Laura Maria Manceriu

Pierre Colson

Anthony Maho

Gauthier Eppe

Ngoc Duy Nguyen

Christine Labrugère

Aline Rougier

Rudi Cloots

Catherine Henrist

Christine Labrugere

Straightforward prediction of the Ni1-xO layers stoichiometry by using optical and electrochemical measurements

Keywords: nickel oxide, thin films, stoichiometry evaluation, impedance spectroscopy, optical properties

Introduction

Nickel oxide (NiO) is a wide band gap p-type semiconductor which is studied in a large range of applications, such as electrochromic coatings [START_REF] Mihelčič | Comparison of electrochromic properties of Ni1-xO in lithium and lithium-free aprotic electrolytes: From Ni1-xO pigment coatings to flexible electrochromic devices[END_REF][START_REF] Denayer | Surfactant-assisted ultrasonic spray pyrolysis of nickel oxide and lithium-doped nickel oxide thin films, toward electrochromic applications[END_REF], new generation solar cells [START_REF] Hod | Characterization and control of the electronic properties of a NiO based dye sensitized photocathode[END_REF][START_REF] Lin | Effect of post-heat-treated NiOx overlayer on performance of nanocrystalline TiO2 thin films for dye-sensitized solar cells[END_REF], gas sensors [START_REF] Ozdemir | Nanostructure modified gas sensor detection matrix for NO transient conversion of NO to NO2[END_REF][START_REF] Zhang | Effect of nickel vacancies on the roomtemperature NO2 sensing properties of mesoporous NiO nanosheets[END_REF] or light-emitting diodes [START_REF] Long | Ultraviolet electroluminescence from ZnO/NiO-based heterojunction light-emitting diodes[END_REF], due to its remarkable chemical stability, unique opto-electronic and magnetic properties. The p-type conductivity property is attributed to the presence of Ni vacancies and from here comes the notation Ni1-xO (in addition described as NiOy when oxygen interstitials are considered as the main defects [START_REF] Tyagi | Postdeposition annealing of NiOx thin films: A transition from n-type to p-type conductivity for short wave length optoelectronic devices[END_REF]), where x < 10 -3 [START_REF] Stokłosa | Defect complexes and defect clusters in Mn1-δO, Co1-δO and Ni1-δO oxides diagrams of the concentrations of point defects[END_REF][START_REF] Sockel | Coulometric titration of transition metal oxides[END_REF], the defects being the expression of a departure from stoichiometry as function of oxygen partial pressure. According to P. Lunkenheimer et al. [11] the x maximum value is 0.2. In the form of thin films, the higher the x value is the more brownish the appearance will be. One nickel vacancy is compensated by the creation of two Ni 3+ sites (eq. 1) and holes (eq. 2) [START_REF] Chen | Property modulation of NiO films grown by radio frequency magnetron sputtering[END_REF], which provide both optical absorption and conductivity.

where,

𝑉 𝑁𝑖 * → 𝑉 𝑁𝑖 ′′ + 2ℎ • (2)
where 𝑁𝑖 𝑁𝑖 * stands for nickel atoms in their normal site, 𝑉 𝑁𝑖 ′′ is the ionized nickel vacancy, 𝑉 𝑁𝑖 * is the non-ionized nickel vacancy and 𝑁𝑖 𝑁𝑖 • is a Ni 3+ site in a normal Ni 2+ site, 𝑂 𝑂 𝑥 represents the oxygen atoms in their normal site and ℎ • are the holes.

Likewise, the excess oxygen in the nickel oxide lattice creates nickel vacancies which are ionized with the formation of Ni 3+ sites and holes [START_REF] Nandy | Effect of oxygen partial pressure on the electrical and optical properties of highly (200) oriented p-type Ni1-xO films by DC sputtering[END_REF].

Nickel oxide is a well known anodic electrochromic material which reversibly switches from transparent to brownish by electrochemical reduction and oxidation, respectively. It was previously observed that the presence of Ni vacancies [START_REF] Denayer | Surfactant-assisted ultrasonic spray pyrolysis of nickel oxide and lithium-doped nickel oxide thin films, toward electrochromic applications[END_REF][START_REF] Wen | Anodic electrochromism for energy-efficient windows: cation/anion-based surface processes and effects of crystal facets in nickel oxide thin films[END_REF], influences the optical properties in the sense that a high initial Ni 3+ content leads to lower transmission in the bleached and colored states as well as to larger optical modulation [START_REF] Wen | Anodic electrochromism for energy-efficient windows: cation/anion-based surface processes and effects of crystal facets in nickel oxide thin films[END_REF][START_REF] Rocha | Electrochromism of non-stoichiometric NiO thin film: as single layer and in full device[END_REF]. In addition, Da Rocha and Rougier [START_REF] Rocha | Electrochromism of non-stoichiometric NiO thin film: as single layer and in full device[END_REF] observed that with increasing Ni 3+ content the open circuit voltage increases along with film resistance decrease. This is not surprising since Voc is a material property which represents in fact the chemical potential (Fermi level) of Ni1-xO measured vs. the reference electrode.

Hence, it is important to find a method to determine the amount of Ni 3+ in the Ni1-xO films as they are involved in many different applications; first for electrochromic applications, where window transparency has to satisfy the customer needs and where the straightforward prediction of the coatings optical performance would be useful; then for p-type dye sensitized solar cells, where the conversion efficiency is directly dependent on the cell Voc (potential difference between Ni1-xO Fermi level and electrolyte Fermi level) and where tuning the material band structure is a key ingredient in increasing performance; or for gas sensors, where sensing performances of Ni1-xO is strongly related to the intrinsic defect concentration.

