Electronic and structural characterization of barrier-type amorphous aluminium oxide

Accepted Manuscript Title: Electronic and structural characterization of barrier-type amorphous aluminium oxide Author: Fabio Evangelisti Michael Stiefel Olga Guseva Raheleh Partovi Nia Roland Hauert Erwin Hack Lars P.H. Jeurgens Francesco Ambrosio Alfredo Pasquarello Patrik Schmutz Claudia Cancellieri PII: DOI: Reference:

S0013-4686(16)32636-6 http://dx.doi.org/doi:10.1016/j.electacta.2016.12.090 EA 28562

To appear in:

Electrochimica Acta

Received date: Revised date: Accepted date:

23-9-2016 18-11-2016 13-12-2016

Please cite this article as: Fabio Evangelisti, Michael Stiefel, Olga Guseva, Raheleh Partovi Nia, Roland Hauert, Erwin Hack, Lars P.H.Jeurgens, Francesco Ambrosio, Alfredo Pasquarello, Patrik Schmutz, Claudia Cancellieri, Electronic and structural characterization of barrier-type amorphous aluminium oxide, Electrochimica Acta http://dx.doi.org/10.1016/j.electacta.2016.12.090 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Electronic and structural characterization of barrier-type amorphous aluminium oxide.

Fabio Evangelisti1*, Michael Stiefel1, Olga Guseva1, Raheleh Partovi Nia1, Roland Hauert1, Erwin Hack1, Lars P.H. Jeurgens1, Francesco Ambrosio2, Alfredo Pasquarello2, Patrik Schmutz1, Claudia Cancellieri1* 1 EMPA,

Swiss Federal Laboratories for Materials Science and Technology, Ueberlandstrasse 129,

8600 Duebendorf, Switzerland. 2 Chaire

de Simulation à l’Echelle Atomique (CSEA), Ecole Polytechnique Fédérale de Lausanne

(EPFL), CH-1015 Lausanne, Switzerland Email: [email protected]*, [email protected]*,

Abstract: The structural, electronic, and dielectric properties of barrier-type anodic Al oxides prepared with various thicknesses have been investigated. The planar and cross morphologies as well as the surface charge distribution were investigated as a function of the voltage applied during growth, i.e. the thickness. Three distinct anodizing potential domains can be clearly identified. A transition in ionic mobilities induces, at anodizing voltage higher than 100 V, the built-up of space charge region in the anodic films. A correlated increased oxide density with growing anodization potential is consistently pointed out by Volta Potential Difference and XPS/Auger measurements. The full dielectric response of the oxides, including both the lattice and electronic components, has been accessed by electrochemical impedance spectroscopy and Auger analysis. The lattice contribution of the dielectric constant is found to be strongly affected by the growth voltage, as a clear increase in the lattice component of the dielectric constant is observed, reaching values close to those of bulk crystalline Al2O3 structures. At variance, the electronic contribution is only slightly affected. The results have been compared to dielectric constants calculated for atomistic amorphous models within the framework of density functional theory. It is shown that amorphous Al2O3 models of higher density lead to dielectric constants that could explain the trend observed in the series of barrier-type anodic oxides prepared in this work.

Keywords: Anodizing, barrier aluminium oxide, surface potential, Electrochemical Impedance Spectroscopy (EIS), capacitance, Auger parameter, dielectric constant.

1. Introduction Aluminium oxide exists in several crystallographic polymorphs and its thin and thick films are used in a wide range of applications including microelectronics and catalysis, diffusion barrier, thermal barrier, and wear resistant coatings for cutting tools [1, 2]. Anodic treatments of aluminium were performed to obtain protective and decorative films on its surface, most frequently porous and amorphous in structure [3, 4]. Applications of porous alumina with a huge surface area and a relatively narrow pore size distribution have been widely investigated and exploited [5-7]. For example, several attempts to fabricate inorganic membranes have been reported [8-10]. Porous alumina is one of the most prominent template materials for acid anodizing preparation of self-ordered porous alumina [11-13] and for synthesis of nanowires or nanotubes with a monodisperse controllable diameter and high aspect ratio [14]. In contrast, barrier-type anodic aluminium oxides have been less investigated from the microstructural and electrochemical point of view despite their potential for applications [15, 16]. The most important commercial use of barrier-type films is in the field of dielectric capacitors and in the protection of vacuum-deposited commercially relevant materials [17], which cannot be achieved using porous films. The high dielectric constant and the stability of amorphous Al2O3, even at high temperatures, make this compound a good candidate for gate insulator materials [18]. Barrier-type anodic aluminium oxides can be obtained in completely insoluble electrolytes (5
those based on porous alumina. This result is expected when taking into account the different morphology and structure, as well as the difference in the effective dielectric constants [21]. Studies on barrier type anodic oxides cover a wide range of applied voltages. In these studies, the oxide growth and eventual incorporation of solvent contaminants [22-24] depend on the choice of electrolyte and pH [25-27]. In this paper, a comprehensive multi-experimental study of the structural, electronic, and dielectric properties of barrier-type anodic aluminium is presented. A wide range of anodizing potentials (up to 350 V) is investigated and a systematic approach is used to analyze the structural properties of the anodic oxides which are grown in specific growth conditions, defined by the choice of the electrolyte type and of pH. This approach will be extended to other growth conditions and oxide types in the future. All the prepared oxides are amorphous with similar roughness and morphology up to 250 V. The surface charge distribution is found to be correlated with thickness and with occurrence of structural defects introduced by the high polarization potential. The complete dielectric response, in which the contributions from electronic and lattice polarization have been disentangled [28], has been derived combining Auger and Electrochemical Impedance Spectroscopy (EIS) techniques. The results show that it is possible to tune the dielectric properties of the amorphous oxide through the applied anodization potential. In particular, it is found that higher anodization voltages correspond to larger values of the dielectric constant, mainly due to an enhanced lattice contribution. The experimental results have been compared with first principle calculations of the dielectric constant of atomistic model structures of amorphous Al2O3, suggesting a correlation between the density of the amorphous oxide and its dielectric properties.

2. Methods 2.1 Materials and growth technique A two electrode electrochemical cell was used for the anodizing experiments consisting of aluminium plates (99.5% Al, 0.5 mm thick; provided in the pre-anodized at 3.4 V form by Novelis Switzerland) for the anode with a surface area of 1 cm2 and a platinum rod with a surface area of 1.6 cm2 as the cathode material. As received from the company and without any further pretreatment, the anode materials were cleaned prior the anodizing process for 5 minutes in an ultrasonic bath using acetone and ethanol, then rinsed with deionized water (18x 106 Ωcm), dried under Ar flow and stored in a dry environment. The aluminium sample was pressed against an O-ring on the side of a Plexiglas cell in order to have a defined, exposed, and analyzed area of 1 cm2 for the subsequent anodizing procedure. A 0.1 mol/l electrolyte solution of citric acid (C6H8O7, Sigma Aldrich) in deionized water adjusted at the pH of 5.8 with 1 mol/l sodium hydroxide solution (Sigma Aldrich) was used for the anodizing process and electrochemical impedance spectroscopy measurements. Anodization of the samples was performed in the potentiostatic domain using two different electrochemical systems. In the low voltage region (lower than 200 V), a Keithley Model 2400 voltage/current source controlled by an in-house LabView software was used for a precise voltage adjustment. Anodization at higher potentials was performed on a second, more powerful, JAISSLE PGU 400V potentiostat system from Electronic Lab Peter Schrems, reaching anodizing values that could not be approached with the Keithley Model 2400. The anodizing procedure was carried out at the final voltages summarized in Tab. 1 without stirring at room temperature and without thermally controlling the bath.

2.2 Characterization methods 2.2.1 Thickness measurements: spectroscopic ellipsometry The film thickness and refractive index were measured by spectroscopic ellipsometry in the 1.5 – 5 eV range. An ellipsometer of the type M-2000 by J.A. Woollam Co., Inc. was used. The samples were measured at three angles α1 = 50 °, α2 = 60 °, and α3 = 70 ° and an UV/VIS spectrum was collected for each angle in the range of λ = 370-1720 nm with an integration time of t = 5 s. The measuring beam was positioned manually at the center of the anodized surface. The sample height and the tilting were adjusted prior to each measurement. Data were fitted with a Sellmeier law using tabulated refractive index values. To investigate the structure (substrate/interface/anodized oxide) and the effect of a possible interface layer, different optical models were compared. The thickness was extracted from the model that gave the best fit.

