The termodynamic model of open-circuit potential for electroless deposition of Ni on silicon

Article abstract of DOI:10.1149/1.2221862

This investigation first proposed that open-circuit potential vs time (OCP-t) is a novel nonlinear potential step controlled by redox reaction and nucleation. A novel thermodynamic model of OCP-t is obtained for electroless deposition of Ni on Pd-activated p-type silicon(100). Thermodynamic transient properties such as capacity of double layer C, surface charge density q, interfacial tension γ, and resistance of chemical reaction Rr are calculated. Results show that the variation of OCP is dependant on the interfacial double layer. The breakdown and rearrangement of the double layer causes surface charge density step, which triggers momentary nucleation of Ni on the substrate. Results also show that reductant pulses would be an effective way to speed nuclei growth.

Full text of DOI:10.1149/1.2221862

Journal of The Electrochemical Society, 153 ͑10͒ C677-C682 ͑2006͒
C677
0
013-4651/2006/153͑10͒/C677/6/$20.00 © The Electrochemical Society
The Termodynamic Model of Open-Circuit Potential for
Electroless Deposition of Ni on Silicon
z
Y. L. Chang, W. C. Ye, C. L. Ma, and C. M. Wang
Department of Chemistry, Lanzhou University, Lanzhou, 730000, China
This investigation first proposed that open-circuit potential vs time ͑OCP-t͒ is a novel nonlinear potential step controlled by redox
reaction and nucleation. A novel thermodynamic model of OCP-t is obtained for electroless deposition of Ni on Pd-activated
p-type silicon͑100͒. Thermodynamic transient properties such as capacity of double layer C, surface charge density q, interfacial
tension ␥, and resistance of chemical reaction Rr are calculated. Results show that the variation of OCP is dependant on the
interfacial double layer. The breakdown and rearrangement of the double layer causes surface charge density step, which triggers
momentary nucleation of Ni on the substrate. Results also show that reductant pulses would be an effective way to speed nuclei
growth.
©
2006 The Electrochemical Society. ͓DOI: 10.1149/1.2221862͔ All rights reserved.
Manuscript submitted February 23, 2006; revised manuscript received April 26, 2006. Available electronically July 26, 2006.
Open-circuit potential vs time ͑OCP-t͒ has been proved a sensi-
tive and effective technique for sensing transient mixed potential at
the interface of solid/solution. It has been applied in monitoring the
Chemicals and materials.— Analytical reagent grade NiSO4
·6H O, NH OH ͑61%͒, HCl ͑36%͒, H O ͑31%͒, HF ͑40%͒, NH F,
2
4
2
2
4
and hydrazine hydrate N H ·H O ͑50%͒ were used. A solution of
2
4
2
1-3
0.05 mol L− NiSO4 was prepared by dissolving 1.3143 g
1
corrosion behavior5 of metal,
hydrogen absorption in Pd
4
6
electrodes, oxygen, carbon monoxide, adsorption in Pt/Pd elec-
NiSO ·H O in 100 mL redistilled water in a flask. Redistilled water
4
2
7
trode, and characterization of acrylic hydrogels. Our group also
reports its application in electroless deposition of Ag. However, the
was used throughout. Nitrogen was purged for solution deaeration.
A p-type crystalline silicon͑100͒ wafer with a resistivity of
10–20 ⍀ cm and a thickness of 525 ± 25 ␮m ͑Beijing Youyan sili-
con villa semiconductor͒ was used.
8
methodology of OCP-t is still undeveloped. Few papers on the
mathematic model of OCP-t are reported. In this work, a novel
thermodynamic model of OCP-t is used to propose for electroless
deposition. We believe that it would be helpful to understand the
process of electroless deposition and develop further applications of
OCP-t.
Wafer treatment and preparation of Pd seeds.— The treatment
of silicon wafer was the same as in Ref. 8. The etched silicon wafer
−
1
is immersed in the solution of 0.005 mol L
+
PdCl2
0.06 mol L− hydrofluoric acid ͑HF͒ for 20 s to obtain the Pd
seeds.
