7406
J. Phys. Chem. B 1998, 102, 7406-7412
Characterization of Electronic and Dielectric Properties of Anodic Oxide Films on Bismuth by Electrochemical Impedance Spectroscopy M. Metikosˇ-Hukovic´ *,† and Z. Grubacˇ ‡ Faculty of Chemical Engineering and Technology, Department of Electrochemistry, UniVersity of Zagreb, 10000 Zagreb, P.O. Box 177, Croatia, and Faculty of Technology, Department of Inorganic Chemistry, UniVersity of Split, 21000 Split, Teslina 10, Croatia ReceiVed: December 3, 1997; In Final Form: June 17, 1998
The results of impedance spectroscopy measurements confirm that different types of anodic films grow on bismuth in slightly alkaline solution and under potentiodynamic and potentiostatic experimental conditions. The band model of solids can describe the behavior of these films. Several approximations were necessary to introduce, since “rapidly” grown oxide films (with R ) 22 nm V-1) were highly nonstoichiometric and amorphous in structure. Numerical analysis showed that two capacitive contributions were involved in the measured impedance spectra, the oxide film capacitance (Cox) and space charge capacitance (CSC), which were used to characterize the semiconducting and dielectric properties of the Bi2O3/electrolyte structure. Both donor concentration (ND) and the critical electrode potential have been determined from Mott-Schottky behavior. The dielectric properties of the oxide film were discussed in terms of a parallel plate capacitor and in accordance with the high-field growth law, and several parameters were determined: the oxide layer thickness (dox), the dielectric constant (), the potential at which oxide electroformation starts (Ed)0 ox ), the thickness of native oxide (din), and the anodization coefficient (R). Potentiostatic anodization confirms the rearrangement within the oxide film under the high electric field detected by impedance spectroscopy. The results indicate that the film formed potentiostatically behaves almost like a capacitor (insulator). The high resistance of the Bi-Bi2O3/electrolyte structure was ascribed to a very high interfacial charge-transfer resistance.
1. Introduction As a result of their applications in areas of optical films, microelectronics, capacitor manufacturing (for electrolytic MOM capacitors), and protection against corrosion, the electrochemistry of most “valve” metals (Al, Ti, Zr, Nb, Ta, Bi, etc.) has been extensively investigated for a long time.1-12 The name “valve” is sometimes used for the range of metals having useful electronic properties for vacuum tube technology. Among valve metals, bismuth occupies a special place, since bismuth anodic films show electrical rectification. The film is a strong insulator in anodic polarization but conducts current easily during cathodic polarization. The formation of anodic films on bismuth is favored in alkaline,1,13 neutral, and acidic14-15 as well as in nonaqueous electrolytes.16 Barrier type oxide films anodically formed on bismuth have been extensively studied in relation to their growth kinetics and their composition and structure.13-22 Nevertheless, thin anodic films are now widely employed in electronic devices, so a considerable interest has arisen in the electrical properties of these films, which are largely dependent on the type of electrical perturbation applied to the metal/solution interface during surface oxide layer formation. Capacitance measurements at estimated frequencies and/or fitting of I-E characteristics are not, however, proper methods for investigating these films.23-25 Electrochemical impedance spectroscopy (EIS)26-30 offers an excellent method to test the equivalent electrical circuit model (EEC) used to describe the metal oxide(semiconductor)/ * To whom correspondence should be addressed. Phone: (+385-1) 4597140. Fax: 4597-139. E-mail:
[email protected]. † University of Zagreb. ‡ University of Split.
