Electrochromic nickel-oxide-based thin films in KOH electrolyte: Ionic and electronic effects elucidated by impedance spectroscopy

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Introduction
Materials that can change their optical properties, reversibly and persistently, as a response to an external electrical potential are called electrochromic (EC) and have important applications in technologies related to energy efficiency (such as smart windows for buildings), information displays, etc. [1][2][3][4][5][6].An EC device construction is usually based on five superimposed layers on one substrate, generally of glass or flexible polyester foil, or positioned between two substrates in a laminate configuration: transparent conducting oxide (TCO) layer/cathodic EC layer/ion conducting layer/anodic EC layer/TCO layer [1,3].Cathodic EC layers color under ion insertion while anodic EC layers color under ion extraction.The central part of the five-layer construction is a purely ionic conductor or electrolyte that can be inorganic (often based on an oxide film) or organic (an adhesive polymer).A particularly well studied combination of thin films in EC device technology uses tungsten oxide as the cathodic layer and nickel oxide as the anodic layer [3,[5][6][7][8][9][10].The electrolyte usually contains H + (protons) or Li + [3], although multivalent ions have also attracted recent interest [11,12].
Recent developments in the field include studies of nanostructured materials [13], additional functionalities [14], as well as a revived interest in other cathodic materials such as TiO 2 [15,16] and V 2 O 5 [17,18].
In the present paper we concentrate on anodic Ni-oxide-based EC layers and study the ion intercalation mechanism in this material.The EC behavior in two types of electrolytes, namely hydroxide solutions and Li + -containing electrolytes, is of considerable interest.The physical properties of Ni-oxide-based films were reviewed previously [8] with attention mainly to EC properties in KOH electrolyte.On the other hand, the EC behavior of such films in Li + -containing electrolytes appears to be complicated.Optical switching is similar in Li + -containing electrolytes and analogous Li + -free ones, which points to the importance of surface redox reactions and that both positive and negative ions are participating [19,20].There exists good evidence that the charge exchange per unit mass is higher in more porous films, suggesting that EC reactions occur mostly at pore surfaces [21].In addition, Elastic Recoil Detection Analysis has demonstrated that both cations and anions from the electrolyte are present in the film, presumably adsorbed at pore surfaces [22].Hence, it is doubtful whether Li + ions can be inserted into the lattice of Ni oxide.The exchanged charge density in films with a thickness of 300 nm is low, specifically of the order of 2 mC/cm 2 [21,22], which can be translated to an ion/Ni ratio less than 0.02 [21].This leads to a transmittance contrast between bleached and colored states which is significantly lower than for cathodic W-oxide-based films [22,23].
EC properties of Ni-oxide-based thin films that were colored and bleached in KOH electrolyte have been discussed in detail by Avendano et al. [24,25].Experiments with Pd-coated Ni-oxide-based films have conclusively shown that the ion exchange involves protons and not the larger OH − and alkali ions [24,26].Expelled protons react with hydroxide ions at the interface to yield water, and the proton insertion process may involve two hydroxide ions reacting to yield water and a proton [26,27].Substantial amounts of ions can be inserted and extracted from Ni-oxide-based films and ratios of protons to Ni in the range of 0.3 and, after extended polarization, even up to 0.6 have been reported [24].The films were found to contain a mixture of Ni oxide and hydroxide phases [25] and the Bode scheme [28,29] of reactions between hydroxide and oxyhydroxide phases was clearly of relevance for understanding the EC properties.It is assumed that coloration occurs by extraction of a proton from Ni(OH) 2 thus forming Ni oxyhydroxide (NiOOH) [24], which exhibits significant optical absorption.However, it appears that the NiO phase is also active in the coloration by forming optically absorbing superoxide (Ni 2 O 3 ), and the Bode scheme has been extended to take this into account [24,25].Bleaching occurs upon insertion of protons by the inverse reactions.The charge density exchange is much larger than in the case of Li + -electrolytes and values in the range 15-30 mC/cm 2 have been obtained [23,24,30].
It would be of interest to take advantage of the large charge density exchange and concomitant transmittance contrast that Ni-oxide-based layers exhibit in for example the KOH electrolyte for EC device technology.Unfortunately, hydroxide electrolytes are not suitable for EC devices, as they are not compatible with a tungsten oxide cathodic layer [23].Using a weak acid protonic electrolyte does not seem to be an alternative, as in this case Ni-oxide-based films exhibit a similar weak coloration as in Li + -containing electrolytes [23].It is therefore of major interest to understand the EC properties of Ni-oxide-based materials in hydroxide electrolytes, and particularly the origin of the large charge exchange density.This could pave the way to major advances in the application of Ni-oxide-based layers in EC devices.In the present paper, we perform a detailed study of charge insertion and transport in V-doped Ni-oxide-based films (referred to as V:NiO) by electrochemical impedance spectroscopy (EIS).The V:NiO films were prepared by reactive sputtering basically as in previous work [24,25].Dopants in NiO have significant effects on the optical absorptance at visible wavelengths [30,31].Some dopants, such as Al or Mg, actually decrease the absorption of NiO, while adding V gives a significantly enhanced absorption [30,31].
In the present study, we incorporated V in the Ni-oxide-based films for technical reasons, specifically to have a deposition process compatible with large-area high-rate magnetron sputter coating.The sputtering process is simplified by the use of non-magnetic targets and the V:NiO alloy target exhibits excellent mechanical properties for this purpose.In addition, X-ray photoelectron spectroscopy studies show that the oxidation state of V is not changed during EC coloration/bleaching [25] and hence the V dopant appears not to be electrochemically active.
EIS is a powerful technique for studying electrochemical reactions, ion intercalation, and ion diffusion phenomena in electrochemical systems [32,33].It has been repeatedly applied to study EC materials, as described in a detailed review [34].In the present case, EIS can give information on interfacial charge transfer and adsorption phenomena, ion diffusion coefficients, and also an effective electrochemical density of states [34].Ho et al. [35] introduced EIS techniques to the study of Li + diffusion in W oxide films and interpreted the results in terms of a Randles equivalent circuit [36].Subsequent work has shown that this model is too simplified, and models based on anomalous diffusion [37] give a better description of EIS data on W oxide thin films [38,39].Theories of anomalous diffusion are relevant for a wide field of applications, as pointed out in a recent review [40].
The present paper is a sequel to our previous impedance studies on EC W-oxide-based thin films [38,39].Impedance spectroscopy on Ni-oxide-based films has been surveyed in the review mentioned above [34].EIS is frequently carried out as a standard analysis tool in studies of EC phenomena, but often only at the open-circuit potential or only in fully bleached and colored states.However, our aim in this paper goes beyond this and we stress that, in order to perform a detailed study of intercalation and diffusion mechanisms, measurements at a number of potentials are necessary.This type of detailed studies of EC Ni-oxide-based films in a KOH electrolyte have been carried out a few times in the past [41][42][43][44], but in our opinion more detailed comparisons with theoretical models are required.Ni oxide films in Li + -based electrolytes have attracted more attention in recent years, and a few detailed impedance studies have appeared [45,46].It should be noted that a previous EIS study on V:NiO in Li + -based electrolyte has been performed by Artuso et al. [47].In addition, the electrochemical density of states of porous Ni oxide films has been studied by Peiris et al. [48].
Below we describe our experiments in Section 2, while Section gives a brief theoretical introduction to the equivalent circuits used to interpret our results and provides the necessary basis for calculations of the diffusion coefficient and the electrochemical density of states.Our results are presented and discussed in Section 4, and a number of conclusions are given in Section 5.