2.2.2 Oxide surface/bulk structure: Electron microscopy and X-Ray diffraction techniques. Transmission electron microscopy (TEM) and Selected Area Diffraction (SAED) measurements were performed to estimate the morphology, the structure, and to further confirm the thickness of the oxide film formed on the anodized aluminium surface. Thin material sections were obtained using a FEI Helios 660 G3 UC Focused Ion Beam (FIB)/SEM system. The thin sections have been analyzed in a JEOL 2200FS field emission TEM. The system was operated at an electron energy of E = 200 keV. For the SAED experiments, a camera length of L = 30 cm was used. In order to investigate possible concentration stoichiometry gradients inside the oxide, energy dispersive x-ray analysis (EDX) data, with a built-in Si(Li)-detector in the TEM, were

recorded. The composition along the measured line was calculated using a less standard CliffLormier correction algorithm.

2.2.3 Oxide homogeneity and electrical properties: Electrochemical Impedance Spectroscopy (EIS) For electrochemical impedance measurements, an Autolab PGSTAT-30 was used in combination with a Frequency Response Analyzer (FRA2) and controlled by NOVA software. An AC amplitude voltage of 10 mV was superimposed to the open-circuit potential and a frequency range of 0.01 Hz to 100 kHz was considered. The electrochemical measurements were carried out at room temperature in a grounded Faraday cage. The EIS measurements were performed without deaerating. A three-electrode electrochemical cell set up was used with the sample connected as working electrode, with an exposed area of 1 cm2, similar to the one used during anodization; a platinum wire rod with a surface area of 1.6 cm2 was used as a counter electrode and a saturated calomel electrode (SCE) with a Luggin capillary as reference electrode. All experiments were carried out in the same solution as used in the anodizing step immediately after anodizing, without taking the sample out of the cell. The experimentally determined complex impedance, 𝑍 = 𝑍 ′ − 𝑗 𝑍 ′′ , where 𝑍 ′ and 𝑍 ′′ are the real and imaginary components of the impedance, is presented in Nyquist (directly - 𝑍 ′′ vs 𝑍 ′ ) and Bode plots, i.e. log|𝑍| vs log 𝑓 and phase shift − 𝜑 vs log 𝑓, where |𝑍| = (𝑍′2 + 𝑍′′2 )1/2 ; −𝜑 = 𝑡𝑎𝑛−1 (

−𝑍 ′′ 𝑍′

); 𝑓 – frequency in Hz. The

experimental EIS data were fitted to an appropriate electrical equivalent circuit using NOVA (1.11) software.

2.2.4 Topography and surface potential: AFM-SKPFM techniques. The topography, the phase, and the chemical reactivity were observed on anodized samples by environmental atomic force microscopy (AFM, VEECO E-Scope). Scanning Kelvin probe force microscopy (SKPFM) characterization mode measurements were performed to retrieve information about the surface topography and surface potential (referred as Volta potential difference) of the sample surface and were collected alternatively in a line scan base using a Pt– Ir metallic coated tip. An AC voltage of 1 V was applied between the SCM-PIT (Pt–Ir coated silicon) tip (Bruker Nano) having a nominal spring constant k=2.8 Nm-1 and a resonance frequency of fres=100 kHz. The Volta potential difference (VPD) was determined with respect to a pure Ni sample surface previously immersed in distilled water, and chosen as reference for its reproducible oxide formed at room temperature [29, 30]. The exact denomination of the measured potential is still a subject of debate but the established potential is of electrochemical nature in environmental conditions, so the most adequate relative reference is a defined metal/oxide/adsorbed water interface structure. Nevertheless, in the case of oxides in contact with the environment, not only the surface charges are giving a contribution to the measured potential. It can even be stated that, in contrast to metals where the electrochemical double layer charging is the key controlling contribution to the potential, migration related space charges in the oxides generated during the high field growth process can dominate the measured signal

2.2.5 Structural and chemical insight: X-Ray Photoelectron Spectroscopy (XPS) X-Ray Photoelectron Spectroscopy (XPS) analysis and Argon sputter depth profiling were carried out with a Physical Electronics (PHI) Quantum 2000 photoelectron spectrometer using

monochromatic Al Kα radiation and a hemispherical capacitor electron-energy analyzer equipped with a channel plate and a position-sensitive detector. The electron take-off angle was 45° and the analyzer was operated in the constant pass energy mode (46.95 eV) for all measurements. Sputtering was performed with Ar+ ions using an acceleration voltage of 2 kV . No effect of preferential sputtering on the surface composition was detected. The sputter rate for depth profiling at 2 kV was determined to be 8 nm/min, using a Ta 2O5 standard. The binding energy calibration was performed using the signals of Au 4f7/2 at 84.0 eV. To partially compensate for surface charging, an electron and an ion gun were operated simultaneously during the analysis. The modified Auger parameter of oxygen, α = O KLL + O BE, was determined by measuring the binding energy of the O 1s peak and the kinetic energy of the O KLL peak originating from the oxide films. The XPS spectra were background subtracted using the non-linear iterative Shirley method and fitted with a mix of Gaussian and Lorentzian functions. The specific binding energy (BE) and kinetic energy (KE) values associated to the Auger peaks were determined by fitting the top region of the concerned peaks.

3. Results 3. 1 Anodization of aluminium samples: Morphological and thickness evaluation The analysis of the structural and the electrical properties of aluminium anodized oxide samples is here reported. Samples were grown in citric acid solution with a pH of 5.8 under potentiostatic polarization at potentials between 10 V and 350 V (Fig. 1, Tab. 1). During the potentiostatic polarization at various final voltages, the current decreases exponentially after a rapid initial raise, a transient evolution typical for a barrier type oxide formation mechanism

(Fig. 1) [19]. Citric acid solution (0.1 M concentration adjusted to pH 5.8), a weak organic acid with low corrosive aggressivity, was used as electrolyte because it allows anodization at high potentials. The mild pH value (5.8) and the low electrolyte concentration (0.1 M) ensure that the inclusion of electrolyte species is kept to a very low level and is under control (c.f. Fig. 4 and section 3.1). The high potential boundary for Al in contact with citric acid was determined with a series of preliminary tests. In such preliminary experiments, the applied anodizing potential profile was defined in terms of the steepness of the initial potential ramp and the overall duration of the process. In the final optimized conditions, an initial steep ramping up for 30 s to the final voltage and a subsequent steady state potential set at the final value for 600 s have been used. In these conditions, the anodization was performed in a reproducible way up to potentials lower by 4-5 V than 250 V. The latter is defined as the dielectric breakdown potential from Volta Potential Difference measurements and from evaluation of pore formation onset. It corresponds to a potential threshold where charge migration is again fast (typical for barrier electrical properties breakdown), resulting in important decrease of the space charges measured by SKPFM. The experiments performed at potentials beyond 250 V have shown low reproducibility, rougher surfaces of the films and surface sparking. Due to the high ionic conductivity (and hence low electronic conductivity) of aluminium oxide films, ionic conduction is the main charge transport mechanism at high applied potentials. t. It is observed that the oxide grown at 50 V has already reached a stable state after 600 s with a current density of 10 A/cm2 At variance, a ten times larger current occurs on the oxide grown at 200 V, denoting a high electrochemical anodic activity.

The formation of the oxide at the metal/oxide interface features the concerted migration of aluminium cations (Al3+) from the metal towards the interface and of oxygen anions (O2-) from the electrolyte to the metal. This ionic conduction requires a high electric field across the interface to allow the migration of ions. Therefore, It is generally accepted that the thickness of barrier-type alumina is mainly determined by the applied voltage [31].

Scanning Electron Microscopy (SEM) characterization of the surface of the amorphous oxides achieved at different final potentials are shown in Fig. 2-a. The surface heterogeneity, which can be related to the roughness at the surface, is found to increase with increasing anodizing potentials. Formation of shallow pores is observed in the SEM images for samples prepared at potentials close or larger than the dielectric breakdown potential (cf. section 3.1 and 3.2, Fig. 2c and 2-d). This is possibly due to the concentration of currents resulting from local heterogeneities in the electronic properties of the oxide. This is a characteristic mechanism of anodic oxide formation, which results in the formation of deep pores in presence of an aggressive electrolyte [8]. The examination by Transmission Electron Microscopy (TEM) of the Focussed Ion beam (FIB) cross sections of the oxides (Fig. 3 a-d) reveals the dense and amorphous nature of the grown oxides over the entire growth potential range. It has to be mentioned that the top layer referenced as Pt-cover in Fig. 3-a-d is a protective coating, which is deposited to protect the oxide layer from beam damage during the thin section preparation in the FIB. The sections also clearly indicate that the lateral heterogeneities identified on the SEM images are mainly of electrical nature and they correspond to shallow pores. These pores are still shallow and do not penetrate the entire oxide when the growth is performed at potentials up to 350 V. For

