N Ziani

E Aubry

N Martin

L Hirsinger

A Billard

P Briois

M Arab

Pour Yazdi

Influence of substrate temperature on delafossite CuFeO2 films synthesized by reactive magnetron sputtering

Keywords: Delafossite, reactive sputtering, substrate temperature, TCO

Delafossite CuFeO2 films have been synthesized by reactive magnetron sputtering at different substrate temperatures from 380 up to 550 °C. The films adopt the rhombohedral structure from 380 to 550 °C. At the highest temperature, the delafossite phase partially dissociates in FCC Cu and Fe3O4 magnetite phases. In addition to the average crystallite size increase, a change of the preferential orientation in the out-of-plane direction from the [012] to [006] directions occurs between 460 and 510 °C. Modelling of the optical properties shows the presence of 2 interband transitions in the visible range. The 1 st main transition at 1.5 eV is ascribed to the absorption component parallel to the c-axis whereas the 2 nd transition (2.10 -2.26 eV) is related to the absorption component in the (a, b) plane. Both evolutions with temperature of the refractive index (~ 2.5) and absorption coefficient (~ 10 -3 cm -1 ) in the infrared suggest the formation of secondary phases having lower oxidation state. The electronic conductivity, dominated by positive charge carrier, varied from 0.01-10 S m -1 according to the preferential orientation and to the presence of secondary phases. A very small amount of a short-range ferromagnetic component (magnetization ~ 10 kA m -1 at 1.5 T) is clearly observed at room temperature thanks to magnetometry confirming the formation of secondary phases undetected by X-ray diffraction. In addition to depend on the

Introduction

The iron is an element of non-negligible quantity in the earth crust (representing about 5% in volume which put it after Si and Al) with advantage of its easy recyclability due to its ferromagnetic property. As a result, iron-based materials are still the subject of interest and research despite the fact that they are already widely used. Among them, delafossite X + Fe 3+ O2 mineral group has a layered structure composed by sheets of linearly coordinated X + cations stacked between distorted FeO6 octahedrons resulting in (FeO2) -layer [START_REF] Marquardt | Crystal chemistry and electrical properties of the delafossite structure[END_REF]. This distinctive characteristic is responsible of the relatively superior in-plane electrical conductivity compared to that along the c axis [START_REF] Benko | Opto-electronic properties of p-and n-type delafossite CuFeO2[END_REF]. According to the sequence of stacking layers, two polytypes (rhombohedral or hexagonal) exist and exhibit high cell anisotropy (the c parameter being around 6 or 4 times longer than a parameter, respectively). It was demonstrated that the top of the valence and the bottom of the conduction band are mainly constituted by Cu-3d states and by Fe-3d states, respectively, while the O-2p states are hybridized with both states [3][4]. This compound exhibits a multi-band spectral absorption which would be advantageous in solar applications. Furthermore delafossite CuFeO2 compound exhibits semiconducting behaviour [START_REF] Dordor | Crystal growth and electrical properties of CuFeO2 single crystals[END_REF] with p-or n-type according to the nature of the dopant [START_REF] Marquardt | Crystal chemistry and electrical properties of the delafossite structure[END_REF] [2], and it can also be considered as a Mott insulator [START_REF] Mackenzie | The properties of ultrapure delafossite metals[END_REF]. In addition to its electrical transport in new regimes, this compound is antiferromagnetic with two reported Néel temperatures at 10.5 and 14 K, which stems from the triangular lattices of Fe 3+ layers separated by nonmagnetic Cu 1+ and O 2-layers [3][4]. This formation is one of the reasons of antiferromagnetic ordering in the structure [START_REF] Mackenzie | The properties of ultrapure delafossite metals[END_REF][7] [START_REF] Moharam | A facile novel synthesis of delafossite CuFeO2 powders[END_REF] and multiferroic properties [START_REF] Daou | Unconventional aspects of electronic transport in delafossite oxides[END_REF]. Theoretical investigations on CuMO2 compounds (with M = IIIA, 3d, 4d, 5d, and rare earth elements) have highlighted the functions of the different substructures in the mechanisms of light absorption, charges separation and transport demonstrating that CuFeO2 is suitable for solar applications such as photovoltaic [START_REF] Zhao | High-throughput screening delafossite CuMO2 (M = IIIA, 3d, 4d, 5d, and RE) optoelectronic functional materials based on first-principles calculations[END_REF]. Some authors have also studied its thermoelectric [START_REF] Daou | Unconventional aspects of electronic transport in delafossite oxides[END_REF][11] [START_REF] Tato | Reactive templated grain growth and thermoelectric power factor enhancement of textured CuFeO2 ceramics[END_REF] and its photocatalytic properties [START_REF] Liu | Fundamental properties of delafossite CuFeO2 as photocatalyst for solar energy conversion[END_REF] [START_REF] Dong | Visible light-induced photocatalytic activity of delafossite AgMO2 (M = Al, Ga, In) prepared via a hydrothermal method[END_REF] [START_REF] Xu | Visible-light photocatalytic reduction of Cr(Ⅵ) using nanosized delafossite (CuFeO2) synthesized by hydrothermal method[END_REF].

However, the synthesis of the single phase delafossite without impurity is non-trivial because the Cu valency must be maintained at its lowest value (+1) while avoiding the formation of the stable spinel CuFe2O4 or other binary compounds. Different processes have been used to produce delafossite CuFeO2-based thin films, e.g. pulsed laser deposition [START_REF] Joshi | Structural and magnetic properties of epitaxial delafossite CuFeO2 thin films grown by pulsed laser deposition[END_REF] [START_REF] Li | Epitaxial growth of delafossite CuFeO2 thin films by pulsed laser deposition[END_REF], spray pyrolysis [START_REF] Omran Alkhayatt | Structure, surface morphology and optical properties of post-annealed delafossite CuFeO2 thin films[END_REF] [START_REF] Mohamed | Synthesis of conducting single-phase CuFeO2 thin films by spray pyrolysis technique[END_REF], sol-gel [START_REF] Chen | Characterization and optoelectronic properties of sol-gel-derived CuFeO2 thin films[END_REF] [START_REF] Chen | Influences of post-annealing conditions on the formation of delafossite-CuFeO2 thin films[END_REF] or radio-frequency sputtering [START_REF] Sinnarasa | Microstructural and transport properties of Mg doped CuFeO2 thin films: A promising material for high accuracy miniaturized temperature sensors based on the Seebeck effect[END_REF][21] [START_REF] Barnabé | Preparation of delafossite CuFeO2 thin films by rf-sputtering on conventional glass substrate[END_REF][23] [START_REF] Li | Effect of lack of oxygen on optical and electrical properties of RF magnetron sputtering deposited CuFeO2-x thin films[END_REF]. It can be noted that an elevated substrate temperature or additional annealing step in neutral atmosphere or in primary vacuum is often required to obtain a crystalline structure, meaning that its synthesis without impurity phase is possible only for a limited range of oxygen partial pressures. To overcome the drawbacks intrinsic to the radio-frequency sputtering (lower deposition rate, higher sputtering pressure, tendency to crack the compound target, efficient cooling system, use of impedance matching box, drift of the chemical composition of the synthesized film due to sputtering yield difference), it is proposed to directly synthesize the delafossite compound from Cu and Fe metallic targets using reactive magnetron sputtering on hot substrates. So far, the role of substrate temperature on the structural, optical, electrical and magnetic properties of delafossite CuFeO2 thin films synthesized by reactive magnetron sputtering have not been explored yet. The changes induced by the increase of the deposition temperature on the structural properties regarding the involved phases and their preferential orientation in the out-of-plane direction is first discussed. In addition to depend on the film orientation, the optical and electrical behaviours suggest the presence of secondary phases with decreasing oxidation state with the increase of the deposition temperature. Besides, the magnetic measurements confirmed the presence of ferromagnetic phase related to the increase of reduction conditions with the deposition temperature, which contributes to the observed optical and electrical properties.

Material and methods

Delafossite CuFeO2 films preparation

CuFeO2 thin films, with a chemical concentration Cu/Fe ratio of 1, were deposited by reactive magnetron sputtering of Cu and Fe metallic targets in a Ar and O2 gas mixture. The sputtering system consists in a 90 L stainless steel vessel (Alcatel SCM 604) equipped with 2 water-cooled and balanced magnetron targets (Ø 50 mm, thickness 3 mm). Prior the deposition step, a base pressure lower than 10 -4 Pa was obtained with a turbomolecular pump unit. The iron and copper targets were supplied with a pulsed Advanced Energy Pinnacle + power generator (JFe = 188-214 A m -2 ) and a DC Advanced Energy MDX 500 power generator (JCu = 14 A m -2 ), respectively, leading to Fe/Cu atomic ratio of 1. The sputtering of ferromagnetic element by conventional magnetron is low and poorly reproducible. It requires a special geometry of the magnetron to ignite and sustain the discharge with an efficient iron sputtering [START_REF] Jouanny | Sputtered Fe1-x(N1-yCy)x films obtained in various (Ar-N2-CH4) reactive plasmas[END_REF], and to increase the reproducibility of the deposition conditions. In addition, the Fe target thickness has been reduced to 1 mm so as to obtain a magnetic field above the targets sufficient to ignite and maintain the discharge. Ar and O2 gases flow rates were controlled with Brooks flowmeters with DAr = 100 sccm and D O 2 = 10 sccm, respectively. It is noteworthy that the O2 flow rate is enough to maintain the sputtering process in the compound mode. MKS Baratron gauge was used to measure the total pressure (Ptot = 2.2 Pa).

