Othman Lagrichi

Laure Guetaz

Olivier Sicardy

Denis Buttard

Arnaud Morin

Laure Guétaz

Platinum-nickel

Keywords: Electrocatalyst, PEMFC, PtNi alloy, Oxygen Reduction Reaction (ORR), Electrode, Anodic Alumina Oxide, Ni Nanowires, Carbon-free electrode

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Introduction

Energy has always been the fulcrum of civilizations and their undeniable pillar of development.

Recently, the effects of climate change are being felt even more intensely [START_REF]Greenhouse Gas Emissions from Energy: Overview, IEA[END_REF]. A wide range of energy sources are already known and have been used until today, such as fossil fuels, natural gas, to name a few. Recently, most of countries are aiming to vault ahead of all fossils due to their horrific effects on the environment. In the world's endless efforts to cut greenhouse gas emissions, scientist suggested possible sustainable pathways for the production of highly demanded fuels and chemicals. Hydrogen vector is coming into the spotlight, which could be used as a fuel to the polymer electrolyte membrane fuel cell (PEMFC) for electricity generation [START_REF] Seh | Combining theory and experiment in electrocatalysis: Insights into materials design[END_REF].

The technology of PEMFCs is a promising power source strongly motivated by its unique energy conversion efficiency of chemical energy of H2 to electricity without emission of greenhouse gas [START_REF] James | Mass Production Cost Estimation for Direct H2 PEM Fuel Cell Systems for Automotive Applications[END_REF]. Its commercialization is still a challenge especially due to durability and cost limitations of the catalyst [START_REF] Wang | Durability studies on performance degradation of Pt/C catalysts of proton exchange membrane fuel cell[END_REF] [START_REF] Alaswad | Technical and Commercial Challenges of Proton-Exchange Membrane (PEM) Fuel Cells[END_REF]. In order to enhance their achievement on the market, it is mandatory to optimize the high costly platinum-based catalyst to increase its activity and stability. This could be reached either by tuning its composition and nanostructure, or by increasing its utilisation during operation via the reduction of mass transport limitations in the electrode, for instance thanks to innovate structures [START_REF] Sun | Advancements in cathode catalyst and cathode layer design for proton exchange membrane fuel cells[END_REF].

Pt-based catalysts such as Pt-Co, Pt-Cu, and Pt-Ni etc. have shown to exhibit higher oxygen reduction reaction (ORR) activity than platinum for PEMFC [START_REF] Wang | Unlocking the door to highly active ORR catalysts for PEMFC applications: polyhedron-engineered Pt-based nanocrystals[END_REF][8] [START_REF] Zhang | Recent advances in Ptbased electrocatalysts for PEMFCs[END_REF]. Commercial Pt-based (PtCo) catalysts (nanoparticles 3-5 nm) supported carbon black are considered as the current standard catalyst offering high surface areas and high specific activity. Unfortunately, they are limited by corrosion of the C and Pt dissolution/agglomeration through Electrochemical Ostwald ripening mechanism, which is reflected by a fast and significant loss of electrochemical surface area (ECSA) over time during fuel cell operation [START_REF] Wang | Durability studies on performance degradation of Pt/C catalysts of proton exchange membrane fuel cell[END_REF] [START_REF] Cherevko | Durability of platinum-based fuel cell electrocatalysts: Dissolution of bulk and nanoscale platinum[END_REF] [START_REF] Dubau | A review of PEM fuel cell durability: materials degradation, local heterogeneities of aging and possible mitigation strategies[END_REF].

Previous studies have demonstrated the benefits of PtNi nanostructures such as nanostructured thin films (NSTF) by 3M Company [START_REF] Debe | Nanostructured Thin Film Electrocatalysts -Current Status and Future Potential[END_REF], unsupported PtNi aerogels [START_REF] Henning | Durability of Unsupported Pt-Ni Aerogels in PEFC Cathodes[END_REF], and platinum-nickel nanowire (PtNiNW) [START_REF] Mauger | Fuel Cell Performance Implications of Membrane Electrode Assembly Fabrication with Platinum-Nickel Nanowire Catalysts[END_REF]. In addition, Pt nanotubes have shown to be an interesting route to reduce Pt loading with improved stability compared to Pt/C structures [START_REF] Galbiati | Supportless Platinum Nanotubes Array by Atomic Layer Deposition as PEM Fuel Cell Electrode[END_REF] [START_REF] Sabarirajan | Atomic layer deposition of Pt nanoelectrode array for polymer electrolyte fuel cells[END_REF]. All these nanostructures have shown very promising performance and stability for low Pt loading.

Our work focuses on reducing the amount of platinum and improving the performance and durability of membrane electrode assemblies (MEAs), aiming to reduce cost and thus encouraging the development of PEMFCs. Accordingly, we aspire to develop and control a new carbon-free architecture of the cathode, made only with vertically aligned PtNi nanotubes (PtNiNTs) supported onto a Nafion ® membrane (figure 1). We can state the differences between all these nanostructures (stated above from literature) compared to our elaborated electrodes: the oriented NSTF nanostructures [START_REF] Debe | Nanostructured Thin Film Electrocatalysts -Current Status and Future Potential[END_REF] were supported on an organic support without carbon. Aerogels [START_REF] Henning | Durability of Unsupported Pt-Ni Aerogels in PEFC Cathodes[END_REF] exhibited larger pores' diameter and are non-oriented with tortuous morphology. For the dispersed PtNiNWs [START_REF] Mauger | Fuel Cell Performance Implications of Membrane Electrode Assembly Fabrication with Platinum-Nickel Nanowire Catalysts[END_REF], the displayed a nonoriented structure as well. The latter used only the external surface of the structures.

In our study, we aimed at developing a carbon-free or support free structure, oriented and organized of PtNiNWs, and above all PtNiNTs structures in order to use both internal and external surface of the tubes. Based on this architecture, we strive to reducing the Pt loading along with the transport limitations, thanks to straight and short routes for transport of species, and optimized volumetric distribution of active sites in the absence of component without any functional properties such as a nonconductive organic support, as in NSTF.

The process is based on an electrochemistry route of Ni electrodeposition inside anodic alumina oxide (AAO) mold which is well described in literature for the growth of oriented structures.