potentials higher than 350 V, the pores might deepen close the oxide-metal interface resulting in an electrical discharge that does not allow to keep macroscopic electric insulation of the surface oxide and the oxide thickness to growth any further (c.f. section 3.1 and Fig. 3-d). Average oxide thicknesses can be derived from TEM micrographs and are reported in Tab. 1. Selected area diffraction patterns (SAED) were measured in the anodized oxides. An example of the results for the oxide grown at 250 V is shown in Fig. 3-f. The SAED pattern was obtained in the region marked in Fig. 3-e. Since neither sharp defined rings nor spots are recognized, it can be stated that the oxide is amorphous. This is further confirmed on the large scale by diffraction (P-XRD) analysis, which resulted in structureless patterns for all the samples (data not shown). Additional energy dispersive X-ray analyses (EDX) along the cross section of the oxide were carried out for the oxide grown at a potential of 200 V, which looks very homogeneous. From the EDX data of the linescan (Fig. 4-a), the composition across the oxide appears to be constant and close to the Al-O 40/60 concentration ratio corresponding to stoichiometric Al2O3 oxide, within the accuracy limit of the measurement. Furthermore, the XPS depth profile evaluation of the samples (Fig. 4-a) indicates a similar constant composition of the oxide across the thickness. The O 1s linetrace, the deconvolution of the two components of the Al 2p peak (Al oxide and Al metal) and the C1s linetrace are reported in Fig. 4-a. The ratio between the O and the Al concentrations is found to be 40/60, in agreement with Rutherford Back Scattering (RBS) measurements (data not shown). The C1s linetrace show the absence of C signal across the entire thickness of the Al2O3 oxide film. Superficial C contamination is observed within the outermost oxide structure. A signal with a noise level of approximately 0.3-0.5 at% is measured for C1s energy range through the oxide thickness (e.g. Fig. 4-a for the sample anodized at 200 V). RBS measurements (data not shown) lead to the same conclusions.

Incorporation of electrolyte species cannot be completely excluded. Nevertheless, the rapid growth which is typical for potentiostatic processes [32] and the major role played by the electrolyte pH solution[33, 34] lead to rule out the influence of inclusion of impurities in the oxide film. Moreover, chemical dissolution of the Al-oxide layer during the anodization can be neglected if the pH used is in the range between 5 and 7 (in the present work a pH of 5.8 is used). This results in the formation of anodic film less prone to incorporate impurities [35, 36]. The oxide thickness was also investigated with ellipsometry measurements ( Fig. 4-b, Tab. 1). Values of thickness measured with TEM (direct) and ellipsometry (indirect) are found to be in good agreement. As expected, the layer thickness increases steadily with voltage, with corresponding growth factors around f = 1.4 nm / V (see inset in Fig. 4-b).

3.2 AFM/ SKPFM and oxide electrical properties The images of the Volta potential difference (VPD) show a laterally homogeneous value of ~1 V (reported versus a Ni reference sample). Non-anodized passive Al would show a VPD value of 0.7 V [29]. This indicates that the anodization performed at the small potential of 1 V already significantly changed the charge distribution in the oxide and on the surface. Since the electrochemical double layer surface contribution is rather small for oxides [37], the significant potential increase can be related to charge distributions (ionic gradients, defects) in the oxide. Visible changes are then observed on the topography images as a result of the use of an higher voltage in the growth process of the anodic film. A general increase of the roughness and a change in the surface morphology is evident when comparing the results with those achieved

with the untreated surface (data not shown). The surface structure corrugation increases monotonically with the applied final potential. At anodizing voltages higher than 250 V, a specific type of roughness is formed as previously evidenced by the TEM/FIB cross section analysis (see Fig. 2 and 3). When moving closer to the electrical breakdown potential of the system, defined from VPD measurements, an increase in the surface roughness is observed along with the appearance of shallow pores. The VPD images and values of the anodized samples (Fig. 5 and Tab. 1) demonstrate a remarkable difference of potential between the low-voltage anodizing domain (oxides grown at potential up to 100 V) and the mid/high-voltage domain (from 100 to 250 V). The average VPD increased from 0.4 to 1.2 V when going from the surface treated at 10 V to that treated at 100 V in the low-voltage domain, a trend similar to that observed in Ref [25]. A steep increase of the VPD to 7.5 V is hence observed in the mid/high- voltage domain. A VPD decrease to 2.7 V is observed for anodizing potentials above the dielectric breakdown potential (Fig. 6).

Our data cannot be interpreted using the linear correlation between VPD and thickness proposed by Yasakau et al. [25] for relative thin oxides (200 nm) and low potentials. In the present work, measurements are extended to relatively thick oxides (> 500 nm), which show a different potential evolution in the mid/high-voltage domain. Linear fitting of the experimental VPD vs thickness dependence yields a slope of 0.025 V/nm (see Fig. 6-b), steeper than the one observed in the low voltage domain. At higher voltages, the slope inverts its sign but keeps the same absolute value. The slope relates to the charge density factor (δ) through the equation

𝛿∙𝑑 , 𝑟 ∙𝜀𝑜

𝑉=𝜀

where εr is the dielectric constant of the oxide, εo the permittivity of vacuum, V the

experimental VPD, and d the measured oxide thickness. The slope sign is mainly affected by the typology of charges (electrons or holes) involved in the gradient density that composes the oxide film. During the double-step anodizing procedure (see section 3.1), the film growth was mainly obtained in the initial rapid process [11]. In the second anodizing step, reaccumulation and redistribution of charge carriers and charged defects occurred in the anodized oxide [38]. In fact, a different organization of charged species (positively charged ions, positively charged defects such as VO2+ and/or Ali3+ or negatively charged defects, VAl3- and Oi2-) and the eventual incorporation of electrolyte species during anodization can contribute to the experimental VPD [39]. The AFM/SKPFM investigation allows one to clearly identify three anodizing potential domains. The low-voltage domain (up to 100 V), for which an almost not-hindered ionic (positively or negatively charged) migration can be envisaged resulting in charge equilibration in the anodized oxide, low VPD and almost constant for this anodizing voltage range. A clearly defined onset point for space charge formation is observed at ~100 V, defined as the transition from the lowvoltage to the mid-high voltage domain. In the mid-high voltage domains (100 -250 V), the ion migration process is hindered, so does not allow ionic charge equilibration and results in the building up of a defined space charge region with a VPD values linearly increasing with the anodizing potential [19]. We define the breakdown potential as the voltage corresponding to the maximum of the Volta Potential Difference measured as a function of the applied potential. Beyond the breakdown voltage domain (> 250 V), the electronic conductivity can be sufficiently high to generate local current discharge. The charge gradient induced by the ionic migration is

perturbed and reduced by induced charge compensation effects. In this domain, the following features are observed: (i) reduction of the measured VPD, (ii) characteristic changes of both surface and in-depth (visible in the FIB cross sections) morphology (Fig. 2 and Fig. 3) [40]. Shallow pores are generated as a result of a locally heterogeneously flowing current and would have produced a porous structure if an aggressive electrolyte had been used. TEM and ellipsometry measurements along with the AFM/SKPFM characterization suggest that not only the structural properties but also the electronic properties could be affected. In order to understand the relation between structural and electronic properties of the oxide, the dielectric properties of the anodized oxides have been investigated with Electrochemical Impedance Spectroscopy measurements (section 3.3) and XPS/Auger analysis (section 3.4).

3.3 Estimation of the dielectric response of the oxide by EIS Electrochemical Impedance Spectroscopy (EIS) measurements were recorded in the same solution as used for the anodization process. The cell was not dismounted and the sample was kept in contact with the solution for 2 hours before EIS characterization. The EIS spectra (in the Bode plot representation) of all the final anodization voltages considered are shown in Fig. 7-a. A high value of the polarization resistance (values at low frequency) is observed and a value of the phase 𝜑 of approximately -90° is inferred, indicating a barrier-type film which is homogeneous in the direction perpendicular to the applied voltage. The anodized film resistance also gradually rises as a function of the applied voltage. The EIS data were then analysed by a suitable equivalent circuit as shown in Fig. 7-b. In this model, Rs is the electrolyte resistance determined at high frequency; Rox is the resistance of oxide film in parallel with a constant phase element (CPE). Due to defects and the varying electrical properties of the

anodized film, even if the oxide is dense and microstructurally homogeneous as observed in Fig. 3, the capacitance element is replaced by a CPE. The impedance of the CPE is given by 𝑍𝐶𝑃𝐸 = 1 (𝑗𝜔)𝑛 𝑄

, where ω is the angular frequency, Q and n are the CPE parameters [41].