Thin film deposition
Thin films of V:NiO were deposited by reactive DC magnetron sputtering from a metallic target onto polyester substrates.The composition of the target was V:Ni (7:93 wt%); the addition of V rendered the target non-magnetic and thus eliminated its interaction with the magnetic field of the sputtering process.Flexible polyester (polyethylene terephthalate) substrates, rather than glass substrates, were used in the present study since they are interesting for device applications [49].The substrates were coated with tin-doped indium oxide (Sn:In 2 O 3 , ITO) with a sheet resistance of 30 Ω/square.Deposition conditions of V:NiO films, as well as their optimization, have been described elsewhere [24,25,30].In the present study, we transferred the deposition conditions used by Avendano et al. [24,30] to a semi-industrial box coater.Prior to the presently reported EIS study, sputtering conditions were optimized and were ensured to give reproducible EC properties, similar to those in the previous studies.The present V:NiO films were produced in an Ar + O 2 + H 2 atmosphere at a pressure of 3.5 Pa, with an O 2 /Ar gas flow ratio of ~0.05, a H 2 /O 2 gas flow ratio of ~0.14, and a power density of 7.2 W/cm 2 .The V:NiO films had a thickness of ~360 nm and were brownish in their as-deposited state with a transmittance of 69% at 550 nm wavelength.Square-shaped films of 2 × 2 cm 2 active area were used in all measurements.

