Properties of ZrO2 passive film formed onto Zr electrode in 1 M NaOH at low voltage

Article abstract of DOI:10.1149/1.2868759

In this paper, results of the potentiodynamic-potentiostatic formation of a homogeneous, passive film of ZrO2 on a Zr electrode in a 1 M NaOH solution at potentials lower than 4.0 V vs saturated calomel electrode are presented. The properties of such a film were investigated by electrochemical impedance spectroscopy (EIS) measurements. After fitting the EIS results by an appropriate equivalent circuit, the capacitance (Cpf) and resistance (Rpf), as well as the space charge capacitance (Csc) and space charge resistance (Rsc) of this film, were determined. The film was found to become an insulator (IN) at the potentials equal to and/or more positive than 2.0 V. In the potential range 0.8 Va transition from a semiconducting to insulating behavior (SC-IN) has been recorded. The donor densities (Nsc), as well as their flatband potentials (Efb) and their space charge layer (dsc) thickness, were determined from the corresponding Mott-Schottky plots recorded in two potential ranges (0.0 V

Full text of DOI:10.1149/1.2868759

Journal of The Electrochemical Society, 155 ͑5͒ C183-C188 ͑2008͒
C183
0
013-4651/2008/155͑5͒/C183/6/$23.00 © The Electrochemical Society
Properties of ZrO Passive Film Formed onto Zr Electrode
2
in 1 M NaOH at Low Voltage
,
z
V. D. Jović* and B. M. Jović
Center for Multidisciplinary Studies, University of Belgrade, 11030 Belgrade, Serbia
In this paper, results of the potentiodynamic–potentiostatic formation of a homogeneous, passive film of ZrO on a Zr electrode in
2
a 1 M NaOH solution at potentials lower than 4.0 V vs saturated calomel electrode are presented. The properties of such a film
were investigated by electrochemical impedance spectroscopy ͑EIS͒ measurements. After fitting the EIS results by an appropriate
equivalent circuit, the capacitance ͑C ͒ and resistance ͑R ͒, as well as the space charge capacitance ͑C ͒ and space charge
pf
pf
sc
resistance ͑R ͒ of this film, were determined. The film was found to become an insulator ͑IN͒ at the potentials equal to and/or
sc
more positive than 2.0 V. In the potential range 0.8 V Ͻ E Ͻ 2.0 V, a transition from a semiconducting to insulating behavior
͑
SC-IN͒ has been recorded. The donor densities ͑N ͒, as well as their flatband potentials ͑E ͒ and their space charge layer ͑d ͒
s
c
f
b
s
c
thickness, were determined from the corresponding Mott–Schottky plots recorded in two potential ranges ͑0.0 V Ͻ E
Ͻ 0.7 V − SC͒ and ͑0.8 V Ͻ E Ͻ 2.0 V − SC-IN͒, where the film behaved as an n-type semiconductor. From the potential
range of the insulating behavior of the film ͑IN͒, its thickness was determined from Cpf.
©
2008 The Electrochemical Society. ͓DOI: 10.1149/1.2868759͔ All rights reserved.
Manuscript submitted August 7, 2007; revised manuscript received December 31, 2007. Available electronically March 11, 2008.
n−1 1/n
Although the anodic behavior of Zr has been the subject of
1
1-14
C = A3
͓1͔
intensive investigations
curves͒, only a few papers have presented the polarization charac-
͑not referring to anodizing charging
f
ͫ
ͩ ͪ
ͬ
R
1
1-3
teristics of Zr in different electrolytes. It was shown in all cases
that at potentials more positive than the corrosion potential, passi-
vation of the Zr electrode occurs, attributed to the formation of a
with n varying from 0.92 to 0.99. The thickness of the passive film
was calculated using the same equation as the one in this paper ͑Eq.
4
; see the Results and Discussion section͒, and a linear dependence
of the film thickness vs applied voltage was obtained. The charac-
ZrO passive film.
2
The properties of the passive ZrO film were mainly investigated
teristic of all these investigations is that the ZrO passive film was
2
2
by electrochemical impedance spectroscopy ͑EIS͒ or capacitance
formed by cycling the potential from 0 to 300 V and measuring the
impedance ͑or capacitance͒ at the open-circuit potential at several
points on the current density vs voltage curve by stopping the
3
-11
measurements.