It is followed by a step of controlled spontaneous galvanic displacement, thermal treatment and acid treatment, leading to the formation of nanotubes. The approach was first developed by Marconot et al. [START_REF] Marconot | Vertically Aligned Platinum Copper Nanotubes as PEM Fuel Cell Cathode: Elaboration and Fuel Cell Test[END_REF] for the fabrication of PtCu nanotubes. Based on his work combined to our original multi-step process, we have chosen PtNi as a promising catalyst which exhibited higher ORR catalytic performance [START_REF] Wang | Unlocking the door to highly active ORR catalysts for PEMFC applications: polyhedron-engineered Pt-based nanocrystals[END_REF].

Finally, the electrodes were integrated in a complete MEA in order to characterize their performance in real operating conditions, followed by Accelerated Stress Tests (AST) to study their stability.

We should point out that the optimization of PtNiNWs and PtNiNWs was described in literature for non-oriented structures but were not tested in real operating conditions in a PEMFC.

Experimental section

Elaboration of PtNiNTs and PtNiNWs

The fabrication process of PtNi nanotubes/nanowires is held by a succession of four steps, as displayed in figure 2 below: i/ the first step consists of elaborating the porous anodic aluminum oxide (AAO) as a sacrificial mold supported onto a Si wafer substrate; ii/ The second step includes the confined growth of nickel nanowires on the silicon substrate, inside the AAO template by the pulsed electrodeposition (PED) process; iii/ This step is followed by the galvanic displacement mechanism; iv/ The AAO is etched in solution of NaOH resulting in self-standing PtNiNWs or PtNiNTs on silicon substrate, v/ Finally, the last step will lead to transferring PtNi nanotubes/nanowires from the Si substrate to a Nafion ® membrane by a hotpressing process to test the electrochemical performance in a complete MEA.

All the steps of the PtNi nanostructure fabrications and their structure will be described in detailed in the results part.

Microstructure

SEM

The morphology of the different nanostructures obtained during the process was analyzed by scanning electron microscopy SEM using a Zeiss Ultra 55 field emission gun (FEG) microscope.

TEM

PtNiNWs and PtNiNTs were analyzed by transmission electron microscopy (TEM). For these analyses, PtNiNWs were pulled off the Si support (or from the membrane) with a razor blade and deposited on a copper TEM grid covered with a lacey carbon film. For PtNiNTs embedded in Nafion ® membrane, a thin section of the membrane (100 nm thick) was prepared by ultramicrotomy at room temperature using a Leica UC6 Ultramicrotome after embedding the sample in epoxy resin.

The analyses were performed using a FEI-Tecnai Osiris operating at 200 kV in the high angle annular dark field (HAADF) with scanning transmission electron microscopy (STEM) mode and equipped with a Super-X X-ray energy dispersive spectrometer (X-EDS). The quantitative analysis of Pt and Ni composition was performed using the Pt-L line and Ni-K line using Cliff-Lorimer k factors given by the EDS Bruker program.

X-Ray diffraction

X-ray measurements were performed in order to determine the crystallographic structure of PtNi after manufacturing. The apparatus used is a two-circles Bruker D8 diffractometer equipped with a Cu-Kα source (λ = 0.15406 nm) and a LYNXEYE linear detector.

Pt loading measurement

UV Spectrophotometry

To quantify the actual amount of metal loaded on the carbon support, UV spectroscopy analysis measurements were carried out by using a Shimadzu 1800 UV spectrometer. The catalysts powder is initially heat treated in a ceramic oven at 600 °C for 15h so that all the components other than Pt are oxidized and vented out of the furnace. The remaining Pt catalyst powder is chemically treated to convert it to the Pt 4+ ionic form, which is needed to perform the UV measurements. The treatment consists in the dilution of the Pt catalyst powder in a solution of 25vol % HNO3 and 75 vol % HCl (Aqua Regia). The solution is completely evaporated at 100 °C into a dedicated glass system. This step is repeated twice with concentrated HCl ( 12M). The obtained dry catalyst is finally diluted in HCl (1M) where the Pt 4+ ions are stable. The obtained solution is analyzed to determine the catalyst concentration. A calibration of the UV spectrometer was made before each measurement by using reference samples.

X-Ray fluorescence

The Pt loadings were also controlled by measuring X-Ray fluorescence spectroscopy (XRF) with a Fischer-scope XDV-SDD, 50 kV, 50W X-Ray source.

Low Pt-loading Pt/C electrode fabrication

In this part, we display the fabrication process of a standard Pt/C electrode whose performance and activity will be compared to those of PtNiNWs and PtNiNTs electrodes under real PEMFC conditions. We targeted to fabricate a low Pt-loading cathode exhibiting substantially the same roughness as the cathodes made of PtNiNWs and PtNiNTs using the same Nafion ® membrane. We integrated these nanostructures onto a Nafion ® HP membrane using the conventional hotpressing process. The hot-pressing process (applied stress, time, and temperature) was optimized to transfer the nanostructures onto the membrane completely (see figure 3).

The hydraulic press (Model SYNTAX) used in assembling MEAs consists of two pedestals heated to 150°C. A loading force was imposed on the upper pedestal to apply stress of 1 MPa for 13 minutes. GDLs and gaskets are used to compensate for eventual unevenness or misalignment on the pedestal surfaces. For both NWs and NTs, once the pressing process is over, we recover the membrane gently with silicon substrate stuck into it. The latter is washed in sulfuric acid H2SO4 0.

Single cell and operating conditions

The MEA were placed in differential fuel cell that allows studying under homogeneous and well-defined conditions for in-depth electrochemical characterization in representative operating conditions.

Single cell

The fabricated MEA was tested under homogeneous and well-defined conditions of relative humidity (RH), cell temperature, and gas flow as demonstrated by Fontana et al. [START_REF] Fontana | Direct growth of carbon nanotubes forests on carbon fibers to replace microporous layers in proton exchange membrane fuel cells[END_REF]. The active area of the flow field is 1.8 cm². Reduced dimensions and high stoichiometric ratios characterize this type of cell. A differential cell's purpose is not to be operated as a technical device but to emulate the local conditions of a larger device and study the effect of different operating parameters at a local scale without the disturbance of along the channel effects [START_REF] Oberholzer | Local Characterization of PEFCs by Differential Cells: Systematic Variations of Current and Asymmetric Relative Humidity[END_REF].