1
Electroless deposition of metal films on silicon such as alumi-
9
9-11
12,13
14
15,16
17
num, copper,
silver,
gold, nickel,
NiP alloy, NiB
1
8
19
6-20
alloy, and CuNi alloy have been investigated. The nucleation and
Electrochemical measuring.— The silicon wafer with Pd seed
layer was fixed on the conductor of the cell ͑see Fig. 1͒. The mea-
1
reaction mechanisms
have also been studied. However, the tran-
sient information of electroless deposition is still blurry and needs to
find a sensitive technique to describe it. OCP-t is an ideal option for
this purpose because it can record transient potential of electroless
surement of OCP-t was done as follows: ͑i͒ stirred with 753.6 rad/s,
−1
͑
ii͒ 0.05 mol L 20 mL NiSO solution was added into the cell at
4
8
deposition effectively. Other transient techniques controlled by
outer circuits such as conventional potential step and current step
make it difficult to acquire actual information of electroless deposi-
tion.
During the electroless deposition process, there are six processes
occurring on the surface of samples, which include: ͑i͒ mass trans-
port of ions, ͑ii͒ migration of ions, ͑iii͒ charge or discharge of double
layer, ͑iv͒ adsorption or desorption of ions, ͑v͒ chemical reaction,
21
and ͑vi͒ nucleation on the substrate. In this experiment, the mass
transport and migration of ions can be ignored because of agitating
strongly. NiSO4 solution and NH NH2 reductant are selected be-
2
cause their reactions are clear. Amperometric i-t is used to acquire
transient current of electroless deposition. Ni film and Pd seed layer
are characterized by atomic force microscope ͑AFM͒ and differen-
tial pulse voltammetry ͑DPV͒.
Experimental
Instruments and software.— AFM ͑Explorer, Veeco Co., USA͒
in contact mode, electrochemical workstation ͑CHI660A, Shanghai,
China͒, and pH meter ͑PHS-3B, Shanghai, China͒ were used. A
homemade electrochemical cell of Teflon with three-electrode con-
figuration ͑shown as Fig. 1͒ was used. A p-Si͑100͒ wafer sample
2
served as the work electrode with a disk area of 12.56 mm . A
saturated calomel reference electrode ͑SCE͒ and a platinum auxil-
iary electrode were used. Data of OCP-t and i-t were fitted with
Origin 7.0 ͑OriginLab Co.͒. The drawing of the cell was done by
Autocad2006 ͑Autodesk Co.͒.
Figure 1. Configuration of electrochemical cell: ͑1͒ SCE, ͑2͒ stirrer, ͑3͒
platinum auxiliary electrode, ͑4͒ cell cover, ͑5͒ cell bulk, ͑6͒ screws, ͑7͒
bottom plate, ͑8͒ sample ͑silicon wafer as work electrode͒, ͑9͒ O-ring, ͑10͒
conductor, ͑11͒ pedestal, and ͑12͒ conduct pole.
z
E-mail: wangcm@lzu.edu.cn
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C678
Journal of The Electrochemical Society, 153 ͑10͒ C677-C682 ͑2006͒
Figure 2. AFM images of samples ͑scan
range was 1000 nm, scan rate was
6.3 ␮m/s, resolution was 300͒: ͑a͒ blank
p-Si ͑100͒, etched in a solution of 10 mL
1
HF ͑40%͒ + 100 mL NH F for 2 min at
4
room temperature, ͑b͒ Pd seeds deposited
−
1
on p-Si ͑100͒, in 0.005 mol L PdCl
−
1
+
0.06mol L HF for 20 s, and ͑c͒ Ni
film deposited on Pd seed layer, in
−
1
0
.05 mol L 20 mL NiSO4 and 500 ␮L
N H ·H O ͑50%͒ for 800 s, stirred with
2
4
2
7
53.6 rad/s.