In most cases, a ZrO passive film was obtained
2
4
-8,10
by anodization at high voltages ͑up to 300 V͒. In some cases,
4
-9
8
cycling at these points. Bardwell et al. formed passive oxide
the capacitance was found to be frequency dependent, while Meis-
9
films on Zr by applying constant current densities ͑0.05, 0.5, and
terjahn et al. reported a frequency-independent capacitance over a
−
2
−2
5
5 mA cm ͒ in steps to 100 mC cm in different solutions ͑bo-
rates, pyrophosphates, and sulfates of pH 8.4͒ and measured the
impedance of such films at the open-circuit potential. They found
that the impedance of the passive film changed with increasing film
thickness, and that the best fit could be obtained by an equivalent
circuit consisting of the parallel connection of CPE and Rp con-
nected in series with the solution resistance Rs. The increase of Rp
with the time of film exposure to the open-circuit potential was
interpreted as “the healing of defects, but not as a thickening of the
film”. At the same time, it was found that “the kinetics of the in-
wide range of frequencies. It was stated by Patrito et al. that the
frequency dependence of the real component of the impedance “in-
dicates that the system Zr/ZrO /electrolyte does not behave as a
2
simple RC series circuit”, and that the oxide is described by a com-
plex dielectric constant. The existence of a bilayered ZrO passive
2
film, composed of a thin, compact inner layer at the electrode sur-
face and a porous outer layer of higher conductivity, has been re-
6,7
6
ported by Pauporte et al. In their first paper, it was shown that in
.5 M H SO and 0.1 M Na SO ͑pH 9͒ the impedance of ZrO
0
2
4
2
4
2
crease of R with time due to the healing of defects become slower
p
passive films formed by cycling the voltage from 0 V vs IrO to 300
10
2
as the thickness increases”. Huot produced and investigated ZrO2
−
1
V vs IrO ͑sweep rate either 100 or 25 mV s ͒ could be fitted by
2
films in a 0.1 M LiOH solution as a function of surface preparation
and the anodic potential by simultaneously measuring the current
an equivalent circuit composed of a constant phase element ͑CPE1͒
−
1
and the solution resistance ͑R ͒ connected in series. However, in 0.1
1
͑v = 50 mV s ͒ and the electrode capacitance ͑1000 Hz, 5 mV͒
during a single cycle of the voltage between 0 and 12 V vs reference
hydrogen electrode. “The actual dependence of C and R on fre-
quency suggested that the Zr/ZrO2/LiOH system does not behave as
an ideal capacitor connected in series with the resistance of the
solution”. It was concluded that a passive film of 28 nm thickness is
obtained at 12 V vs saturated calomel electrode ͑SCE͒, which is a
M NaOH, the transformation from one to two layers occurred at
voltages higher than 25 V and a complex equivalent circuit com-
posed of CPE ͑representing the compact oxide layer͒, the parallel
3
connection of CPE and R ͑representing the porous oxide layer͒,
2
2
and the solution resistance ͑R ͒ could be used to fit the impedance
1
6
7
spectra. In their second paper, the ZrO passive film was formed
3
2
typical insulator. Recently, Chen et al. investigated the electro-
and investigated by EIS measurements in 0.1 M ͑NH ͒ B O . The
4
2
4
7
chemical behavior of Zr in a borate buffer solution of pH = 6.94 at
6
EIS spectra revealed a bilayer structure ͑as in the previous paper ͒,
but the fitting was performed with an equivalent circuit composed of
the serial connection of CPE and R , representing a simplification
2
50°C and a pressure of 62 bars by measuring the current, imped-
ance, and capacitance as a function of the potential. Passive oxide
films were formed at different potentials for 24 h and their thickness
was determined from the capacitance measurements ͑using the same
equation as in Ref. 7; see also the Results and Discussion section͒,
since it was found that the capacitance of such a passive oxide film
is practically independent of the frequency at f Ͼ 1 kHz. The EIS
spectra recorded for all passive films revealed well-defined de-
pressed semicircles with a Warburg-like impedance at low frequen-
cies. Assuming that the interfacial capacitance could be obtained
from C = −1/␻ZЉ, and neglecting the contribution of the Helmholtz
3
1
valid for the high-frequency part of the EIS spectra. Because the
n
impedance of the CPE was written as Z = 1/A ͑j␻͒ , the capacity
3
3
of the passive film was obtained from the equation
*
Electrochemical Society Active Member.
E-mail: vladajovic@ibiss.bg.ac.yu
z
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C184
Journal of The Electrochemical Society, 155 ͑5͒ C183-C188 ͑2008͒
Table I. ␣ and GF values for EIS results recorded at different potentials.
