milchev, L. Heerman, Electrochim. Acta 48 (2003) 2903.

[4] V. Tsakova, D. Borissov, B. Ranguelov, Ch. Stromberg, J.W.

Schultze, Electrochim. Acta 46 (2001) 4213.

[5] R. Keding, C. R€ussel, J. Non-Crystal. Solids 278 (2000) 7.

[6] V. Guterman, Yu. Averina, V. Grigor’ev, Electrochim. Acta 45

(1999) 873.

[7] T. Vargus, R. Varma, in: R. Varma, J.R. Selman (Eds.),

Techniques for Characterization of Electrodes and Electrochem-

ical Processes, Wiley, New York, 1991, p. 717.

[8] J.E. Garland, C.M. Pettit, M.J. Walters, D. Roy, Surf. Interface

Anal. 31 (2001) 492.

[9] M. Palomar-Pardav�e, M. Miranda-Hern�andez, I. Gonz�alez, N.

Batina, Surf. Sci. 399 (1998) 80.

[10] M.H. H€ozle, C.W. Apsel, T. Will, D.M. Kolb, J. Electrochem.

Soc. 142 (1995) 3741.

[11] J.V. Zoval, R.M. Stiger, P.R. Biernacki, R.M. Penner, J. Phys.

Chem. 100 (1996) 837.

[12] R.J. Nichols, D. Schr€oer, H. Meyer, Electrochim. Acta 40 (1995)

1479.

[13] S. Fletcher, T. Lwin, Electrochim. Acta 28 (1983) 237.

[14] S. Fletcher, Electrochim. Acta 28 (1983) 917.

[15] S. Fletcher, C.S. Halliday, D. Gates, M. Westcott, T. Lwin, G.

Nelson, J. Electroanal. Chem. 159 (1983) 267.

[16] S. Cer�e, M. Vazquez, S.R. de S�anchez, D.J. Schiffrin, J. Electro-

anal. Chem. 505 (2001) 118.

[17] G. Kokkinidis, J. Electroanal. Chem. 201 (1986) 217.

[18] F. Ebrahami, A.J. Liscano, Mater. Sci. Eng. A301 (2001) 23.

[19] L. Chen, N. Magtoto, B. Ekstrom, J. Kelber, Thin Solid Films 376

(2000) 115.

[20] D.M. Tench, J.T. White, J. Electrochem. Soc. 137 (1990) 3061.

[21] M.E. Hyde, R.G. Compton, J. Electroanal. Chem. 549 (2003) 1.

[22] L. Heerman, A. Tarallo, J. Electroanal. Chem. 470 (1999) 1.

[23] M. Sluyters-Rehbach, J.H.O.J. Wijenberg, E. Bosco, J.H. Sluy-

ters, J. Electroanal. Chem. 236 (1987) 1.

[24] E. Budevski, G. Staikov, W.J. Lorenz, Electrochim. Acta 45

(2000) 2559.

[25] R. de Levi, in: H. Gerischer, C.W. Tobias (Eds.), Advances in

Electrochemistry and Electrochemical Engineering, 13, Wiley,

New York, 1984, p. 1.

[26] M. Fleischmann, H.R. Thirsk, in: P. Delahay (Ed.), Advances in

Electrochemistry and Electrochemical Engineering, vol. 3, Wiley,

New York, 1963, p. 123.

[27] R.L. Deutscher, S. Fletcher, J. Chem. Soc., Faraday Trans. 94

(1998) 3527.

[28] A.J. Bard, L.R. Faulkner, Electrochemical Methods: Fundamen-

tals and Applications, Wiley, New York, 1980.

[29] R.S. Nicholson, Anal. Chem. 37 (1965) 1351.

[30] D.M. Kolb, in: H. Gerischer, C.W. Tobias (Eds.), Advances in

Electrochemistry and Electrochemical Engineering, 11, Wiley,

New York, 1978, p. 125.

[31] G. Gunawardena, G.J. Hills, I. Montenegro, B. Scharifker, J.


[32] G.J. Hills, D.J. Schiffrin, J. Thompson, Electrochim. Acta 19

(1974) 657.

[33] B. Scharifker, J. Mostany, J. Electroanal. Chem. 177 (1984)

13.

[34] M.J. Walters, C.M. Pettit, D. Roy, Phys. Chem. Chem. Phys. 3

(2001) 570.

[35] J.E. Garland, K.A. Assiongbon, C.M. Pettit, S.B. Emery, D. Roy,

Electrochim. Acta 47 (2002) 3113.

[36] M.J. Walters, J.E. Garland, C.M. Pettit, D.S. Zimmerman, D.R.

Marr, D. Roy, J. Electroanal. Chem. 499 (2001) 48.