Various chemical and physical approaches have been developed to produce Ni1-xO films including spray pyrolysis [START_REF] Wu | Effect of annealing temperature on the characteristics of the modified spray deposited Li-doped NiO films and their applications in transparent heterojunction diode[END_REF][START_REF] Chan | Characteristics of p-NiO thin films prepared by spray pyrolysis and their application in CdS-sensitized photocathodes[END_REF], sputtering [START_REF] Rocha | Electrochromism of non-stoichiometric NiO thin film: as single layer and in full device[END_REF][START_REF] Kim | Nickel vacancy behavior in the electrical conductance of nonstoichiometric nickel oxide film[END_REF][START_REF] Yang | Effect of heat treatment on the properties of nonstoichiometric p-type nickel oxide films deposited by reactive sputtering[END_REF], pulsed laser deposition [START_REF] Bouessay | Electrochromic degradation in nickel oxide thin film: A self-discharge and dissolution phenomenon[END_REF][START_REF] Rubin | Electrochromic lithium nickel oxide by pulsed laser deposition and sputtering[END_REF], atomic layer deposition [START_REF] Thimsen | Energy Levels, Electronic properties and rectification in ultrathin p-NiO films synthesized by atomic layer deposition[END_REF], electrodeposition [START_REF] Nakaoka | Semiconductor and electrochromic properties of electrochemically deposited nickel oxide films[END_REF], chemical vapor deposition [START_REF] An | Aerosol-chemical vapor deposition method for synthesis of nanostructured metal oxide thin films with controlled morphology[END_REF], etc. In parallel, different strategies were used to modify the Ni1-xO stoichiometry such as annealing in oxygen rich or oxygen poor atmosphere [START_REF] Thimsen | Energy Levels, Electronic properties and rectification in ultrathin p-NiO films synthesized by atomic layer deposition[END_REF][START_REF] Yang | Effect of heat treatment on the properties of nonstoichiometric p-type nickel oxide films deposited by reactive sputtering[END_REF][START_REF] Nalage | Sol-gel synthesis of nickel oxide thin films and their characterization[END_REF], doping [START_REF] Wu | Effect of annealing temperature on the characteristics of the modified spray deposited Li-doped NiO films and their applications in transparent heterojunction diode[END_REF][START_REF] Thimsen | Energy Levels, Electronic properties and rectification in ultrathin p-NiO films synthesized by atomic layer deposition[END_REF], modification of the O2 partial pressure [START_REF] Chen | Property modulation of NiO films grown by radio frequency magnetron sputtering[END_REF][START_REF] Kim | Nickel vacancy behavior in the electrical conductance of nonstoichiometric nickel oxide film[END_REF], etc. Nevertheless, all these strategies lead to modifications in layer structure and morphology with important consequences on electrochemical measurements since the electrochemically active surface changes, which issue is rarely considered during elemental analysis. For investigating the Ni1-xO stoichiometry, energy-dispersive X-ray spectroscopy (EDS), X-ray photoelectron spectroscopy (XPS), Rutherford Backscattering Spectrometry (RBS)

or electrochemical methods are typically used.

EDX allows micrometer range profiling with medium detection sensitivity (0.1-1.0 at. %) but is mistakenly used to determine the O/Ni ratio since light elements like O cannot be properly quantified and is highly sensitive to surface roughness. XPS allows surface quantification (up to 10 nm), reaching even lower detection limits (0.1 at. %). However it is sensitive to organic contamination and quantitative determination of Ni 3+ is still delicate because it is very much dependent on the fitting and calculation approach [START_REF] Chen | Property modulation of NiO films grown by radio frequency magnetron sputtering[END_REF][START_REF] Usha | Improved electrochromic performance of a radio frequency magnetron sputtered NiO thin film with high optical switching speed[END_REF]. RBS is considered more reliable than XPS due to the higher analysis depth (1 µm) with detection limits ranging from 10 -3 at. % for heavy elements to 10 at. %. However, if not coupled with Nuclear Reaction Analysis (NRA), it can give false information about the oxygen content. Electrochemical methods like cyclic voltammetry or impedance spectroscopy rely on the proper selection of set-up and measuring conditions since these measurements are highly sensitive to sample or electrolyte contamination, defective contacts, analysis parameters (media, pH, scanning speed, etc.) or sample structure.

Given that the techniques have different capabilities, limitations, and depths of analysis, they can provide differing results even for highly homogenous films. Kim and Lee [START_REF] Kim | Nickel vacancy behavior in the electrical conductance of nonstoichiometric nickel oxide film[END_REF] have analyzed the stoichiometry of R.F. sputtered Ni1-xO layers and observed that the content of Ni 3+ is over estimated by XPS (x = 0.020) with report to RBS (x = 0.006). When analyzing the Ni1-xO layers prepared by R.F. sputtering at P(O2 ) = 6%, Chen et. al [START_REF] Chen | Property modulation of NiO films grown by radio frequency magnetron sputtering[END_REF] noted that the x values calculated from the O/Ni ratio are much lower (x = 0.076) compared to x values derived from the Ni 3+ /Ni 2+ ratio (x = 0.13). They explained this by Ni 3+ enrichment at the surface of nanostructures. The x value determined from cyclic voltammetry curves [START_REF] Rocha | Electrochromism of non-stoichiometric NiO thin film: as single layer and in full device[END_REF] is much smaller (x =0.035) than the x value obtained by RBS [START_REF] Wen | Anodic electrochromism for energy-efficient windows: cation/anion-based surface processes and effects of crystal facets in nickel oxide thin films[END_REF] (x = 0.32, considering that for each oxygen interstitial one nickel vacancy is formed) for Ni1-xO film with similar thickness, even if the pristine transmission level at 550 nm is lower (44% vs. 62%, respectively), suggesting higher Ni 3+ content.