Fused silica glass slides were used as substrates (76 x 26 x 1.1 mm 3 ), and were located on a heating and rotating substrate-holder parallel to the surface target at about 60 mm. The substrate-holder was referenced to ground and its rotation speed was fixed at 60 rpm. The substrate temperature was varied from 380 to 550 °C with a graphite electrical resistance heater placed behind the substrateholder while keeping constant other deposition parameters.

CuFeO2 films characterization

The film thickness (fixed at 440 ± 16 nm) was determined from the cross-section observation of the films via a Field Emission Scanning Electron Microscope (FE-SEM JEOL JSM -7800F) and by using spectrophotometry. The structural features of the films were investigated by using a Bruker D8 focus diffractometer (Co K α 1+2 radiation) equipped with the LynxEye linear detector in a Bragg Brentano configuration (0.02° step). The total optical transmittance and reflectance of the films were measured with a Shimadzu UV-3600 spectrophotometer equipped with ISR-3100 integrating sphere in the range 220-2600 nm. Standard white board BaSO4 was used for the baseline. Optical simulations of the transmittance and reflectance spectra were realized with the SCOUT software to determine some optical properties such as refractive index, absorption coefficient [26]. The electrical conductivity of the films was determined from the sheet resistance measured using conventional four probe method (Jandel system). A detailed study of the electrical properties was carried out by measuring the charge carrier concentration and mobility by Hall effect in the temperature range 30-200 °C by means of a homemade system based on the van der Pauw method with a magnetic field of 0.8 T perpendicularly applied to the sample surface. Magnetometry measurements in static mode (point by point, 16 kA m -1 ) were performed with a vibrating sample magnetometer (Microsense model EZ7) at room temperature with a magnetic field (up to ± 1.5 T) applied to the plane of the films. The diamagnetic contribution of the substrate holder was removed from the measured magnetization. The Seebeck coefficient was measured at room temperature by means of a homemade system. For hot and cold sources, copper material was used as superconductor and the temperature of hot source was maintained constant at set point value by hot water circulation inside of hot source (25 °C). The real-time value of temperature was determined with CHY 505 RTD thermometer (Centenary Materials Co. Ltd., Hsin-Chu City, Taiwan) and the difference of potential between hot and cold side of the sample was performed using a frame grabber of National Instrument USB-4065 (Electronic Test Equipment, Cary, NC, USA). The relative Seebeck coefficient (µV K -1 ) was calculated by using the following formula:

α = -∆V/∆T (1)
Where ∆V is the potential difference (µV) and ∆T is the temperature difference (K) between hot and cold side of the samples, respectively. In order to find the absolute values of Seebeck coefficient, the absolute Seebeck value for Cu (2 µV K -1 [START_REF] Zhou | Impact of the film thickness and substrate on the thermopower measurement of thermoelectric films by the potential-Seebeck microprobe (PSM)[END_REF]) was subtracted from each measured value. The Seebeck coefficient of each sample was measured 4 times and the errors in the measurement were evaluated to be within 5 %.

Results and discussion

Structural properties

X-ray diffractograms of thin films deposited at different substrate temperatures are shown in Fig. 1. From 380 up to 510 °C, the crystallisation of the delafossite structure in the trigonal R3 ̅ m space group without the presence of secondary phase is observed. At 550 °C, deposition conditions (substrate temperature and O2 partial pressure) become sufficiently reductive to lead to the partial dissociation of the delafossite structure in semimetallic magnetite Fe3O4 and metallic Cu phases.

The use of grazing incidence X-ray diffraction (GIXD) does not underline the occurrence of a specific phase (Fe3O4 or Cu) at the sample surface, but rather reveals a fairly homogeneous distribution of the different phases through the film thickness (not shown). If the O2 partial pressure is high enough to form CuFeO2 compound at low deposition temperature, it can be assumed that, for a constant O2 partial pressure, the deposition temperature elevation would lead to the reduction of the oxygen content in the growing film (stronger oxygen thermal desorption at more elevated temperature and incapacity to adsorb oxygen during the cooling in vacuum).

Below 510 °C, the delafossite structure exhibits a preferential orientation towards the [012] direction, while higher temperatures lead to a preferential growth along the [00l] axis. Considering spherical crystallites independent on crystallographic directions, their average size has been estimated using the Scherrer's formula from the Full Width at Half Maximum (FWHM) by deconvolution of the 3 most intense peaks corresponding to the (006), ( 101) and ( 012) planes (cf.

Fig. 2). The instrumental contribution on the line broadening is assumed to be negligible compared to that induced by the size of crystallites. The average crystallite size is stable up to 440 °C, and after deposition at TS 460 °C, while (006) diffraction line was detected, the average crystallite strongly increases for all crystallographic directions. At 550 °C, the crystallite size calculated from the (006) diffraction line is still growing contrary to those measured from other directions. This result is consistent with the observed change in the preferential growth with the deposition temperature. The dislocation density can be approached, for low amount, considering it as the inverse of the square of crystallite size [START_REF] Williamson | Dislocation densities in some annealed and coldworked metals from measurements on the X-ray debye-scherrer spectrum[END_REF]. A decrease of the dislocation density when increasing the temperature during the film growth is thus assumed. Besides, it can be observed that the change in the preferential orientation from [012] to [006] occurs in rather reductive conditions as the deposition temperature increases. It is worth noting that previous observations also reported a preferential orientation along the c-axis direction in rather reductive conditions, e.g. by implementing a crystallization post-treatment of sol-gel films at high temperature (> 600-850 °C)

and at O2 partial pressure of about 10 -3 -10 -2 atm [START_REF] Chen | Influences of post-annealing conditions on the formation of delafossite-CuFeO2 thin films[END_REF]. Other authors observed it during the posttreatment of radiofrequency sputtered CuFeO2 films in a primary vacuum at 450 °C as confirmed by the additional crystallization of metal Cu and spinel Fe3O4 phases [START_REF] Barnabé | Copper and iron based thin film nanocomposites prepared by radio frequency sputtering. Part I: elaboration and characterization of metal/oxide thin film nanocomposites using controlled in situ reduction process[END_REF].

Optical properties

Transmittance and reflectance spectra are displayed in Fig. 3. Transmittance spectra exhibit interference fringes in the near infrared region with a steep fall of the transmittance at around 860 nm corresponding to optical absorption by interband electronic transitions. It is noteworthy that the region of the transmittance fall is more abrupt compared to previous studies [START_REF] Omran Alkhayatt | Structure, surface morphology and optical properties of post-annealed delafossite CuFeO2 thin films[END_REF][18] [START_REF] Deng | Characterization of amorphous p-type transparent CuFeO2 thin films prepared by radio frequency magnetron sputtering method at room temperature[END_REF]. Indeed, some authors observed a progressive decay of the transmittance through the visible range [19][23].

In our case, the transmittance drops from 60 to 5 % through only 150 nm, whereas the same loss was reported through 550 nm [19][23][30]. This corresponds to a poor transparency of delafossite films (only about a few percent and up to 30 % transmittance loss at 420 nm). The average transmittance in the visible range progressively decreases when increasing the deposition temperature to become fully opaque at 550 °C due to the crystallization of magnetite and copper phases (Table 1) [START_REF] Aubry | Synthesis of iron oxide films by reactive magnetron sputtering assisted by plasma emission monitoring[END_REF]. Optical properties cannot be determined with our used methods due to their strong absorbance and reflectance in the studied wavelength.

The absorption coefficient spectrum ( ) was determined from transmittance and reflectance spectra using three different methods. For the first one, the simplified absorption coefficient was calculated from the equation below :

α(λ)= 1 t ln ( (1-R(λ)) T(λ) ) ( 2
)
Where t is the thickness in cm, R( ) and T( ) are the reflectance and transmittance spectra, respectively. The second method implies the simulation of transmittance and reflectance spectra, by implementing dispersion models. In the first one, designed hereafter by "Cauchy", the refractive index n and the extinction coefficient k were calculated by using the well-known empirical Cauchy model. It should be specified that this model is suitable for low absorption domain (i.e., > 1000 nm in our case):

n(λ)=A+ B λ 2 + C λ 4
(3)

k(λ)=D+ E λ 2 + F λ 4 (4)
where A, B, C, D, E, and F are constants. A more sophisticated dispersion model taking into account the strong optical absorption located around 750 nm was also used (Fig. 3). The optical absorption was then modelled with the so-called O'Leary-Johnson-Lim (OJL) model valuable for interband electronic transitions assuming that tail states exponentially decay into the band gap [START_REF] O'leary | The relationship between the distribution of electronic states and the optical absorption spectrum of an amorphous semiconductor: An empirical analysis[END_REF].

Considering the multi-band response of the CuFeO2 material, it is admitted that 3 mains electronic transitions at 1.15, 2.03 and 3.35 eV strongly influence the optical properties [START_REF] Ong | Electronic structure and optical properties of AFeO2 (A = Ag, Cu) within GGA calculations[END_REF]. However, only two OJL transitions were necessary to achieve a satisfactory fit of transmittance and reflectance spectra in agreement with a previous study [START_REF]Role of CuAlO2 as an absorber layer for solar energy converter epitaxial thin film by photoconductivity[END_REF], and also with the abrupt fall of the transmittance.