Graphite flow fields with multi-straight and parallel channels are used on both the anode and the cathode side.

Operating conditions

The cell was mounted in an in-house test stand that allows a precise control of the conditions protocol during operation, as summarized in

Conditioning

Prior to testing, the MEA was pre-conditioned (break-in step) via voltage cycling using a labdeveloped protocol as referred in Support Information SI 2. The MEA conditioning was carried out in H2/O2 at 1.5 bar and relative humidity of 100% (fully humidified gases) at 80°C for several hours to reach the maximum performance of the cell.

Electrochemical characterisations

Electrochemical surface area measurement

Cyclic Voltammetry (CV) measurements are performed in order to determine the specific electrochemical surface area. It refers to the catalyst's surface area in contact with the electrolyte, accessible to protons from the membrane, and electrically connected to the current collector. The experiment was carried out at 80°C with a Biologic © potentiostat monitored by the EC-Lab program, with a fully humidified flow of H2 and N2 at the electrode that is used as the anode and at the cathode in fuel cell operation, respectively.

The roughness is calculated from hydrogen desorption coulometry after underpotential deposition (HUPD) and determined according to the following expression (equation 1). Further details are expressed in Support Information SI 3.

𝑹𝒐𝒖𝒈𝒉𝒏𝒆𝒔𝒔 = 𝑸 𝒅𝒆𝒔

𝟎.𝟐𝟏 × 𝑺 𝒆𝒍𝒆𝒄𝒕𝒓𝒐𝒅𝒆 Equation 1

where: -Selectrode refers to the real geometric surface area of the electrode in cm²geo;

-Roughness: in cm²Pt/cm²geo; -Qdes: charge obtained by integrating the dashed blue area in C.

Ohmic resistance measurements

The ohmic resistance as a function of RH was measured thanks to impedance measurement at different relative humidity under H2/N2, as for ECSA measurements. Potentiostatic Electrochemical Impedance Spectroscopy (PEIS) measurements were held from 200kHz to 100Hz at 0.4VRHE, where no adsorption/desorption reactions are observed in this region, as confirmed by the absence of redox peaks in the CV. We performed measurements in a potentiostatic mode, where a perturbation around a fixed value of voltage (10mV) is applied.

Simultaneously, its current response is measured (the amplitude of the applied signal should be small to be in the linear regime). Considering the PEIS experiments carried out in this work and the very thin CL used in cathode, we could not dissociate the losses related to protons transport through the active layer. Thus, we will settle for the high-frequency resistance (the value of impedance for which the imaginary part is equal to zero at high frequency) to quantify the ohmic resistance of the cell Rohmic.

We will settle for the high-frequency resistance (the value of impedance for which the imaginary part is equal to zero at high frequency) determined by PEIS at 0.65VRHE to correcting the polarization curves from the ohmic drop, and to compare the performance accurately (refer to Support Information SI 2 for further details).

𝑬 𝒄𝒆𝒍𝒍,𝒊𝑹-𝒇𝒓𝒆𝒆 = 𝑬 𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅 + 𝑹 𝑶𝒉𝒎 . 𝒋

Equation 2

Where Ecell,iR-free is the ohmically-corrected potential, Emeasured is the measured cell potential, Rohm is the ohmic resistance, and the j is the current density.

Results

PtNiNTs and PtNiNWs fabrication and structure

Anodic Alumina Oxide (AAO) fabrication

In order to obtain straight aligned and organized Pt-Ni nanowires and nanotubes, we leaned out to use tuned mold-based templates made of aluminum oxide. To that end, several steps are required to obtain the desired structure of the anodic alumina. The first step will consist of the manufacturing of the nanoporous alumina template with vertically oriented organized pores.

Its design will govern the final organization of the electrode. Tuning the parameters of anodization, the achieved template will be used as a mold for the growth of the nickel nanowires, which are considered precursors for the PtNi nanotubes.

Here, we report the process of double anodization after optimization to obtain nanostructures with the desired dimensions, ranging from 50 to 150 nm in pores' diameter and 0.1 to 1 µm in depth. A detailed fabrication process was described exhaustively elsewhere ii. Nanopores initiation and growth of parallel nanochannels;

iii. Wet etching process in an acidic solution, which leads to the formation of hollow and ordered nanocells.

By tuning the anodization parameters, which directly impact the kinetics of the pores' formation, we tend to control the thickness of AAO, which would be the final length and diameter of the nanowires when grown onto the matrix. The first anodization has two main interests: i/ removing a controlled thickness of aluminum and ii/ obtaining a pre-patterned aluminum surface after the wet etching. The latter, performed in the right conditions, would predict the final pores' size (i.e., porosity and density).

In our experiment, we used the mild double anodization process as described by Masuda et al. As evidenced in the literature, the etching rate is dependent on the chemical composition of the pore wall oxide of AAO [START_REF] Han | In Situ Determination of the Pore Opening Point during Wet-Chemical Etching of the Barrier Layer of Porous Anodic Aluminum Oxide: Nonuniform Impurity Distribution in Anodic Oxide[END_REF]. More details about the evolution of pore diameter (Dp) are referred in Supporting Information SI 5.

Figure 6 below exhibits the AAO template obtained by double-anodization process with almost uniform pores' size throughout this work alumina phase transformation (i.e., crystallization) to γ-alumina, which is resistant to chemical etching [START_REF] Marsal | Fabrication and optical characterization of nanoporous alumina films annealed at different temperatures[END_REF]. Also, since we are using an Al/Si substrate, annealing temperature should not reach the aluminum melting point (~650°C) to create AlSi alloy during thermal treatment. For such conditions, the annealing temperature is therefore chosen to be 450°C. This step is mandatory and provides a framework onto which we can not only reduce organic contaminants and anions from the electrolyte (oxalate and phosphate anions) incorporated in nanoporous alumina [START_REF] Nielsch | Self-ordering Regimes of Porous Alumina: The 10 Porosity Rule[END_REF] but also to get rid of water molecules which can, thereafter, react with vapor HF during deoxidation step.