E/V
4.0
0.98 0.98 0.99 0.99 0.98 0.98 0.98 0.99 0.98 0.98 0.98 0.98 0.98 0.97 0.97 0.97 0.96 0.96 0.96
1.7 2.2 36 39 5.1 6.1 7.2 12 18 13 25 12 25 6.9 2.1 7.8 12 27 37
3.8
3.6
3.4
3.2
3.0
2.8
2.6
2.4
2.2
2.0
1.5
1.3
1.1
0.9
0.7
0.5
0.3
0.1
␣
4
GF ϫ 10
layer capacitance, the measured capacitance was found to be equal
Contact of the Zr ͑99.8% Goodfellow͒ sample ͑1.0 ϫ 1.0
3
to the space charge capacitance, C . By direct measurement of
ϫ 0.2 cm ͒ with a copper wire on the back side of the electrode
sc
−
1
Mott–Schottky ͑MS͒ plots at a sweep rate of 25 mV s , a donor
was made with a silver conductive epoxy paste ͑Alfa Aesar͒; the
17
18
−3
2
density of the order of 10 –10 cm of the n-type semiconduct-
ing property of the film was determined, while the shift of the inter-
cepts on the vertical and horizontal axes was explained by the pres-
ence of a series combination of the voltage-independent capacitance
electrode was sealed in an epoxy resin so that an area of only 1 cm
was exposed to the solution. Once mounted, the electrode was pol-
ished first with emery papers ͑1200, 2400, and 4000͒ and then with
polishing clothes impregnated with alumina down to 0.05 ␮m ͑1,
0.3, and 0.05 ␮m͒, cleaned in an ultrasonic bath for 10 min ͑to
remove traces of the polishing alumina͒, thoroughly washed with
extrapure UV water, and transferred to the electrochemical cell,
where the polarization and EIS measurements were performed.
A polarization diagram was recorded in 1 M NaOH at a sweep
rate of 1 mV s− starting from the cathodic limit of −1.05 V and
finishing at 4.0 V. At the end of the polarization diagram ͑4.0 V͒, the
Zr electrode was held at this potential for 1 h for a passive oxide
film to grow. After passive oxide film formation, EIS spectra were
recorded at different potentials, covering the potential range
0.0 V Ͻ E Ͻ 4.0 V, starting from the upper limit and finishing at
the lower limit. After finishing these measurements, EIS spectra at
certain potentials in the range 0.0–4.0 V ͑exactly at 0.0, 0.5, 1.0, 2.0,
3.0, and 4.0 V͒ were recorded again to determine whether the prop-
erties of the passive film changed during this procedure. It was
found that the maximum difference between the first and repeated
experiments was in the range of ±5%, confirming that the properties
of the passive film remained the same during the impedance mea-
surements. The EIS spectra recorded in the potential range 0.6 V
Ͻ E Ͻ 4.0 V were obtained in the frequency range from 0.1 Hz to
of the outer insulating layer ͑C ͒ and the space charge capacitance
ox
͑
C ͒ of the barrier layer, using a modified MS dependence given by
sc
Eq. 17 in Ref 3. An identical equation ͑Eq. 2 in Ref. 11͒ was used to
11
explain the semiconducting properties of the ZrO2 passive film
formed at 12 V vs SCE in 1 M H PO . The MS plot was obtained by
3
4
1
the same procedure as in Ref. 3, except that the frequency used was
−
2
5
00 Hz ͑with the same assumption that C = −1/␻ZЉ͒. C was al-
most independent of the potential in the region from 0 to 12 V, while
at potentials more negative than 0 V, a sharp, linear change in the
slope of the C vs E dependence was recorded, with a minimum at
about −0.6 V and a sudden increase of C values at more negative
potentials. According to the authors, the existence of this minimum
on the MS plot was caused by the interface or surface states.
In the paper by Schweinsberg et al., anodic passive ZrO films
formed potentiodynamically ͑20 mV s ͒ on a polycrystalline Zr
electrode in 0.5 M H SO4 were investigated on single grains by
−
2
−
2
1
2
2
−
1
2
anisotropy microellipsometry ͑AME͒. The results showed a strong
texture dependence of the growth of the passive ZrO2 film on a
polycrystalline Zr electrode.
The photoelectrochemical properties of ZrO films formed on Zr
2
13
1
0 kHz or 40 kHz, while the EIS spectra at lower potentials were
electrodes were investigated by Di Quarto et al. The measurements
were performed in different non-deaerated electrolytes on oxide
films formed at the open-circuit potential, as well as on oxide films
formed after an additional anodization at 5 V on differently prepared
Zr metal surfaces. The photo-electrochemical behavior was inter-
preted by assuming the formation of a duplex oxide film with the
possibility of the presence of a hydrated oxide layer formed after
immersion in the solution at the open-circuit potential.
obtained in the frequency range from 0.01 Hz to 40 kHz ͑the ac
amplitude was 10 mV͒. The EIS spectrum recorded at 0.7 V was
repeated in the frequency range from 0.01 Hz to 100 kHz.