In the infrared range where the absorption of light is related to the free charges, a simple Drude model was also introduced to contribute to the dielectric dispersion. No roughness surface or interface was used in this model. The deviation (mean square difference between simulated and measured data) was less than 10 -4 for the transmittance part and less than 6 x 10 -4 for the reflectance part. The higher deviation for the reflectance part is ascribed to the BaSO4 absorption bands from the integration sphere which alter the reflectance spectra in the near infrared range. This dispersion model is named "OJL" in the rest of the study.

Fig. 4 shows the spectral dependency of the absorption coefficient. Far from the absorption edge, the three methods lead to fairly similar results, namely an increase of the deposition temperature gradually degrades the near infrared absorption. This could be related to the absorption of free charge carrier, in which the promotion of already excited charge carrier to an unoccuped state inside the same band (intraband absorption) occurs. Considering the Drude model which reports the charge carrier transport properties due to intraband transition in a metallic solid, the absorption coefficient related to the imagery part of the dielectric constant is then proportional to the charge carrier concentration [START_REF] Fox | Optical properties of solids[END_REF]:

ε 1 =ε opt (1- ω P 2 τ 2 1+ω 2 τ 2 ) (5)
ε 2 = ε opt ω P 2 τ ω(1+ω 2 τ 2 ) (6)
ω P =√ Ne 2 mε 0 (7)
α free charge carrier = Ne 2 mε 0 ncτω 2 (8)
with 1, 2 are the real and imaginary parts of the dielectric function, respectively, opt the dielectric constant far from absorption edge (= n 2 in the transparent region), the pulsation (s -1 ), P the plasma pulsation (s -1 ), lifetime of charge carrier (s), N the quantity of the charge carrier (m -3 ), e the elementary charge, m the effective mass (kg), and 0 the vacuum permettivity. A decrease of the infrared absorption would therefore be linked to that of the charge carrier concentration.

Besides, the presence of a secondary phase absorbing infrared in increasing proportion with the deposition temperature would also explained the decay of the absortion coefficient in this range.

For wavelengths lower than 1000 nm, the "Cauchy" model is no more valid. The graphical method for the determination of the absorption coefficient still remains relatively consistent in the medium absorption range ( < 800 nm), while a slight discrepency in the absorption coefficient can be observed in the strong absorption range ( < 540 nm) due to the addition of a 2 nd OJL transition.

In this range, the absorption coefficient increases up to 10 5 cm -1 for the films deposited at 380 and 440 °C and becomes even larger for higher deposited temperatures. The strong optical absorption at < 800 nm is consistent with previous article [START_REF] Liu | Fundamental properties of delafossite CuFeO2 as photocatalyst for solar energy conversion[END_REF], in which the authors observed similarly strong absorption, while it started at 1000 nm. It was ascribed to the direct transition O-pz Fe-dxz, -dz2 at 1.55 eV (O-2p Fe-3d) with the possible contribution of the indirect transition O-px, -py Fedxy, -dxz, -dyz, -dx2-y2, -dz2 at 1.54 eV.

Spectral dependancies of the refractive index, determined by "Cauchy" and "OJL" models, are presented in Fig. 5. Far from the absorption edge, the refractive index lies between 2.4 and 2.6, with an order of magnitude consistent with the extracted values from ellipsometric spectroscopy [START_REF] Jiang | Electronic structure and performance bottlenecks of CuFeO2 photocathodes[END_REF]. Refractive index follows the same trend with the deposition temperature up to 1000 nm, wavelength for which the "Cauchy" model is no more valid. The measured refractive index in infrared range is affected by the presence of other phases. As a first approximation, the measured refractive index is proportionnal to the volume of the relative phases. Based on our previous assumption, on which oxygen content would be affected by the temperature deposition, a progressive decrease of the refractive index would then be expected with the deposition temperature elevation. In previous study dealing with the annealing conditions of sputtered CuFeO2 films [START_REF] Ben Jbara | Effect of thermal annealing on the optoelectronic properties of Cu-Fe-O thin films deposited by reactive magnetron co-sputtering[END_REF], it was observed that a slight enhancement of the reductive conditions (increase of annealing temperature in primary vacuum) leads to the formation of Cu2O and Fe2O3 phases from rhombohedral delafossite phase, while with even more reductive conditions (same temperature range combined with secondary vacuum) only Cu and Fe3O4 phases crystallize. Refractive indices of Cu2O and Fe2O3 are 2.6 to 2.27 and 2.78 to 2.66 in the infrared range (1000 to 2600 nm, respectively) [START_REF] Polyanskiy | Refractive index database[END_REF], and the refractive indices of metallic Cu included from 0.46 to 1.09 and of the spinel Fe3O4 are included from 2.13 to 2.85 at 1000 to 2600 nm, respectively. [START_REF] Polyanskiy | Refractive index database[END_REF]. The formation of phases with relative high refractive index such as Fe2O3 hematite and Cu2O would explain the observed increase of the refractive index at 460 °C. It is noteworthy that the bandgap energy of Fe2O3 (~ 600 nm) is consistent with the absorption range of the films, and to the progressive drop of transmittance in the visible [START_REF] Aubry | Synthesis of iron oxide films by reactive magnetron sputtering assisted by plasma emission monitoring[END_REF]. At 510 °C, the crystallization of Cu and Fe3O4 phases having lower refractive indices than Cu2O and Fe2O3 phases would be one reason of the decrease of the refractive index in infrared range. For lower wavelengths (< 1000 nm), the "OJL" dispersion model taking into account the strong optical absorption exhibits two maxima in the refractive index which are related to the two OJL interband electronic transitions. In agreement with the absorption spectra, a slight difference of the refractive index behaviour can be observed according to the deposition temperature, which is suppposed to be related to the change in the preferential orientation. Indeed, a few studies underline the anisotropic behaviour of the optical properties in delafossite compounds [37][38]. Furthermore, electronic structure calculations on delafossite compound such as CuAlO2 reported on the different optical behaviour according to the cristallographic directions [39][40]. It was shown that both refractive index and dispersion are smaller in the direction parallel to the c-axis than in its perpendicular direction. A similar behaviour, based on the computed anisotropic absorption spectra in CuFeO2, would also be responsible of the slight decrease of the refractive index at 510 °C.

Optical gap energy (Fig. 6(a)) was determined using the graphical method in which the absorption coefficient calculated from the equation (2) was used in Tauc's plots considering direct interband electronic transition. In agreement with our above observations on the poor average transmittance in the visible and of the modelled dielectric functions to simulate transmittance and reflectance spectra, only two linear regions were observed indicating the presence of two direct transitions (not shown here), while 3 main transitions are computed in the visible range [3][4]. A first transition at 1.62 eV is independent on the deposition temperature, whereas the 2 nd transition decreases from 2.26 to 2.10 eV as the deposition temperature increases from 380 to 510 °C. Other references experimentally showed by spectrometry and photoconductivity presence of both transitions [4][33]. The 2 nd transition could be ascribed to O-px, -py Cu-dz2 (O-2p Cu-3d) and O-px, -py Fe-dxy, -dxz, -dyz, -dx2-y2, -dz2 (O-2p Fe-3d) at 1.92 eV [START_REF] Liu | Fundamental properties of delafossite CuFeO2 as photocatalyst for solar energy conversion[END_REF]. Furthermore, it is noteworthy that, with the deposition temperature elevation, the amplitude ratios of the 1 st transition over the 2 nd transition determined from "OJL" model increase (x 3.5 at 380 °C to x 9.5 at 510 °C). This means that the 1 st transition prevails over the 2 nd one while both amplitudes increases with temperature.

The 1 st transition at 1.4 -1.62 eV involves transition along the c direction (O-2pz -> Fe-3dz2 at 1.55

eV) [START_REF] Liu | Fundamental properties of delafossite CuFeO2 as photocatalyst for solar energy conversion[END_REF]. The prevailing of the 1 st transition is then consistent with the observed change of the preferential orientation along the [006] direction at elevated deposition temperature. Moreover Ong et al. [START_REF] Ong | Electronic structure and optical properties of AFeO2 (A = Ag, Cu) within GGA calculations[END_REF] demonstrated that the optical bandgap energies at 1.8 and 2.15 eV are well ascribed to absorption components parallel and perpendicular to the c-axis direction, respectively.

Accordingly, the slight difference in the observed absorption spectra below 500 nm could then be related to the observed change in the preferential orientation. However it should be mentionned that in highly oriented thin films along the c axis, containing small amount of cuprospinel phase, the transition at 2.1 eV is still observed meaning that many transition modes are implied simultaneously [START_REF]Role of CuAlO2 as an absorber layer for solar energy converter epitaxial thin film by photoconductivity[END_REF].