electrolyte or metal oxide (insulator)/electrolyte interface. It is particularly desirable to be able, using impedance measurements, to represent the metal oxide/electrolyte interface in terms of passive electronic elements in the equivalent circuit, the physical significance of which can be ascertained by variation of the electrode potential. It is also important to assign the passive elements to a spatial configuration of the various charge accumulation modes. The present paper is a study of a bismuth oxide layer/ electrolyte system by means of EIS, over a wide frequency range. The purpose of this paper is to analyze the dielectric properties of the potentiodynamically and potentiostatically formed Bi oxide films on Bi and to provide more detailed information concerning their electronic properties. We attempted to fit the impedance data using different EECs in such a way as to simulate a complete set of data (from 30 mHz to 60 kHz) using a minimum number of passive elements within a relative error less than 5%. A Maxwell-type five-element circuit, involving surface states, could be excluded as a reasonable model for the impedance data combined with the results of Mott-Schottky measurements.26 The EEC model presented in this paper is very helpful for the quantitative analysis of the Bi oxide/electrolyte interface. 2. Experimental Section Electrochemical impedance and photoelectrochemical measurements were carried out in a borate buffer solution of pH ) 9.2, an electrolyte that has no dissolution action on the oxide films electrochemically formed on bismuth. A borate buffer solution, pH ) 9.2, consisting of 0.1 mol dm-3 H3BO3 + NaOH was prepared from reagent grade chemicals and triply distilled water. The working electrode was prepared from spectroscopi-
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J. Phys. Chem. B, Vol. 102, No. 38, 1998 7407
cally pure bismuth rods (Johnson-Matthey) and sealed into a glass tube with epoxy resin. Prior to each experiment the exposed surface (0.197 cm2) of the working electrode was polished to a mirror finish with 0.05 µm alumina powder, degreased in trichlorethylene, and afterward repeatedly rinsed with triply distilled water. All measurements were carried out on freshly prepared electrodes that were first cathodically polarized at -1.6 V in the working solution for 15 min to remove any previously formed surface film. The reference electrode was a saturated calomel electrode (SCE) to which all potentials were referred. EIS measurements were performed in the wide frequency range, from 60 kHz to 30 mHz, by use of an ac voltage amplitude of (5 mV, an EG&G PAR lock-in amplifier M5301A for a single-sine type of experiment (60 kHz to 5 Hz), and the M273 potentiostat/galvanostat for a multisine type of experiment (5 Hz to 30 mHz). The frequency spectra are analyzed in the complex plane using the software for complex nonlinear leastsquares (CNLS) fitting developed by Boukamp.31-33 Electrochemical impedance measurements were applied to in situ characterize the Bi oxide/electrolyte interface. Anodic oxide films were produced using the potentiodynamic and potentiostatic experimental techniques. In dynamic conditions, oxide films were formed with the sweep rate of 20 mV s-1 starting from the hydrogen evolution potential region up to various anodic potential limits (the potential range between -1.6 and 2.0 V). The impedance data were collected every 200 mV. This would typically take 30 min due to the low frequencies investigated. Potentiostatic experiments were done according to the following procedure. The first potential step from -1.6 to -1.2 V was applied to achieve a reproducible electroreduced Bi surface. After a potential holding at -1.2 V for 60 s was achieved, the second potential step from -1.2 V to different formation potentials, Ef, was applied. The potential was then progressively stepped 200 mV in the positive direction, and after waiting 30 min, impedance data were collected. For calculations of the oxide thickness, the geometric surface area was corrected using the roughness factor 1.8 that was obtained from the Coulometric and the capacitance data. Photoelectrochemical measurements were performed in a single compartment cell with a quartz window. The incident light of a 100 W tungsten-halogen lamp was chopped using a modified Brookdeal 9479 variable frequency chopper. The duration of the consecutive light and dark periods were 0.56 and 30 ms, respectively. Therefore, a condition related to the separation of nonequilibrium light-generated carriers and the establishment of a stationary photoeffect was achieved. Photocurrent was recorded during a linear potential sweep of 10 mV s-1. 3. Results and Discussion 3.1. Semiconducting Properties of Potentiodynamically Formed Oxide Films on Bismuth. The general features of the passivation of bismuth in a borate buffer solution under controlled potential sweep are illustrated in Figure 1. Two characteristic potential regions can be distinguished during the anodic scan. In the initial potential region, the current shows a sharp maximum, which corresponds to the growth of a bismuth oxide layer of monomolecular dimensionssthe monolayer region. The reaction34,35
2Bi(s) + 3H2O(aq) f Bi2O3(s) + 6H+(aq) + 6e
(1)
which has an equilibrium potential of Er ) -0.413 V vs SCE
Figure 1. Linear sweep voltammogram of a Bi electrode in a Na borate buffer solution, pH ) 9.2, sweep rate 20 mV s-1, and linear sweep voltammogram of a Bi electrode covered by the Bi2O3 film with superimposed photocurrent peaks. Electrode was illuminated with the rectangular light impulses of 100 W quartz halogen lamp via rotating chopper.