Nickel nanowires (NiNWs) confined growth inside AAO

Nanoporous aluminum oxide was found to be ideal for the growth of dense nanowire arrays, providing ordered, parallel, and uniform pore channels with a high aspect ratio and mechanical support to fragile nanowires [35][36].

In this study, we have chosen the pulsed electrochemical deposition (PED) in an aqueous solution for NiNWs growth. PED's main advantages, which allowed better control over the deposition parameters and the length of NiNWs, rely on its flexibility to adjust the amplitude and duration of the voltage pulses. It offers the possibility of introducing a delay pulse to refresh the metallic ions concentration at the deposition interface, promoting uniform nanowire growth [START_REF] Nielsch | Uniform Nickel Deposition into Ordered Alumina Pores by Pulsed Electrodeposition[END_REF].

Prior to electrodeposition, the electrical contact at the bottom of the pores is not homogeneously ensured due to the silicon electrochemical oxide formed at the end of anodization. A silicon deoxidization step by vapor HF was added to the process to overcome this issue (Supporting Information SI 6). Figure 7 below shows the homogeneous deposition of NiNWs inside the AAO template. Nickel nanowires were grown in AAO mold, using the Watts bath solution: a mixture of 300 g/L NiSO4.6H2O, 45 g/L NiCl2.6H2O, and 45 g/L H3BO3 as a buffer [START_REF] Benaben | Electrolytic nickel coating[END_REF][38] (see Supporting Information .

The magnetic stir bar was put in the container containing the solution to be stirred at 35-40°C.

The pH of the solution was measured to be 4. It has been suggested that boric acid stabilizes the pH and enhances metal deposition.

To perform Ni PED, the sample is maintained inside an adequate homemade electrochemical cell (same electrochemical cell as the one used for aluminum anodization) where the electrical contact between the electrolyte and the working electrode is ensured at the bottom of nanopores on the conductive silicon substrate.

Finally, the electrodeposited nickel into porous alumina templates created ordered nanowires as depicted in figure 8-a-b andc). Pulsed currents helped improve the deposits' quality by smoothing surface may be due to Ni oxidation, and allowing good adherence to the substrate).

The deposition time was varied to control the length of the nanowires. The slight difference in NiNWs length in figure 8-c) is attributed to the aluminum deposition's surface unevenness on silicon.

PtNiNTs fabrication

On the other hand, the elaboration of PtNiNTs has followed a different process. Firstly, the self-standing NiNWs on Si were dipped in a Potassium tetrachloroplatinate (K2PtCl4) solution without HCl at 80°C for 90 minutes (details were given in Support Information SI 9 -PtNiNTs Fabrication).

After several sets of experiments regarding the temperature's effect, we noticed that temperature has a significant effect on the rate of the reaction. Once the experiment is over, the sample was rinsed in distilled water. The PtNiNWs were analyzed by TEM (figure 11). The Ni and Pt X-EDS elemental maps (figure 11) reveal that the reaction had led to the deposit of a thin layer containing Pt of ~4-5 nm onto the Ni nanowires. A higher magnification HAADF/STEM image coupled X-EDS analyses of a single PtNiNWs was performed (figure 12). These analyses clearly reveal an oxide shell serving as a Ni protective shell from the deposition of Pt cations during the reaction, which might inhibit the GD reaction to take place. From this analysis, we can conclude that PtCl4 is likely to be deposited instead of pure Pt as demonstrated by the presence of Cl. Once the PtNi nanowires were entirely transferred to the ionomer membrane, the latter is then immersed in the 0.5M sulfuric acid solution for dealloying (acid leaching process), reacidifying the membrane, and helps to tear off gently the polymer from the silicon substrate.

For the acid leaching (AL), however, the goal was not to remove all the nickel but the soluble nickel of the PtNiNWs that was not alloyed to the Pt. Finally, after AL, we obtain a forest of well-organized PtNiNTs on the membrane as can be seen in figure 14. To sum up, several steps were involved in the formation of PtNiNTs (figure 16). In Supporting Information (SI 9) section, we stated in detail the experimental process alongside TEM and XRD analysis.

The synthesized electrodes will further be transferred to MEA then evaluated and applied as the cathode catalysts for a single differential cell.

The SEM images in figure 17 show the cathode's final self-supported nanostructures after the complete integration of PtNiNWs and PtNiNTs on the Nafion ® HP membrane. We designed the PtNi nanostructure to reach a Pt loading of about 0.1 mg/cm² for the PtNi nanotubes, with a diameter of 50 nm, which defined the final length of the nanostructures being about 250-300 nm. We chose this dimension so as the inner diameter of the tubes is around 30 to 40 nm that corresponds roughly of the size of the secondary pores in the conventional Pt/C nanostructure.

Pt loading of PtNiNWs and PtNiNTs electrodes is respectively 100 and 15 µg/cm². Thus, the final loading of the nanostructure is far lower than calculated considering bulk structures. This means that the PtNi nanowires and the walls of the PtNi nanotubes are porous and are made of PtNi alloy nanoparticles, as shown on SEM and TEM images.

The Pt loading of the PtNiNWs and PtNiNTs can be tuned by changing the diameter, length, of the nanostructure, the composition of the PtNi. However, these parameters are not independent and changing the dimensions of the nanostructure will induce modification of the size and composition of the PtNi nanoparticles that make the tubes.

The synthesized electrodes are transferred to the membrane to obtain an MEA, and then evaluated as the cathode in single differential cell tests.

PtNiNWs and PtNiNTs performance and stability vs conventional Pt/C electrode

This part will depict the electrochemical characterizations in relevant operating conditions of the MEA made of conventional Pt/C catalyst at low Pt loading, PtNiNWs, and PtNiNTs as cathodes. Studies have been completed and intended to quantify the performance compared with standard Pt/C electrodes and quantify the activity and transport limitations in different operating conditions, especially in dry or wet conditions. The robustness towards the accelerated stress test has also been evaluated.

Electrochemical surface area

In our experiment performed on the Pt/C, PtNiNWs and PtNiNTs electrodes whose Pt loading is respectively 35, 100 and 15 µg/cm². The roughness reads about 7.3 cm²Pt/cm²geo, 6 cm²Pt/cm²geo and 3.7 cm²Pt/cm²geo, respectively, as displayed in figure 18 (a-c) below. The difference in the shape between the CV obtained with PtNiNWs and PtNiNTs on figures 18b and 18c respectively indicate that the nanostructure of the PtNi nanoparticles, that is to say size, shape and crystalline orientations most probably differ between the two electrodes.