In the case of Gamry software ͑used for fitting the experimental
impedance diagrams͒, “goodness of fit” is the parameter which de-
fines the precision of the fitting. The goodness of fit is similar to
Boukamp’s chi-squared. It is a mathematical quantification of how
close the experimental points are to the line fitted by complex non-
linear least-squares analysis and is represented by the relation ͑chi-
squared͒/number of points. The smaller the value, the better the fit,
Concerning the growth mechanism of passive ZrO films, there
2
is still some controversy. The most accepted high field mechanism
1
4-17
18
͑
HFM͒
͑until 1976͒ was recently criticized by Zhang et al.,
−
4
with the value of the goodness of fit 1 ϫ 10 for the best fit. In our
who pointed out that the point defect mechanism ͑PDM͒ provides a
better account of the experimental data than the HFM.
case, this value was between 1.67 ϫ 10− and 3.91 ϫ 10 and is
4
−3
given in Table I for several potentials.
Four experiments were repeated on the same sample of Zr elec-
trode with the same procedure of sample surface preparation ͑pol-
In this study, an attempt was made to grow a passive ZrO film in
M NaOH electrolyte by combining potentiodynamic and potentio-
2
1
static techniques at potentials lower than 4.0 V vs SCE, and to
investigate its insulating and semiconducting properties by the EIS
technique.
ishing͒ and ZrO film formation, and an average response ͑the varia-
2
tion of results was ±4%͒ is presented in the paper.
Experimental
Results and Discussion
All experiments were carried out in a three-compartment stan-
dard electrochemical cell at room temperature in an atmosphere of
purified nitrogen. Before each experiment, the electrolyte was
purged with N for 30 min. The same N atmosphere was main-
tained over the solution during the experiment to minimize oxygen
contamination. A platinum mesh counter electrode and the reference,
an SCE, were placed in separate compartments. The latter was con-
nected to the working electrode by a Luggin capillary. All solutions
were made from analytical grade NaOH ͑Merck͒ and extrapure UV
water ͑Smart2PureUV, TKA͒.
Polarization diagram.— The polarization diagram recorded in 1
M NaOH is shown in Fig. 1. The diagram is characterized by a
corrosion potential at about −0.9 V followed by a sharp increase of
2
2
the current density from about 10− to about 10 A cm and a
current density plateau at this value up to about 0.5 V. A sharp
increase in the current density with a peak at about 1.0 V and a
9
−5
−2
−
4
−2
current density maximum at about 2 ϫ 10 A cm and another
current density plateau ͑at about 1.5 ϫ 10− A cm ͒ characterize
the polarization diagram at more positive potentials. As can be seen
in Fig. 1, after holding the electrode at 4.0 V for 1 h, the current
4
−2
Polarization and EIS measurements were performed by a
computer-controlled Gamry potentiostat ͑Reference 600͒ using the
corrosion software DC 105 and the electrochemical impedance soft-
ware EIS 300.
density dropped to about 8 ϫ 10− A cm .
5
−2
There are only a few papers reporting the polarization character-
istics of Zr electrode in different solutions. In two of them, the
1
,2
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Journal of The Electrochemical Society, 155 ͑5͒ C183-C188 ͑2008͒
C185
Figure 1. Polarization diagram recorded on a Zr electrode at a sweep rate of
−
1
1
mV s in 1 M NaOH solution by holding the potential at 4.0 V for 1 h.
polarization characteristics of Zr were presented in the potential
range −0.5 to 2.0 V vs SCE in 0.5 M H SO , while in another
2
4
3
paper the polarization characteristics of Zr were presented in the
potential range −0.7 to 1.1 V vs standard hydrogen electrode ͑SHE͒
in 0.1 M B͑OH͒ + 0.001 M LiOH. In all cases, the polarization
3
curves were characterized by a passive region at potentials more
positive than the corrosion potential, with some increase of the cur-
Figure 2. ͑a͒ ZЈ–ZЉ diagrams recorded in 1 M NaOH at different potentials
͑Ǣ: 4.0 V; ᭺: 3.0 V; △: 2.4 V; ▽: 1.0 V; छ: 1.5 V; b: 0.6 V͒ for a passive
rent density ͑peak͒ at a potential of about 1.3 V in 0.5 M H SO .