These facts are motivating our original approach, i.e. the prediction of the Ni1-xO stoichiometry by using optical and electrochemical measurements. (Aldrich, 99.999%) solution to which polyethyleneglycol PEG (Aldrich, average Mn 400) was added in mass ratio Ni(NO3)2 : PEG = 1 : 3. As previously described [START_REF] Denayer | Surfactant-assisted ultrasonic spray pyrolysis of nickel oxide and lithium-doped nickel oxide thin films, toward electrochromic applications[END_REF], the USP equipment is an ExactaCoat © apparatus from Sonotek © equipped with an AccuMist © nozzle operated at 120 kHz, atomizing the solution into very fine droplets which are then conveyed by a carrier gas towards the heated substrate where the pyrolysis (precursor conversion and surfactant decomposition) takes place, forming the Ni1-xO films. The USP deposition parameters [START_REF] Denayer | Surfactant-assisted ultrasonic spray pyrolysis of nickel oxide and lithium-doped nickel oxide thin films, toward electrochromic applications[END_REF] involved a nozzle-substrate distance of 5.5 cm, a solution flow rate of 0.25 mL/min, and the use of air as carrier gas (6025 Pa). Deposition follows a "x,y" patterning above the surface with a Sshaped move (4 mm spacing) at a constant speed of 40 mm/s. The "x,y" deposition was performed 10 consecutive times, keeping exactly the same pattern every odd passages and shifting "x" (or "y") coordinate by 2 mm every even passages. Likewise, deposition was done onto standard, non-conducting glass substrates for X-Ray characterization. After deposition, the Ni1-xO thin films were annealed at 350, 400, 500 and 600 ⁰C in air for 3 h to modify their stoichiometry. Sample names correspond to the applied annealing temperatures.

Thin films characterization

The Ni1-xO coatings thickness was determined in cross-section by scanning electron microscopy (SEM) on an ESEM-FEG XL 30 FEI instrument, operated at 15 kV in the backscattered electron mode. The following values were obtained (average of 10 measurements): 293 ± 12 nm (350°C), 200 ± 13 nm (400°C), 242 ± 20 nm (500°C) and 202 ± 15 nm (600°C). Atomic Force Microscopy (AFM, Digital Instrument Nanoscope III microscope from Veeco) was also exploited to record surface topography of the Ni1-xO films and allowed for determining roughness and grain size distribution. The image acquisition was performed in tapping mode with a super sharp (tip diameter 5 nm)improved super cone probe (Team Nanotec). Surface porosity was also evaluated through contact angle measurements (KSV instruments, static contact angle mode) using glycerol as testing liquid since water was readily absorbed by the porous samples and did not allow qualitative measurements. X-ray diffraction (XRD) was used to assess the crystalline nature of the Ni1-xO layers. Analysis were realized on a Bruker D8 Discovery diffractometer (grazing incidence, Cu Kα radiation, α = 0.154 nm, 32° < 2θ < 48°, step width 0.02°, 1.5 s/step, 2⁰ incidence angle).

A UV/VIS spectrometer in the 350 -700 nm wavelength range (slit width 1 nm, beam cross section at focal point 0.6 mm x 9 mm) using air as blank. The contribution of the FTO substrate was substracted from the initial absorption spectra of the annealed Ni1-xO films for more accurate correlation with the film composition.

Results and discussion

Structural and morphological characterization

The X-Ray diffraction patterns of Ni1-xO deposited onto standard glass annealed at different temperatures were acquired (Fig. 1) to evaluate temperature related changes in crystallinity and stoichiometry. The (1 1 1) and (2 0 0) X-ray peaks were observed at 2θ angles of approximately 37.2⁰ and 43.2⁰, respectively, which constitutes a proof of cubic phase (PDF # 00 047 1049 from PDF-4+ database of International Center for Diffraction Data) formation. No evidence of Ni2O3 or other phase formation was found. The average crystallite size for each sample was calculated for the (2 0 0) peak using the Debye-Scherrer formula:

D = 0.9λ Bcosθ ( 3
)
where D is the crystallite size in nm, λ is the wavelength of the incident radiation (Cu Kλ= 0.154 nm), θ is the Bragg angle and B is the FWHM of the diffraction peak in radians. The lattice constant "a'' was calculated with the following formula (standard deviation of calculated values is ± 0.005 nm):

a = d(h 2 + k 2 + l 2 ) 1/2 (4)
where h, k and l are the Miller indices of the (2 0 0) peak and "d" is the interplanar distance obtained from the Bragg law (d = λ/2sinθ). Both "D" and "a" values are plotted in Fig. 1. The crystallinity of the Ni1-xO films increases with increasing annealing temperature (Fig. 1a), with crystallites size ranging from around 9 nm to 21 nm. A slight shift of the patterns towards higher 2𝜃 angles is observed (2θ is 43.19⁰, 43.27⁰, 43.32⁰ and 43.33⁰ for sample 350, 400, 500 and 600, respectively), corroborated with the decreasing lattice parameter values (Fig. 1b).

Since the crystallite size increases, particle size increase is also expected and consequently changes in layer roughness. These aspects are very important for our approach since it was already shown that the Ni1-xO electrochemically active surface is dependent on layer crystallinity and morphology [START_REF] Wen | Anodic electrochromism for energy-efficient windows: cation/anion-based surface processes and effects of crystal facets in nickel oxide thin films[END_REF]. The AFM images confirm the XRD results, i.e. the particle size increase with annealing temperature, with a granular morphology characterizing all the samples. Particle size distribution was calculated based on the AFM images by using the ImageJ software and shown next to the topographies in Fig. 2. All layers were characterized by low roughness values (Fig. 2), slightly increasing when going from 400 to 600 ⁰C annealing temperature due to particle size increase. The average particle sizes were slightly different than the crystallite sizes since the particles are polycrystalline and their size was calculated for the Ni1-xO thin films deposited on different substrates, FTO and glass, respectively. Contact angle measurements were performed on the Ni1-xO film using glycerol as testing liquid since in the case of water the drop was readily absorbed. As it can be observed in Fig. 3 the glycerol contact angle is rather constant for the Ni1-xO films annealed at 350 and 400 ⁰C but increases for higher temperatures along with roughness increase. We suppose that is the combined effect of surface roughness, increasing film density and dehydroxylation of the surface. A rougher surface has an increased air trapping capability rendering a hydrophobic effect [START_REF] Qing | Large-Area Fabrication of Superhydrophobic Zinc Surface with Reversible Wettability Switching and Anticorrosion[END_REF]. Pictures of the glycerol droplet formed on the film surface are also shown for each case.

Optical properties

The absorption spectra of the Ni1-xO films deposited on FTO were recorded versus air and normalized with the film thickness. The transmission spectra were obtained by mathematical conversion (T = 10 2-A ). The optical results confirm that the annealing was effective in modifying the Ni1-xO film stoichiometry, i.e. absorption increases/transmission decreases (Fig. 4a andb)

with increasing annealing temperature due to increasing Ni 3+ concentration. and 600⁰C for 3h.