The employed circuit provides the ideal fit of the data measured for samples anodized at voltages up to 50 V (Fig. 7 c-d, 10 V-curve), thus indicating the presence of one time constant. In contrast, the fit is not perfect for samples obtained at higher voltages, thus suggesting the presence of two time constants (Fig. 7-d, 150 V curve). In the present work the goal is not to focus on the fitting procedure, but to estimate the dielectric properties of the surface layer from the fitting parameters and the values for film thickness determined by the ellipsometry technique. Thus, the same equivalent circuit depicted in Fig. 7-b was used for all the anodization conditions. The crucial step in the EIS analysis is often not related to the fitting procedure but on how properly the effective capacitance value (𝐶𝑒𝑓𝑓 ) is extracted from CPE parameters (Q, n). The dielectric constant of the layer can then be derived using the values of the effective capacitance 𝐶𝑒𝑓𝑓 and the thickness values 𝑑 as 𝜀 =

𝑑 𝐶𝑒𝑓𝑓 𝜀0 𝐴

, where 𝐴 is the surface area of the

film (1 cm2). The evaluation of 𝐶𝑒𝑓𝑓 from the CPE parameters has been addressed by Orazem et al. [42]. They introduced different approaches to extract the correct dielectric constant value. In this work, a normal time-constant distribution through the surface layer is assumed and the global impedance response of the electrode includes additive contributions from each part of the layer. This approach takes into account the film inhomogeneity across the thickness and leads to 1

the expression for the effective capacitance as 𝐶𝑒𝑓𝑓 = 𝑄 𝑛 ∙ 𝑅𝑜𝑥 (

1−𝑛 ) 𝑛

. According to Refs. [42]

and [43], the CPE behaviour is valid for the high frequency domain, where the imaginary part of

the impedance (- Z’’) shows a perfect linear behaviour in a log-log plot. This is the case for all samples in the frequency range of 0.02 Hz – 100 kHz, which was used for the fitting. A similar range was selected by Orazem et al [42] in the study of oxides formed on stainless steel. The fitted parameters of the circuit and corresponding values of 𝐶𝑒𝑓𝑓 and ε are reported in Tab. 2. It should be noted that the Helmholtz double layer capacitance at oxide/electrolyte interface can be neglected for all oxides studied in this work. In fact, the error in the capacitance induced by the addition of the double layer capacitance (approximately 70 μF/cm2, 1-nm-thick layer in water) does not exceed 1%, even for the thinnest film anodized at 10V. The values of the dielectric constant show that two types of oxide layers can be distinguished: oxides anodized in the low voltage domain (<100 V) with an average dielectric constant of 10.3 and oxides anodized in the mid-high voltage domain (100 – 250 V) with an average dielectric constant of 12.6. These two domains correspond to those identified through the AFM/SKPFM characterization. The average value measured in the low voltage domain (10.3) is comparable with the value of 10.5 measured for sintered alumina [44]. Films anodized at low voltages (<100 V) are homogeneous in nature. In contrast, films obtained at higher voltages (> 100 V) show heterogeneous dielectric behavior, which results in higher dielectric constants. This is also visible in the shape of the phase in EIS spectra of the film anodized at 150 V (Fig. 7-d). Inhomogeneity appears in the presence of two time constants. This effect becomes more distinguishable at increased voltages (Fig. 7-b). Nevertheless, the heterogeneity is not very pronounced and the high impedance and barrier properties are preserved until and beyond the dielectric breakdown potential value.

3.4 Local chemical state of O in the grown oxide layers

The depth-resolved local chemical state of O in the grown oxide layers (as compared to the respective bulk reference states in α-Al2O3 and γ-Al2O3) was evaluated from the (modified) Auger Parameter of O (α). This was measured by XPS as a function of sputter-profiling depth. The modified Auger parameter of O corresponds to the sum of the kinetic energy (KE) of the O KLL Auger line and the binding energy (BE) of the respective O 1s photoelectron line (i.e. α = KE(O KLL) + BE(O1s), which is independent of the incident photon energy, of the reference level, and of charging effects [45-47]. A change in the local chemical state of O (i.e. a change in α ) with respect to a crystalline reference state (γ-Al2O3) is associated with different chemical shifts in BE(O1s) and KE(O KLL). This is due to the difference in extra-atomic relaxation (or polarization) energy Rea of the final state for the singly and doubly charged core-hole states, respectively [47-49]. γ-Al2O3 has been chosen as standard for direct reference due to the negligible differences in the local chemical states of Al and O when compared with the amorphous phase [47]. A major contribution to Rea is related to the electron response of the local chemical environment of the atom (i.e. the electronic polarization) upon creation of a core hole or of two core holes in the photo-ionization and the Auger process, respectively [47-49]. The local chemical environment comprises the average coordination, bond angles, and bond distances between the core-ionized atoms and its first-neighboring atoms. As demonstrated in Ref [50], the measured change of the Auger parameter ∆α between two different local chemical states is given by Δα = 2ΔRea , where ΔRea is the difference in Rea between the two different states. For very thin (< 2 nm) oxide films on metals, the electronic screening of charges in the oxide film by the metal substrate introduces an additional contribution to the polarization energy [50, 51], which can be neglected for the thick oxide layers grown in the present study.

The values of α for the oxide layers, as grown at various anodizing potentials and after different sputter cycles (corresponding to different depths below the oxide surface), are collected in the so-called chemical state (or Wagner) plot in Fig. 8-a. α values were measured for selected anodizing voltages within the complete list of prepared samples (see Tab. 1). This chemical state plot was obtained by taking KE(O KLL) as ordinate and BE(O1s) as the opposite of the abscissa. Hence, equal values of α (corresponding to similar local chemical states of O) lie on parallel lines of slope +1. The measured values of α for different potentials and sputter depths approximately fall between 1037.0 and 1040.5 eV, which can be compared to the range of 1038.7 – 1039.9 eV reported for amorphous and crystalline Al-oxide films grown on Al metal substrates by thermal oxidation [46]. Results collected in Fig. 8-b and Fig. 9 show that the O Auger parameter of the anodized oxide layers not only varies with anodizing potential (Fig. 8-a and 9), but also exhibits a distinct trend with sputter depth. Considering the values measured for the sample prepared at 200 V as an instructive example, it is observed that α initially decreases from 1038.8 eV at the surface (cycle 0) to 1037.8 eV in the central region of the oxide layer (cycle 4). It hence increases to 1038.4 eV, near the metal-oxide interface (cycles 8-10). From measurements performed in the same conditions on bulk α-Al2O3 and γ-Al2O3 references, the resolved reference values of α are observed to be constant with increasing sputter depth. This indicates that the observed change of α with increasing sputter depth for the anodized oxide layers (Fig. 8-b) is not induced by sputtering artefacts (e.g. preferential sputtering of O), but originates from actual changes in the local chemical state of O across the oxide layer. For the unsputtered surface, the value of α decreases from α = 1040.4 eV at 10 V to α = 1039.2 eV at 250 V, with an overall α decrease of 1.2 eV (Fig. 9, black dots). A similar, but more pronounced trend is observed after the first sputter cycle, as the value of α decreases by 1.9 eV

, from 1039.8 eV at 10 V to 1037.9 eV at 250 V (Fig. 9, red dots). The most pronounced variation in α as a function of the anodizing potential is observed for the central parts of the oxide layers, where α ranges from 1040.0 eV at 10 V to 1037.8 eV at 250 V (the overall variation being 2.2 eV) (Fig. 9 blue dots). In the sputtered region near the metal-oxide interface, a decrease of α from 1039.9 eV at 10 V to 1038.4 eV at 250 V is observed (Fig. 9, pink dots). Hence, for all probed oxide depths, the measured values of α decrease with increasing anodizing potential covering a range going from 1.2 to -2.2 eV. This effect is larger than the one observed in oxide films grown by thermal oxidation in a temperature range of 373 – 773 K (from 0.4 eV to 1.2 eV) [46]. Therefore the polarization potential has a larger effect on the variation of the local chemical state than the oxidation temperature. From the Clausius-Mossotti relation [52] one infers that the O Auger parameter and the material density are inversely proportional. Therefore, the measured values of the O Auger parameter as a function of the applied voltage (Tab 3) indicate a potential-dependent increase of the density. At variance, the variation of the O Auger parameter at different depths suggests density variations across the oxide layer, with lower densities near the surface and the metaloxide interface. These results could also arise from small changes in the stoichiometry across the thickness. However, such variations were not detected in our measurements. Furthermore, the large VPD measured by SPKFM (Fig. 6) suggest the occurrence of a gradient of ionic species [25] , which could induce the observed polarization effects.