In the crystalline solids, material disorder stems from local composition (doping, substitution), structure (vacancy, dislocation, deviation from stoichiometry) or temperature changings (lattice thermal vibrations), and manifests through the presence of localized states near the band edges forming absorption tail at energies below Eg [START_REF] Studenyak | Urbach rule in solid state physics[END_REF]. Only structural disordering is presuming to have a significant effect in our case, because of the constancy of the chemical composition in sputtered films and because measurements have been done at ambient temperature. While the origin of the tail state remains unclear, their distribution shows an exponential dependence with the energy below the bandgap [START_REF] O'leary | The relationship between the distribution of electronic states and the optical absorption spectrum of an amorphous semiconductor: An empirical analysis[END_REF]. In the "OJL" interband electronic transition, the parameter describes the width of the tail states exponentially decaying into the bandgap (Fig. 6(b)). Besides, the wellknown Urbach tail, expressing the width of the exponential tail in the absorption spectrum for energies below the bandgap has been also computed using the equation:

α(hν)=α 0 exp ( hν-E 0 E u ) (9)
where is the absorption coefficient (cm -1 ), h the Planck's constant, the frequency of the incident electromagnetic wave (Hz), 0 and E0 are characteristic parameters related to the materials corresponding to the convergence point of the Urbach bundle (extrapolation of lines ln( ) vs.

energy for different temperatures) [41][43]. Eu is the Urbach energy (eV) and expresses the width of the band associated to the disorder. Both methods result in the same order of magnitude and the same trend, namely a progressive decrease of the band width related to the disorder when increasing the deposition temperature. Despite the relatively large values for the film deposited at 380 °C, the and Eu parameters are consistent with values reported previously for delafossite CuFeO2 thin films (~ 130 nm) [START_REF] Omran Alkhayatt | Structure, surface morphology and optical properties of post-annealed delafossite CuFeO2 thin films[END_REF], and also for sputtered crystallized oxides such as undoped NiO [START_REF] Jamal | Effects of growth temperature on the photovoltaic properties of RF sputtered undoped NiO thin films[END_REF], or undoped ZnO [START_REF] Rai | Analysis of the Urbach tails in absorption spectra of undoped ZnO thin films[END_REF]. It has to be specified that, in reason of the 1 st transition located below the energy of the 2 nd transition, the determination of the Urbach energy cannot be obtained. Estimated by modelling, the 2 nd transition displays a very large energy (~ 0.3-0.45 eV). The relaxation of the intrinsic stress which develops during the film growth is probably responsible of the decrease of the disorder with the elevation of the deposition temperature rather than thermal tensile stress which appears due to the difference of thermal expansion coefficient between the substrate (0.5 10 -6 K -1 ) and the film (2.61 10 -6 K -1 [START_REF] Salke | Raman spectroscopic studies of CuFeO2 at high pressures[END_REF]) during the cooling step. The growth of crystallite size combined with the dislocation density supports this observation.

Electronic transport properties

The temperature dependence of the electrical conductivity along with the charge carrier concentration vs. mobility is depicted in Fig. 7(a) and (b). The film deposited at 510 °C is too resistive to be characterized by our Hall effect setup. To confirm its poor electrical conductivity, the 4 probes method has been implemented on the samples (Table 1). Both methods (4 probes method or Hall effect) indicate that the electrical conductivity of the films deposited between 380 and 460 °C has the same order of magnitude. According to Mayadas and Shatzkes model [START_REF] Mayadas | Electrical-resistivity model for polycrystalline films: The case of arbitrary reflection at external surfaces[END_REF], the electrical conductivity is driven by the charges scattering at the grain boundaries. This effect becomes more significant with the grain size reduction in metallic environment (< 30 nm in Al) [START_REF] Harper | Mechanisms for microstructure evolution in electroplated copper thin films near room temperature[END_REF]. The mean free path of charge carrier in CuFeO2, calculated from the charge carrier concentration and mobility, being less than 1 nm and about 350 times lower than that of a Cu single-crystal (~ 39 nm) [START_REF] Harper | Mechanisms for microstructure evolution in electroplated copper thin films near room temperature[END_REF] cannot ascertain the dependency of the electrical conductivity on the grain boundary for the films deposited at temperatures lower than 510 °C.

As expecting for a semi-conductor, the electrical conductivity well increases with the temperature, due to the increase of carrier concentration with the temperature elevation (Fig. 7(a)). The Seebeck coefficient, representing the thermoelectric response induced by a temperature difference, was also measured (Table 1). The Seebeck coefficient is related to the charge carrier diffusion towards the cold side due to a temperature gradient. Then, according to the sign convention, a positive coefficient means that the electrical conductivity is dominated by positive charge carriers. The previously established hypothesis that oxygen deficiencies, which lead to the formation of donor levels [START_REF] Dordor | Crystal growth and electrical properties of CuFeO2 single crystals[END_REF], would be created by increasing the substrate temperature is then not verified. Based on Cu2O chemistry, it could be assumed that the defects responsible of the p-type behaviour would be rather related to copper vacancies, the delafossite having weak tolerance for Cu non-stoichiometry, and/or interstitial oxygen defects while having higher activation energy and thus a lower probability to occur [1][47]. However, a study dealing with the cationic vacancy in CuGaO2 revealed that the p-type charge carrier is rather related to oxygen overstoichiometry [START_REF] Ashmore | Electrical and structural characteristics of non-stoichiometric Cu-based delafossites[END_REF].

Furthermore, the linearity of the plots ln( ) vs. T -1/4 implies that a mechanism of hopping occurs [5][49].

The temperature dependence of the electrical conductivity is almost not more perceptible at 550 °C due to the presence of metallic and semi-metallic phases, and also confirmed by the weak evolution of the charge carrier concentration with the temperature. The crystallization of highly electrical conductive phases such as Cu or semimetal Fe3O4 having an electrical conductivity of about 3 10 6 and 10 4 S m -1 , respectively [START_REF] Aubry | Synthesis of iron oxide films by reactive magnetron sputtering assisted by plasma emission monitoring[END_REF][50], is responsible of the observed increase in the electrical conductivity. Likewise, the formation in weak proportion of Fe2O3 and Cu2O phases (Cu2O 10 -2 S m -1 , Fe2O3 10 -8 to 10 -2 S m -1 ) in agreement with the absorption coefficient and refractive index observations in the infrared would explain the rather low electrical conductivity for film deposited at 460 °C.

Previous articles have reported that the electrical conductivity via the charge carrier mobility exhibits a relatively strong anisotropy along or perpendicular to the c direction, and that the charge carrier mobility strongly depends on the nature of the majority charge carrier [2] [START_REF] Dordor | Crystal growth and electrical properties of CuFeO2 single crystals[END_REF]. Indeed, Benko et al. [START_REF] Benko | Opto-electronic properties of p-and n-type delafossite CuFeO2[END_REF] demonstrated that the mobility of charge carrier in p-type CuFeO2 (~ 10 -5 m 2 V -1 s -1 ) is higher than n-type compounds (~ 10 -10 m 2 V -1 s -1 ). Furthermore, Shannon et al. [START_REF] Shannon | Chemistry of noble metal oxides. III. Electrical transport properties and crystal chemistry of ABO2 compounds with the delafossite structure[END_REF] observed an anisotropic electrical conductivity according to the crystallographic orientations. Indeed, the electrical conductivity ratio /// _|_ or mobility ratio µ///µ_|_ (// parallel to c axis), estimated from Dordor et al. [START_REF] Dordor | Crystal growth and electrical properties of CuFeO2 single crystals[END_REF] data, is around 2.1 10 -3 for n-type whereas it tends to 2.6 10 -1 in p-type compound,

showing the promotion of the electrical conductivity along the (a,b) plane, i.e. parallel to the Cu + layers. The order of magnitude of the charge carrier mobility in the CuFeO2 films deposited from 380 to 460 °C and their electrical conductivity of about few S m -1 ascertains the positive nature of the majority charge carrier. According to the above statements, the change in the preferential orientation towards the [006] direction because of the strong anisotropic behaviour of the electrical conductivity of the delafossite structure could then be partially responsible of the decrease of the electrical conductivity for films deposited at TS 460 °C (Fig. 7(a)). In our case, the electrical conductivity ratio 510 °C/ 440 °C is around 10 -3 which is lower than the expected electrical conductivity ratio ( 510 °C/ 440 °C ≈ 0.26), meaning that the electrical conductivity for film having a

[006] preferential orientation is lower than expected (~ 2 10 -1 S m -1 ). Again, the presence of secondary phases in a weak proportion, such as Fe2O3 or Cu2O phases would contribute to the low electrical conductivity as observed by the 4 probe methods.

Magnetic properties

Magnetization loops measured at room temperature for delafossite films deposited at different deposition temperatures are displayed in Fig. 8(a). The quasi-linear dependency of the magnetization on the applied magnetic field in addition with the absence of saturation magnetization suggests that paramagnetic behaviour dominates as expected at this temperature, largely higher than the Néel transition temperatures for the delafossite compound [52][53].

Assuming a pure paramagnetic behaviour, the mean volume susceptibility (i.e. the ratio between the variation of the magnetization and the applied magnetic field) has been calculated for a magnetic field greater than 0.5 T (Table 1). Up to 510 °C, these mean volume susceptibilities are about 2.5 x 10 -2 , which is between 2 and 9 times higher than the previously reported values at room temperature for single crystal [54][55]. It is noteworthy that these values are anisotropic only in the antiferromagnetic state [START_REF] Hua-Kun | The magnetic anisotropy and complete phase diagram of CuFeO2 measured in a pulsed high magnetic field up to 75 T[END_REF]. The variations in the mean volume susceptibility reveal local fluctuation in the chemical composition (e.g. Cu vacancy, O insertion, etc) of the paramagnetic CuFeO2 phase [START_REF] Cullity | Introduction to magnetic materials[END_REF].