Electrochemical and electrical properties

Given that in our approach we were searching a correlation between the optical and When the Ni1-xO films are put into contact with the electrolyte, the equilibration of the Fermi level occurs along with majority carrier (holes) migration towards the interface. This produces a negative space charge layer in the semiconductor (also called depletion layer) and a positive space charge layer in the electrolyte (also called the Helmholtz layer), resulting in band bending.

The separation of charge results in a measurable capacitance (C) in the mid-frequency region, which comprises the contribution of the semiconductor space charge layer (Csc) and that of the Helmoltz layer (CH), i.e. 𝐶 -1 = 𝐶 𝑠𝑐 -1 + 𝐶 𝐻 -1 . The Nyquist plots (example given for sample 600 in Fig. 5b) and phase angle vs. frequency plots (example given for sample 600 in Fig. S2 from supplementary information) as function of applied bias represent additional evidence that it is the capacitive element in the mid-frequency region (Q2) that strongly changes as function of potential, and thus considered for the Mott-Schottky plot.

The electrolyte was prepared in order to be sufficiently concentrated (addition of 1M KCl) so that the Gouy layer [START_REF] Thimsen | Energy Levels, Electronic properties and rectification in ultrathin p-NiO films synthesized by atomic layer deposition[END_REF] can be neglected. Since the CH is considerably higher than the Csc (the Helmoltz layer thickness is lower than the space charge layer thickness), the overall measured capacity is dominated by the space-charge capacitance (Csc) and its variation with the applied potential is described by the Mott-Schottky equation:

1 C sc 2 = - 2 eεε 0 NA 2 (E -Φ fb - kT e ) (5)
where A is the effective surface area of the semiconductor (specific surface area evaluated from AFM [START_REF] Antony | Size-dependent specific surface area of nanoporous film assembled by core-shell iron nanoclusters[END_REF] (140, 136, 32 and 22 m 2 /g for sample 350, 400, 500 and 600, respectively, see supporting information) and the entire film thickness were considered), E is the applied potential, Φ fb is the flat band potential, k is the Boltzman constant, T is the temperature in K, ε is the dielectric constant of NiO (15, [29]), ε0 is the vacuum permittivity, N is the carrier concentration within the depletion region and e is the electron charge. The Mott-Schottky plot corresponding to the 1.0 kHz frequency is shown in Fig. 6a. The space charge capacitance was found to be frequency dependent with a higher spreading for the sample annealed at 350 ⁰C. The 1 kHz frequency was chosen from the scanned frequency range (15 kHz -300 Hz) as saturation was achieved for all samples and because starting with this frequency the N/Φfb dispersion was reduced [START_REF] Ramesham | Determination of flat-band potential for boron-doped diamond electrode in 0.5 m NaCl by ac-impedance spectroscopy[END_REF] (as example the Mott-Schottky plots in the 1 kHz -300 Hz range for samples 350 and 600 are shown in Fig. S3 from supplementary information). The intercept of the linear fit In addition, the Mott-Schottky plots were registered at different pH for the 350 Ni1-xO layer (Fig. 6b). The Φfb value decreased with 0.052(3) V per unit of pH, which is close to the expected value of 0.059 V for an ideal semiconductor-aqueous electrolyte interface, meaning that suitable measuring conditions were chosen. Exceptionally for the solution with pH 10 there was a higher deviation probably due to partial film dissolution.

Table 1. Effect of annealing temperature on the open circuit potential (Voc), carrier density (N), flat-band potential (Φfb), valence band position (EVB), the potential at which the semiconductor is fully depleted (Φ vs. Ag/AgCl and SHE), the potential drop across the space charge region (ΦSC) and depletion layer thickness (LSC) of Ni1-xO thin films.

When E < Φfb the band bending increases, acting as a barrier for the passage of holes through the junction resulting in increased charge transfer resistance (the semicircle in the mid-frequency region increases at E < 0.4 V, Fig. 5b), whereas for E > Φfb the band bending is decreased favoring the holes diffusion and thus explaining the decrease in charge transfer resistance (the semicircle in the mid-frequency region almost disappears at E > 0.4 V, Fig. 5b).

The open circuit potential (Voc) of each film (350, 400, 500 and 600) was measured with report to the Ag/AgCl sat. KCl reference electrode in the aqueous electrolyte (surface of electrode in contact with the electrolyte is 0.15 cm 2 ) and values are given in Table 1. The Voc increased with annealing temperature, indicating Ni 3+ enrichment.

The valence band edge position can be calculated using the following equation for nondegenerated p-semiconductors [START_REF] Thimsen | Energy Levels, Electronic properties and rectification in ultrathin p-NiO films synthesized by atomic layer deposition[END_REF]:

E VB = Φ fb + kT e ln ( N V N ) (6)
where𝑁 𝑉 is the effective density of holes in the valence band defined as:

N V = 2( 2πm h * kT h 2 ) 3/2 (7)
where h is the Planck constant and 𝑚 ℎ * is the effective mass of holes (0.9 𝑚 0 [START_REF] Choi | Electrical conduction and effective mass of a hole in single-crystal NiO[END_REF], 𝑚 0 is the mass of an electron. Thus, NV for Ni1-xO is estimated to be 2. flat band values the valence band edge can be tuned by annealing, i.e. lowered by increasing annealing temperature (Table 1) due to carrier concentration enhancement.

The width of the depletion layer (LSC) is given by:

L sc = (2εε 0 Φ sc /eN) 1/2 (8)
where e is the electron charge, Φsc is the potential drop across the depletion region (Φ sc = Φ fb -Φ, where Φ is the potential at which Ni1-xO layer is fully depleted and is determined from Fig. 6a at the turning point of the linear region towards negative region) and e, N, ε and ε0have already been defined. The depletion layer width decreases with increasing carrier concentration and except for sample 350 for which it extends to the entire layer thickness (293 nm), for all the other samples it is confined at the layer surface, most probably due to reduced charged mobility.