MEA performance

In this work, and after conditioning, we have tested the fuel cell's performance under wet H2/O2 gas flow at different relative humidity values at 80°C, by keeping the partial pressure of O2 at the inlet constant.

We compared performance of each MEA at different relative humidity. Polarization curves for Pt/C, PtNiNWs and PtNiNTs were recorded at 80°C in H2/O2 and H2/Air at 80% RH and 100%RH, at a total pressure of 1,5 bar and 1,38 bar, respectively. The ohmic resistance decreases as RH increases thanks to the enhancement of proton conductivity of the ionomer upon hydration.

Thus, the polarization curves were corrected from the derived ohmic resistances from EIS measurements as depicted in figure 19 below. Therefore, the only difference in performance is due to the operation of the electrode that depends on the activity of the catalyst and on its utilization related to the O2 and H + transport limitations.

Comparison under O2:

From the polarization curves, we notice that the RH affects the PtNiNWs and PtNiNTs electrodes' performance, while the Pt/C electrode is much less impacted. The performance of the PtNiNWs decreases significantly from 100% to 80% RH at low current density, below 0.8 A/cm². This is ascribed to a decrease in the use of the catalyst surface area due to H + transport limitations. Indeed, there is no ionomer on the ~250 nm long PtNiNWs. At 100%RH, one can expect proton transport on the surface of the hydrated catalyst (NWs/NTs) up the end of the reduced length nanostructure, that-is-to-say close to the GDL, even in the absence of ionomer thanks to proton transport phenomenon similar to that suspected to rule the operation of NSTF, as described by Eikerling [START_REF] Chan | A Pore-Scale Model of Oxygen Reduction in Ionomer-Free Catalyst Layers of PEFCs[END_REF], or Zenyuk [START_REF] Medici | Understanding Water Transport in Polymer Electrolyte Fuel Cells Using Coupled Continuum and Pore-Network Models[END_REF]. In the absence of ionomer, the amount of water content on the surface of the catalyst is most probably significantly reduced at 80%RH, if exists. Thus, the proton transfer must be drastically limited in this condition resulting in electrochemical reaction restricted to the area very close to the membrane surface where there is ionomer, namely on a much lower surface than at 100%RH. 20).

At 80%RH, the PtNiNTs electrode has the lowest voltage below 0.2 A/cm² but gives the best performance above 0.8 A/cm², while the PtNiNWs electrode is the least performing at high current density. It shows here how sensitive to RH these nanostructures are, which has also been reported for NSTF [START_REF] Debe | Nanostructured Thin Film Electrocatalysts -Current Status and Future Potential[END_REF]. These results also emphasize the potential interest of PtNiNWs or PtNiNTs electrodes depending on RH. More results of the effect of RH at the Anode and Cathode respectively are described in the supplementary information. The best performance was achieved at 100% RH for Pt/C, and PtNiNWs, and 80%-100% RH (anode and cathode, respectively) for PtNiNTs.

Comparison under Air:

The performance of the electrodes were also compared under Air (figure 20). If the current density for a given voltage is much lower than under pure O2 due to the five times reduced oxygen partial pressure, the overall trends are similar. Compared to PtNiNTs electrode, The PtNiNWs electrode shows the best performance above 0.75V, so at low current density, but seems the more sensitive to flooding, while the PtNiNTs electrode shows the opposite trend and offer the best performance, better than Pt/C, below 0.6V. Compared to PtNi NSTF electrode having a much higher Pt loading and a loading of about 0.125 mgPt/cmgeo² and 20 cm²Pt/cm²geo, respectively, and which results from more than two decades of considerable efforts of research and development, our electrodes show lower absolute performance in similar operating conditions (80°C, under Air and 60%RH) [START_REF] Steinbach | Recent Progress in Nanostructured Thin Film (NSTF) ORR Electrocatalyst Development for PEM Fuel Cells[END_REF]. However, the maximum current per specific surface that can be drawn from PtNiNTs electrodes is about 0.15 A/cm²Pt, that is about 2 times higher than for NSTF. It seems to indicate that the oriented nanotubes architecture allows better O2 accessibility compared to nanowires or nanowiskers architectures, and makes this nanostructured electrode less sensitive to flooding.

Effect of Accelerated Stress Test on performance

Not only the performance of the electrodes was compared but also the stability upon Accelerated Stress Tests (AST).

The AST test was inspired from "AST Protocol from the DOE", as described by the DOE [START_REF]Multi-Year Research, Development, and Demonstration Plan, Protocols for Testing PEM Fuel Cells and Fuel Cell Components[END_REF] (figure 21-a). Drawing upon the degradation of the catalyst layer at the cathode side, the purpose of this study was to assess its durability under harsh conditions: 50K square wave potential cycles from 0.6 VRHE to 1.0 VRHE during 3 s, at a Tcell of 80°C, under H2/N2 at 100% RH and a total pressure of 1 bar. In this potential range, platinum oxidation and reduction occur, causing dissolution and redeposition of the catalyst, inducing low carbon corrosion (which takes place at a higher potential range >1.2 VRHE).

Cyclic Voltamperometry (CV) measurements were conducted at 80°C, 100%RH before and after AST, as shown on figure 21-b, c andd. However, there are so many coupled electrochemical and physical processes that govern the performance that the comparison of the raw polarization curves of electrodes differing in the type of catalyst, nanostructure and specific electrochemical surface area can hardly allow understanding the causes of the limitations. As a first step to estimate the interest of PtNiNTs and PtNiNWs, it is beneficial to compare specific and mass activities of these electrodes and their evolution upon AST. This result is not really surprising considering that the PtNiNWs behave probably similarly to bulk material that shows better specific activity compared to nanoparticles. This PtNi-based electrocatalyst nanostructure shows improved activity compared to Pt/C, as expected from the different studies in the literature. However, the enhancement compared to Pt/C, being about 13 times and 60% for specific and mass activities, respectively, before AST, that is modest compared to what has been previously reported for this latter value.