0
1
s, ͑iii͒ 500 ␮L N H ·H O ͑50%͒ was injected into the cell at
000 s, and ͑iv͒ measurement was stopped at 1800 s. The sample
Figure 2a shows the AFM images of blank p-Si͑100͒. It can be
seen that the silicon wafer is flat; the tested average roughness de-
gree ͑Ra͒ was 0.99 nm. The images represent the surfaces of a
2
4
2
was taken out and rinsed with redistilled water and dried by nitrogen
gas to acquire AFM images or do DPV. The inner wall of the cell
and O-ring are immersed into 0.1 mol L HNO for 30 min, then
rinsed by redistilled water. The procedure of i-t is the same as that of
OCP-t. Initial E was set as the value of OCP at 0 s. All measure-
ments were performed at room temperature.
22
hydrogen-terminated silicon substrate.
−
1
3
Figure 2b shows the AFM images of Pd seed layer on the silicon
wafer. Pd islands form on the active sites of hydrogen-terminated
silicon, and the surface of silicon is not completely covered, which
suggests that the nucleation was an island model or a Volmer–Weber
In the measurement of DPV, the supporting electrolyte was
8
,23
−
1
͑
VW͒ model,
and the growth of Pd nuclei was a gradual
0
.1 mol L HNO and applied potential was from −1 to 1.3 V.
3
8
nucleation. The Pd particles have an average size of about 85 nm
and the tested average roughness Ra is 13.22 nm.
Results and Discussion
Figure 2c shows the AFM images of Ni films on a Pd-activated
silicon wafer. The Pd seed layer is covered completely by Ni film,
and the tested average roughness Ra is 11.28 nm. It can be seen that
the nucleation of Ni is also VW model.
Characterizations of Ni film and Pd seed layer.— The Ni film
and Pd seed layer deposited on p-Si͑100͒ are characterized by AFM
and DPV.
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Journal of The Electrochemical Society, 153 ͑10͒ C677-C682 ͑2006͒
C679
␸i = − 0.11e−t/110.83 + 9.0 ϫ 10 t − 0.63 ͑0 Ͻ t ഛ 1000͒
−5
R2 = 0.9919
͓1͔
␸s = − 0.10 + 0.92/͑1 + e͑t−999.81͒ϫ100/5.60͒ ͑1000 Ͻ t ഛ 1000.4͒
R2 = 0.9972
͓2͔
␸e = − 0.43 + 132.26e−t/149.83 ͑1000.4 Ͻ t ഛ 1800͒ R = 0.9906
2
͓
3͔
−
t/8.43
−6
2
ii1 = ͑29.28e
+ 3.32͒ ϫ 10 ͑0 Ͻ t ഛ 13͒ R = 0.9962
͓
4͔
t−102.46/183.17
ii2 = ͑12.72 − 11.41/͑1 + e
͒͒
Figure 3. The curve of DPV in 0.1 mol L−1 HNO3 solution: ͑1͒ Pd seed
layer, ͑2͒ Ni film on blank silicon ͑right axis͒, and ͑3͒ Ni film on Pd seed
layer.
ϫ 10−6 ͑13 Ͻ t ഛ 1000͒ R = 0.8818
2
͓5͔
−
4
i = 1.78 ϫ 10 ͑t − 1000͒ ͑1000 Ͻ t ഛ 1000.4͒ R = 0.98509
s
͓
6͔
ie = 0.16e−t/120.72 + 5.95 ϫ 10−5 ͑1000.4 Ͻ t ഛ 1800͒ R = 0.9962
7͔
Curve 1 of Fig. 3 shows the differential pulse stripping peak of
Pd. The stripping peak of Pd appeared at −0.3 V. After 0.5 V, the
stripping current approaches 0 A because of the oxidation of Si
substrate.
2
͓
2
+
Curve 2 of Fig. 3 shows the differential pulse stripping peak of
The explanation of OCP-t and i-t.— Ni
is easy to form
2
+
2+
Ni film on blank p-Si͑100͒. The peak at −0.03 V is the first electron
Ni͑H O͒ in NiSO solution. Because some of Ni͑H O͒ is hy-
2
6
4
2
6
0
+
24
transfer, Ni → Ni + e, and the peak at 0.6 V is the second elec-
drolyzed, the solution presents as acidic
+
2+
tron transfer, Ni → Ni + e.