at pH ) 9.2, takes place. In the plateau region, the current is nearly constant, indicating a thickening of the film under a constant electric field by high-field ion migration in the film.12 By illumination of the interface of a Bi oxide/electrolyte with short light impulses, having a quantum energy hν > Eg, the observed photoeffect (photocurrent) can be interpreted as the result of the space charge separation of electron hole pairs in the depletion layer of the film by the applied field. The anodic photocurrent, which appears at the end of the monolayer region, increases and continues to increase in the plateau region. The onset potential of anodic photocurrent, i.e., the potential value at which the sign of photocurrent changes, corresponds to the flat-band potential, Efb ) 0 V.36-38 Metal oxides are compounds of variable composition for which deviation from stoichiometry is a common and expected phenomenon. Depending on the character of deviation, i.e., whether the excess anion or cation vacancies prevail in the oxide lattice, charge carriers can be mostly electrons (n-type) or mostly holes (p-type). The presence 0 of anion vacancies (V2+ 0 + 2e h V0) formed during the Bi(III) oxide growth under the swept potential control causes n-type conductivity of the oxide film18,19 as follows from Figure 1. The oxide film determines the structure of the double layer charge distribution and the potential drop both in the steady state and during electrode polarization, which have been studied using impedance spectroscopy. Selected impedance spectra of a Bi-Bi2O3 electrode at different formation potentials, Ef, in the form of Bode plots, are illustrated in Figure 2. In the fitting procedure we have shown that a better agreement between the theoretical and experimental data is obtained if a constant phase element (CPE) is introduced instead of a pure capacitance. The need to include a CPE element is the consequence of nonidealities of the solid Bi interface and has been extensively discussed by several authors.39-42 For frequencies ranging from 60 kHz to below 1 Hz, the electrode impedance, Z, may be precisely described by a constant-phase element CPE in series with a resistor, RΩ
Z ) Z(CPE) + RΩ ) [Q(iω)n]-1 + RΩ
(2)
where i is the imaginary number (i2 ) -1), Q is the frequencyindependent real constant, ω is the angular frequency, n is the
7408 J. Phys. Chem. B, Vol. 102, No. 38, 1998
Metikosˇ-Hukovic´ and Grubacˇ TABLE 1: CNLS Fit Values for the Electrical Equivalent Circuit Shown in Figure 2a E/V
106 × CPE/Ω-1 cm-2 sn
n
R1/Ω cm2
R2/kΩ cm2
106 × C2/F cm-2
-0.30 -0.24 0 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80
61.40 48.90 13.90 7.10 4.96 4.03 3.29 2.82 2.14 1.62 1.61 1.43 1.28 1.32 1.05 0.83 1.06
0.616 0.620 0.774 0.789 0.815 0.900 0.905 0.818 0.914 0.885 0.898 0.900 0.914 0.871 0.819 0.893 0.780
27 32 32 41 72 63 89 27 63 30 45 41 79 55 46 56 42
19.0 15.6 29.4 41.1 41.4 68.3 73.5 79.5 73.1 89.7 88.6 99.0 92.9 88.0 133.0 111.0 122.0
70.00 47.60 27.00 12.00 9.51 7.22 6.20 5.71 5.22 4.85 4.81 4.18 3.95 3.87 4.00 3.81 3.74
a
Figure 2. Simulated impedance spectra in the Bode plot of the potentiodynamically formed Bi2O3 films on Bi in a Na borate buffer solution, pH ) 9.2, at potentials of (b) 0, ([) 0.2, and (2) 2.0 V. Dependence of the (a) phase angle Θ and (b) absolute impedance |Z| on the applied frequency. The inset shows data for EEC used to fit the impedance spectra.