PtNiNTs electrode shows both lower specific and mass activity compared to Pt/C and PtNiNWs at the beginning of the test. There could be two explanations for that. First, while all the electrochemical surface area of the PtNiNTs can be probed using Hupd, a significant part might not be accessible to O2, as about a 25% of the length of the NTs is impregnated into the membrane as shown in figure 15. Thus, the ECSA overestimates the real active surface area, leading to an underestimation of the specific activity. Second, it is known that for most of the PtNi nano-electrocatalyst, an in-situ dealloying step, in addition to the acid leaching after synthesis, is necessary to reach the maximum performance. The non-dealloyed catalyst can show poor activity. This is probably the case for our PtNiNTs as both the specific and mass In this context, this paper offered a fresh and broader perspective for NTs (with post-processing optimization) as a promising route to be more investigated. Further experiments on larger nanotubes arrays are needed to better understand the behaviour of these structures. The integration of ionomer while increasing the surface area, GDL optimization and integration of an intermediate layer between the electrode and the GDL, as for NSTF could help to limit or avoid flooding at high relative humidity.

Figure 1 .

 1 Figure 1. Scheme of the cross-section of an oriented carbon-free PtNi nanotubes (PtNiNTs) arrays transferred onto the Nafion ® membrane.

Figure 2 .

 2 Figure 2. Methodology of the elaboration process of PtNi nanowires and nanotubes.

Figure 3 .

 3 Figure 3. Schematic illustration of the hot-pressing process used to integrate the supported PtNiNWs and PtNiNTs electrodes on the Nafion ® HP membrane.

[ 21 ]

 21 [START_REF] Lee | Porous Anodic Aluminum Oxide: Anodization and Templated Synthesis of Functional Nanostructures[END_REF][23][START_REF] Masuda | Highly ordered nanochannel-array architecture in anodic alumina[END_REF][25][START_REF] Gorisse | Highly organised and dense vertical silicon nanowire arrays grown in porous alumina template on <100> silicon wafers[END_REF][27][28][29]. The anodization process follows a multi-step procedure to obtain the desired geometry of nanoporous AAO templates: i. Formation of massive alumina layer at the beginning of the process;

[ 29 ]

 29 as shown in figure 4. It is used for highly ordered and homogeneous templates at a slow rate growth of nanochannels. It exhibits low current density at a fixed voltage (i.e., low anodizing potential) and a low concentration of acidic solution.

Figure 4 . 5 .

 45 Figure 4. Scheme of the two-step anodization process for the fabrication of a nanoporous alumina template, where the green side refers to the Silicon substrate and the black bulk to aluminum layer. A) formation of irregular AAO pores after 1 st anodization, B) first AAO etching in orthophosphoric acid leaving nanobowls on the aluminum surface, C) regular pores formation after 2 nd anodization and D) pores widening process in orthophosphoric acid.

Figure 5 .

 5 Figure 5. Electrochemical cell setup used for anodizing aluminum on p-type silicon substrate (Left picture) and 3D model of the PVC cell (right picture) composed of: a) Stirrer, b) PVC core, c) Metal cap that ensures electrical contact and mechanical cohesion between the cell and the sample (electrode), d) Flowing cooling Liquid system to adjust the temperature of the electrolyte, e) Cylindrical platinum gauze as counter-electrode.

Figure 6 .

 6 Figure 6. A scanning electron microscope (SEM) image of the nanoporous anodic aluminum oxide fabricated during this work through the double-step anodization process in 3%wt oxalic acid, under potentiostatic regime, with an applied voltage of 34 V at 23°C.

Figure 7 .

 7 Figure 7. SEM micrographs of top view a) homogeneous NiNWs inside alumina template and a crosssectional view b) of NiNWs growth inside anodic aluminum oxide, with HF deoxidation step, which is mandatory to obtain homogenous NiNWs deposit.

Figure 8 .

 8 Figure 8. Scanning Electron Microscopy (SEM) observations of Nickel nanowires grown inside porous anodic alumina template (PAAT), a) SEM top view of Nickel nanowires before alumina etching, b) SEM Top view of Nickel nanowires after alumina etching, and c) SEM cross-sectional view of Nickel nanowires after alumina etching.

Figure 9 .

 9 Figure 9. SEM cross section view (a) and top-view (b) structural characterization of PtNiNWs after exposing NiNWs/Si to a K2PtCl4 solution in 0.05 M HCl at 35°C for 8 minutes.

Figure 10

 10 Figure 10 below summarizes the reproducible fabrication process of PtNiNWs as follows:

Figure 10 .

 10 Figure 10. Schematic illustration of various stages involved in fabricating PtNi nanowires.

Figure 11 .

 11 Figure 11. HAADF/STEM image and the associated Pt and Ni X-EDS elemental maps for PtNiNWs (intermediate step before the formation of PtNiNTs) Pt species are in red, and Ni species are in green.

Figure 12 .

 12 Figure 12. a) HAADF/STEM images and the associated Pt, Ni, O and Cl X-EDS elemental maps of the PtNiNWs as-synthesized (without HCl addition), obtained after galvanic displacement in K2PtCl4 at 80°C. Red mapping refers to Pt, Green mapping refers to Nickel, Light-green mapping refers to

Figure 13 .

 13 Figure 13. A schematic diagram of the annealing process in RTA (Rapid Thermal Annealing) temperature.

Figure 14 .

 14 Figure 14. SEM image of top view of PtNi nanotubes transferred to Nafion ® membrane after acid leaching.

Figure 15 .

 15 Figure 15. a) a) HAADF-TEM image and associated X-EDS Pt, Ni and F elemental maps of the porous PtNiNTs embedded onto the Nafion ® membrane. b) The corresponding Pt and Ni elemental maps showing gradient of composition and the Ni and Pt composition quantified in the two different areas.

Figure 16 .

 16 Figure 16. A schematic illustration of the complete process of the steps involved in the elaboration PtNi nanotubes.

Figure 17 .

 17 Figure 17. SEM images of top-view of the sample a) PtNiNWs and b) PtNiNTs array structures transferred onto the Nafion ® membrane by the hot-pressing process.

Figure 18 .