2
6
+
+
5
+
+
Ni͑H O͒ → Ni͑H O͒ OH + H → Ni͑H O͒ ͑OH ͒ + 2H
Curve 3 of Fig. 3 shows the differential pulse stripping peak of
Ni film on the Pd seed layer. The peak at 0.04 V is the first electron
2
2
ad
2
4
ad 2
͓8͔
0
+
transfer, Ni → Ni + e, and the peak at 0.4 V is the second elec-
−
2+
+
+
2+
A weak bond exists for 2 OH to Ni͑H2O͒4 . H is dissociative
and pH is 3.0. When aqueous NiSO solution is added into the cell,
H is adsorbed to the Pd seed layer immediately. The specific ad-
sorption layer of H forms first, and the potential rises gradually but
tron transfer, Ni → Ni + e. The peak of Pd does not appear, in-
4
dicating that the Pd seed layer is completely covered.
+
+
Thermodynamic model of electroless deposition of Ni on Pd-
current decays quickly to a limit due to saturation of specific adsorp-
actived silicon.—
Mathematic description of OCP-t and i-t.—
2+
6
+
tion within 13 s. As the diffusion layer of H and Ni͑H O͒ form,
2
Curve a of Fig. 4 shows OCP-t. The curve is made up of three
segments. Before 1000 s, the potential changes gently because of
potential remains raised because of concentration polarization, and
current also rises slowly because of ions diffusion. After 300 s, the
potential decays linearly because of the formation of an anion layer
at the interface of diffuse layer; current also decays but lags to
potential due to a charge of double layer.
adsorption and desorption of ions, i.e., initial potential ␸ ͑seg. 1͒;
i
from 1000 s to 1000.4 s, a potential step ␸ appears due to break-
s
down of the double layer ͑seg. 2͒; after 1000.4 s, potential exponen-
tially shifts to negative because of redox reaction and nucleation,
−1
N H ·H O is easy to hydrolyze. The pH of 0.5282 mol L
2
4
2
i.e., end potential ␸ ͑seg. 3͒.
e
N H ·H O is 10.81
2
4
2
Curve b of Fig. 4 shows the response curve of i-t under OCP,
+
−
which is also made up of three segments: initial current i ͑seg. 1Ј͒,
N H ·H O → N H + OH
͓9͔
i
2
4
2
2
5
current step i ͑seg. 2Ј͒, and end current i ͑seg. 3Ј͒.
s
e
According to Ref. 24, when N H ·H O is used as a reductant, the
2
4
2
OCP-t and i-t are fitted accurately with Origin 7.0.
electroless deposition of Ni is divided into four steps in acidic solu-
tion. Hydrolyzation first takes place on the surface of the active
sample, and then other reactions follow
+
−
2
H O → 2H + 2 OH
͓10͔
͓11͔
͓12͔
͓13͔
͓14͔
2
Ni2+ + 2 OH → Ni͑OH͒
−
2
Ni͑OH͒ + N H → Ni + N H ͑OH͒ + 2H
2
2
4
2
2
2
N H ͑OH͒ + 2H → N + 2H O + H
Overall: Ni2+ + N H → Ni + N + H + 2H
In fact, when N H ·H O is added into aqueous NiSO solution,
2
2
2
2
2
2
+
2
4
2
2
2
4
2
4
−
+
+
−
OH rushes to the H layer and neutralization of H and OH first
takes place, then the double layer of H collapses immediately. Con-
+
sequently, a remarkable potential step and current step appear ͑seg. 2
of OCP-t and seg. 2Ј of i-t͒. Then the double layer rearranges and a
2
6
+
new layer of Ni͑H O͒ forms. When Reactions 11–13 occur on the
2
Figure 4. The curves of OCP-t and i-t of electroless deposition of Ni on Pd
seed layer: ͑a͒ the curve of OCP-t, and ͑b͒ the curve of i-t; ͑1͒ initial poten-
tial ␸ , ͑2͒ potential step ␸ , and ͑3͒ end potential ␸ ; ͑1Ј͒ initial current i ,
surface of the Pd seed layer, the potential exponentially shifts to
negative and the current exponentially decays ͑seg. 3 of OCP-t and
seg. 3Ј of i-t͒. DPV and AFM affirm the formation of Ni film.
i
s
e
i
͑
2Ј͒ current step i , and ͑3Ј͒ end current i .
s
e
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C680
Journal of The Electrochemical Society, 153 ͑10͒ C677-C682 ͑2006͒
Figure 5. Scheme of equivalent circuit of electroless deposition: ͑R ͒, resis-
1
tance of solution, ͑R ͒, resistance of redox reaction, and ͑C͒ capacity of
r
double layer.