CPE power (n ) R/(π/2)), and R is the phase angle of the CPE. The factor n is an adjustable parameter that usually lies between 0.5 and 1.39-42 The CPE only describes an ideal capacitor when n ) 1. Otherwise, for 0.5 < n < 1, the CPE describes a distribution of dielectric relaxation times in frequency space. The resistive component measured at the high-frequency limit, RΩ, was independent of potential and was subtracted from the data presented in Figure 2. This resistance, typically 45 Ω cm2, is attributed to the solution resistance between the Luggin capillary and the working electrode and uncompensated resistance due to the ionic motion. The complete basic data are listed in Table 1. The EEC model of the Bi oxide/electrolyte structure, presented as the inset in Figure 2, fits the experimentally obtained impedance data. A value of χ-quadrate of 10-4 or less indicates a reasonable good fit using a minimum number of passive elements within an error of 5%. Numerical analysis shows that all the impedance spectra comprise two overlapping time constants. One of them (τ1) can be associated with the oxide response, and the other (τ2) can be related to a space charge. This enabled us to extract two capacitive contributions involved
Bi/potentiodynamically formed Bi2O3/Na borate buffer pH ) 9.2.
in the measured impedance, the oxide film capacitance, Cox and the space charge capacitance, CSC, used to characterize the semiconducting and dielectric properties of the potentiodynamically formed oxide layer. The capacitance, C2 (Table 1), obtained by the CNLS fitting procedure of the experimentally measured impedance data, is related to the space charge capacitance, CSC, and the Helmholtz double layer capacitance, CH by C2-1 ) CSC-1 + CH-1 assuming that contributions from surface states can be neglected. It was assumed that the surface states are characterized by one time constant, which does not significantly overlap with the time constants of any other states.43 All capacitance values were corrected taking the Helmholtz capacitance of 20 µF cm-2. During the anodic polarization of the electrode, electrons are 0 drawn (captured in the anion vacancies, V2+ 0 + 2e ) V0) from the oxide/electrolyte interface toward the metal/oxide interfaces, causing the band edges to bend upward. Thus, at the interface to the electrolyte side, the positive space charge of fixed ionized donors is formed, i.e., an exhausted layer. When the anodic polarization is increased, the thickness of the space charge layer dSC is increased. The Mott-Schottky relation23,24,44-46 describes the corresponding diminution of the space charge capacitance CSC that can be expected.
CSC-2 ) 2/0e0ND(|∆φs| - kT/e)
(3)
where and 0 are the oxide and vacuum dielectric constants, respectively, ND is the donor density, Efb is the flat-band potential, ∆φ is the voltage drop over the space charge layer (equals the difference between the electrode potential E and electrode potential at the flat-band condition) ∆φs ) E - Efb. The linearity of the relation CSC-2 vs E (3) implies that the main voltage drop occurs over the space charge layer. The positive slope of the Mott-Schottky straight line indicates that the potentiodynamically formed oxide film on bismuth behaves like an n-type semiconductor, which is coherent with results found by photopotential measurements.18,19 From the slope, using the eq 3 and taking the value of ) 46, the donor concentration, ND, of the oxide studied was calculated to be 1.7 × 1020 cm-3. The estimated value of the donor concentration is on the same order of magnitude as ND obtained for other semiconducting metallic oxides.23,46 The intercept at C2SC ) 0 corresponds to a critical potential, E0 ) 0.1 V. The measured E0 differs from Efb by the factor (-r + ln r)kT/e. An estimate
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J. Phys. Chem. B, Vol. 102, No. 38, 1998 7409
Figure 3. Schottky-Mott plot for the potentiodynamically formed Bi2O3 films on Bi in Na borate buffer solution, pH ) 9.2.