3.5 Theoretical analysis of dielectric constants of amorphous Al2O3 In this section, density-functional calculations were used to investigate the connection between the structural properties of the barrier-type amorphous Al2O3 samples produced in this work

and their dielectric response. From Tab. 3, it is evident that the static dielectric constants (εr EIS) of the samples obtained at mid-high voltage (> 100 V) are larger than both those measured for samples at lower voltage (< 100 V) and those recorded in the literature for ALD-prepared Al2O3 [53, 54] . This suggests differences between the structural features of these materials. The theoretical determination of the dielectric constants was performed combining density functional theory (DFT) calculations with a formulation of the polarization based on a discrete Berry phase [55, 56]. Calculations were carried out in the presence of a finite electric field of 0.001 a.u. Wave-function optimizations and structural relaxations in the presence of the electric field were performed to evaluate the high-frequency dielectric constant εele and the static dielectric constant εr, respectively. All calculations are performed with the Quantum-ESPRESSO suite of codes [57]. The exchange-correlation functional developed by Perdew, Burke, and Ernzerhof (PBE) [58] was employed. A plane-wave basis set with a kinetic energy cut-off of 70 Ry was used for valence electrons. The core valence-interactions were described by normconserving pseudopotentials. First, the dielectric constants of various crystalline phases of Al2O3 were calculated in order to establish the accuracy of the theoretical results with respect to experiment. α-Al2O3 and κ-Al2O3 were modelled as described in Ref. [59]. For the defective spinel γ phase, a 40-atom model with two octahedral Al vacancies was employed, as proposed in Ref. [60]. For α-Al2O3, the calculated results for εele agree with experimental values within ~0.1. For the various components of εr, the calculated values systematically overestimate their experimental counterparts by 0.9-1.4 (cf. Tab. 4). From Tab. 4, it is inferred that εele does not vary by more than 0.1 among the various crystalline phases despite noticeable variations in the mass density ρ and in the structural

arrangement as evidenced by the average Al coordination number nAl. The static dielectric constants undergo larger variations which appear to increase with ρ and nAl. The same methodology was employed to calculate the dielectric constants for a model of amorphous Al2O3 (model Am-1). This model was generated in Ref [59]. and shows a mass density of ρ=3.31 g/cm3 along with structural and electronic properties falling within the range of available experimental data for ALD-prepared samples [53]. The calculated values of the electronic and static dielectric constants are in overall good agreement with their experimental counterparts (cf. Tab 4). The slight overestimation is consistent with that observed for the crystalline phases. It should be noted that the calculated εele remains close to the values of the crystalline phases, whereas εr is considerably lower. This can be interpreted with the lower density and the lower average Al coordination number of amorphous model Am-1, thereby confirming the qualitative trend observed for the crystalline phases. The structure of model Am1 could represent that of barrier-type Al2O3 samples generated at low voltages (< 100 V) as the calculated values of εr are consistent with the dielectric constants measured in Tab 3 (9.8510.01). However, the higher εr (12.19-13.11) measured at mid-high voltages (> 100 V) suggest the occurrence of significant structural modifications with respect to model Am-1. For this reason and in view of identifying a qualitative relationship between ρ and ε r, a second amorphous model at an increased density of ρ=4.10 g/cm3 was constructed. To obtain such a model, the atomic coordinates of model Am-1 were firstly homogeneously shrunk. Then, an ab initio molecular dynamics simulation was performed for a period of 10 picoseconds (ps) at constant volume and with a temperature set at 2000 K. A high temperature was chosen to accelerate the transition of energy barriers in times affordable to the molecular dynamics simulations. The structure achieved at the end of the molecular dynamics simulation was

further relaxed. The final model Am-2 is employed to calculate the dielectric constants. Compared to model Am-1 (ρ=3.31 g/cm3), model Am-2 does not only feature an increased mass density (ρ=4.10 g/cm3) but also a higher average Al coordination number (nAl=5.41, compared to nAl=4.40 for model Am-1). The calculated dielectric constants in Tab. 4 show that model Am-2 features larger values of εr than model Am-1, which mainly result from an enhanced lattice contribution. It can be remarked that the Cartesian components of εr for model Am-2 range between 13.05 and 13.65. This range is similar to the values measured for barrier-type Al2O3 at anodizing voltages > 100 V (cf. Tab. 3). These considerations suggest that an increase in density could be at the origin of the high dielectric constants measured for the anodic samples in this work. However, the density increase which is necessary to achieve dielectric constants close to the measured ones appears to be larger than typical densities of amorphous Al2O3, which range between 3.05 to 3.65 g/cm3 [61, 62]. It should be noted that in the experiment, the high value of the dielectric constant results from a measurement in the sole growth direction and could thus be achieved with a lower density than in our model am-2, which has been achieved through isotropic shrinking. However, it cannot be excluded that the high measured values might also result from the incorporation of electrolyte species (not detected in our case) or of other defects.

4. Discussion EIS , SKPFM, and Auger measurements provide results that can be consistently interpreted with the occurrence of different voltage domains. In particular, three different domains at low-(< 100 V), mid-(100 -250 V), and high (> 250 V) voltages can be distinguished.

At anodizing potentials higher than the breakdown potential (>250 V, see section 3.1 and 3.2 for discussion on the experimental evaluation), the oxide films show a clearly different morphology, higher roughness, and different charge compensation effects (Fig. 2, 3 and Fig. 6-a,b), when compared to the oxides anodized at lower voltages. These highly defective porous samples were not analyzed by EIS and XPS. A fully experimental Auger evaluation was carried out for the low- and mid-voltage anodizing domains. At anodizing voltages lower than 250 V a clear turning point is observed at ~ 100 V, which separates the low and the mid voltage domains. Below this value, the VPD value is almost independent of the anodizing voltages (Fig. 6-a and Tab. 1), thus indicating a homogeneous and not-hindered ionic charge migration process in the electric field established by the anodizing potential. In the mid-voltage region, the ion migration becomes dependent on the anodizing potential (Fig. 6-a and Tab. 1). The electric-field driven transport of O and Al during the anodic growth yields the formation of pronounced space charge regions in the grown oxide film. Due to the charge selectivity of the oxidation process, negative charges are supposed to accumulate near the oxide-electrolyte interface due to the presence of positively charged defects, building up a characteristic outer space charge region. Depending on the applied potential (electrical field strength) , ion migration through space charged regions could be influenced by the average oxide density over the thickness of the grown oxide. The variation of the VPD values with the anodizing voltage is consistent with the potential-dependent evolution of the O Auger parameter (Tab. 3). In fact, the O Auger parameter is found to decrease with the applied voltage. It is also found to change with depth. These trends can be related to the different densities of the oxide samples generated at various anodization potentials and with variations of the density within the same material.

From Ref. [46], the overall reduction of free-volume in the random network of densely packed oxygen atoms in amorphous Al-oxides (i.e. the oxide densification) is also generally accompanied by a decrease of the O Auger parameter. This is due to the overall decrease of the electronic polarizability around the core-ionized O atoms. The consistency between the growing oxide density and the lower O Auger parameters measured for samples obtained at higher voltages indicates that the ionic charge migration process (and the consequent building up of a space charged region, see section 3.2 and Fig. 6) is hindered at higher density, while it is facilitated at lower density.

A clear separation between the low- and mid-voltage domains is also observed for εr-EIS values. (described in section 3.3) as a function of the anodizing potential. Values of εr-EIS ~ 10 are measured in the low voltage range (< 100 V) and values of ~12-13 in the mid-voltage range (100250 V) (section 3.3 and Tab. 2) evidencing a clear change of the dielectric properties of the oxides obtained in these two domains.

In the following, the dielectric behavior of the anodized materials is further investigated, in particular, the correlation between structural properties and the lattice and electronic contributions to the dielectric constant. An estimation of the electronic contribution εele to the bulk dielectric constant can be derived from the chemical state analysis (O Auger parameter) presented previously. Since the Auger parameter depends on the electronic polarizability, its value can be related to the high frequency contribution (εele). The electronic polarizability referred to an oxide reference state (γ-Al2O3) is given by ΔEpol ≈ ΔRea . ΔEpol can be related to the electronic contribution of the dielectric constant εele with the following expression [63] :

∆𝐸𝑝𝑜𝑙 = −

𝑒2 2

(4𝜋𝑟)−1 ( 𝛆

1 𝑒𝑙𝑒

−𝛆

1 𝑒𝑙𝑒−𝑟𝑒𝑓

)

(eq.1)

In Eq. 1, e is the electronic charge and r is an effective orbital radius. εele and εele-ref are the highfrequency dielectric constants of the material of interest and of the reference material (γ-Al2O3), respectively. In order to use Eq. 1 for the calculation of εele of the amorphous oxides prepared in this work, an estimation of r has to be provided. Using the difference between the α values measured for bulk crystalline α-Al2O3 and γ-Al2O3 (1038.91 eV and 1038.53 eV, respectively) and the respective difference in the theoretical εele reported in Tab. 4, a value of r=0.09 Ȧ is obtained.