 18 Figure 18. Cyclic voltammograms (CV) of a) Pt/C, b) PtNiNWs and c) PtNiNTs, recorded in fully humidified H2/N2 gas flow from 0.1 VRHE to 1.2 VRHE at 80°C with a sweep rate of 200mV/s.

Figure 19 .

 19 Figure 19. Comparison of fuel cell's ohmically-corrected polarization curves of Pt/C, PtNiNWs and PtNiNTs cathodes at operating conditions in the order of anode/cathode in H2/O2, a cell temperature of 80°C, at a) 100% RH and 1.5 bar, and b) 80% RH and 1.38 bar.

Figure 20 .

 20 Figure 20. Comparison of H2/Air polarization curves for the low-Pt loading cathode Pt/C (black), PtNiNWs (red) and PtNiNTs (blue).

Figure 21 .

 21 Figure 21. a) Cell voltage vs. time during voltage cycling from 0.6 VRHE to 1.0 VRHE to fasten the dissolution of Pt. Comparison of voltammograms before degradation and after 50K cycles conducted in H2/N2 at 80°C and relative humidity of 100% and a total pressure of 1 bar, recorded at a potential sweep rate of 200 mV/s, for b) Pt/C MEA, c) PtNiNWs MEA and d) PtNiNTs MEA.

Figure 22 .

 22 Figure 22. Comparison of fuel cell's ohmically-corrected polarization curves of Pt/C, PtNiNWs and PtNiNTs MEAs at operating conditions in H2/O2, cell temperature of 80°C, at different relative humidity values and total pressure (in the order of anode/cathode: 100% RH and 1.5bar, 80%-100% RH and 1.38-1.5 bar), before and after 50K load cycles.

4. 2 . 4

 24 Activity before and after AST To have a better insight into the performance and stability of the electrodes, figure 23 summarizes the evolution of the specific activity (SA) (a) and mass activity (MA) (b) at 0.8 VRHE, the ECSA (c) and the roughness (d), before and after AST. Interestingly, PtNiNWs have shown the best specific activity while PtNiNTs have shown the highest mass activity, but only after AST.

  activities are strongly enhanced after AST. The comparison of activities has demonstrated noticeable stability of PtNiNTs compared to PtNiNWs and Pt/C toward AST cycles as depicted in figure 23-c and d below.Table S4 in support information sums up the comparison between our tested electrodes and NSTF electrodes.

Figure 23 .

 23 Figure 23. Comparison of the tested MEAs in this study (Pt/C, PtNiNWs and PtNiNTs as cathodes) before degradation and after 50K potential cycles in H2/O2. Data recorded at EiR-free=0.8 VRHE.: a) Specific Activity before and after degradation, b) Mass Activity before and after degradation, c) ECSA before and after degradation, d) Roughness before and after degradation, e) Current density at 0.8VRHE before and after degradation, and f) Platinum Surface before and after degradation. All resulted were obtained at 80°C, 1.5 bar, 100%RH.

see Erreur ! Source du renvoi introuvable.).

	sprayed onto the PTFE substrate. We quantified the Pt loading by two methods: UV-Visible
	Spectroscopy and X-ray Fluorescence spectroscopy (XRFS). Both techniques demonstrated a
	final loading of about 35-40 µgPt/cm².
	3.5 MEA preparation
	3.5.1	Half Catalyst Coated Membrane (CCM) with Pt/C electrode
	The Pt/C electrode on its PTFE substrate was transferred on the Nafion ® membrane by hot-
	pressing at 150°C and 2 MPa for 10 minutes. The so-obtained half Catalyst Coated Membrane
	(CCM) was integrated in MEA. The active area for the Pt/C electrodes is 1.8 cm² equals to that
	of the flow field of the cell (3.5.2 Half Catalyst Coated (CCM) with PtNiNWs and PtNiNTs electrodes
	The cathode-type Pt/C catalytic ink was prepared by mixing: 0.7g of catalyst powder
	TEC10V50E (47.2 w%Pt Tanaka ® Pt NPs (~3 nm) deposited onto carbon support Vulcan XC72
	(~40-50 nm)), 4.5 g of Nafion ® solution D520, 20 mL of Propanol as a solvent and 20 mL
	Ultrapure water 18.2 MΩ.cm. The ink preparation was held in a glovebox because of safety
	issues related to the handling of nanopowders. The weight ratio between ionomer and carbon
	is 67%. After the dispersion, the ink was stirred for 72 hours with a magnetic stirrer.
	Before depositing the ink onto a Poly-tetrafluoroethylene (PTFE) (250 µm) substrate, the ink
	was premixed in a sonicator bath beforehand for 10 minutes at room temperature to improve
	its homogeneity. Using the ultrasonic coating process provided by Sono-Tek © the ink was

Table 1 .

 1 active area allow to check that the difference in temperature between the anode and cathode plates is negligible, namely less than 0.2°C. During the test, the active gases used are Air or Oxygen at the cathode and Hydrogen at the anode. Operating conditions for testing differential cells.

	Experimental values

table 1 below. The cell temperature is controlled via circulation of hot water on both anode and cathode plates. Thermocouples placed very closed to the

  At higher current density, above 0.8 A/cm², the increase in water production probably leads to local water condensation in or close to the catalyst layer even at 80%RH in the channel. The proton conduction path would then be restored allowing reaching better performance at 80% RH than at 100% RH, probably because of the lower O2 transport limitations in GDL less saturated with liquid water. This phenomenon is not observed in the Pt/C based electrodes that contain ionomer. Regarding the PtNiNTs electrodes, that is also free of ionomer, if a decrease in voltage is observed from 100% to 80% RH for current density lower than 0.2 A/cm², the performance is much better at 80% RH than at 100% RH above 0.2 A/cm². This electrode seems to very sensitive to flooding compared to PtNiNWs when reaching high relative humidity but is able to keep some hydration at low RH maybe thanks to capillary condensation in the porous wall of the tubes or in the inner of the tubes. When comparing the performance of the electrodes at 100% RH, one can see that the PtNiNWs electrodes perform better at low current density than the two others, but its performance decreases drastically above 0.6 A/cm².