N+ D /ND
of Efb is therefore difficult because the ratio r ) remains unknown. The (Efb - E0) difference is equal to kT/e (∼25 mV at 25 °C) for r ) 1 (i.e., complete donor dissociation in the bulk of oxide). This is not, however, the usual case for anodically grown films.23 Generally, for crystalline semiconductors, the concentration of conducting electrons, resulting from donor dissociation, depends on donor energies ED that corresponds to the average of ED.47 Cooper et al.48 studied the influence of preparation techniques on the semiconducting properties of TiO2 and found that linearity of the Mott-Schottky plot did not guarantee that the value of a flat-band potential was incorrect or meaningful. This can be also easily seen from our results (Figure 3) where the Mott-Schottky plot shows good linearity but does not give a flat-band potential consistent with values obtained using other measuring techniques. The results of photocurrent measurements (Figure 1) showed that the curve recorded from the anodic to cathodic side yields the correct value for the onset potential of the anodic photocurrent, which in this case equals the flatband potential. According to literature data36-38,46-48 the electrode polarized in the described manner contains less surface states. The estimated thickness of the space charge layer, dSC ) (20|E - Efb|(eND))1/2 at 0.8 V is 4.6 nm. Since it is considerably smaller than the oxide layer thickness (see below), it provides a good basis for the use of the band theory. The charge in this region is eNDdSC )12 µC/cm2. 3.2. Dielectric Properties of Potentiodynamically Formed Oxide Films on Bismuth. The dielectric properties of the oxide film formed under the swept potential control were examined in terms of a parallel plate capacitor, eq 4, and in accordance with the high-field growth law, eq 5. According to the “highfield” law,1,2,15-17 a linear relationship between the oxide capacitance and formation potential, Ef, is expected, since the behavior of bismuth during anodic oxidation resembles the kinetics of anodization of valve metals.3-10,12-15 Thus
C-1 ox )
dox REf ) 0γA 0γA
(4)
where the second equality stands for
dox ) REf ) R(Ea,l - Ed)0 ox )
(5)
Figure 4. Dependence of the reciprocal capacity, C-1, of the potentiodynamically formed Bi2O3 films on the oxide, film thickness, dox. The inset shows the dependence of the reciprocal capacity, C-1, of the potentiodynamically formed Bi2O3 films on the electrogenerated oxide film thickness, ∆d. The solid line is the linear regression.
and dox is the oxide layer thickness, R is the anodization coefficient that indicates the rate of oxide growth in nm V-1, is the Ea,l is the upper (anodic) potential limit, and Ed)0 ox electrode potential at which oxide formation starts. It refers to a hypothetical thickness dox ) 0. In fact, the total oxide thickness, dox is composed of din, the thickness of the initial oxide present after the polishing step, and ∑∆d, resulting from the successive anodization steps. Thus
dox ) din +
qaVM
∑∆d ) din + nFAγ
(6)
were qa ) ∑∆qa. The reciprocal oxide capacitance Cox-1 can also be written as the sum of two terms Ca-1 and Cin-1, because the capacitance of the “electrogenerated oxide” is in series with the capacitance of the “initial oxide”. Now, Cexp-1 ) Cox-1 + CH-1. The value of Cexp was calculated from the time constant (τ1) that was obtained by the CNLS fitting procedure of impedance spectra (Table 1). CH commonly used in the literature is 20 µF cm-2.4,5 The reciprocal capacitance of the oxide layer, measured at the formation potential and plotted against the thickness of the oxide layer, is shown in Figure 5. The thickness was calculated from the anodic charge using Faraday’s law according to eq 6, in which the molar volume of the bulk Bi2O3 (VM ) 52.1 cm3/ mol) was used.49 The strong linear dependence shown in Figure 4 means that the capacity is only a function of the anodic charge or thickness and is independent of other factors. The extrapolation of the straight line to the abscissa yields the thickness of the film present initially (the spontaneously grown oxide film thickness), din ) 0.04 nm. The dielectric constant of ) 46 for the oxide film is obtained from the slope and using eq 4. This value agrees well with the values of reported by Williams,18 Bojinov,50 and Kanazirski.51 The variations of the reciprocal oxide capacitance and the corresponding value of the film thickness, as a function of the formation potential, are presented in Figure 5. The oxide film thickness increases linearly with Ef as can be expected for a valve metal. The anodization ratio, R, obtained using Figure 5
7410 J. Phys. Chem. B, Vol. 102, No. 38, 1998
Metikosˇ-Hukovic´ and Grubacˇ
Figure 5. Dependence of the reciprocal capacity, C-1, of the potentiodynamically formed Bi2O3 films on the formation potential, Ef. The inset shows the dependence of the oxide film thickness, dox, on the formation potential, Ef. The solid line is the linear regression.