The model of equivalent circuit.— Electroless deposition of Ni
on the Pd seed layer can be modeled as a novel nonlinear potential
step controlled by redox reaction and nucleation, which is more
complicated than traditional transient techniques. However, it obeys
the basic principles of potential steps and can be described with the
Figure 6. The curve of C-t for electroless deposition of Ni on Pd seed layer:
͑
1͒ initial capacity C , ͑2͒ capacity step C ͑3͒ end capacity C .
i
s
e
21
method of equivalent circuit.
The model of equivalent circuit for electroless deposition is
shown in Fig. 5. The capacity of double-layer C connects in parallel
␸e
− 0.43
5.95 ϫ 10−5
r
R = lim
r
=
= − 7.22 ϫ 103
͓23͔
͓24͔
with the resistance of chemical reaction R , and the resistance of
t→ϱ ie
solution R connects to the circuit in series.
1
In electroless deposition, the redox reaction and nucleation are
C = − 0.18e−
0.0016t
− 0.02 ͑1010 Ͻ t ഛ 1800͒
dominant factors, so R is far less than R generally. Moreover, R
e
1
r
r
can be treated as a constant when redox reaction carries out at a
To confirm the presumption of R /R Ϸ 0, a traditional potential
1 r
21
steady rate, i.e., R /R Ϸ 0, R = constant. The capacity of the
step is used to estimate the scale of R and R approximatively
1 r
1
r
r
double layer is a key step to calculate other thermodynamic param-
eters.
because electroless deposition would not rigorously satisfy the con-
dition of a traditional potential step.
Using Laplace transform and reverse transform for Eq. 16, we
obtain
Model of capacity.— Capacity can be derived from potential and
current with the above equivalent circuit. The equation of current i
can be derived from Ohm’s law without polarization of concentra-
tion
␸k
Rr
e−t/RC
i =
ͫ
1 +
ͬ
͓25͔
R1 + Rr
R1
␸
− iR1
d
+
C
͑␸ − iR ͒ = i
͓15͔
͓16͔
1
=
R
1
1
1
Rr
dt
+
͓26͔
͓27͔
R1 Rr
d␸
␸
+
di
dt
R1
Rr
C
= R C
+
ͩ
1 +
ͪ
i
␸k = lim␸e = − 0.43
1
dt
Rr
t→ϱ
When R /R Ϸ 0, Eq. 11 can be simplified as
Comparing Eq. 25 with Eq. 7, we obtain
1
r
Rr = − 7.22 ϫ 103
d␸
␸
C
+
= i
͓17͔
͓18͔
dt
Rr
R1 = − 2.75
i − ␸/Rr
d␸/dt
C =
R1/Rr Ϸ 0
Results show that the presumption is appropriate.
It can be seen from the figure that the magnitude of the initial
When no redox reactions take place, R = ϱ, Eq. 18 can be sim-
r
plified as
−11
−7
−2
capacity is from 10
end capacity is exponentially decayed from −5.58 to −3.07
to 10 ; capacity step reach −5.58 ϫ 10 ,
i
−
2
C =
͓19͔
ϫ 10 . A noticeable focus is the time interval of the capacity step,
which is not synchronous with potential or current step. The poten-
tial or current step finishes within 0.4 s, but the capacity step re-
mains 10 s; the cause may be the rearrangement of the double layer
d␸/dt
Equation 19 can also be derived from the definition of capacity
dq idt
i
+
C =
=
=
͓20͔
after the breakdown of the H layer.
d␸ d␸ d␸/dt
Model of surface charge density.— Surface charge density can
be derived from the definition of capacity ͑Eq. 20͒, but cannot be
calculated with current directly because the current is made up of
faradaic current and nonfaradaic current. Faradaic current is caused
by redox reaction; however, nonfaradaic current is caused by charge
of the double layer. Only nonfaradaic current contributes to surface
charge density
At the stage of the initial potential and potential step, no redox
reaction occurrs, so Eq. 14 is adopted. For end potential, Eq. 13
must be adopted because redox reaction occurrs and a new Ni layer
forms. Differential capacity is calculated out and plotted on a graph.