The Φ fb and EVB values are in good agreement with the values already reported for NiO films prepared by chemical solution processes [START_REF] Chan | Characteristics of p-NiO thin films prepared by spray pyrolysis and their application in CdS-sensitized photocathodes[END_REF][START_REF] Nakaoka | Semiconductor and electrochromic properties of electrochemically deposited nickel oxide films[END_REF][START_REF] Natu | Valence band-edge engineering of nickel oxide nanoparticles via cobalt doping for application in p-type dye-sensitized solar cells[END_REF]. The Voc values are scarcely reported and they show the same trend as for our samples, i.e. increasing with Ni 3+ concentration [START_REF] Wen | Anodic electrochromism for energy-efficient windows: cation/anion-based surface processes and effects of crystal facets in nickel oxide thin films[END_REF][START_REF] Rocha | Electrochromism of non-stoichiometric NiO thin film: as single layer and in full device[END_REF][START_REF] Bouessay | Electrochromic degradation in nickel oxide thin film: A self-discharge and dissolution phenomenon[END_REF].

It is interesting to observe that lower Voc values are reported for NiO films obtained by sputtering [START_REF] Wen | Anodic electrochromism for energy-efficient windows: cation/anion-based surface processes and effects of crystal facets in nickel oxide thin films[END_REF] which according to RBS analysis should have higher Ni 3+ content when compared to our samples. Moreover, higher Voc and transmission values are reported for NiO layers prepared by R.F. sputtering with 2% and 10% O2 [START_REF] Rocha | Electrochromism of non-stoichiometric NiO thin film: as single layer and in full device[END_REF] characterized by lower Ni 3+ concentration as opposed to NiO layers prepared by D.C. sputtering with the same amount of oxygen and similar layer thickness [START_REF] Wen | Anodic electrochromism for energy-efficient windows: cation/anion-based surface processes and effects of crystal facets in nickel oxide thin films[END_REF].

Films conductivity

The films resistivity (ρ) was measured by two points contact measurement in vertical geometry (contact surface 0.8 mm 2 ) and used along with carrier concentration (N) to calculate the mobility (μ) according to the formula:

μ = 1 ρNe (9)
Film resistivity decreases (from 5.9 kΩ.cm for the sample 300 to 0.6 kΩ.cm for the sample 600)

along with increasing carrier concentration and a radical drop in mobility was registered (0.36 cm 2 /(V•s) for sample 350 compared to 0.0021cm 2 /(V•s) for sample 600) which could be related to ionized impurity scattering (Fig. 7).

Stoichiometry and optical properties prediction

To begin, the Voc values of the films (Table 1) were plotted versus the corresponding transmission values at 550 nm (Fig. 8a) and a linear dependency was found. The correlation of optical and electrochemical parameters allows for determining the initial transmission of an unknown Ni1-xO sample by simply dipping the film in the electrolyte and taking the Voc value.

When plotting the transmission or the open circuit potential vs. carrier concentration (Fig. 8b andc, respectively) linearity is again observed. It is to note that absorption values could also be used for building these curves. The inverse exercise could be made as well, for determining the transmission level of an unknown sample, carrier concentration or simply the Voc have to be measured. The proposed method could be applied for determining the stoichiometry in Ni1-xO films prepared by other methods, to Li-doped NiO, or other films which show important change in optical properties (either in the visible or near-infrared region) with carrier concentration/ stoichiometry modification (i.e. highly sub-stoichiometric titanium oxide or transparent conducting oxides). Such correlations have never been done before and allow for the straightforward determination of the carrier concentration and stoichiometry by measuring film transmission or Voc since x in Ni1-xO is given by [START_REF] Sørensen | Nonstoichiometric oxides. Chap. 1 Thermodynamics and defect structure of nonstoichiometric oxides[END_REF]:

x = [V Ni " ] * M ρ * N A (10)
where nickel vacancy concentration [V Ni " ] is equal to carrier concentration N if we consider that all the vacancies are ionized ( NA is the Avogadro number, and ρ and M are the NiO density and molar mass). The x values for sample 300, 400, 500 and 600 are given in Table 2 next to the number of Ni 3+ sites per unit cell (Ni 3+ MS) obtained by considering that for one nickel vacancy two Ni 3+ sites are formed (eq.1).

Table 2. Stoichiometry variation with annealing temperature. To verify our theory, we registered the transmission spectra of a Ni1-xO sample which was annealed at 500 ⁰C for 8 h in Ar atmosphere and used the calibration curve in fig. 8b to determine the carrier concentration. For a transmission level of 85.8% at 550 nm, N was found to be 2.2•10 16 cm -3 . The Voc was also measured (0.195 V vs. Ag/AgCl sat. KCl) as previously described and lead to similar carrier concentration when extrapolated in Fig. 8c. At the same time the carrier concentration was determined by Mott-Schottky measurements (Fig. S4 in supplementary information), in the same conditions as all the other samples, giving a similar value i.e. N = 2.3•10 16 cm -3 . Furthermore, the carrier concentration of the sample annealed at 500 ⁰C in Ar atmosphere (2.2•10 16 cm -3 ) was lower than the one of the same sample annealed in air (5.8•10 17 cm -3 ), as expected.

For comparison, the number of Ni 3+ sites was also determined by performing a cathodic scan of fresh non-cycled films in 0.5 M LiClO4 in PC electrolyte at 20 mV/s scan rate (Fig. 9), starting from the equilibrium potential towards -0.5 V vs. Ag/AgCl (3M KCl saturated with AgCl) reference electrode and ending when cathodic current reached 0. The charge capacity was extracted from the electrochemical curves for all the samples by integration and further used for calculating the number of Ni 3+ sites (eq.12) [START_REF] Wen | Anodic electrochromism for energy-efficient windows: cation/anion-based surface processes and effects of crystal facets in nickel oxide thin films[END_REF].

Ni 3+ CV = Q A * M edρN A (11)
The number of Ni 3+ sites determined by cathodic scan is higher than the one derived from the Mott-Schottky plots. These differences might originate from the used scanning speed as the surface of cyclic voltammetry and thus the charge capacity modifies with scanning speed, or from a trace contamination of the electrolyte or sample.