In fact, each magnetization loop in Fig. 8(a) exhibits a low coercive field and a low residual magnetization combined with a change in the slope of the magnetization at low applied magnetic field. It is noteworthy that the magnetization loops are similar to that of canted antiferromagnetic materials [START_REF] Cullity | Introduction to magnetic materials[END_REF]. However, this phenomenon probably not occur due to the large temperature difference between Néel's temperature and room temperature [START_REF] Shukla | Griffith-like phase in Crednerite CuMnO2[END_REF][58] and also to the presence of secondary phases as deduced from the optical and electrical studies. This shows that in addition to the overall paramagnetic behaviour, a small fraction of short-range ferromagnetic phase is present.

This phase could be attributed to the chemical ordering at the nanoscale or to ferromagnetic clusters, as suggested by the crystallization of magnetite at the highest deposition temperature.

Subtracting the paramagnetic component to the measured magnetization, the saturation magnetization related to the ferromagnetic component has been estimated in Fig. 8(b). These values are rather stable at 10 kA m -1 up to 460 °C. Afterwards the saturation magnetization progressively increases with the deposition temperature, confirming the increase of the ferromagnetic component with the deposition temperature. The saturation magnetization is too high to correspond to pure hematite Fe2O3 (Ms ~ 1-2 kA m -1 ). The crystallisation of the cuprospinel CuFe2O4 seems improbable considering the rather reductive conditions with the deposition temperature increase.

Assuming the crystallization of magnetite cluster (or eventually of -Fe2O3) which exhibits a theoretical saturation magnetization of about 477 (350) kA m -1 [59] could be responsible for such ferromagnetic behaviour, the volume fraction of this ferromagnetic phase would only be 2 (3) % for the films deposited below 460 °C, 3 (5) % for film deposited at 510 °C and up to 10 % for film grown at 550 °C finally showing X-ray detectable magnetite phase. In addition to the paramagnetic behaviour, a short-range ferromagnetic component is shown even at low deposition temperature (380 °C), while its presence by X-ray diffraction is not detected. It is suggested that an increase of the deposition temperature at a constant oxygen partial pressure would progressively dissociate the delafossite phase in addition to change its preferential orientation. This would occur by forming phases with decreasing oxidation state contributing to the optical and electrical behaviour by their nature and their proportion. It is believed that the decrease of the relative poor transmittance in the visible range is ascribed to the presence of such phases growing with temperature.

Conclusions

Delafossite

Figures caption

Fig.

  CuFeO2 films have been synthesized by reactive magnetron sputtering on heated fused silica substrate. CuFeO2 films crystallize in the rhombohedral structure from 380 to 550 °C, with a preferential orientation change from [012] to [006] direction between 460 and 510 °C. It is shown that the increase of deposition temperature makes the deposition conditions more reductive, leading to the formation of secondary phases with decreasing oxidation state, detected from optical and electrical studies. Beyond 510 °C, the partial reduction of the delafossite in Cu and Fe3O4 phases occurs. By optical modelling, two absorption peaks were assigned to the light absorption in the parallel and perpendicular directions to the c-axis. The electrical conductivity, dominated by positive charge carrier, exhibits a relatively strong dependency on the crystallographic orientation.

Fig. 2

 2 Fig. 1 X-ray diffractograms of CuFeO2 films deposited at different temperatures.

Fig. 3

 3 Fig. 3 Transmittance and reflectance spectra of delafossite CuFeO2 films deposited at different temperatures (solid and dashed lines, respectively). Open circles and diamonds correspond to the simulated spectra with the model based on two OJL interband transitions combined with Drudelike dispersion, respectively.

Fig. 4

 4 Fig. 4 Absorption coefficient spectra determined with different methods (solid line: 2 OJL interband transitions with Drude-like dispersion model, dotted line: Cauchy model, dashed line: from transmittance and reflectance spectra).

Fig. 5

 5 Fig. 5 Refractive index vs. wavelength of delafossite thin films measured using two different models (solid line: 2 OJL interband transitions with Drude-like dispersion model and dotted line: Cauchy model).

Fig. 6 (

 6 Fig. 6 (a) Optical band gap energy vs. deposition temperature determined using two different methods: (i) modelling of the dielectric function (2 OJL interband transitions with Drude-like model), and (ii) graphical method by using Tauc's plot for direct transitions. (b) Evolution of broadening spread of band tails in OJL interband transition model and of Urbach energy of the transition at 1.62 eV vs. deposition temperature (Urbach energy of the 2 nd transition (2.26-2.10 eV) cannot be obtained in reason of the presence of the 1 st transition at lower energies).

Fig. 7 (

 7 Fig. 7 (a) Evolution of ln( ) vs. T -1/4 and (b) of charge carrier mobility vs. concentration for the CuFeO2 films deposited at different temperatures.

Fig. 8 (

 8 Fig. 8 (a) M-H loops and (b) evolution of the coercive field and of the magnetization at saturation once subtracting the paramagnetic component for CuFeO2 films deposited at various deposition temperatures.

Figure 1

 1 Figure 1

Figure 2

 2 Figure 2

Figure 3a

 3a Figure 3a

Figure 3b

 3b Figure 3b

Figure 4

 4 Figure 4

Figure 5

 5 Figure 5

Figure 6a

 6a Figure 6a

Figure 6b

 6b Figure 6b

Figure 7a

 7a Figure 7a

Figure 7b

 7b Figure 7b

Figure 8a

 8a Figure 8a

Figure 8b

 8b Figure 8b

Table caption Table 1

 caption1 Average transmittance in visible range, electrical conductivity measured at room temperature using the 4 probes method, Seebeck coefficient and mean volume susceptibility determined from M-H loops of the CuFeO2 films sputtered at different temperatures

	Deposition temperature (°C)	Average transmittance in visible range	Electrical conductivity at 20 °C (S m -1 )	Seebeck coefficient (µV K -1 )	Mean volume susceptibility
	380	0.056	0.8 10 0	295	2.5 10 -2
	440	0.035	1.3 10 0	101	2.1 10 -2
	460	0.025	3.2 10 0	196	2.1 10 -2
	510	0.020	3.4 10 -3	101	2.4 10 -2
	550	0.001	1.3 10 2	194	1.4 10 -2

Table

  Click here to access/download;Table;Table 1.docx

Acknowledgement

The authors thank the community "Pays de Montbéliard Agglomération" for his financial support and would like to express their gratitude for the financial support received from Mouloud Mammeri University of TiziOuzou, Algeria


Ole Bang

Peter Uhd Jepsen

John Dudley

Thibaut Sylvestre
email: thibaut.sylvestre@univ-fcomte.fr

Ryszard Buczynski

Mariusz Klimczak

Bettina Heise

Markus Brandstetter

Johann Troles

Goery Genty

Clemens Kaminski

Oliver Hadeler

Patrick Bowen

Peter Moselund

Philippe Leproux

Guillaume Huss

Juha Toivonen

Jaani Silvennoinen

Shreesha Rao

Gaoyuan Li

Manoj Dasa

Kyei Kwarkye

Amar Nath

Solveig Perret

Xavier Forestier

Tanvi Karpate

Zorin Ivan

Marcello Meneghetti

Zahra Eslami

Chetan Poudel

Etienne Genier

Fathima Shabana

Abba Saleh

Supercontinuum broadband light sources covering UV to IR applications (SUPUVIR EU Project)

We review our recent advances in supercontinuum (SC) generation in specialty optical fibres in the context of the European H2020-MSCA-ITN-2016 project called SUPUVIR. Significant scientific progress was made in emerging UV and mid-IR wavelength ranges for biomedical applications and molecular spectroscopy, evidenced by many scientific publications and the development of new compact and reliable mid-IR SC fibre sources. As a result, supercontinuum technology and its industrial applications have been matured considerably.

Introduction

A standing challenge since the invention of the laser has been to use nonlinear processes to convert laser light to new wavelengths as lasers only operate efficiently at distinct wavelengths. Supercontinuum (SC) generation offers an elegant solution to this, as it massively broadens the laser spectrum. In its simplest case a powerful narrowband laser is sent into a short piece of fibre to generate a rainbow of colours at the output, pertaining the brightness and spatial coherence of the laser. This allows access to both new wavelengths and new applications exploiting coherent broadband laser radiation that are not available with conventional laser technology.

The scientific challenges addressed in the European project SUPUVIR was to overcome current shortcomings of SC sources in terms of wavelength coverage, noise, power density and robustness to offer a truly unique and disruptive technology for societal and industrial challenges, such as pollution and food quality monitoring, bio-imaging, molecular spectroscopy, detection and monitoring of key diseases, such as cancer and glaucoma.

15 Ph. D students (early stage researchers, ESR) were trained and involved in different work packages ranging from glass chemistry, fibre design and drawing, to the development of next generation SC sources and their applications.

Significant scientific progress was made in emerging UV and mid-IR wavelength ranges, evidenced by many publications, and some SC light-based demonstrators were developed in the project. As a result, supercontinuum technology and its industrial applications have been matured considerably.

The major advances in SUPUVIR beyond state-of-the-art are:

1. The development of a deep understanding of low-noise coherent so-called all-normal-dispersion (ANDi) supercontinuum (SC) generation and how is depends on pump laser noise and the birefringence of the optical fibre. This has enabled SUPUVIR researchers to develop these low-noise ANDi SC sources and demonstrate unrivalled performance in optical coherence tomography (OCT) imaging and scanning near-field optical microscopy in terms of sensitivity and penetration depth. This will allow faster and more accurate diagnosis of important diseases, such as skin cancer and glaucoma.