Electrochemical and optical measurements
Electrochemical measurements on V:NiO films were carried out in ambient atmosphere.Counter, reference, and working electrodes were a Pt foil, an Ag/AgCl (3 mol/L KCl) electrode, and the V:NiO film under study, respectively.To observe the applied potential dependence of different charge transport and charge storage parameters, various potentials associated with a change in the transparency from fully bleached state to fully dark state were used.All potentials stated in this paper are given vs. the Ag/AgCl reference.The electrolyte was 0.01 M KOH.EIS measurements on the films were carried out with a Solartron electrochemical interface together with a Solartron 1260 frequency E. Pehlivan et al. response analyzer.An AC signal of 10 mV amplitude was superimposed on an applied DC potential.The frequency of the signal was scanned between 10 − 2 and 10 5 Hz with 10 data points per decade.DC potentials from − 0.75 V to 0.75 V, with 0.1 V between successive potentials, were used in the EIS measurements.Before starting each EIS measurement, the potential was applied to the film during a pretreatment time of 15 min to achieve a stable electrochemical state.The EIS measurements started at the most bleached state of the films, i.e., at − 0.75 V.The measurement (15 min pretreatment time and ~35 min EIS recording) at each potential was repeated at least twice to make sure that the data were stable and reproducible.Then, the potential was increased to the next potential (− 0.65 V) and a new measurement was performed.This procedure was repeated until the EIS measurement was completed at the darkest state of the film, namely at 0.75 V.
Optical transmittance measurements were carried out on films immersed in the electrolyte by an Ocean Optics fiber optics spectrometer in the wavelength range 350-800 nm.The transmittance of a quartz cell filled with electrolyte was taken as 100% reference for the optical transmittance measurements.

Equivalent circuit analysis
An equivalent circuit model was employed to analyze the EIS measurements.In this approach, the data are modeled by a circuit containing resistances together with capacitances and/or constant phase elements (CPEs).The impedance of a CPE is represented by the equation where τ is a generalized capacitance and gives the amplitude of the CPE, n is a power-law exponent, and ω is the angular frequency.The equivalent circuit should contain elements that model the resistance of the electrolyte, adsorption and charge transfer at the electrolyte-film interface, diffusion in the film, and processes occurring at the film-substrate interface.From the fitted values of the elements in the equivalent circuit, we subsequently obtained various physical parameters.
In the present case, we employed different circuits in different potential ranges.Considering first positive and low negative values of the applied DC potential, we used a generalization of the basic Randles circuit introduced to the study of EC materials by Ho et al. [35].Instead of the normal diffusion impedance, we introduced an anomalous diffusion impedance, Z d , as shown in Fig. 1a, into this circuit.In particular, the anomalous diffusion models referred to as AD1a and AD1b in work by Bisquert and Compte [37] were used to fit the EIS data.These models are based on a direct generalization of ordinary diffusion to the case of fractional diffusion [37].We now give a brief explanation of how these models differ from ordinary diffusion.The ordinary diffusion equation can be written as where c is concentration, D is the diffusion coefficient, and x is a spatial coordinate.This equation is derived by combining Fick's law, which states that the flux is proportional to the concentration gradient, with the continuity equation, which is a conservation law for the diffusing particles [37].The ordinary diffusion equation can be generalized in two ways.First, the continuity equation can be generalized so that the number of diffusing particles is no longer conserved.This leads to the anomalous diffusion model labeled AD1a, in which the generalized diffusion equation is given by [37], (3) It should be noted that the derivative on the left-hand side is a fractional derivative of order n, which is a number between zero and unity.Bisquert [50] has shown that a multiple-trapping model leads to a fractional diffusion equation of the AD1a type.In the second case, a fractional derivative can be introduced into Fick's law, while the continuity equation remains valid.These assumptions lead to the AD1b model, where the generalized diffusion equation is of the same form as Eq.(3) [37], but with a different fractional exponent, 1 -n.The AD1b model is consistent with a treatment of hopping conduction in the framework of the Continuous Time Random Walk model [37,50].The solutions of the generalized diffusion equations, to obtain the diffusion impedance Z d , have been given in detail by Bisquert and Compte [37].There are distinct differences between the solutions for the AD1a and AD1b models, as we return to below.Fig. 1a shows the generalized Randles equivalent circuit, drawn so that all versions of AD models are included, as well as the corresponding physical system.In this figure, R hf is the high-frequency resistance due to the electrolyte and the substrate, CPE dl is a constant-phase element describing the double-layer at the front (electrolyte/EC film) interface, and R ct is the charge transfer resistance at the front interface.In many cases (such as the present one), an intermediate ion adsorption step at the electrolyte-film interface [51] cannot be distinguished experimentally from the CPE dl -R ct combination.The anomalous diffusion impedance, Z d , describes diffusion in the film as well as back (EC film/ITO) interface effects since the diffusion is assumed to be blocked at the back interface.It is common to use a distributed element representation (generally a transmission line) for Z d , as shown in Fig. 1a, where χ and ζ are general impedances per unit length and impedance-lengths, respectively.They have different interpretations in the various anomalous diffusion models.In the AD1a model, χ is a resistance (per unit length) with amplitude r and ζ is a CPE (with parameters τ and n), while in AD1b χ is a CPE and ζ is a capacitance (per unit length).We have also introduced the notation AD1ab for the case where both χ and ζ are CPEs.
This phenomenological model contains one parameter more than the AD1a and AD1b models and was found to be useful to obtain accurate fits at negative potentials between − 0.05 V and − 0.25 V.
At potentials more negative than − 0.25 V we did not find any clear evidence of ion diffusion in the film, and hence the simpler equivalent circuit shown in Fig. 1b was used.It includes a high-frequency resistance, R hf , as before in series with a parallel combination of a CPE and a leak resistance, R lf .The leak resistance may be due to side reactions occurring in the film or in the electrolyte.
Equivalent-circuit fitting of experimental data for V:NiO thin films in KOH electrolyte was carried out by use of the software ZView® [52].Data points above frequencies of about 2 kHz were influenced by parasitic effects that may be related to the counter and reference electrodes and were excluded from the fits.To describe the quality of the fits, we use the weighted-sum-of-squares (WSSQ) deviation [52].