Once a value of r has been determined, the electronic part of the dielectric constant for the anodized oxides is given as an average εaveele over the values obtained from each measured point during the sputtering across the oxide thickness (see Fig. 10 and Tab. 3). εr originates from the sum of the contributions of the electronic polarization (εele) and of the crystal structure lattice vibrations (εlat) [28].Therefore, an average lattice contribution (εavelat) can be obtained from the measured values of εr-EIS and εaveele (see Fig. 10 and Tab. 3). The experimental εaveele values show a very small variation in both the low and mid-voltage domains Fig. 10 and Tab. 4. The average value of 3.10 is found to be comparable to previous experimental and calculated values for εele, (Fig. 10 and Tab. 4). The experimental value of εele for α-Al2O3 (3.075) is close to the values measured for the anodized oxide prepared at high voltages (Fig. 10 and Tab. 4). In contrast, the low voltage anodizing domain shows lower values. A large difference is observed when comparing the values calculated in the present work for anodized oxides with the ones obtained for ALD-prepared Al2O3 (2.6-2.8 from Refs. [53, 54])

Values of εavelat for anodized oxides (Tab. 4 and Fig 9) are found to increase with anodizing potential, with 6.7<εavelat<7.7 in the low-voltage domain and 9.0<εavelat< 10.2 in the mid-voltage domain. The measured dielectric constants are compared to those achieved from DFT calculations performed on various crystalline and amorphous Al2O3 models. Notwithstanding a general overestimation of the calculated values with respect to experimental data from literature, DFT calculations strengthen the connection between the measured dielectric constants and the structural properties of the amorphous oxides prepared in this work. Values of εavelat for the oxides prepared in the low-voltage domain are found to be comparable to those calculated for an amorphous model of low density (Am-1), for which the structural and electronic properties were found to be in excellent agreement with ADL-prepared oxides [59]. These results suggest that the structure of barrier-type oxides achieved at low voltages should be similar to those of ALD-prepared oxides. At variance, εavelat of samples prepared in the mid-voltage domain do not fall in the experimental range of values measured for ADL-prepared oxides. Interestingly, their values are found to be close to those measured and calculated for crystalline phases of Al2O3. Moreover, values in the mid-voltage domain are found to be comparable to those calculated for a second amorphous model (Am-2), with a density close to the experimental density of α-Al2O3 . The combination of experimental and calculated results suggest that, as the oxide becomes more dense at higher voltage, the space available for each ion is reduced and a larger degree of long-range order could be envisaged, with formation of multiple sub-ordered units within the amorphous oxide structure [64].

5. Conclusion In this study, the structural and electronic properties of barrier-type aluminium oxides were investigated by means of a multi-experimental and theoretical characterization. Systematic surface and cross-section structural, morphological, and electrochemical investigations were carried out as a function of the applied anodizing final voltages. Evaluation of the AFM, TEM morphology and Volta Potential Difference (VPD) clearly define three different potential domains: - a low-voltage domain (up to 100 V) showing a very weak dependence of the VPD on the anodizing voltage thus indicating a not-hindered ionic migration. - a space-charge onset point is observed around 100 V, indicating the transition to the midvoltage domain (100-250 V). In this range of voltages, ion migration process becomes slower to allow ionic charge equilibration and it is associated to a higher densification of the oxide. - the breakdown voltage domain is observed above 250 V, the high voltage domain. In this region, misbalance in the charge gradient is produced, with consequent local current discharge and reduction of the VPD values. A defined change in roughness is outlined in the FIB cross sections and SEM data. The reduction of the measured O Auger parameter values with the anodic growth potential observed up to 250 V is a consequence of the increased material density as pointed out by the VPD measurements. It is suggested that the densification is related with the development of a larger degree of long-range order at higher applied potentials. The average values of εaveele and εavelat derived from EIS and Auger analysis show different voltage-dependent behaviors. In particular, εaveele is found to be only marginally affected by the

anodizing voltage. At variance, εavelat, is largely influenced by the applied growth potential with a clear distinction between the low- and mid-voltage domains. The comparison of measured values with results achieved with DFT calculations performed on various crystalline and amorphous models having different densities further supports the connection between the anodization potential and the density of the barrier-type oxide. The results presented in this work indicate that the anodization process is a precise technique for achieving barrier-type oxides with tunable structural and dielectric properties.

Acknowledgements The authors thank Davide Colleoni and Giacomo Miceli from the Ecole Polytechnique Fédérale de Lausanne (EPFL) (Lausanne, Switzerland ) for fruitful discussions and for providing the coordinates of the amorphous Al2O3 model generated in Ref. [59]. This work has been performed within the frame of the National Center of Competence in Research (NCCR) ``Materials' Revolution: Computational Design and Discovery of Novel Materials (MARVEL)'' of the Swiss National Science Foundation. We used computational resources of the Swiss National Supercomputing Centre (CSCS) and of the Chair of Atomic Scale Simulation (CSEA) at the EPFL.

References [1] I. Levin, D. Brandon, Metastable Alumina Polymorphs: Crystal Structures and Transition Sequences, Journal of the American Ceramic Society, 81 (1998) 1995-2012. [2] D.H. Trinh, K. Back, G. Pozina, H. Blomqvist, T. Selinder, M. Collin, I. Reineck, L. Hultman, H. Högberg, Phase transformation in κ- and γ-Al2O3 coatings on cutting tool inserts, Surface and Coatings Technology, 203 (2009) 1682-1688. [3] V.F. Henley, Chapter 1 - Principles of Anodizing, Anodic Oxidation of Aluminium and its Alloys, Pergamon ,1982, pp. 3-5. [4] G.W. Critchlow, D.M. Brewis, Review of surface pretreatments for aluminium alloys, International Journal of Adhesion and Adhesives, 16 (1996) 255-275. [5] C.R. Martin, Nanomaterials: A Membrane-Based Synthetic Approach, Science, 266 (1994) 1961-1966. [6] S.Z. Chu, K. Wada, S. Inoue, M. Isogai, Y. Katsuta, A. Yasumori, Large-Scale Fabrication of Ordered Nanoporous Alumina Films with Arbitrary Pore Intervals by Critical-Potential Anodization, Journal of The Electrochemical Society, 153 (2006) B384-B391. [7] G. Patermarakis, H.S. Karayannis, The mechanism of growth of porous anodic Al2O3 films on aluminium at high film thicknesses, Electrochimica Acta, 40 (1995) 2647-2656. [8] K. Itaya, S. Sugawara, K. Arai, S. Saito, Properties of porous anodic aluminum oxide films as membranes, Journal of Chemical Engineering of Japan, 17 (1984) 514-520. [9] A.T. Shawaqfeh, R.E. Baltus, Fabrication and characterization of single layer and multi-layer anodic alumina membranes, Journal of Membrane Science, 157 (1999) 147-158. [10] T. Kyotani, W. Xu, Y. Yokoyama, J. Inahara, H. Touhara, A. Tomita, Chemical modification of carboncoated anodic alumina films and their application to membrane filter, Journal of Membrane Science, 196 (2002) 231-239. [11] S. Akiya, T. Kikuchi, S. Natsui, N. Sakaguchi, R.O. Suzuki, Self-ordered Porous Alumina Fabricated via Phosphonic Acid Anodizing, Electrochimica Acta, 190 (2016) 471-479. [12] K.R. Hebert, S.P. Albu, I. Paramasivam, P. Schmuki, Morphological instability leading to formation of porous anodic oxide films, Nat Mater, 11 (2012) 162-166. [13] R.A. Mirzoev, A.D. Davydov, D.K. Kurmyalevskaya, A.N. Bazylyk, S.I. Vystupov, Conditions for transition from barrier to porous oxidation of aluminum in phosphoric acid solutions, Electrochimica Acta, 184 (2015) 214-218. [14] S. Shingubara, Fabrication of Nanomaterials Using Porous Alumina Templates, Journal of Nanoparticle Research, 5 (2003) 17-30. [15] J. Chen, M. Yao, X. Yao, Electromechanical Breakdown of Barrier-Type Anodized Aluminum Oxide Thin Films Under High Electric Field Conditions, Journal of Electronic Materials, 45 (2016) 892-898. [16] D. Veys-Renaux, N. Chahboun, E. Rocca, Anodizing of multiphase aluminium alloys in sulfuric acid: in-situ electrochemical behaviour and oxide properties, Electrochimica Acta, 211 (2016) 1056-1065. [17] P.H. Lu, K. Wang, Z. Lu, A.J. Lennon, S.R. Wenham, Anodic Aluminum Oxide Passivation For Silicon Solar Cells, IEEE Journal of Photovoltaics, 3 (2013) 143-151. [18] B. Abad, J. Maiz, M. Martin-Gonzalez, Rules to Determine Thermal Conductivity and Density of Anodic Aluminum Oxide (AAO) Membranes, The Journal of Physical Chemistry C, 120 (2016) 5361-5370. [19] J.W. Diggle, T.C. Downie, C.W. Goulding, Anodic oxide films on aluminum, Chemical Reviews, 69 (1969) 365-405.