Likewise, for comparison purposes, a physical method i.e. XPS was used for determining the degree of non-stoichiometry in the samples 400 and 600. The core level spectra of the Ni 2p3/2 states for the 400 and 600 Ni1-xO thin films are presented in Fig. 10a andb, respectively. The biding energy at 853.9 eV is attributed to the Ni 2p3/2 main peak, the shoulder at 856.1/856.2 eV is the surface component, and the biding energies at 855.3/855.4 eV are indexed to Ni 3+ states.

Meanwhile, the biding energies at 861.0 and 863.7/863.8 eV were attributed to the charge transfer satellite peaks [START_REF] Usha | Improved electrochromic performance of a radio frequency magnetron sputtered NiO thin film with high optical switching speed[END_REF][START_REF] Preda | Interface effects in the Ni 2p x-ray photoelectron spectra of NiO thin films grown on oxide substrates[END_REF].

Comparison with literature

In view of the difference in "x" values between the electrochemical and XPS analysis, a literature survey was undertaken concerning the different methods for determining the stoichiometry of Ni1-xO films synthesized by chemical or physical processes (Table 3). In addition, wherever carrier concentration was given we have calculated the x values (assuming a constant value for the layer density and molar mass) by using the eq. 11, and compared the results with our own (the values are written in bold in Table 3). The stoichiometry results show that the sample 600 has a higher Ni 3+ concentration than sample 300 and should thus have a higher transmission modulation. However, the electrochromic experiments show the contrary. The lower performance was attributed to the layer structure. In fact sample 600 is more crystalline according to XRD results and has lower specific surface. This is in agreement with previous studies [START_REF] Chen | Property modulation of NiO films grown by radio frequency magnetron sputtering[END_REF][START_REF] Chen | Highly porous nickel oxide thin films prepared by a hydrothermal synthesis method for electrochromic application[END_REF] which link the reduced transmission modulation to the increasing layer crystallinity and compactness which hampers Li + ions diffusion.

Conclusions

Compact p-type Ni1-xO layers with 0.7•10 -6 <x <3.7•10 -5 (and corresponding N values of 3.9•10 16 and 5.0•10 18 ) were synthesized by ultrasonic spray pyrolysis (USP) and subsequently annealed in air at 350, 400, 500 and 600 ⁰C. The Ni 3+ content in the films increased with rising annealing temperature as confirmed by XRD, optical absorption and Mott-Schottky analysis.

Giving the low x values, we conclude that NiO films with higher carrier concentration can only be prepared by USP when doping is used or by physical methods. The x values determined by electrochemical measurements were significantly lower compared to XPS values. This leads us to conclude that the elemental analysis of non-stoichiometric oxides is challenging from the point of view of selecting the appropriate analysis tool and the accurate and universal interpretation of results.

The particle size increases with increasing annealing temperature resulting in increased film compactness, as proven by the rising contact angle values, and consequently to decreasing specific surface. The changes in specific surface were taken into consideration during the electrochemical analysis. A lower electrochromic performance was obtained for films with higher Ni 3+ concentration due to the increased film compactness and crystallinity. Film conductivity is increased (hole concentration enhances) with rising temperature leading to a lower charge transfer resistance at the electrolyte/Ni1-xO interface.

The original correlation transmission (T)-open circuit potential (Voc)-carrier concentration (N)

demonstrated in this study allowed the straightforward evaluation of stoichiometry in unknown Ni1-xO films and the prediction of their optical properties. The transmission in the initial, colored and bleached state is lowered with increasing x. The Voc is a valuable material property as information about stoichiometry can be obtained by simply following its evolution, i.e. Voc increases for decreasing x values.

  Thermo Fisher Scientific K-Alpha spectrometer (monochromatized AlKα source, hν=1486.6 eV, spot size 200 μm) was used for surface XPS analysis of the Ni1-xO thin films.The full spectra (0-1150 eV) were obtained with constant pass energy of 200 eV and high resolution spectra with constant pass energy of 40 eV. Quantification of Ni 3+ was done based on the fits of the high resolution Ni 2p3/2 spectra using the AVANTAGE software (Thermo Fisher Scientific).The Ni1-xO films resistance was studied by 2-points contact measurements (considering a vertical geometry, contact diameter 0.12 cm) using a PhysTech RH 2035 system. The carrier concentration, flat band potential and NiO/electrolyte interface properties were determined by electrochemical impedance spectroscopy analysis in aqueous media (0.1M NaH2PO4 + 1M KCl, pH adjusted to 7 with NaOH to guarantee constant pH and ionic strength) in the 50 Hz -800 kHz frequency range (51 points uniformly distributed over a logarithmic scale) under variable potential. In the case of Mott-Schottky measurements, the frequency scanning was started from the negative potential values towards positive values. Electrolyte solutions of pH 8, 9 and 10 were also prepared for studying the variation of the flat band potential with pH. The area of the electrode which was exposed to electrolyte was 0.15 cm 2 . The electrolyte was purged with Ar for 30 min before the analysis to remove any dissolved oxygen. The electrochemical measurements were carried out in a custom three-electrode cell using a potentiostat (Biologic SP300 with frequency response analyzer), a platinum counter electrode, an Ag/AgCl in saturated KCl reference (0.248V vs. SHE, XR300 Radiometer Analytical) electrode for the aqueous media and an Ag/AgCl in 3M KCl saturated with AgCl (0.208V vs. SHE, REF361 Radiometer Analytical) for the non-aqueous media. The cyclic voltammetry and chronoamperometry experiments were carried out in a solution of lithium perchlorate 0.5 M (99.99%, Aldrich) in propylene carbonate (anhydrous 99.7%, Sigma Aldrich) in the -0.5 to 1.2V potential range. The absorption spectra of the initial, colored and bleached Ni1-xO films were registered using a Perkin Elmer Lambda 25

Fig. 1 X

 1 Fig. 1 X-Ray diffraction patterns (a) and crystallite size and lattice parameter (b) values of the Ni1-xO films on glass substrate annealed at 350, 400, 500 and 600 ⁰C for 3 h.