2
4
The passive region was attributed to the formation of a ZrO film.
ZrO film. Frequency range: 40 kHz to 0.1 Hz. ͑b͒ ZЈ–ZЉ diagrams recorded
2
2
Figure 1 shows that a similar behavior was recorded in 1 M NaOH,
with the first current density plateau between about −0.8 and about
in the same solution at different potentials ͑Ǣ: 0.5 V; ᭺: 0.4 V; △: 0.3 V;
▽: 0.2 V͒. Frequency range: 40 kHz to 0.01 Hz. Experimental points are
presented by squares, circles, triangles, etc., while solid lines represent fitting
curves.
0
.5 V. With a further increase of the potential, the current density
again increased, followed by a passive region up to 4.0 V, indicating
that a new process occurred at the passive ZrO film. Because a
2
breakdown of the passive film on Zr was found not to occur up to
6
1−␣ 1/␣
300 V, this current density increase could be attributed to further
Cpf = ͓Y0͑Rpf͒
͔
͓2͔
͓3͔
oxidation of the passive ZrO layer, but not to oxygen evolution,
20
2
which is derived from the equation
because such a process was not detected in the investigated potential
region ͑it should be characterized by much higher current densities͒.
Hence, on holding the potential at 4.0 V for 1 h, further oxidation of
␣
−1
Cpf = Y0͑␻mЉ͒
where Y0 represents the constant in the equation for the constant
ZrO occurred at the electrode surface, followed by a slight decrease
21
2
phase element, present in all commercially available software
of the current density.
given in ⍀ cm−2 s ͒, ␻Љ is the frequency of the maximum on
−1
␣
͑
m
the −ZЉ vs log ␻ dependence ͑independent of the value of ␣͒ and ␣
is the factor of homogeneity of the space charge distribution in the
passive oxide film. It is important to note that in such approach it is
EIS results and MS plot analysis.— Some of the ZЈ–ZЉ dia-
grams recorded at different potentials in the potential range 0.7 V
Ͻ E Ͻ 4.0 V are presented in Fig. 2a, while some of the ZЈ–ZЉ
diagrams recorded at different potentials in the potential range
assumed that both components of the passive film ͑C and R ͒ are
pf
pf
1
9,20,22
dependent on ␣ ͑these equations
are generally developed for
0.0 V Ͻ E Ͻ 0.5 V are presented in Fig. 2b ͑experimental points
parallel connection of CPE and R͒. The frequency dispersion of the
capacity as a consequence of the passive film heterogeneity–
homogeneity ͑expressed as ␣͒ is closely related to the space charge
are given as squares, circles, triangles, etc., while the fitting curves
are presented as solid lines͒. The fitting was performed with the
equivalent circuit shown in Fig. 3, composed of a resistance ͑Rpf͒
and a CPEpf connected in parallel ͑representing the passive film
impedance͒, with the solution resistance ͑R ͒ in series with them.
s
The fitting parameters Rpf ͑R ͒, C ͑C ͒ are presented in Fig. 4a
sc
pf
sc
and 5b, respectively, while the ␣ values and the goodness of fit ͑GF͒
are given in Table I for several potentials. As can be seen, all ZЈ–ZЉ
diagrams are characterized by well-defined semicircles, and in all
cases very good fits were obtained, indicating that the total electrode
impedance is dominated by the impedance of the passive oxide film,
and that the contribution of the double-layer capacity can be ne-
glected. A small dissipation of points does exist in some cases at
lower frequencies, giving a higher value of the GF, up to about
−
3
3
.9 ϫ 10 ͑see GF in Table I͒. Taking into account that an ideal GF
−
4
value amounts to 1 ϫ 10 , and that the total measured impedance
varies from about 12 to about 10 M⍀ cm , all fits are satisfactory.
2
Figure 3. Schematic representation of the equivalent circuit used to fit the
In order to obtain the dimensionally correct value for the capaci-
tance, the following equation was used
experimentally obtained impedance results: R : resistance of the passive
pf
19
oxide film; CPE : CPE of the passive oxide film; R : solution resistance.
pf
s
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C186
Journal of The Electrochemical Society, 155 ͑5͒ C183-C188 ͑2008͒
Figure 4. ͑a͒ Rpf vs E and Cpf vs E dependences obtained by fitting ZЈ–ZЉ
diagrams recorded in the potential range 1.0–4.0 V. ͑b͒ Corresponding dpf vs
E dependence is obtained using Eq. 4.