[20] M. Pashchanka, J.J. Schneider, Origin of self-organisation in porous anodic alumina films derived from analogy with Rayleigh-Benard convection cells, Journal of Materials Chemistry, 21 (2011) 1876118767. [21] S. Wen, D.D. Chung, Effect of Stress on the Dielectric Constant of Alumina, Journal of Electronic Packaging, 127 (2004) 235-236. [22] K. Shimizu, H. Habazaki, P. Skeldon, G.E. Thompson, G.C. Wood, Migration of oxalate ions in anodic alumina, Electrochimica Acta, 46 (2001) 4379-4382. [23] K. Shimizu, G.M. Brown, H. Habazaki, K. Kobayashi, P. Skeldon, G.E. Thompson, G.C. Wood, Impurity distributions in barrier anodic films on aluminium: a GDOES depth profiling study, Electrochimica Acta, 44 (1999) 2297-2306. [24] G.C. Wood, P. Skeldon, G.E. Thompson, K. Shimizu, A Model for the Incorporation of Electrolyte Species into Anodic Alumina, Journal of The Electrochemical Society, 143 (1996) 74-83. [25] K.A. Yasakau, A.N. Salak, M.L. Zheludkevich, M.G.S. Ferreira, Volta Potential of Oxidized Aluminum Studied by Scanning Kelvin Probe Force Microscopy, The Journal of Physical Chemistry C, 114 (2010) 8474-8484. [26] H. Habazaki, R. Nishimura, K. Okitsu, H. Inoue, I. Kiriyama, F. Kataoka, M. Sakairi, H. Takahashi, The effects of film thickness and incorporated anions on pitting corrosion of aluminum with barrier-type oxide films formed in neutral borate and phosphate electrolytes, Journal of Solid State Electrochemistry, 18 (2014) 369-376. [27] J. Chen, M. Yao, R. Xiao, P. Yang, B. Hu, X. Yao, The application of the barrier-type anodic oxidation method to thickness testing of aluminum films, Review of Scientific Instruments, 85 (2014) 094101. [28] H. Momida, T. Hamada, Y. Takagi, T. Yamamoto, T. Uda, T. Ohno, Theoretical study on dielectric response of amorphous alumina, Physical Review B, 73 (2006) 054108. [29] P. Schmutz, G.S. Frankel, Characterization of AA2024‐T3 by Scanning Kelvin Probe Force Microscopy, Journal of The Electrochemical Society, 145 (1998) 2285-2295. [30] W. Jeitschko, Transition metal stannides with MgAgAs and MnCu2Al type structure, Metallurgical Transactions, 1 (1970) 3159-3162. [31] S. Tajima, M.G. Fontana, R.W. Staehle., Advances in Corrosion Science and Technology Plenum Press: New York, London, 1970. [32] D. Hasenay, M. Šeruga, The growth kinetics and properties of potentiodynamically formed thin oxide films on aluminium in citric acid solutions, Journal of Applied Electrochemistry, 37 (2007) 10011008. [33] T. Hurlen, A.T. Haug, Corrosion and passive behaviour of aluminium in weakly alkaline solution, Electrochimica Acta, 29 (1984) 1133-1138. [34] S.-M. Moon, S. Pyun, II, Growth mechanism of anodic oxide films on pure aluminium in aqueous acidic and alkaline solutions, Journal of Solid State Electrochemistry, 2 (1998) 156-161. [35] P.L. Cabot, F.A. Centellas, J.A. Garrido, E. Pérez, Comparative study of the potentiodynamic behaviour of aluminium at low potentials in barrier layer and in pore-forming electrolytes, Journal of Applied Electrochemistry, 17 (1987) 104-112. [36] M. Šeruga, D. Hasenay, Electrochemical and surface properties of aluminium in citric acid solutions, Journal of Applied Electrochemistry, 31 (2001) 961-967. [37] P. Campestrini, E.P.M. van Westing, J.H.W. de Wit, Influence of surface preparation on performance of chromate conversion coatings on Alclad 2024 aluminium alloy: Part II: EIS investigation, Electrochimica Acta, 46 (2001) 2631-2647. [38] K. Ozawa, T. Majima, Anodization behavior of Al, and physical and electrical characterization of its oxide films, Journal of Applied Physics, 80 (1996) 5828. [39] W. Vedder, D.A. Vermilyea, Aluminum + water reaction, Transactions of the Faraday Society, 65 (1969) 561-584.

[40] N. Sato, A theory for breakdown of anodic oxide films on metals, Electrochimica Acta, 16 (1971) 1683-1692. [41] G.J. Brug, A.L.G. van den Eeden, M. Sluyters-Rehbach, J.H. Sluyters, The analysis of electrode impedances complicated by the presence of a constant phase element, Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, 176 (1984) 275-295. [42] M.E. Orazem, I. Frateur, B. Tribollet, V. Vivier, S. Marcelin, N. Pébère, A.L. Bunge, E.A. White, D.P. Riemer, M. Musiani, Dielectric Properties of Materials Showing Constant-Phase-Element (CPE) Impedance Response, Journal of The Electrochemical Society, 160 (2013) C215-C225. [43] B. Hirschorn, M.E. Orazem, B. Tribollet, V. Vivier, I. Frateur, M. Musiani, Determination of effective capacitance and film thickness from constant-phase-element parameters, Electrochimica Acta, 55 (2010) 6218-6227. [44] C.M. K. Wefers, Oxides and hydroxides of aluminum, Alcoa technical paper, Alcoa Laboratories: Pittsburg, PA, 19 (1987). [45] C.D. Wagner, A. Joshi, The auger parameter, its utility and advantages: a review, Journal of Electron Spectroscopy and Related Phenomena, 47 (1988) 283-313. [46] P.C. Snijders, L.P.H. Jeurgens, W.G. Sloof, Structure of thin aluminium-oxide films determined from valence band spectra measured using XPS, Surface Science, 496 (2002) 97-109. [47] L.P.H. Jeurgens, F. Reichel, S. Frank, G. Richter, E.J. Mittemeijer, On the development of long-range order in ultra-thin amorphous Al2O3 films upon their transformation into crystalline γ-Al2O3, Surface and Interface Analysis, 40 (2008) 259-263. [48] C.D. Wagner, H.A. Six, W.T. Jansen, J.A. Taylor, Improving the accuracy of determination of line energies by ESCA: Chemical state plots for silicon-aluminum compounds, Applications of Surface Science, 9 (1981) 203-213. [49] G. Moretti, Auger parameter and Wagner plot in the characterization of chemical states by X-ray photoelectron spectroscopy: a review, Journal of Electron Spectroscopy and Related Phenomena, 95 (1998) 95-144. [50] V.I. Nefedov, Extra-atomic relaxation in surface systems, Journal of Electron Spectroscopy and Related Phenomena, 63 (1993) 355-378. [51] A. Pasquarello, M.S. Hybertsen, R. Car, Spherosiloxane H8Si8O12 clusters on Si(001): First-principles calculation of Si 2p core-level shifts, Physical Review B, 54 (1996) R2339-R2342. [52] N. W. Ashcroft, N.D. Mermin, Solid State Physics, Saunders 1976. [53] Y.T. Chu, J.B. Bates, C.W. White, G.C. Farlow, Optical dielectric functions for amorphous Al2O3 and γ‐ Al2O3, Journal of Applied Physics, 64 (1988) 3727-3730. [54] G.D. Wilk, R.M. Wallace, J.M. Anthony, High-κ gate dielectrics: Current status and materials properties considerations, Journal of Applied Physics, 89 (2001) 5243-5275. [55] P. Umari, A. Pasquarello, \textit{Ab initio} Molecular Dynamics in a Finite Homogeneous Electric Field, Physical Review Letters, 89 (2002) 157602. [56] P. Umari, A. Pasquarello, Polarizability and dielectric constant in density-functional supercell calculations with discrete {k} -point samplings, Physical Review B, 68 (2003) 085114. [57] G. Paolo, B. Stefano, B. Nicola, C. Matteo, C. Roberto, C. Carlo, C. Davide, L.C. Guido, C. Matteo, D. Ismaila, C. Andrea Dal, G. Stefano de, F. Stefano, F. Guido, G. Ralph, G. Uwe, G. Christos, K. Anton, L. Michele, M.-S. Layla, M. Nicola, M. Francesco, M. Riccardo, P. Stefano, P. Alfredo, P. Lorenzo, S. Carlo, S. Sandro, S. Gabriele, P.S. Ari, S. Alexander, U. Paolo, M.W. Renata, QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials, Journal of Physics: Condensed Matter, 21 (2009) 395502. [58] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized Gradient Approximation Made Simple, Physical Review Letters, 77 (1996) 3865-3868. [59] D. Colleoni, G. Miceli, A. Pasquarello, Band alignment and chemical bonding at the GaAs/Al2O3 interface: A hybrid functional study, Applied Physics Letters, 107 (2015) 211601.