2. The development of SC cascading towards the mid-IR, which is a very complicated process in which a broadband SC is used to pump another optical fibre to generate an SC extending to even longer wavelengths. This knowledge has profound importance for the development of the future long-wavelength mid-infrared SC sources extending past 10 µm to cover the so-called molecular fingerprint region. Such sources are of key importance for pollution and food quality monitoring, as well as for performing ultra-fast optical biopsies of cancer tissue.

Through the scientific advanced industrial partner NKT

Photonics is developing a new low noise SC laser product series with more than an order of magnitude lower noise than current state-of-of-the-art. Likewise industrial partners LEUKOS and NORBLIS have developed compact and reliable mid-infrared cascaded fibre SC laser product series that for the first time extends to wavelengths longer than 10 µm. 4. A fully automated multimodal fluorescence microscopy platform has been developed at UCAM incorporating an SC laser, which is capable of intensity, lifetime, and spectral imaging at unprecedented speeds (orders of magnitude faster than conventional approaches) without sacrificing accuracy or. The system fills a major gap in biomedical diagnostics and provides new opportunities for drug research in cells or organism models. The novel platform has already enabled SUPUVIR researchers to make significant contributions in the fields of neuroscience, stem cells, gene delivery, and material science. 6. Industrial partner VALMET has been able to develop a short-range SC laser-based LIDAR system for remote profiling of the temperature and gas composition inside thermal devices, such as industrial furnaces and boilers. This represents the first non-contact system to be able to provide a profile (not just an average) of the temperature and gas composition. 7. A multimodal MIR OCT-Spectroscopy system based on SC light source has been developed and demonstrated by RECENDT for structural non-destructive testing.

8. New low-loss heavy-metal-oxide and chalcogenide glass photonic crystal fibres have been designed and successfully fabricated by UR1 and IMIT (formely ITME) for SC generation towards the mid-IR. New UVgrade silica PCFs have been also designed by CNRS. 9. Improved numerical modeling of SC generation and nonlinear dynamics in optical fibers, including input noise and all laser parameters, has been performed by CNRS and DTU, validated by real-time SC experimental measurements.

Figure 1 .

 1 Figure 1. Photograph of the optical setup of the multimodal microscope including a SC light source. 5. A near-infrared SC laser with extremely high pulse energy has been developed and used as the light source in a new optical-resolution photoacoustic microscope (OR-PAM). The new system has allowed the researchers to demonstrate real-time in vivo hyper-spectral PAM of lipids and endogenous agents inside live tadpoles. The results have underlined the suitability of high-pulse energy SC lasers in endoscopic multi-spectral OR-PAM systems for the detection of atherosclerosis, a key disease in an increasingly obese society.


PhD Ali Gharaviri

Simone Pezzuto

PhD Mark Potse

MD, PhD Giulio Conte

PhD Stef Zeemering

MSc Vladimír Sobota

PhD Sander Verheule

PhD Rolf Krause

MD, PhD Angelo Auricchio
email: angelo.auricchio@cardiocentro.org

MD, PhD Ulrich Schotten

Synergistic antiarrhythmic effect of inward rectifier current inhibition and pulmonary vein isolation in a 3D computer model for atrial fibrillation

Keywords: Antiarrhythmic drug, Inward rectifier currents, Catheter ablation, Atrial Fibrillation recurrence, In-silico study. Condensed

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

What's new

• We simulated the efficacy of inward rectifier current blockade and its combination with PVI on prevention of AF initiation in different degrees of atrial fibrosis.

• The combination of inward rectifier blockade with PVI synergistically reduced the likelihood of AF initiation in simulations with severe atrial fibrosis.

• The inward rectifier current blockade adjunctive to PVI strongly reduced the number of fibrillation wavesand new wavefront generation rate, while increasing the wave size, and thereby strongly prevented AF induction.

Introduction

Despite the development of pharmacological therapies for patients with atrial fibrillation (AF), a large proportion of AF patients are not arrhythmia-free. [START_REF] Rillig | Comparing Antiarrhythmic Drugs and Catheter Ablation for Treatment of Atrial Fibrillation[END_REF] Pharmacological therapy is less effective in non-paroxysmal AF patients than in paroxysmal AF patients, indicating the significance of structural remodelling in the efficacy of pharmacological therapy. If the treatment with antiarrhythmic drugs (AAD) fails, patients receive catheter ablation (CA) as a second-line treatment. [START_REF] Hakalahti | Radiofrequency ablation vs. antiarrhythmic drug therapy as first line treatment of symptomatic atrial fibrillation: systematic review and meta-analysis[END_REF] CA is also associated with a rather disappointing long term outcome, as after one year AF reoccurs in up to 30% of patients after PVI, despite proven complete PV isolation supporting the presence of driver mechanisms of AF located outside the PV area. [START_REF] Vogler | Pulmonary Vein Isolation Versus Defragmentation: The CHASE-AF Clinical Trial[END_REF][START_REF] Kuck | Cryoballoon or Radiofrequency Ablation for Paroxysmal Atrial Fibrillation[END_REF] The recent EAST trial stresses the need for early and effective rhythm control strategies [START_REF] Kirchhof | Early Rhythm-Control Therapy in Patients with Atrial Fibrillation[END_REF] and combination of AADs with CA may be a strategy to achieve this. In a recent study, Duytschaever et al. demonstrated that continuing previously ineffective treatment with AAD after CA is associated with lower prevalence of atrial tachyarrhythmias after one year. [START_REF] Duytschaever | PulmOnary vein isolation With vs. without continued antiarrhythmic Drug trEatment in subjects with Recurrent Atrial Fibrillation (POWDER AF): results from a multicentre randomized trial[END_REF] However, the mechanisms underlying this synergistic inhibition of AF recurrences is not well understood. Also, current AADs having potential side effects such as ventricular proarrhythmia. For these reasons, atrial-selective AADs that do not affect ventricular conduction or repolarization have been developed. Examples are blockers of the ultra-rapid inward rectifier current (IKur), small-conductance Ca 2+ -activated K + -currents (SK), and the G-proteingated acetylcholine-activated inward rectifier current (IKAch). A blocker of IKAch (XAF-1407) has recently been demonstrated to effectively suppress AF in an experimental equine model. [START_REF] Fenner | Effect of selective IK,ACh inhibition by XAF-1407 in an equine model of tachypacing-induced persistent atrial fibrillation[END_REF] Here, we tested whether inward rectifier current blockade reduces AF inducibility and whether the combination of inward rectifier blockade with PVI prevents AF recurrences in a computer model of human atria.

Methods

Computational model of AF

Computer simulations were performed on a highly detailed 3D model of human atria. [START_REF] Gharaviri | Epicardial Fibrosis Explains Increased Endo-Epicardial Dissociation and Epicardial Breakthroughs in Human Atrial Fibrillation[END_REF] The model geometry was based on magnetic resonance imaging data of a subject with normal atria with manually added anatomical structures and properties such as three layers of fibre orientations, endocardial trabeculated network, Bachmann's bundle, wall thickness heterogeneities, and left atrial appendage trabeculated network. [START_REF] Gharaviri | Epicardial Fibrosis Explains Increased Endo-Epicardial Dissociation and Epicardial Breakthroughs in Human Atrial Fibrillation[END_REF] Several studies have shown that these structures have an essential role in AF initiation and maintenance. [START_REF] Whitaker | The role of myocardial wall thickness in atrial arrhythmogenesis[END_REF][START_REF] Verheule | Role of endoepicardial dissociation of electrical activity and transmural conduction in the development of persistent atrial fibrillation[END_REF] The model consisted of approximately 5 million nodes spaced at 200µm. Action potential propagation was simulated with a monodomain reaction-diffusion equation using the Courtemanche-Ramirez-Nattel atrial cell model. [START_REF] Courtemanche | Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model[END_REF] AF-induced changes in ionic currents were incorporated by setting the conductivities for Ito, ICa,L, and IK1 at 40%, 35%, and 200% of their normal values, respectively. [START_REF] Gharaviri | How disruption of endo-epicardial electrical connections enhances endo-epicardial conduction during atrial fibrillation[END_REF] Simulations were performed using the propag-5 software [START_REF] Krause | Hybrid Parallelization of a Large-Scale Heart Model[END_REF] and run on a Cray XC50 supercomputer with GPU support.