Diffusion coefficients and chemical capacitance
The impedance Z d of the transmission line in Fig. 1a has been given by Bisquert and Compte [37].From their results one can directly obtain the impedance for the general AD1ab anomalous diffusion.Below we consider the AD1a and AD1b models, which will be compared in the Results section, and for which it is possible to derive effective diffusion coefficients.In the AD1a model, the diffusion impedance is given by [37], Here, R ω is a pre-factor, the so-called "diffusion resistance", ω is the angular frequency, ω d is a characteristic frequency, and n is the powerlaw exponent of the CPE element, which can have values between zero and unity.The corresponding impedance in the AD1b model is found to be [37], which is distinctly different from Eq. ( 4).
In cases where CPEs are involved in describing the diffusion process, it is not straightforward to derive expressions for the diffusion coefficient [37,53].However, one may define an effective diffusion coefficient, D, by the procedure outlined in Ref. 53.In the case of the AD1a model, D depends on the fit parameters as well as the diffusion length, L (in our case the film thickness), and is given by the expression [38], A corresponding expression for the AD1b model can be obtained by the same procedure [38].Finally, we address the relationship between the charge capacity of the film and the asymptotic low-frequency capacitance in an EIS measurement.This quantity is often called the chemical capacitance, C chem [54], and its potential dependence shows how the inserted charge, i.e., the number of inserted ions, changes as the applied potential is altered.The chemical capacitance can be expressed as [53,54], Here, N is the number of inserted ions, which is equal to the number of charge-compensating electrons from the back contact.Hence dN/dU also gives the number of electrons inserted or extracted per unit potential, which is related to the electronic density-of-states (DOS).
It is clearly of interest to know how many ions per host atom are transferred when the applied potential, and therefore the energy, varies.In the present case, monovalent ions are inserted/extracted into/from V: NiO and the amount of ions is simply given by the exchanged charge.We define x as the number of inserted ions, N ion , per host metal atom, N host , in the film, which is easily computed from where Q ion is the inserted or extracted charge, M is the molar mass of the host material in which the ions are inserted/extracted, e is the elementary charge, A is the active area of the film, d is the thickness of the film, ρ is the density of the film, and N A is Avogadro's constant.It is seen that dN/dx in Eq. ( 7) is equal to N host .The quantity dx/dU is called the electrochemical density-of-states (EDOS) and shows the number of ions per host metal atom exchanged at a certain potential.It is also a function of potential.Transforming the potential scale to an energy scale, and noting that the number of electrons/holes inserted from the back contact is equal to the number of inserted/extracted ions, it is realized that dx/ dU is an effective electron DOS.It has been shown several times that this EDOS is able to give an at least qualitative picture of the electron DOS of nanostructures and disordered thin films [55][56][57][58][59][60].