Fig. 2

 2 Fig. 2 AFM images (500 nm x 500 nm) and particle size distribution for the Ni1-xO films annealed at 350, 400, 500 and 600 ⁰C for 3 h. Roughness values are also shown on the pictures.

Fig. 3

 3 Fig. 3 Contact angle values of the Ni1-xO films annealed at 350, 400, 500 and 600 ⁰C for 3 h.

Fig. 4

 4 Fig. 4 Absorption (a) and transmission (b) spectra of the Ni1-xO films annealed at 350, 400, 500

Fig. 5

 5 Fig. 5 Nyquist plots of the samples 350, 400, 500 and 600 at 0.2V (a), Nyquist plots of the sample 600 as function of applied potential (b).

  with the x axis (fit was done in the linear region) was used to determine the flat band potential whereas the carrier concentration was determined from the slope. Both carrier concentration and flat band potential values are summarized in Table1. It can be clearly observed that the carrier concentration increases with annealing temperature along with flat band potential indicating a lowering of the valence band edge.

Fig. 6

 6 Fig. 6 Mott-Schottky plots for the 1.0 kHz frequency for the Ni1-xO samples annealed at different temperatures (a) and the flat band variation as function of pH for the 350 case (b).

Fig. 7

 7 Fig. 7 Variation of the carrier concentration (N), resistivity (ρ) and mobility (μ) of Ni1-xO films as function of annealing temperature.

Fig. 8

 8 Fig. 8 Transmission (at 550 nm) vs. the open circuit potential Voc (a), transmission (at 550 nm) vs. carrier concentration (b), and open circuit potential Voc vs. carrier concentration (c).

  -Schottky analysis, CVcyclic voltammetry and XPS -X-ray spectroscopy analysis

Fig. 9

 9 Fig. 9 First reduction curves of the Ni1-xO samples in 0.5 M LiClO4 in PC electrolyte (specific surface was considered).

Fig. 10 Fig

 10 Fig. 10 Fig. 10 XPS spectra of the Ni 2p3/2 states in Ni1-xO thin films annealed at 400 (a) and 600 °C (b) along with the deconvolution.

Fig. 11

 11 Fig. 11 Cyclic voltammetry curves (a) and colored and bleached state transmission spectra (b) of the samples 350 and 600.

  1•10 19 cm -3 . As already confirmed by the

	Sample	N (m -3 )	Voc (V/SHE)	Φfb (V/SHE)	EVB (eV/vacuum)	Φ (V vs. Ag/AgCl)	Φ (V /SHE)	Φsc (V/SHE)	Lsc (nm)
	350	2.87•10 21	0.382	0.211	-4.64	-0.226	-0.027	0.185	292
	400	3.94•10 22	0.401	0.312	-4.74	-0.081	0.118	0.194	81
	500	5.80•10 23	0.432	0.467	-4.90	-0.008	0.191	0.276	25
	600	5.00•10 24	0.452	0.651	-5.08	0.031	0.230	0.421	10

Table 2 .

 2 Based on the XPS

	quantification the formula of the Ni1-xO films can be written as Ni0.90O or Ni 0.97 2+ Ni 0.02 3+ O in the
	case of sample 400, and Ni0.84O or Ni 0.984 2+ Ni 0.032 3+ O for sample 600. It can be clearly observed
	that by XPS considerably higher Ni 3+ concentrations are obtained compared to Mott-Schottky
	analysis for both samples.

Table 3 .

 3 Literature survey on x determination in Ni1-xO films prepared by different methods. Layer thickness (d), transmission at 550 nm (T550 nm), carrier concentration (N), flat band potential (Φfb), open circuit potential (Voc) and valence band edge position (EVB) are also given.

	Ref.	Deposition method/ heat treatment	d [nm]	T550 nm [%]	x value/ method	N [cm -3 ]	Φfb vs. SHE pH [V]/ media/	EVB [eV]	Voc vs. SHE [V]
	20	PLD, PO2=10 -1 mbar	30	80-95	-	-	-	-	0.68
	25	Spin coating, 400 ⁰C in air	906	32	2.4•10 -4	1.3•10 19 /2-P	-	-	-
		Spin coating, 700 ⁰C in air	500	11	6.9•10 -4	3.7•10 19 /2-P	-	-	-
	16	Spray pyrolysis, 400 ⁰C in air	350	75	0.56/ XPS	1.8•10 17 /	-	-	-
					3.3•10 -5	4-p HE
	22	ALD, 300 ⁰C in Ar atm.	71	85	0.2•10 -5	1.1•10 17 / MS	0.19/ aq/ 10	-5.2	-
		ALD, 300 ⁰C in O2 atm.	71	-	5.0•10 -4	2.7•10 19 / MS	0.69/ aq/ 10	-5.2	-
		ALD, 600 ⁰C in O2 atm.	71	-	0.14	7.3•10 21 / MS	0.73/ aq/ 10	-5.2	-
	17	Spray pyrolysis, 450 ⁰C in air	100	70	9.1•10 -4	4.9•10 19 / MS	0.36/naq/10	-4.8	-
	32	Blade coating, 450 ⁰C in air	600	-	0.55/ XPS	1.2•10 18 / MS	0.37/ aq/ 7	-4.8	-
					2.2•10 -5
	18	R.F. sputtering, 30% O2	100	-	0.006/ RBS vs.		-	-	-
					0.020/ XPS
		R.F. sputtering, 100% O2	100	-	0.05/ RBS vs.		-	-	-
					0.027/XPS
	12	R.F. sputtering, 6% O2	360	-	0.076/ XPS I vs.		-	-	-
					0.13/ XPS II
		R.F. sputtering, 80% O2	360	-	0.083/ XPS I vs.		-	-	-
					0.19/ XPS II
	14	D.C. sputtering, 2% O2	300	84	0.16/ RBS	-	-	-	0.13
		D.C. sputtering, 10% O2	300	62	0.32/ RBS	-	-	-	0.23
	15	R.F. sputtering, PO2 =2%	250	92	0.009/ CV	-	-	-	0.54
		R.F. sputtering, PO2 =10%	250	44	0.035/ CV	-	-	-	0.84
	26	R.F. sputtering, Ar atm.	900	55	0.19/ XPS	-	-	-	-
	23	Electrodep., 400 ⁰C in air	-	-	3.3•10 -2	1.8•10 21 / MS	0.50/ aq/ 10	-4.9	-
	35	R. F. sputtering, PO2 =10%	60	50	1.0•10 -2	5.5•10 21 /	-	-	-
						4-p HE
	36	R. F. sputtering, PO2=10 -4	-	60	0.5•10 -5	2.6•10 17 /	-	-	-
		mbar				4-p HE
	19	R.F. sputtering, PO2 =50%,	100	-	0.44/ XPS	1.8•10 21 /4-p	-	-	-
					3.3•10 -2	HE
		R.F. sputtering, PO2 =50%,	100	-	0.36/ XPS	2.5•10 20 /4-p	-	-	-
		100 ⁰C in N2			4.6•10 -3	HE
		Spray pyrolysis, 400 ⁰C in air	200	86	0.7•10 -6	3.9•10 16 / MS	0.31/ aq/ 7	-4.7	0.40
	This study	Spray pyrolysis, 600 ⁰C in air	200	83	0.2•10 -4 / CV 0.010/ XPS 0.7•10 -4 / CV 3.7•10 -5	5.0•10 18 / MS	0.65/ aq/ 7	-5.0	0.45
					0.016/ XPS