Modelling of inward rectifier current blockade

The inward rectifier background current (IK1) and the G-protein-gated acetylcholine-activated inward rectifier current (IKAch) show identical current-voltage relationships and are, therefore, indistinguishable on the single cell level. [START_REF] Dobrev | The G proteingated potassium current I(K,ACh) is constitutively active in patients with chronic atrial fibrillation[END_REF] Thus, both currents are adequately represented by one total inward rectifier conductance in computer models. For this reason, inhibition of IKAch was simulated by reduction of this total inward rectifier current. The conductance of the current was reduced by 30% resulting in a prolongation of the atrial action potential duration by approximately 20ms, which is in the range of experimental studies. [START_REF] Dobrev | Molecular basis of downregulation of G-protein-coupled inward rectifying K(+) current (I(K,ACh) in chronic human atrial fibrillation: decrease in GIRK4 mRNA correlates with reduced I(K,ACh) and muscarinic receptor-mediated shortening of action potentials[END_REF][START_REF] Voigt | Constitutive activity of the acetylcholineactivated potassium current IK,ACh in cardiomyocytes[END_REF]

Distribution of tissue fibrosis

The effect of structural remodelling was simulated by different degrees of fibrosis. The conditions without, with moderate, and with severe fibrosis were modelled by setting 0%, 50%, and 70% of the elements in the model as fibrotic, respectively. Fibrotic elements remained conductive along the fibre direction and isolated in the two transverse directions. This modelling of atrial tissue fibrosis agrees with the experimental study by Spach et al. that revealed loss of side-to-side electrical connections between atrial muscle bundles in fibrotic atrial tissue. [START_REF] Spach | Relating extracellular potentials and their derivatives to anisotropic propagation at a microscopic level in human cardiac muscle. Evidence for electrical uncoupling of side-to-side fiber connections with increasing age[END_REF] The fibrosis was distributed within the subepicardial layer, while the atrial bundles remained intact. The spatial distribution of fibrosis was uneven, with patches or island presenting higher degree of fibrosis. Such distribution was based on spatially correlated, anatomy-tailored random fields. [START_REF] Gharaviri | Epicardial Fibrosis Explains Increased Endo-Epicardial Dissociation and Epicardial Breakthroughs in Human Atrial Fibrillation[END_REF][START_REF] Pezzuto | Beat-tobeat P-wave morphological variability in patients with paroxysmal atrial fibrillation: an in silico study[END_REF]

Modelling of Pulmonary vein isolation

In PVI simulations, two antral circumferential lines isolated the PV from the atria. Virtual ablation lesions consisted of tissue volumes modelled by non-conductive elements.

AF initiation in pre-and post-catheter ablations

AF initiation likelihood was assessed by applying incremental pacing at 20 different locations in both atria and compared between the control (no inward rectifier current inhibition and no CA), inward rectifier current blockade (IK blockade), PVI, and IK blockade + PVI groups.

Pacing locations were selected based on reported possible sources of extra-PV ectopic focal activity in AF patients, including the area between the PVs, left atrium, left atrial appendage, right atrial appendage, coronary sinus, superior caval vein, inferior caval vein, and right atrium. [START_REF] Santangeli | Techniques for the provocation, localization, and ablation of non-pulmonary vein triggers for atrial fibrillation[END_REF] All pacing sites were located outside the ablated area. In each simulation, AF was initiated by applying incremental pacing with a duration of 2 seconds at a selected pacing site. In total, 14 stimuli were applied with the pacing cycle length gradually reducing from 280ms to 124ms. After the pacing period, the simulations were continued for another 3 seconds with no pacing.

Definition of successful AF initiation

The stimulation protocol outcome was analysed in terms of the type of self-sustained rhythm after 2 seconds of stimulation. If no activation after pacing was noted, the initiation was considered unsuccessful. Otherwise, a distinction between AF and atrial flutter (AFL) was made, with the latter not being considered as successful AF initiation. AF and AFL conduction patterns were differentiated by analysing the reconstructed 12-lead ECGs, as described in detail in the supplementary material.

Detection and tracking of fibrillation waves

A fibrillation wave was defined as a contiguous volume in which all nodes had transmembrane voltage above -60 mV. Wave size was defined as the number of model elements within this contiguous volume. Both the number of waves and wave sizes were calculated at each millisecond of simulated time.

Fibrillation waves were tracked in both time and space, as described in our previous study. [START_REF] Gharaviri | A computer model of endo-epicardial electrical dissociation and transmural conduction during atrial fibrillation[END_REF] Briefly, the temporal dynamics of waves can be described by three events:

• Generation: appearance of a new wave either due to wave break or transmural conduction.

• Fusion: the merge of two or more waves into one wave.

• Extinction: the extinction of a wave, due to encountering either a boundary or unexcitable tissue.

Statistics

All statistical analyses were performed using GraphPad Prism software version 8.0. The values are expressed as means ± SD. Statistical tests were performed to compare the effect of three parameters (fibrosis levels, IK blockade, and PVI) in AF initiation rate, using two-way ANOVA followed by post hoc Bonferroni test. A value of P < 0.05 was considered to be significant.

Results

In total, 240 simulations were performed. The simulations consisted of 4 groups: control (no interventions), inward rectifier current blockade (IK blockade), PVI, and the combination of inward rectifier current blockade and PVI (IK blockade + PVI). Twenty simulations were performed for each degree of fibrosis, resulting in the total of 60 simulations performed in each group.

AF initiation

Fibrillation pattern complexity

Overall, a significant increase in AF cycle length was observed in all simulation groups when compared to control, regardless of the fibrosis degree, as shown in Table 1. When compared to control, no significant differences in the excitable gap were detected in any simulation group (see Table. Examples of wave lifespans in control, IK blockade, PVI, and PVI accompanied with IK blockade simulations with severe fibrosis are illustrated in figure 4A. An increase in the fibrosis degree in control simulations led to a significant increase in fibrillation wave generation rate, quantified as the slope of the fitted line to the wave lifespans, and therefore a significant increase in AF conduction pattern complexity, quantified as the average number of waves per cycle (Figure 4B &C). The increase in conduction pattern complexity was due to the reduction of wave size and higher rate of new wavefront generation, while wavefront lifespan medians remained unchanged (Figure 4D &E). In the simulations without fibrosis, IK blockade caused a significant reduction in the average number of waves per cycle, by increasing the wave sizes and significantly reducing the rate of wavefront generation.

However, this effect of IK blockade disappeared in the simulations with moderate and severe fibrosis. PVI significantly reduced new wavefront generation rate in the simulations without fibrosis as well as in the simulations with moderate fibrosis. Nevertheless, this effect faded in PVI simulations with severe fibrosis. In IK blockade combined with PVI simulations, the synergistic interaction between the wave size enlargement caused by IK blockade and the reduction in atrial tissue mass caused by PVI further reduced the available space for wavefront interactions. This resulted in significantly decreased rate of new wavefront generation, and therefore in a smaller number of fibrillation waves.

Discussion

We investigated the isolated and combined effects of inward rectifier current blockade and PVI on AF initiation in the presence of various degrees of atrial fibrosis. Both inward rectifier blockade and PVI effectively reduced the rate of AF induction at low degrees of atrial fibrosis but lost their efficacy in severely fibrotic atria. In the simulations with severe fibrosis the combination of inward rectifier blockade and PVI effectively suppressed AF recurrences, while either of the interventions was not efficient individually. The synergy between both interventions resulted in reduction in the number of fibrillation waves. The main underlying mechanism behind this effect was a reduction in the rate of new wavefront generation, leaving the lifespan of fibrillation waves unaffected.

Effect of inward rectifier current blockade and PVI in previous in-silico studies

So far, several in-silico studies investigated the effect of different antiarrhythmic drugs (single-channel or multiple-channel block) or CAs on AF initiation, perpetuation and termination. [START_REF] Grandi | Computational modeling: What does it tell us about atrial fibrillation therapy?[END_REF][START_REF] Grandi | Antiarrhythmic mechanisms of beta blocker therapy[END_REF] Among the large variety of potassium channels expressed in human atria, the inward rectifier currents IK1 and IKAch play a significant role in AF perpetuation. Heterogeneous shortening of the atrial effective refractory period caused by vagally modulated IKACh channels are thought to be the mechanism underlying vagally-induced AF. [START_REF] Rattanawong | Drug Therapy for Vagally-Mediated Atrial Fibrillation and Sympatho-Vagal Balance in the Genesis of Atrial Fibrillation: A Review of the Current Literature[END_REF] Hence, inhibition of IKAch may minimize the effect of IKACh modulations and could be a future therapeutic option for vagallyinduced AF. [START_REF] Rattanawong | Drug Therapy for Vagally-Mediated Atrial Fibrillation and Sympatho-Vagal Balance in the Genesis of Atrial Fibrillation: A Review of the Current Literature[END_REF] Dobrev and colleagues have demonstrated that an increase of constitutively active IKAch strongly contributes to atrial action potential shortening in human persistent AF. [START_REF] Dobrev | The G proteingated potassium current I(K,ACh) is constitutively active in patients with chronic atrial fibrillation[END_REF] Also IKAch is active in atrial but not in ventricular cells so that inhibition of IKAch is not expected to prolong ventricular action potential. For these reasons inward rectifier currents are an attractive target for antiarrhythmic treatment of AF. [START_REF] Grandi | Antiarrhythmic mechanisms of beta blocker therapy[END_REF][START_REF] Sanchez | Atrial Fibrillation Dynamics and Ionic Block Effects in Six Heterogeneous Human 3D Virtual Atria with Distinct Repolarization Dynamics[END_REF] Importantly, IK1 and IKAch only differ in their single channel conductance but their single cell level current-voltage relationships are identical. [START_REF] Dobrev | The G proteingated potassium current I(K,ACh) is constitutively active in patients with chronic atrial fibrillation[END_REF] Thus, both currents are adequately represented by the total inward rectifier conductance in computer models.