Results and discussion
Fig. 2 shows transmittance as a function of wavelength for a V:NiO film at different applied potentials between − 0.75 V and 0.75 V.The transmittance clearly depends on the potential and the coloration/ bleaching process was found to be reversible.Supplementary measurements show that the transmittance in the bleached and colored states remain stable over 100 color/bleach cycles (results not shown).The bleached state at − 0.75 V displays high visible transmittance, which decreases progressively for wavelengths shorter than 550 nm.We interpret the decrease towards short wavelengths as a result of sub-bandgap absorption in the films, probably due to transitions between localized states in a band tail.It has been shown that V doping significantly increases the absorption of Ni-oxide-based films at wavelengths below about 500 nm [31].Therefore, the absorption tail in Fig. 2 can, to a large extent, be assigned to the V impurity.The colored state at 0.75 V exhibits a very low visible transmittance, that increases steadily towards long wavelengths.The transmittance value in the mid-visible at 550 nm goes from ~80% in the bleached state to ~10% in the colored state, which signifies excellent optical contrast.
We can define three potential regions, with reference to the optical characteristics in Fig. 2: Bleached states of the film at potentials of − 0.35 V and lower, intermediate states at potentials between about Fig. 2. Optical transmittance of a ~360-nm-thick V:NiO film in the 350-800nm wavelength range for applied potentials between − 0.75 V and 0.75 V with 0.1 V increment.Arrow indicates the evolution of the spectral transmittance for stepwise decrease of the applied potential, as detailed in the main text.− 0.25 V and 0.25 V, and dark states at potentials more positive than 0.25 V. Fig. 3 shows the absolute value of the impedance of a V:NiO film as a function of potential at different frequencies.It is observed that the low-frequency impedance is high at the bleached states, decreases progressively in the intermediate region, and converges at a lower value at the dark states.
Corresponding impedance response data are given as isotropic complex impedance plots in Fig. 4, specifically for low potentials in panel (a), for intermediate potentials in panel (b), and for high potentials in panel (c).Specific fitting parameters are given in Tables A1-A3 in the Appendix.It was not possible to draw impedance responses at all potentials in the same graph owing to the very different order of magnitude of the values at different applied potentials.Furthermore, the impedance varies as a function of frequency over orders of magnitude, and therefore the high-frequency region is shown in insets to clearly display all important features.
It is observed that low applied potentials gave large impedance values, and it is also seen that the fits to the equivalent circuits in Fig. 1 demonstrated excellent agreement; generally, the WSSQ deviation was in the range 0.001-0.01,with the largest values at the borders between the three potential ranges discussed below.No good fit could be found for the most positive potential (0.75 V), and corresponding data are therefore excluded from Fig. 4c and Table A3.As noted above, the response was significantly different in three potential regions; they are therefore discussed separately below.
(i) -0.75 to -0.35 V.Here the data can be fitted excellently to the equivalent circuit in Fig. 1b, comprising a resistance in series with a parallel combination of a resistance and a CPE.Values of the fitting parameters are given in Table A1.The high-frequency resistance is mainly due to the electrolyte, while the lowfrequency resistance is very high and is interpreted as being a leak resistance or arising from a hypothetical parasitic reaction.The absence of a diffusion process may seem problematic since it can be seen from Fig. 2 that a low degree of coloration occurs at these potentials.However, it was recently shown that an interfacial adsorption process [51] also gives rise to coloration [61] and this might give a contribution to the large semicircle seen in part in Fig. 4a.We also note that − 0.35 V could be in a crossover region where AD diffusion effects might be relevant.
(ii) -0.25 V to 0.25 V. Part of this interval refers to a crossover region where we found it necessary to use the phenomenological AD1ab circuit.At least at the two lowest potentials, we found that a combination of the AD1a and AD1b models gave an improved fit to experimental data.This is hardly surprising, since this so called AD1ab model contains one additional parameter.Therefore, we found this latter model to be valuable in a potential region where the other models start to deviate from experimental data.The AD1ab model is without clear physical interpretation and probably signifies that the processes discussed under (i) above and anomalous diffusion are both significant.In Fig. 5 we compare the WSSQ deviations of fits from the AD1a and AD1b models to experimental data.It is clearly seen that the fits to the AD1a model are vastly superior, both at intermediate and dark states of the film.It is also instructive to compare the fits from the AD1ab and AD1a models in the intermediate region (see Tables A2 and A3).At potentials below − 0.05 V, the AD1ab fit is significantly better, while very little difference between the fits is observed at positive potentials.The AD1ab fits are also somewhat over-determined since some fitting parameters exhibit large uncertainties.For the reasons outlined above, the AD1a model should be preferred at positive potentials.
(iii) 0.35 V to 0.75 V. Here, the AD1a theory is clearly preferred (Fig. 5) and the fitting is generally excellent.However, the determination of the AD1a resistance parameter r is uncertain, and it actually becomes ill-determined at potentials of 0.45 and larger.In Table A3, it is seen to be much smaller than the charge transfer resistance, which at the same time is increasing towards high potentials.The effects of r on the spectra are therefore small, hidden beneath the contribution of R ct and not possible to detect by fitting to the present model.In the discussion below, we will focus on the use of the AD1a parameters for obtaining physical information.
We now discuss the fitting parameters and concentrate on fits involving the AD1a diffusion element (Table A3).The high-frequency resistance R hf was almost the same at all potentials and was much larger than in our previous work on W oxide films [39].This is evidently due to the use of different electrolytes in the two cases.The charge transfer resistance R ct was of the order of 40 Ω at low/intermediate potentials and started to increase at 0.35 V, eventually reaching values in excess of 100 Ω.The associated CPE exhibits a generalized capacitance in the μF region and an exponent in the range 0.8-1, where the latter value corresponds to an ideal capacitance.These values were interpreted as due to the properties of the electrochemical double-layer at the electrolyte-film interface.The AD1a parameters show a characteristic variation with potential.The resistance r steadily decreases, and the CPE amplitude increases, as the potential is increased.For potentials above 0.35 V, the resistance parameter exhibited large uncertainties, and at 0.45 V and higher it was not significantly different from zero.It is observed that, in this potential range, r was much smaller than the charge transfer resistance and therefore the diffusion resistance could not be reliably determined from the data.The AD1a power-law exponent exhibited values in the range of 0.8-0.9.Hence, the associated CPE is significantly different from an ideal capacitance, although the difference is not a major one.We emphasize that, in the AD1a model, the low-frequency asymptotic behavior is a CPE.This means that there exist slow transients in the EIS data, and an eventual approach to a steady state is not detectable within the frequency range we employed.The CPE asymptotic behavior is best interpreted within a multiple-trapping approach [50], which means that some charge carriers are situated in trap states.This effect might be related to the observed gradual increase of charge density of V:NiO films over many insertion/extraction cycles [25].