MS -Mott-Schottky measurement, HE -Hall Effect measurement, 2-Ptwo point measurements, 4-P four point measurement in Van der Paw configuration, CVcyclic voltammetry.

Acknowledgements

The authors are thankful to the Walloon Region of Belgium for the funding of the Exactacoat Ultrasonic Spray Pyrolysis equipment through the SMARTSPRAY project (n°1117339, Greenomat). Laura Manceriu is grateful to the Walloon Region and AGC Flatglass ("Nouveaux produits CVD" Project, Convention de sous-traitance n°7428) for post-doctoral financial support.

Anthony Maho thanks "Fonds de la Recherche Scientifique" (FNRS) for post-doctoral financial support (FC 86864). The authors would also like to thank Gilles Sronck (GREEnMat) for films deposition and Cédric Malherbe (Analytical Chemistry and Electrochemistry Departement, University of Liège,) for optical measurements.

When looking at the table we first note that different techniques applied on the same sample render very different results [START_REF] Kim | Nickel vacancy behavior in the electrical conductance of nonstoichiometric nickel oxide film[END_REF]. Even more, there are significant differences reported for the same technique. Chen et. al [START_REF] Chen | Property modulation of NiO films grown by radio frequency magnetron sputtering[END_REF] extracted higher x values from the O/Ni ratio than from the Ni 3+ /Ni 2+ ratio and explained this by Ni 3+ enrichment at the surface of nanostructures.

It is likely possible that the difference comes from not removing the O related to organic contamination. Usually the content of Ni 3+ determined by XPS is higher compared to values obtained by RBS, cycling voltammetry or the values calculated by our approach. A very thin layer of Ni(OH)2 [START_REF] Bouessay | Electrochromic degradation in nickel oxide thin film: A self-discharge and dissolution phenomenon[END_REF] could be present at the film surface which is not detected by RBS leading to x overestimation. Some contradictions are also found, the x value determined from cyclic voltammetry curves [START_REF] Rocha | Electrochromism of non-stoichiometric NiO thin film: as single layer and in full device[END_REF] is smaller (0.035) than the x value obtained by RBS [START_REF] Wen | Anodic electrochromism for energy-efficient windows: cation/anion-based surface processes and effects of crystal facets in nickel oxide thin films[END_REF] (0.32, considering that for each oxygen interstitial one nickel vacancy is formed) for NiO film with similar thickness, even if the transmission level at 550 nm is lower (44% vs. 62%, respectively), suggesting higher Ni 3+ content.

Regarding our method for assessing x, we see that by applying it to other groups samples similar results are obtained when dealing with same range of carrier concentrations [START_REF] Wu | Effect of annealing temperature on the characteristics of the modified spray deposited Li-doped NiO films and their applications in transparent heterojunction diode[END_REF][START_REF] Thimsen | Energy Levels, Electronic properties and rectification in ultrathin p-NiO films synthesized by atomic layer deposition[END_REF][START_REF] Natu | Valence band-edge engineering of nickel oxide nanoparticles via cobalt doping for application in p-type dye-sensitized solar cells[END_REF], validating our results. Moreover, for higher carrier concentrations (10 20 -10 21 cm -3 ) the values calculated by our method come near the x values determined by XPS or RBS [START_REF] Yang | Effect of heat treatment on the properties of nonstoichiometric p-type nickel oxide films deposited by reactive sputtering[END_REF][START_REF] Thimsen | Energy Levels, Electronic properties and rectification in ultrathin p-NiO films synthesized by atomic layer deposition[END_REF][START_REF] Nakaoka | Semiconductor and electrochromic properties of electrochemically deposited nickel oxide films[END_REF][START_REF] Chen | Tunable electrical properties of NiO thin films and p-type thin-film transistors[END_REF] validating our approach.

Electrochromic activity

Since initially the films were intended for EC applications, the evaluation of their performance is investigated in a non-aqueous electrolyte. The electrochromic behavior of the two samples representing the extremes in terms of annealing temperatures (samples 350 and 600) were tested in the 0.5M LiClO4 in PC electrolyte in the -0.5 -1.2V potential range by cyclic voltammetry (CV) at 20 mV/s scan rate. The in situ cycling of the as-deposited Ni1-xO samples, previously performed in our group [START_REF] Denayer | Surfactant-assisted ultrasonic spray pyrolysis of nickel oxide and lithium-doped nickel oxide thin films, toward electrochromic applications[END_REF], showed that the bleaching was finished at around -0.5 V vs Ag/AgCl sat KCl. For more negative potentials (going up to -1.4 V) no change in optical and electrochemical capacity were registered. The 10 th CV cycle is shown fig. 11a.