The curve of C-t ͑shown in Fig. 6͒ is also made up of three
segments, i.e., initial capacity C , capacity step C , and end capacity
i
s
Ce
␸
e
C = − 2.48 ϫ 10− + 1.25 ϫ 10−10et/110.08 ͑0 Ͻ t ഛ 1000͒
10
q =
Cd␸/A
͓28͔
i
͵
␸
i
͓
21͔
2
Submitting ␸ , ␸ , ␸ , C , C , C , and A = 12.56 mm into
i
s
e
i
s
e
C = − 5.65 ϫ 10−
3
͑
t − 1000
͒
͑1000 Ͻ t ഛ 1010͒
͓22͔
Eq. 28, acquire
s
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Journal of The Electrochemical Society, 153 ͑10͒ C677-C682 ͑2006͒
C681
Figure 8. Curve of ␥-t for electroless deposition of Ni on Pd seed layer: ͑1͒
initial interfacial tension ␥ , ͑2͒ step of interfacial tension ␥ , ͑3͒ end inter-
Figure 7. Curve of q-t for electroless deposition of Ni on Pd seed layer: ͑1͒
initial surface charge density q , ͑2͒ step of surface charge density q , ͑3͒ end
i
s
i
s
−
6
facial tension ␥ , and ͑3Ј͒ amplification of end interfacial tension 10 ␥ .
surface charge density q , and ͑3Ј͒ amplification of end surface charge den-
e
e
e
−
4
sity 10 q .
e
−
7
remains about 10 s; the end interfacial tension increases from −10
−
4
q = 1.11 ϫ 10−13et/111.54 + 4.37 ϫ 10−13 ͑0 Ͻ t ഛ 1000͒
to −10 . The step of interfacial tension first increases and then
decreases; the signal direction changes from positive to negative,
proving that the double layer collapses first and then rearranges.
i
͓
29͔
−
2
q = 9.70 ϫ 10 ͑t − 1178͒ ͑1000 Ͻ t ഛ 1010͒
͓30͔
Conclusions
s
OCP-t is a novel nonlinear potential step controlled by redox
reaction and nucleation. The thermodynamic model of OCP-t for
electroless deposition can be set up by modeling of the double layer
and equivalent circuit. Thermodynamic parameters such as capacity
of double layer, resistances of chemical reaction, surface charge
density, and interfacial tension can be derived from OCP-t and i-t.
Thermodynamic curves all include three segments but have different
characters. The potential and current step are synchronous, indicat-
ing they have the same mechanism, but the capacity step lags to
them because of the charge of double layer.
Results show that surface charge density is an important factor
because nuclei growth may be dependant on surface charge density.
Reductant pulse can cause very high surface charge density and
triggers momentary nucleation, but the step time is only 10 s. Rep-
etitious reductant pulses may be an effective way to speed nuclei
growth and form different configures.
q = − 1.53e−
t/120.48
− 0.21e−t/149.83
e
+
5.98 ϫ 10−4 ͑1010 Ͻ t ഛ 1800͒
͓31͔
The curve of q-t is shown in Fig. 7. The initial surface charge
−
15
−10
density q is from 10 to 10 , the step of surface charge density
i
q reaches −17.15 within 10 s, and the end surface charge density q
s
e
−
4
rebounds to 10 . Compared with the initial surface charge density,
the step is so high that nucleation is very easy to trigger. A Ni
monolayer or submonolayer may be deposited on a Pd seed layer
instantaneously because the surface charge density decreases from
−
17.15 to 3.39 ϫ 10−6 within 1 s. The end surface charge density
−
6
−4
increases from 3.40 ϫ 10 to 5.95 ϫ 10 and remains steady after
600 s, which shows that, after 1600 s, the diffusion of ions in the
1
boundary layer still plays an important role although agitated
strongly, so the growth of Ni nuclei may be gradual.