[37] M.A. Lovell, M.J. Walters, D. Roy, Phys. Chem. Chem. Phys. 1

(1999) 1985.

[38] M.A. Lovell, D. Roy, Electrochim. Acta 43 (1998) 2117, Erratum,

44 (1999) 2327.

[39] A.N. Correia, M.C. dos Santos, S.A.S. Machado, L.A. Avaca, J.


[40] S. Floate, M.E. Hyde, R.G. Compton, J. Electroanal. Chem. 523

(2002) 49.

[41] K. M�arquez, R. Ortiz, J.W. Schultze, O.P. M�arquez, J. M�arquez,

G. Staikov, Electrochim. Acta 48 (2003) 711.

[42] L. Massot, P. Chamelot, F. Bouyer, P. Taxil, Electrochim. Acta

48 (2003) 465.

[43] R. Schrebler, P. Cury, M. Orellana, H. G�omez, R. C�ardova, E.A.

Dalchiele, Electrochim. Acta 46 (2001) 4309.

[44] M. Kleinert, H.-F. Waibel, G.E. Engelmann, H. Martin, D.M.

Kolb, Electrochim. Acta 46 (2001) 3129.

[45] H.-F. Waibel, M. Kleinert, L.A. Kibler, D.M. Kolb, Electrochim.

Acta 47 (2002) 1461.

[46] G. Oskam, P.C. Searson, Surf. Sci. 446 (2000) 103.

[47] S. Jaya, T. Prasada Rao, G. Prabhakara Rao, Electrochim. Acta

31 (1986) 343.

[48] M. Palomar-Pardav�e, I. Gonz�alez, A. Soto, E.M. Arce, J.


[49] R. Srinivasan, P. Gopalan, Surf. Sci. 338 (1995) 31.

[50] D. Grujicic, B. Pesic, Electrochim. Acta 47 (2002) 2901.

[51] L.H. Mascaro, E.C. Pereira, J. Electroanal. Chem. 485 (2000)

81.

[52] D.M. Kolb, H. Gerischer, Surf. Sci. 51 (1975) 323.

[53] G. Nagy, D. Roy, J. Phys. Chem. 98 (1994) 6592.

[54] A. Piotrowski, T. Kolowski, Acta Phys. Polonica B 31 (2000)

89.

[55] N.W. Ashcroft, N.D. Mermin, Solid State Physics, Saunders

College, Philadelphia, 1976, p. 364.

[56] M. Palomar-Pardav�e, I. Gonz�alez, N. Batina, J. Phys. Chem. B

104 (2000) 3545.

[57] A.A. Gewirth, B. Niece, Chem. Rev. 97 (1997) 1129.

[58] T. Suzuki, T. Yamada, K. Itaya, J. Phys. Chem. 100 (1996) 8954.

[59] S. Lecuyer, A. Quemerais, G. Jezequel, Surf. Interface Anal. 18

(1992) 257.

[60] F. Di Quarto, C. Gentile, S. Piazza, C. Sunseri, Corros. Sci. 35

(1993) 801.

[61] Y. Bouizem, F. Chao, M. Costa, A. Tadjeddine, G. Lecayon, J.


[62] O. Kerrec, D. Devilliers, H. Groult, M. Chemla, Electrochim.

Acta 40 (1995) 719.

[63] M.J. Mehl, D.A. Papaconstantopoulos, Phys. Rev. B 54 (1996)

4519.

[64] A.I. Danilov, J.E.T. Andersen, E.B. Molodkina, Yu. M.

Polukarov, P. Møller, J. Ulstrup, Electrochim. Acta 43 (1998)

733.

[65] M.J. Walters, K.A. Assiongbon, D.R. Marr, B.T. Shepardson, D.

Roy, Int. J. Hydrogen Energy 28 (2002) 275.

[66] V. Macagno, J.W. Schultze, J. Electroanal. Chem. 180 (1984) 157.

[67] P.P. Prosini, M.L. Addonizio, A. Antonaia, Thin Solid Films 298

(1997) 191.


[68] M.Y. Abyaneh, J. Electroanal. Chem. 530 (2002) 82.

[69] M.H. H€olzle, U. Retter, D.M. Kolb, J. Electroanal. Chem. 371

(1994) 101.

[70] R.D. Armstrong, M. Fleischmann, H.R. Thirsk, J. Electroanal.

Chem. 11 (1966) 208.

[71] J.T. Hinatsu, F.R. Foulkes, J. Electrochem. Soc. 136 (1989) 125.

[72] M. Tomellini, M. Fanfoni, Surf. Sci. 393 (1997) L99.

[73] E. Herrero, L.J. Buller, J. Li, A.C. Finnefrock, A.B. Salom�on, C.Alonso, J.D. Brock, H.D. Abru~na, Electrochim. Acta 44 (1998)

983.

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