It is also interesting to plot the EIS data in the complex capacitance  (C ″ vs. C ′ ) representation, as shown in Fig. 6.Capacitance data were calculated from the impedance for every applied potential by using the relation C = 1 iωZ .The C ″ vs. C ′ curves were arc-shaped, except for potentials in the region of bleached states that were discussed above.In addition, the curves exhibit different radii for each potential.Extrapolations of the curves to low frequencies, i.e., to high real capacitances, would in principle give the chemical capacitance C chem .However, in the AD1a model, the asymptotic low-frequency behavior follows a CPE pattern (or pseudo-capacitive behavior) rather than looking like an ideal capacitance.The departure from ideal capacitive behavior is not very large, as noted above, and one might attempt a graphical extrapolation of the arcs in Fig. 6 to obtain an estimate of the chemical capacitance as a function of potential.It is observed in Fig. 6 that fits to a semicircle work very well for the majority of the arc-shaped curves.Hence, the data were fitted to a semicircle and extrapolated to obtain the intercept of the semicircle with the C ′ axis.Because the experimental data only cover part of the semicircle, errors in the extrapolated intercept could amount to as much as 20%.However, we used these extrapolations to estimate chemical capacitances; the obtained values of C chem increased from ~5 mF/cm 2 at − 0.15 V to ~21 mF/cm 2 at 0.75 V.For negative potentials, close to the bleached state, the curves were not semicircle-shaped and became almost straight lines.The departure from the arc-shape increased for more negative potentials.Fig. 7 shows EDOS, represented by dx/dU as discussed above, as a function of applied potential.To interpret these data, we first note that the energy scale is the inverse of the potential scale.Hence, high potentials correspond to low energies.Secondly, V:NiO films color by ion extraction and simultaneous extraction of electrons from the valence band of the material.Hence, the EDOS in Fig. 7 should correspond to the unoccupied states close to the top of the valence band.It is seen that dx/ dU is maximum in the darkest state, as expected, and decreases nearly uniformly when the applied potential decreases towards the bleached state.As noted above, the EDOS could not be obtained for potentials lower than − 0.25 V.The shape of the EDOS curve is close to the one expected for a band edge.However, it is uncertain whether the displayed states are at the top of the valence band or in a band tail of localized states extending into the band gap.It should be noted that a previous determination of the EDOS for nanostructured Ni oxide was interpreted in terms of an exponential distribution of band gap states [48].However, the position of the top of the NiO valence band edge has been Fig. 4. Imaginary impedance as a function of real impedance in the frequency range 0.01 Hz-3 kHz of a ~360-nm-thick V:NiO film at the shown applied potentials.For clarity, the data are given in three separate panels, denoted (a)-(c), pertaining to the film being in bleached, intermediate, and dark states.Insets illustrate the high-frequency region of the curves.Symbols show measured data points and arrows point at the data points for indicated frequencies at some potentials.Full curves show the fits to the experimental data by the equivalent circuits in Fig. 1.
E. Pehlivan et al. determined by Nakaoka et al. [62], using Mott-Schottky analysis, to be situated at 0.32 V. Therefore, it seems that the EDOS in Fig. 7 shows the crossover between the upper part of the valence band at high potentials and a band tail of localized states at low potentials.
Effective diffusion coefficients, D, were obtained from Eq. ( 6) from the equivalent-circuit analysis using the AD1a diffusion impedance.In addition to the data in Table A3, an AD1a fit was attempted at two more negative potentials.In these cases, an acceptable fit was obtained only in part of the frequency range.At potentials above 0.35 V, the AD1a resistance was too uncertain to permit meaningful calculations of D. The effective diffusion coefficient is shown in Fig. 8 as a function of applied potential.The values obtained for D for the two lowest potentials in Fig. 8 are just estimates, as explained above, but we believe they are of the correct order of magnitude.The errors in the determination of effective diffusion coefficients are dominated by the uncertainty of the resistance parameter r.It increases from roughly 4 % at − 0.15 V to nearly 30 % at 0.35 V.The diffusion coefficient exhibits a strong increase of about four orders of magnitude as the potential increases.Previous work has identified two phase transitions at about − 0.1 V and 0.23 V, that were detected in electrochemical measurements on V:NiO films [24].These phase transitions could not be seen in the present measurements, which were conducted at relatively few potentials.The onset of fast diffusion in Fig. 8 is in the region of the first of these phase transitions, which has been identified as the transformation of β-Ni (OH) 2 to the more porous α− Ni(OH) 2 phase in the Bode reaction scheme [24].It seems natural that this transition would facilitate diffusion in the film.Interestingly, the second transition, from α-nickel hydroxide to γ-nickel oxyhydroxide [24], seems to be associated with a stronger increase of the EDOS in Fig. 7.
It can be deduced by comparing Figs.7 and 8 that D increases when dx/dU increases.As explained above, dx/dU being small means that the number of electrons extracted from the valence band, as well as the number of extracted protons, is small at low potentials.On the other hand, at high potentials many electrons and protons have been extracted    from the film.In this case there are plenty of unoccupied sites, the EDOS is high, and diffusion is easy.However, the diffusion coefficient becomes unexpectedly high at high potentials, actually orders of magnitude higher than reported in previous work.Values in the region 10 − 11 to 10 − 12 cm 2 /s were found by galvanostatic intermittent titration [24], and similar values have been reported for diffusion coefficients pertinent to Li + [47].It should be kept in mind that we determined effective diffusion coefficients in the framework of the AD1a anomalous diffusion model, and this technique may not be directly comparable to diffusion coefficients determined by other methods.Secondly, the AD1a model implies that there exist long-time transients that are modeled by the CPE component in Z d .This feature must be interpreted within a multiple-trapping scheme [50], and this means that the effective diffusion coefficient in Fig. 7 describes only the diffusion of the un-trapped ions [50].