and eqs 4 and 5 results in R ) 17.6 nm V-1 and relates to the electric field strength, E h , of about 6 × 105 V cm-1. The value of E h is consistent with literature results.1,12,15 The potential at which oxide formation starts Ed)0 ox is more than 200 mV more positive (Figure 5) than the equilibrium potential, since it includes the overpotential at the metal/oxide and oxide/ electrolyte interfaces depending on the current, i.e., sweep rate. 3.3. Electric and Dielectric Properties of Potentiostatically Formed Oxide Films on Bismuth. A typical Bode and Nyquist plot of the passive bismuth electrode with the potentiostatically formed oxide film is given in Figure 6. The fitting procedure using the simple equivalent circuit (parallel RC combination), shown as the inset in Figure 6, resulted in a very good agreement between the experimental and theoretical data. A standard deviation χ-quadrate was on the order of of 10-5, and the relative error was less than 5%. A complete listing of the basic data is given in Table 2. The exponent “n” of CPE points to a high degree of bismuth surface homogeneity. The Bode plot shows that the log |Z| against log f curves show three distinctive segments. In the higher frequency region, the log |Z| against log f relationship tends to become zero, with phase angle values falling rapidly toward 0°. This is a response typical of a resistive behavior and corresponds to a solution resistance. In the medium-frequency region, a linear relationship between log |Z| against log f with a slope close to -1 and phase angle approaching -90° can be observed. This is the characteristic response of a capacitive behavior. In the low-frequency region the resistive behavior of the electrode is reached. The lowfrequency limit, where |Z| does not depend on f, represents the sum of the electrolyte resistance RΩ and the charge-transfer resistance Rct that is defined by the equation
Rct ) lim Re {Zf} ωf0
(7)
where Re{Zf} denotes the real part of the complex faradic impedance Zf and ω corresponds to the frequency of the ac signal (ω ) 2πf). The radius of the semicircle in the Nyquist plot increases with increasing potential and indicates a very high interfacial charge-transfer resistance, Rct. The magnitude of the Rct is between 88 and 167 kΩ cm2.
Figure 6. Simulated impedance spectra in the Nyquist and Bode plots for the potentiostatically formed Bi2O3 films on Bi in a Na borate buffer solution, pH ) 9.2, at potentials of (b) 0.0, (2) 0.2, (9) 0.6, and (1) 1.8 V. The inset shows data for EEC used to fit the impedance spectra.
TABLE 2: CNLS Fit Values for the Electrical Equivalent Circuit Shown in Figure 6a E/V
Rct/kΩ cm2
106 × CPE/Ω-1 cm-2 sn
n
-0.20 0.20 0.60 1.00 1.40 1.80
11.67 61.20 87.90 110.50 121.66 166.50
39.32 11.85 5.50 3.48 2.54 2.13
0.772 0.847 0.892 0.915 0.926 0.934
a
Bi/potentiostatically formed Bi2O3/Na-borate buffer pH ) 9.2.