The influence of inward rectifier current inhibition on AF initiation, termination, and conduction pattern was investigated in several computational studies. [START_REF] Grandi | Computational modeling: What does it tell us about atrial fibrillation therapy?[END_REF][START_REF] Grandi | Antiarrhythmic mechanisms of beta blocker therapy[END_REF] Sánchez et al. demonstrated that inward rectifier inhibition led to higher arrhythmia organization by enlarging wave sizes, increasing wave meandering, and reducing the number of secondary wavelets. [START_REF] Sanchez | Atrial Fibrillation Dynamics and Ionic Block Effects in Six Heterogeneous Human 3D Virtual Atria with Distinct Repolarization Dynamics[END_REF] These findings are in line with our results of inward rectifier current inhibition in the atria without fibrosis in the present study. However, we observed significant efficacy loss of inward rectifier current blockade in reducing the number of fibrillation waves and AF termination or initiation in the presence of moderate or severe fibrosis.

The effectiveness of PVI to terminate AF in representative virtual atria was assessed in several studies. [START_REF] Rotter | Impact of varying ablation patterns in a simulation model of persistent atrial fibrillation[END_REF] Recent proof-of-concept in-silico studies investigated the role of atrial fibrosis in ablation failure using detailed patient-specific image-based models. [START_REF] Grandi | Anti-arrhythmic strategies for atrial fibrillation: The role of computational modeling in discovery, development, and optimization[END_REF] These studies demonstrated that both the patient-specific degree and the distribution of fibrosis are a determining factor in AF initiation and maintenance. [START_REF] Mcdowell | Virtual electrophysiological study of atrial fibrillation in fibrotic remodeling[END_REF] McDowell et al. demonstrated that modelling of ablation lesions in the persistent rotor core meandering regions renders AF uninducible. [START_REF] Mcdowell | Virtual electrophysiological study of atrial fibrillation in fibrotic remodeling[END_REF] Here, we simulated the combination of PVI and inward rectifier current blockade and studied the mechanisms underlying the synergy between these two treatment options on prevention of AF initiation.

Synergism between inward rectifier inhibition and PVI to prevent AF recurrence

The development of efficient therapy against AF remains an important unfulfilled clinical need. Treatment with AADs has been considered as the first-line therapy [START_REF] Hakalahti | Radiofrequency ablation vs. antiarrhythmic drug therapy as first line treatment of symptomatic atrial fibrillation: systematic review and meta-analysis[END_REF] and recently has been demonstrated to reduce major cardiovascular adverse events in patients with AF. [START_REF] Kirchhof | Early Rhythm-Control Therapy in Patients with Atrial Fibrillation[END_REF] However, the efficacy of AADs decreases with AF progression. [START_REF] Hakalahti | Radiofrequency ablation vs. antiarrhythmic drug therapy as first line treatment of symptomatic atrial fibrillation: systematic review and meta-analysis[END_REF] CA has been recognized as an alternative therapeutic modality in AF treatment, which has been highlighted in several studies to be more efficient than AAD therapy to prevent AF recurrences. [START_REF] Grandi | Computational modeling: What does it tell us about atrial fibrillation therapy?[END_REF] Nevertheless, CA results remain suboptimal, particularly in non-paroxysmal AF patients. [START_REF] Verma | Approaches to catheter ablation for persistent atrial fibrillation[END_REF] Recently, there has been a growing interest in the effect of AAD continuation after CA. [START_REF] Duytschaever | PulmOnary vein isolation With vs. without continued antiarrhythmic Drug trEatment in subjects with Recurrent Atrial Fibrillation (POWDER AF): results from a multicentre randomized trial[END_REF] As reported in the POWDER-AF trial, the AADs, despite being inefficient before ablation, are becoming efficient in reducing AF recurrence after CA. [START_REF] Duytschaever | PulmOnary vein isolation With vs. without continued antiarrhythmic Drug trEatment in subjects with Recurrent Atrial Fibrillation (POWDER AF): results from a multicentre randomized trial[END_REF] The mechanisms underlying this synergy between AADs and CA in AF recurrence prevention were so far not well understood.

Our simulations showed that either inward rectifier current inhibition alone or PVI alone can significantly prevent initiation of AF only in the presence of no or moderate fibrosis, while both became inefficient in the presence of severe fibrosis. When both strategies were combined, little contribution to further reduction of AF inducibility in the simulations with no or moderate fibrosis was observed. In severe fibrosis, inward rectifier blockade in combination with PVI strongly reduced the number of fibrillation waves, increased their size and strongly prevented successful AF induction. This effect was associated with significant decline in the rate of new wave generation while wavefront lifespan remained unaltered. The observed synergism might be explained by the fact that both PVI as well as the wavelength prolongation by the inward rectifier blockade restrict the available space for wave-frontwave-tail interactions which reduces the likelihood for wave break and generation of new waves. Our results indicate that the newly developed inhibitors of IKACh have a potential to show the observed synergism with PVI to prevent AF induction in a clinical setting.

Limitations

Inter-individual variabilities in anatomy, atrial size, fibre orientation, and wall thickness were not considered in our study. Several clinical and simulation studies reported the effect of variability in atrial geometry and the pattern of fibrosis on initiation of fibrillatory waves. [START_REF] Grandi | Anti-arrhythmic strategies for atrial fibrillation: The role of computational modeling in discovery, development, and optimization[END_REF][START_REF] Boyle | Using personalized computer models to customtailor ablation procedures for atrial fibrillation patients: are we there yet?[END_REF][START_REF] Zahid | Feasibility of using patient-specific models and the "minimum cut" algorithm to predict optimal ablation targets for left atrial flutter[END_REF][START_REF] Ali | Arrhythmogenic propensity of the fibrotic substrate after atrial fibrillation ablation: a longitudinal study using magnetic resonance imaging-based atrial models[END_REF] Studying the effect of variations in the pattern of atrial fibrosis on AF inducibility is certainly warranted. Although based on clinical data, the pattern of atrial fibrosis was generated algorithmically in this study. We investigated the effect of inward rectifier current inhibition, whereas several other currents have been shown to play an important role in AF termination. Moreover, we did not investigate inhibition of multiple ion channels on AF dynamics. Finally, heterogeneity in ionic parameters in our model has not been implemented on purpose in order to avoid confounding factors.

Conclusion

This study shows that adding inward rectifier current inhibition to PVI caused a significant reduction in AF recurrences even in the atria with severe fibrosis, whereas both treatments alone failed to prevent AF initiation in severely fibrotic atria. This reduction in AF recurrence rate is due to the synergistic effect of the two treatments to reduce the number of wavefrontwavetail interactions, thereby lowering the rate of new wavefront generation and thus the number of active fibrillation waves.

Figure

  Figure 1A displays several action potentials recorded during simulated AF episodes in the

Figure 2

 2 Figure 2 depicts representative conduction patterns and corresponding ECG leads of IK

Figure 3

 3 Figure3shows initiation rates of atrial tachycardia in all simulation groups in the presence of

  1).

Figure 1 :

 1 Figure 1: A) Simulated action potentials during AF episodes in control and IK blockade

Figure 2 :

 2 Figure 2: Consecutive snapshots of conduction patterns and corresponding ECG leads (II,

Figure 3 :

 3 Figure 3: Atrial fibrillation (AF) and atrial flutter (AFL) initiation likelihood in control (no

Figure 4 :

 4 Figure 4: Electrophysiological parameters. A) Examples of wave life spans in control, IK

Table 1 .

 1 Atrial fibrillation cycle length (AFCL) and Excitable gap (EG) in simulation groupswith different degrees of fibrosis.

	Simulation Groups
		Control	IK blockade	PVI	PVI + IK blockade
	Fibrosis					P Value
	AFCL (ms)	147.12 ±15	210.52 * ±14 187.12*±13	202.12* ±15	*P < 0.05
	without
	EG (ms)	55.28 ± 4.3	59.2 ± 3.1	58.2 ± 2.9	57.9 ± 4.2	P > 0.05
	AFCL (ms)	152.28 ±18	224.06* ±16	192.28*±14	204.06*±16	* P < 0.05
	moderate
	EG (ms)	53.78 ± 3.1	58.77 ± 4.2	57.77 ± 3.3	57.77 ± 3.6	P > 0.05
	AFCL (ms)	197.13 ±12	229.12 * ±17 228.44*±11	219.12*±13	* P < 0.05
	severe
	EG (ms)	54.64 ± 2.9	59.6 ± 3.8	57.6 ± 3.8	57.6 ± 3.1	P > 0.05

Sources of funding

This work was supported by the Swiss National Supercomputing Centre (CSCS) under project ID s778 and by grants to US from the Netherlands Heart Foundation (CVON2014-09, RACE V: Reappraisal of Atrial Fibrillation: Interaction between hypercoagulability, Electrical remodelling, and Vascular Destabilisation in the Progression of AF), and the European Union (ERACoSysMED H2020 ERA-NET, Marie Sklodowska-Curie grant agreement No. 675351). Dr Conte is supported by the Swiss National Foundation (SNF) (Ambizione grant no PZ00P3_180055 / 1). 8 Conflict of interest Angelo Auricchio (AA) is a consultant to Boston Scientific, Backbeat, Biosense Webster, Cairdac, Corvia, Microport CRM, Philips, Radcliffe Publisher. He received speaker fee from Boston Scientific, Medtronic, and Microport. He participates in clinical trials sponsored by Boston Scientific, Medtronic, Philips. He has intellectual properties with Boston Scientific, Biosense Webster, and Microport CRM. Ulrich Schotten (US) received consultancy fees or honoraria from Johnson & Johnson, Roche Diagnostics, and Bayer Healthcare. US is cofounder and shareholder of YourRhythmics BV. He holds intellectual property with Roche and YourRhythmics BV. The other authors have nothing to declare.