Conclusions
In this paper we performed a detailed electrochemical impedance spectroscopy study of V:NiO films in a KOH electrolyte.The films exhibited pronounced electrochromic switching between bleached and colored states.The EIS measurements were carried out at different potentials in the range from − 0.75 V to 0.75 V vs. Ag/AgCl.In the bleached state at low potentials, EIS data indicated a pseudo-capacitive behavior together with a leak resistance probably due to parasitic chemical reactions.At potentials higher than − 0.25 V, the spectra were fitted to a Randles-type model, wherein the diffusion impedance was described by the anomalous diffusion 1a model introduced by Bisquert and Compte [37].
Our data have several implications for the understanding of the dynamics of electrochromism of Ni-oxide-based thin films in hydroxide electrolytes.First, the AD1a model can be interpreted in terms of multiple trapping of ions.It seems that there exist both free and trapped ions in the films, and this may have consequences for the electrochromic properties, especially for the stability of the electrochromic response.Diffusion coefficients were too low to be measured at potentials below − 0.35 V where only little coloration takes place, probably by a surface process.At higher potentials, the diffusion coefficient increases steeply up to values of the order of 10 − 8 cm 2 /s.This increase occurs in the range where the Bode reaction from β-Ni(OH) 2 to the more porous α− Ni(OH) 2 phase should take place.The coloration is believed to occur by further reactions producing absorbing NiOOH and subsequently Ni 2 O 3 [24,25].It was inferred from the electrochemical density of states that the charge-compensating electrons are present in a band tail at low potentials (high energy) and at the top of the valence band at high potentials (low energy).It seems that the high charge capacity and transmittance switching as well as the remarkably fast ion kinetics of Ni-oxide-based thin films in KOH are dependent on the presence of significant amounts of a porous nickel hydroxide phase that is transformed according to the Bode reaction scheme [28,29].Further studies are necessary for evaluating the implications of these findings for the behavior of Ni-oxide-based films in protonic and Li + -containing electrolytes.