The capacitive nature of the passive electrode is readily apparent in Figure 7. The reciprocal capacitance is directly proportional to the thickness of the oxide film and can be obtained either from the Z(CPE) values (Table 2) at a frequency of 0.158 Hz, when the impedance data give, in the Bode plot, a straight line with a slope of -1, or from the value of the imaginary part of impedance, Zim, at the same frequency using the relation C-1 ) ωZim(ω)2πf). The anodization ratio (R ) 11.5 nm V-1) and the electric field within the oxide layer (E h ≈ 1 × 106 V cm-1), determined from the results in Figure 7 and using eqs 4 and 5, are noticeably different from the previous data for the oxide film formed under the swept potential control. The potential at which the film formation starts (Ed)0 ox ) -400 mV) shows less deviation from the equilibrium potential in comparison with the oxide formed potentiodynamically. Consequently, the charge distribution could be due to deep levels in the band gap that could not be detected in the potential range studied. The carrier concentration must be less than 1018 cm-3. In other words, space charge contributions to the electric field in the oxide film are found to
Characterization of Anodic Oxide Films
Figure 7. Dependence of the reciprocal capacity, C0.16Hz-1, of the potentiostatically formed Bi2O3 films on the formation potential, Ef. The inset shows the dependence of the oxide film thickness, dox, on the formation potential, Ef. The solid line is the linear regression.
be negligible, indicating either a less disordered amorphous structure or a more stoichiometric character of the Bi2O3 films produced under potentiostatic conditions in comparison with the films formed under potentiodynamic conditions. 4. Conclusions The results of impedance spectroscopy measurements confirmed that different types of anodic films grow on bismuth in slightly alkaline solution and under potentiodynamic and potentiostatic experimental conditions. Impedance spectra were characterized by two time constants relating to semiconducting and dielectric properties of the potentiodinamically grown Bi2O3 films. A combination of EIS data with photoelectrochemical measurements was useful in order to obtain reliable information about the electronic structures of these films: donor concentration, critical (flat-band) potential, potential of anodic photocurrent onset. The dielectric properties of Bi2O3 films were interpreted and analyzed in terms of a parallel plate capacitor and using a constant phase element model. Potentiostatically grown Bi2O3-film/electrolyte structure could be well described using a simple RC combination. The result indicated that the film behaved almost like a capacitor. Acknowledgment. The Ministry of Science of the Republic of Croatia supported this work through Grant 125011. Glossary A C Ca Cexp CH Cin Cox CPE
surface area capacitance capacitance of the anodic film total experimental capacitance Helmholtz capacitance capacitance of the “initial oxide” film total capacitance of the oxide film constant phase element
J. Phys. Chem. B, Vol. 102, No. 38, 1998 7411 CSC Css da din dox dSC e E Ef E h Efb Eg Erev F f I Iph j M n ND qa R Rct RΩ VM Z0 ZCPE
space charge capacity of a semiconductor capacitance induced by the presence of surface states thickness of the “electrogenerated oxide” thickness of the “initial oxide” total thickness of the oxide layer depletion layer thickness magnitude of electronic charge potential formation potential electric field strength flat-band potential width of band gap reversible potential Faraday constant frequency (f ) ω/2π) electric current photocurrent current density molar or atomic mass characteristic parameter of a CPE donor density quantity of electricity involved in the formation of the oxide resistance charge-transfer resistance ohmic resistance molar volume of the oxide formed absolute impedance at f ) 0.158 Hz impedance of a distributed element (CPE)
Greek symbols R 0 δ ω F η Θ τ Fs
anodization coefficient permittivity of vacuum relative permittivity roughness factor angular frequency density overpotential phase angle of a CPE time constant voltage drop over the space charge layer
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