Figure 5. ͑a͒ MS plot obtained in the potential range 0.0–4.0 V. ͑b͒ Rsc vs E
and Csc vs E dependences obtained by fitting ZЈ–ZЉ diagrams recorded in the
potential range 0.0–0.8 V ͑linear MS plot͒.
A detailed analysis of the MS plot is shown in Fig. 5a. Three
potential regions with different shapes ͑slope͒ of the MS plot are
detected: an insulating behavior ͑IN͒ of the passive film ͑E
Ն 2.0 V͒, a transition potential region ͑0.7 V Յ E Յ 2.0 V͒
marked with SC-IN, and a space charge region ͑SC͒ at potentials
distribution in the film; these two parameters are mutually depen-
2
3
dent. Such a statement was also pointed out by Van Meirhaege in
24
the analysis of the capacity of semiconductors. According to these
two references, “the frequency dependence of the capacity must be
accompanied by a frequency-dependent parallel resistance.” The pa-
rameter ␣, which defines the homogeneity of the space charge dis-
tribution in the passive oxide film, was found to vary between 0.96
and 0.99 ͑Table I͒, indicating an almost homogeneous space charge
distribution in the oxide film.
1
1
E Յ 0.7 V. From the slope of the SC region ͑3.28 ϫ 10
−
2
4
−1
F
cm V ͒ of this linear dependence, the donor density of the
1
9
−3
SC layer, Nsc = 1.96 ϫ 10 cm , was determined, while the flat-
band potential, Efb = −0.1 V vs SCE, represents the intercept on the
1
1
potential axis. From the slope of the SC-IN region ͑0.23 ϫ 10
After the fitting procedure and calculation of Cpf and R , these
pf
−
2
4
−1
F
cm V ͒ of this linear dependence, the donor density of the
values were used to plot the dependences shown in Fig. 4a. As can
be seen, Cpf is practically independent of the potential in the poten-
1
9
−3
SC layer, Nsc = 27.9 ϫ 10 cm , was determined, while the flat-
band potential, Efb = −10.65 V vs SCE, represents the intercept on
the potential axis. Both values of the donor density are in a rela-
tial range 2.0–4.0 V, with the average value being C ͑av͒
pf
−
2
=
1.83 ␮F cm . Hence, in this potential region, ZrO behaves as
2
9
tively good agreement with the one reported by Meisterjahn for a
an insulator and accordingly its thickness could be determined by
the equation
zirconium passive film formed at ambient temperature, but they are
almost two orders of magnitude higher than the one reported by
3
␧
␧0
Chen for a zirconium passive film formed in 0.1 M B͑OH͒3
dpf
=
͓4͔
+
0.001 M LiOH at an elevated temperature and high pressure
Cpf
1
7
18
−3
3
͑
10 –10 cm ͒. In comparison with the statement of Chen et al.
3
where the dielectric constant of ZrO is ␧ = 22 and the permittivity
2
that “the film is only lowly-doped with electron donors” ͑which is
most probably the consequence of a low value for potentials used
for the passive film formation in Ref. 3, 0.3–0.6 V vs SHE͒, it is
obvious that the films formed at potentials equal to and/or more
positive than 2.0 V in 1 M NaOH are highly doped, and that the
level of doping increases as the potential region of insulating behav-
ior ͑E Ն 2.0 V vs SCE͒ is approached.
−
14
−1
of the free space is ␧ = 8.85 ϫ 10
F cm . The results of such
0
calculations, with the average value of the thickness of the ZrO film
2
being d ͑av͒ = 10.56 nm, are presented in Fig. 4b. A small increase
pf
in the value of Cpf could be detected in the potential range 1.0–2.0
V, while Cpf ͑C ͒ and R ͑R ͒ significantly increase in the potential
sc
pf
sc
range 0.0–0.8 V ͑Fig. 5b͒.
In order to obtain more detailed information about the semicon-
Concerning the value of the flatband potential, there is a discrep-
ancy between our results and the results cited in the literature. In
ducting behavior of the ZrO film, the MS plot was analyzed.