[60] G. Gutiérrez, A. Taga, B. Johansson, Theoretical structure determination of γ−Al2O3, Physical Review B, 65 (2001) 012101. [61] Y. Oka, T. Takahashi, K. Okada, S.-i. Iwai, Structural analysis of anodic alumina films, Journal of NonCrystalline Solids, 30 (1979) 349-357. [62] S.M. Lee, D.G. Cahill, T.H. Allen, Thermal conductivity of sputtered oxide films, Physical Review B, 52 (1995) 253-257. [63] S. Kohiki, S. Ozaki, T. Hamada, K. Taniguchi, Characterization of silicon compounds using the Auger parameter in X-ray Photoelectron Spectroscopy (XPS), Applied Surface Science, 28 (1987) 103-110. [64] G. Scaduto, M. Santamaria, P. Bocchetta, F. Di Quarto, The effect of hydration layers on the anodic growth and on the dielectric properties of Al2O3 for electrolytic capacitors, Thin Solid Films, 550 (2014) 128-134. [65] C. Arhammar, A. Pietzsch, N. Bock, E. Holmstrom, C.M. Araujo, J. Grasjo, S. Zhao, S. Green, T. Peery, F. Hennies, S. Amerioun, A. Fohlisch, J. Schlappa, T. Schmitt, V.N. Strocov, G.A. Niklasson, D.C. Wallace, J.E. Rubensson, B. Johansson, R. Ahuja, Unveiling the complex electronic structure of amorphous metal oxides, Proceedings of the National Academy of Sciences, 108 (2011) 6355-6360.

Figure and Table captions

Fig. 1: Characteristic transient curves for the anodizing process. Current density as a function of time during the potentiostatic polarization at different final voltages of 50 V (red), 100 V (black), 150 V (blue) and 200 V (pink), respectively.

Fig. 2: Scanning Electron Microscopy (SEM) images of the anodized oxide surfaces grown at a) 50 V, b) 200 V, c) 250 V and d) 350 V

Fig. 3: Bright field Scanning Transmission Electron Microscope (STEM)-micrographs recorded from samples anodized at a) 50 V, b) 200 V, c) 250 V and d) 350 V, e): zoomed view of the oxide grown at 250 V, f): Selected area diffraction pattern (tube length = 30 cm) of region marked in e)

Fig. 4: (a) TEM/EDX-linescan and XPS depth profile analysis of an oxide grown at 200 V; (b) Thickness measurements by spectroscopic ellipsometry of the anodized samples, as a function of the final anodizing potential values. The straight line corresponds to a linear regression of the data and its analytical expression is given as inset.

Fig. 5: Surface topography (left) and Volta potential difference (VPD) (right) images of the anodized aluminium samples at the respective final voltages: 50 (a), 100 (b), 200 (c), 250 V (d). The scale bar is 2 μm.

Fig. 6: Plot of the VPD of the anodizing process (a) as a function of the final anodizing potential (black dashed line is a guide to the eye) and (b) as a function of the experimentally measured thickness of the anodic oxide.

Fig. 7. (a) Bode plot representation (measured at the OCP in 0.1 M citric acid solution, pH 5.4) for the complete range of anodizing potential considered; (b) Equivalent circuit model used to fit EIS data, (c) Nyquist and (d) Bode plot of impedance data for two selected anoding voltages corresponding to the low anodizing domain (10 V) and mid-high anodizing domain (150 V)

Fig. 8: (a) Chemical state plot for O in the anodic oxide films for various anodizing potentials and sputtering cycles (denoted by increasing numbers), (b) The Auger parameter, α, versus the relative thickness of the anodic oxides and of two standards, α-Al2O3 and γ-Al2O3 (orange and violet dashed lines respectively) explored during the sequential sputtering cycles for representative anodizing potentials of 50 V (red), 200 V (black) and 250 V (blue). Dashed lines are only guides to the eye. Measurements are averaged over 3 repetition sets.

Fig. 9: Measured values of the O Auger parameter versus anodizing potential (from 10 to 250 V) for: i) the unsputtered surface (no sputtering cycle; black), ii) after the first sputter cycle (red), iii) at mid-way distance between the surface and the metal-oxide interface (blue) iv) and at the metal-oxide interface (last sputtering cycle - pink). Dashed lines are guide to the eye. The results of the measurements were averaged over 3 repetition sets.

Fig. 10: (a) Electronic contribution to the dielectric constant (black dots - εaveele) of the metal oxide vs. the anodizing potential. (b) Evaluation of the lattice contribution to the dielectric constant (black squares - εavelat.). For both εaveele and εavelatt layouts are also reported the

experimental values of εele and εlat for α- Al2O3 (blue) taken from Ref [63]. averaged over the spatial directions (experimental εlat along the z-axis for α- Al2O3 is also reported) and the εele and εlat for the amorphous Al2O3 (magenta) taken from Ref [53, 54]. obtained as described in section 3.5. The black dashed line is only a guide to the eye. .

Tab. 1: Average oxide thickness measurements obtained from TEM micrographs, where V is the final polarization potential, VPD stands for Volta Potential Difference obtained through AFM/SKPFM technique. Anodizing V/ V

Thickness by Ellipsometry / nm

10 30 50 100 150 200 250 285 300 350

43± 5 65± 10 124± 10 177± 10 243± 10 304± 10 370± 10 405± 10 496± 10

Thickness by TEM / nm

75± 2

275 ± 5 335 ± 5

495± 30

VPD / V 0.4 ± 0.1 0.4± 0.1 1.1± 0.1 1.2± 0.1 2.6± 0.2 5.6± 0.2 7.5± 0.2 8.5± 0.2 5.7± 0.2 2.7± 0.2

Tab. 2: Results of EIS data modelling using the circuit of Fig. 7-b; thickness values evaluated by linear regression of experimental data obtained by ellipsometry in the range of 30 - 250 V, and the resulting values of the effective capacitance Ceff and dielectric constant εr . Anodizing voltage, V Blank (7.1) 10 30 50 100 150 200

Rs, Ωcm2 35.2 32.2 43.6 29.9 43.8 23.6 21.8

R, M Ωcm2 234.9 137.4 105.3 195.5 89.4 161.3 65.4

250

20.1

169.3

Q,

n

d, nm

616.7 486.5 213.3 126.6 80.4 53.3 45.6

0.98 0.98 0.97 0.98 0.96 0.96 0.95

34.1

0.95

nF/s(1-n)

cm2,

𝑪𝒆𝒇𝒇,𝑸 ,

εr

13.6 17.1 40.9 64.6 124.1 183.6 243.1

nF/cm2 676.1 527.7 233.9 134.8 87.9 58.1 48.4

10.4 10.2 10.8 9.8 12.3 12.1 13.3

302.6

37.1

12.7

Tab. 3: Measured values of the O Auger parameter (α) for the unsputtered surface (α0) and after the first sputter cycle (αn1), at mid-way distance between the surface and the metal-oxide interface (αmid) and at the metal-oxide interface (αinterf) as plotted in Fig. 9. The average electronic contributions to the bulk dielectric constant (εaveele) of each sputtered point across the oxide thickness are also reported. Anodizing V

α0 (eV)

αn1 (eV)

αmid (eV)

αinterf (eV)

εaveele

εr EIS

εavelat

10 V 30 V 50 V 100 V 150 V 200 V 250 V

1040.4 1040.5 1039.5 1039.4 1039.4 1038.8 1039.2

1039.8 1038.9 1038.7 1038.3 1037.8 1037.9 1037.9

1040.0 1039.2 1038.7 1038.4 1038.3 1038.2 1037.8

1039.9 1039.0 1038.9 1038.6 1038.6 1038.4 1038.4

3.033 3.087 3.122 3.115 3.129 3.125 3.105

10.2 10.8 9.8 12.3 12.1 13.3 12.7

7.2 7.7 6.7 9.2 9.0 10.2 9.6

Tab. 4: Calculated values of the equilibrium mass density ρ (g/cm3), average Al coordination number nAl, and dielectric constants εele and εr, for α-, γ- ,κ-, and two models of amorphous Al2O3 (Am-1 and Am-2). Dielectric constants are reported for each Cartesian direction and as average values. Experimental values for α-Al2O3 [41] and amorphous Al2O3 [33,34] are reported in parentheses. Note that the experimental values of εele are obtained from the square of the optical refractive index.

Phase

ρ

nAl

εele x

y

εr z

Average

3.20 3.20 3.18 3.19 (3.077) (3.077) (3.072) (3.075)

x

y

z

Average

10.80 (9.4)

10.80 (9.4)

12.74 (11.6)

11.44 (10.13)

α

3.86

6

γ

3.42

5.25

3.11

3.09

3.09

3.10

11.83

11.36

11.85

11.68

κ

3.65

5.5

3.10

3.16

3.18

3.15

12.20

11.94

12.25

12.16

Am-1

3.31

4.40

3.02

3.03

3.05

3.03 (2.6-2.8)

9.75

9.78

9.70

9.74 (8.0-9.0)

Am-2

4.10

5.41

3.18

3.20

3.19

3.19

13.36

13.65

13.05

13.35