Based on the above discussion, we can make the conclusion that
the nucleation rate may depend on surface charge density. Reductant
pulse may be an effective way to speed nuclei growth because pulse
can increase surface charge density. A special deposition layer may
be obtained by special reductant pulse.
Acknowledgment
This paper was supported by the Special Doctoral Foundation of
the Education Ministry of China ͑grant no. 20030730014͒
Lanzhou University assisted in meeting the publication costs of this
article.
Model of interfacial tension.— The interfacial tension of electrode/
solution plays an important role for adsorption and diffusion of ions.
It interacts with surface charge density and can be calculated with
25
the Lippmann equation
List of symbols
␸
e
␥
= −
qd␸
͓32͔
͓33͔
A
area of electrode ͑mm2͒
Ci initial capacity ͑F͒
Cs capacity step ͑F͒
Ce end capacity ͑F͒
capacity ͑F͒
Faraday constant ͑C͒
ii1 specific adsorption current ͑A͒
ii2 diffuse current ͑A͒
is current step ͑A͒
ie end current ͑A͒
response current ͑A͒
qi initial surface charge density ͑C/mm ͒
qs step of surface charge density ͑C/mm ͒
qe end surface charge density ͑C/mm ͒
͵
␸
i
Submitting ␸ , ␸ , ␸ , q , q , and q into Eq. 32, we acquire
i
s
e
i
s
e
−
2
−5 2
C
F
␥i = 10.79 − 3.90 ϫ 10 t + 8 ϫ 10 t
−
8 3
−
6.25 ϫ 10 t ͑0 Ͻ t ഛ 1000͒
␥s1 = − 5 ϫ 10−3 ln͑t − 999.7͒ − 0.89/͑t − 999.7͒
2.97 ͑1000 Ͻ t ഛ 1000.4͒
i
+
͓34͔
͓35͔
2
2
−
2
␥s2 = − 25.13 + 2.34 ϫ 10 t ͑1000.4 Ͻ t ഛ 1010͒
2
R1 resistance of solution ͑⍀͒
Rr resistance of chemical reaction ͑⍀͒
␥e = 764.18 − 7.72 ϫ 104e−t/222.19 ͑1010 Ͻ t Ͻ 1800͒ ͓36͔
The curve of ␥-t is shown in Fig. 8. The initial interfacial tension
R
t
␸
parallel resistance of R1 and R ͑⍀͒
time ͑s͒
open-circuit potential ͑V͒
r
−
11
−13
is from 10 to 10 ; the step of interfacial tension increases from
−
12
−
7.37 ϫ 10
to 1.70 within 0.4 s, then decreases to −1.65 and
␸i initial potential ͑V͒
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C682
Journal of The Electrochemical Society, 153 ͑10͒ C677-C682 ͑2006͒
␸
s
potential step ͑V͒
Soc., 148, 784 ͑2001͒.
␸
␥
␥
␥
e
end potential ͑V͒
13. F. Jin, H. Tong, L. B. Kong, and C. Wang, Appl. Phys. A: Mater. Sci. Process.,
initial interfacial tension ͑N/mm͒
interfacial tension step ͑N/mm͒
end interfacial tension ͑N/mm͒
A80, 597 ͑2005͒.
I
1
1
4. D. Niwa, T. Homma, and T. Osaka, J. Phys. Chem., B108, 9900 ͑2004͒.
5. P. Gorostiza, M. A. Kulandainathan, R. Díaz, F. Sanz, P. Allongue, and J. R.
Morante, J. Electrochem. Soc., 147, 1026 ͑2000͒.
s
e
1
1
6. T. K. Tsaia and C. G. Chaoa, Appl. Surf. Sci., 233, 180 ͑2004͒.
7. D. I. Ma, L. Shirey, D. McCarthy, and A. Thompson, Chem. Mater., 14, 4586
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