2
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Journal of The Electrochemical Society, 155 ͑5͒ C183-C188 ͑2008͒
C187
2
4
Morrison’s book, the value of the flatband potential for ZrO is
ducting oxide, resulting in the formation of an insulator, because the
2
2
5-27
given as −1.8 V vs SHE, taken from three cited references
Table V.1. on p. 183͒. After an inspection of citations in the book,
we found that two of these references ͑Ref. 26 and 27͒ do not
correspond to the properties of ZrO . In Ref. 26, the value of the
flatband potential for ZrO is given in Table II, being −1.0 V vs
SHE ͑not −1.8 V vs SHE͒, and was taken from Ref. 25, while in
thickness of the SC layer ͑d ͒ is practically identical to the thick-
sc
2
4
͑
ness of the passive oxide film ͓d ͑av͔͒.
pf
The impedance of the process occurring in the semiconducting
2
oxide film could be represented by the parallel connection of Cpf and
2
Rpf ͑see Fig. 6a and c͒ or the serial connection of Cpf and R ͑see
s
Fig. 6b and d͒, respectively. The simplification of the process occur-
ring at the semiconducting electrodes, assuming either the serial
connection of Cpf and R or the parallel connection of C and Rpf
Ref. 27, the properties of YFeO were investigated and ZrO was
3
2
not even mentioned. In Ref. 25 the data concerning the flatband
potential for ZrO2 do not exist, except for the diagram with the
intensity of the photocurrent as a function of potential ͑Fig. 2͒,
where the intercept on the potential axis for a ZrO film formed at 8
V vs SCE ͑no data about the time of anodization͒ was about −1.5 V
vs SCE. As stated in Morrison’s book ͑p. 135͒, “any other un-
known voltage sources located outside the semiconductor space
charge region such as IR drop or a battery will shift the voltage axis
s
pf
͑with Cpf being a parallel plate capacitor͒, is very often used in the
3,11,30-35
literature.
In the case of the serial connection of Cpf and Rs,
2
the capacitance is calculated directly from the value of Z , i.e.,
Љ
Cpf = 1/2␲fZЉ, while in the case of the parallel connection of C
24
pf
and R , the capacitance is calculated directly from the value of YЉ,
pf
i.e., Cpf = YЉ/2␲f. The results of such an analysis ͑C vs E͒ are
pf
presented in Fig. 6 for different frequencies ͑Ǣ: 10 kHz; ᭺: 1 kHz;
by the amount of the voltage, and appear as a shift in E . A common
fb
△
: 100 Hz, and ▽: 10 Hz͒ for the passive ZrO film in the potential
2
source of such an unknown voltage is a separate phase, a film, on
the surface.” Hence, one of the reasons could be an additional ohmic
resistance, either from the electrode contact or from the cell con-
range 0.9–4.0 V ͑Fig. 6a and b, insulating behavior͒ and in the
potential range 0.0–0.7 V ͑Fig. 6c and d, semiconducting behavior͒.
As can be seen in all cases, for frequencies higher than 10 Hz, Cpf is
practically independent of potential, and well-defined linear Cpf vs E
plots are obtained. For the potential range 0.9–4.0 V ͑Fig. 6a and b,
insulating behavior͒, this is in accordance with the plots presented in
Fig. 4a, but the values of Cpf were found to depend on the frequency
struction which could cause very negative values of E . Considering
fb
Ref. 3 and 11, after assuming simplification of the system by a serial
connection of the resistance and capacitance, the MS plots show
extremely negative values of Efb and, in order to explain such a
behavior, the authors had to assume the existence of a duplex oxide
for both the assumption of the serial connection of Cpf and R and
s
film, with the properties of the second oxide film, C , being unde-
ox
the parallel connection of Cpf and R . Moreover, neither of the
pf
fined. In this paper it has been shown that such a simplification
could give wrong results, even for very homogeneous films ͑see
further discussion͒.
average Cpf values matches the one obtained from Fig. 4a. At the
same time, for the potential range 0.0–0.7 V ͑Fig. 6c and d, semi-
conducting behavior͒, instead of the Cpf vs E plot presented in Fig.
5b, linear Cpf vs E plots independent of potential were obtained
The thickness of the SC layer ͑d ͒ is calculated by the
sc
2
8,29
equation
͑
except for f = 10 Hz͒. It is most likely that the change of the
values of Cpf as a function of the frequency is the consequence of
the fact that the passive film capacitance is not exactly a parallel
plate capacitor, but is represented by the CPE and, although the
values of ␣ are close to unity ͑0.96–0.99͒, the values of Cpf are
sensitive to such small deviations from unity. Usually such an ap-
1
/2
2
␧␧0
kT
e
dsc
=
ͫ
ͩ
E − Efb
−
ͪ
ͬ
͓5͔
eNsc
where E is the potential of the passive oxide film formation, while e,
k, and T have their usual meaning. In the case of the semiconducting
potential region ͑SC͒, the value of E was 0.8 V, the first point where
this oxide film behaves differently; the change of the slope on the
MS plot ͑see Fig. 5a͒. In the case of the transition potential region
3
,11,30-35
proach is used
at only one constant frequency ͑1 kHz in
most cases͒, assuming that, at such a particular frequency, the sys-
tem could be described by the serial connection of the solution re-
sistance and oxide film capacitance ͑neglecting the contribution of
the double-layer capacitance͒. This is a correct assumption, but, for
impedance spectra of almost all electrochemical systems, this as-
sumption ͑simplification͒ is valid and the question arises as to
whether the obtained values for the donor density and the flatband
potential are correct. In this paper it is shown that such an assump-
tion can lead not only to the wrong values, but also to a different
dependence of the passive film capacity on frequency ͑Fig. 6͒.