Table A3
Parameters obtained from fitting of experimental electrochemical impedance spectroscopy data shown in Fig. 4b and c to the equivalent circuit depicted in Fig. 1a.The AD1a model was used in the fitting.Data are given on high-frequency resistance (R hf ), double-layer CPE parameters (τ int , n int ), charge transfer resistance (R ct ), diffusion resistance (r), AD1a CPE (τ c , n c ), and weighted sum of squares of the fit (WSSQ).Resistance and capacitance values were normalized to 1 cm 2 of electrode area and the AD parameters were normalized to unit length.Parameters within parentheses exhibited uncertainties of more than 30%.

Fig. 1 .
Fig. 1.(a) Equivalent circuit (solid lines) used in the present study and corresponding physical system shown in color: an EC film (not drawn to scale) immersed in an electrolyte.Here R hf is the high-frequency resistance, CPE dl is an interfacial constant-phase element, and R ct is the charge transfer resistance at the interface.A transmission line representation of the diffusion impedance, Z d , for "anomalous diffusion", where χ and ζ are distributed impedances, is indicated within the dashed rectangle.(b) Equivalent circuit used for potentials more negative than − 0.25 V.

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.Pehlivan et al.

Fig. 3 .
Fig. 3. Absolute value of the impedance at the frequencies given in the figure as a function of applied potential for a ~360-nm-thick V:NiO film.The three potential regions mentioned in the text are indicated.The borders between them are not strictly defined as indicated by the white areas.

Fig. 5 .
Fig.5.Weighted sum of squares deviation of fits of the AD1a and AD1b models to impedance data for a ~360-nm-thick V:NiO film at potentials giving intermediate and dark states.

Fig. 6 .
Fig. 6.Imaginary capacitance as a function of real capacitance (C ″ vs. C ′ ) for ~360-nm-thick V:NiO films at the shown potentials.Inset reports similar graphs for the potentials where semicircle behavior was not observed.Symbols indicate measured data points and lines show fitting of a semicircle to the data.

Fig. 7 .
Fig. 7. Electrochemical density of states, represented by dx/dU, as a function of applied potential for ~360-nm-thick V:NiO films.

Fig. 8 .
Fig. 8. Effective diffusion coefficient for H + ions as a function of potential for ~360-nm-thick V:NiO films.