Hence, according to the results presented in this work, it appears
reasonable to avoid direct MS ͑or Cpf vs E͒ plots and obtain correct
values of Cpf by fitting EIS results and then plotting the correspond-
ing MS ͑or Cpf vs E͒ dependences.
͑
SC-IN͒ this value was 2.0 V, the first point where this oxide film
behaves as an insulator. By the analysis of the MS plot recorded in
the SC-IN region in Fig. 5a, an extremely negative and unrealistic
value for the Efb was obtained ͑Efb = −10.65 V vs SCE͒, but the
thickness of the SC layer ͑calculated using Eq. 5͒ remained practi-
cally the same as the one recorded for the semiconducting ͑SC͒
region ͓d ͑SC͒ = 10.4 nm, d ͑SC-IN͒ = 10.0 nm͔ and was prac-
tically identical to the thickness of the insulating oxide film
dpf͑av͒ = 10.56 nm͔. Such a behavior indicates that in the transi-
tion potential region it is possible to obtain linear MS plots with the
reasonable values for the donor densities. Extremely negative values
for Efb could be explained either by the introduction of a duplex
oxide film, as it was the case in Ref. 3 and 11, or by the presence of
the transition potential region. Taking into account that the values of
sc
sc
͓
Conclusions
dsc and d ͑av͒ are practically identical and that there is no indica-
pf
This paper showed that a homogeneous passive ZrO film could
2
tion of the presence of a second semicircle ͑corresponding to an-
other oxide layer͒ in the EIS results ͑Fig. 2͒, it appears that the
assumption of the existence of a duplex oxide film is unrealistic for
this case.
be formed on a Zr electrode in 1 M NaOH by a combination of
potentiodynamic and potentiostatic techniques at potentials more
negative than 4.0 V vs SCE. The film was found to become insulator
͑IN͒ at the potentials equal to and/or more positive than 2.0 V as a
result of a depletion ͑exhaustion͒ layer formation. In the potential
range 0.8 V Ͻ E Ͻ 2.0 V, a transition from a semiconducting to
insulating behavior ͑SC-IN͒ has been recorded. The donor densities
24
According to Morrison, by changing the cell voltage the ex-
periment can produce four different forms of the SC layer. One of
them is a depletion layer, sometimes termed an exhaustion layer.
This layer forms if the majority carriers are extracted in moderate
amounts, the surface region is “depleted” of majority carriers, and
minority carriers are not present, thus the surface region is depleted
͑
N ͒, as well as their flatband potentials ͑E ͒ and their thicknesses
s
c
f
b
of the SC layer ͑d ͒, were determined from the corresponding MS
sc
plots recorded in two potential ranges ͑0.0 V Ͻ E Ͻ 0.7 V
− SC͒ and ͑0.8 V Ͻ E Ͻ 2.0 V − SC-IN͒, where film behaved as
an n-type semiconductor. It was also shown that it seems reasonable
͑
exhausted͒ of both forms of mobile carriers. In such a case, the
surface region is essentially insulating. Hence, it is most likely that
with an increasing potential such a process occurs in the semicon-
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C188
Journal of The Electrochemical Society, 155 ͑5͒ C183-C188 ͑2008͒
Figure 6. ͑a and c͒ Cpf vs E dependences obtained by the analysis of EIS results for different frequencies ͑Ǣ: 10 kHz; ᭺: 1 kHz; △: 100 Hz; and ▽: 10 Hz͒
assuming a parallel connection of Cpf and R . ͑b and d͒ C vs E dependences obtained by the analysis of EIS results for different frequencies ͑Ǣ: 10 kHz; ᭺:
pf
pf
1
kHz; △: 100 Hz; and ▽: 10 Hz͒ assuming a serial connection of Cpf and R .
s
1
1
1
1
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͑
or Cpf vs E͒ dependences.
8. L. Zhang, D. D. Macdonald, E. Sikora, and J. Sikora, J. Electrochem. Soc., 145,
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