	The best performing in this condition is the Pt/C electrode, while the PtNiNTs shows the lowest
	performance. Similar performance with low loaded Pt/C electrode can be found in the
	literature, as demonstrated by Liu et al. who reported better performance with 20wt% Pt/C
	catalyst from JM with a loading of 50 µg/cm² under pure O2 Erreur ! Source du renvoi
	introuvable.. With such Pt loading, and roughness, the performance dramatically decreases in
	air (Figure

AUTHORS INFORMATION

Corresponding author: arnaud.morin@cea.fr

Email

ASSOCIATED CONTENT

Supporting Information

The Supporting Information is available free of charge on the ACS Publications website at DOI: XXXXXX.

-Anodic Alumina Oxide template fabrication -Details on manufacturing and characterisations of the PtNiNWs and PtNiNTs electrodes -Corrected and uncorrected polarisation curves under O2 and Air Get the PDF from here.

ACKNOWLEDGMENTS:

This work was supported by CEA Grenoble and Université Grenoble Alpes. Authors want to thank PTA and BCAi for clean room facilities. Also, authors are thankful for LCP lab for complete fuel cell facilities and INAC lab for materials' elaboration apparatus and structural characterization.


Patrice Salzenstein
email: patrice.salzenstein@femto-st.fr

David Bassir
email: david.bassir@cmla.ens-cachan.fr

David Perez De Lara
email: david.perezdelara@gtiit.edu.cn

Fiber to resonator coupling multicriteria optimization with COMSOL multiphysics

Keywords: Optical resonator, Coupling, optimization, COMSOL wave guide

In this paper, we discuss the principle of coupling an optical signal to an optical resonator. We give the broad outlines of the principle and the experimental parameters then we look at how to optimize this coupling using finite element simulations on COMSOL software. Simulation of the coupling is based on straight and ring waveguides placed very close to each other so the waveguide can be transmitted from one to other.

INTRODUCTION

We have seen that optical resonators with a very high quality factor, at least 100 millions, are useful for various types of applications in metrology, sensors or oscillators [1 -5]. Studies in the literature concerning the modeling of coupled device based on optical fiber with crystalline resonators which involve the aspect of simulation and optimization [1 -7]. It is also necessary to take into account the technological constraints of manufacture for the coupling [START_REF] Salzenstein | Electrically driven thermal annealing set-up dedicated to high quality factor optical resonator fabrication[END_REF]. The first step of multi-criteria optimization shows that we can simulate and then find an optimal design. The sensitivity analysis shows a relatively good correlation between the experimental Q factor obtained, and that obtained with the simulation by the finite elements. This optimization process incorporates certain constraints related to the manufacturing process, and to the thermal analysis of the resonator. However, some parameters require a domain which is non-continuous, it is chosen between fixed positions, but this makes the convergence more complicated to achieve. We therefore focus on the implementation of the experimental concept and on the coupling of crystalline resonators under a straight waveguide and the simulation is based on the multi-physics software COMSOL [9 -11]. We present simulation results and also the comparison with the experiment.

COUPLING OF A RESONATOR TO A GUIDE

Need to couple the optical resonator

If we want to mount optical resonators in oscillator mode, or if it is simply necessary to characterize it, it is necessary to proceed by coupling. An optical resonator considered as a cavity could be ideal if we had a totally closed system being isolated from the world outside. The propagation of a signal inside this cavity could then correspond to a high and intrinsic quality coefficient of the resonator. Nevertheless, in reality, an optical resonator, i. e. a resonant cavity, is not a closed system at all. We must measure its quality coefficient parameters. However, it is obvious that any external intervention could break the insulation of a cavity. It is necessary to be able to inject and of course recover the information. The main objective is to inject an optical signal inside the cavity. Figure 1 shows how a resonator is to an optical tapered fiber. There are of course other methods to inject a signal. What comes to mind first is to illuminate the cavity with lighting of which the power would be quite significant. However, this method could not highlight the strong quality coefficients, which, at the opposite, require a certain finesse. There is the possibility of sending a signal by using a prism, which is convenient in the case of a compact and robust component. We could also use a tapered fiber or tip, which approaches the resonator sufficiently closer to be able inject signal in the resonant cavity. The method we find easier to do in the lab is to use a stretched and tapered fiber. We first remove the sheath of the fiber, then we stretch from each end, performing this stretch under a flame [START_REF] Salzenstein | Experimental study of a crystalline-resonator based optoelectronic oscillator[END_REF]. We therefore act on the principle that the resonator is coupled to a tapered fiber. (e,L) refer respectively to the thickness and to the width of the Si3N4 microring and the ridge. (D, g) refer respectively to the diameter and to the gap between the Si3N4 microring and the ridge. N-C (Not Known) show that the parameter was not described or listed in the reference.

Main active parameters

In Table 1, we give the typical parameters that are involved in the comparison of the Q factor for optical resonators of micro disk type. They are all silicon nitride on a silicon chip so they are better comparable.

Unfortunately, not all references describe and give full details of their experiences. However, it is very interesting to give a narrow range of variation of the factor Q obtained as well as the associated parameters such as the thickness, the diameter and the width of the micro ring Si3N4 and of the ridge. Authors at Cornell University have obtained a good Q-factor with a propagation loss within the ring equal to 4.2 dB/m and we estimate the absorption loss to be 71%.

3. Main parameters for the crystalline material: MgF2 and Ca F2:

For analysis, we select two materials. The first material is the Magnesium Fluoride (MgF2), which is characterized by its refractive index, for the ordinary and extraordinary ray between (No, Ne) respectively equal to 1.37 and 1.38, for a Transmission Range between 0.12 and 8.5 µm. The MgF2 is density is 3.148g/cm 3 . The second material is the Calcium fluoride (CaF2), which is characterized by it is refractive index for the ordinary and extraordinary ray between (No, Ne) respectively equal to 1.42 and 1.44 with a Transmission Range between 0.2 and 9 µm. The CaF2 is density is 3.18g/cm 3 . Typical parameters are involved in the Q-factor comparison for the silicon nitride micro-rings and ridge on a silicon chip. We have reported the results in reference [START_REF] Bassir | Optimal design of a crystalline and integrated resonator coupled with optical fibre[END_REF]. A number of references give a more accurate picture of typical parameters [13 -16]. Thickness is between 320 nm and 910 nm. Width of the Si3N4 micro-ring vary in the range of 500 nm to 1.8 µm, when diameter of the ring vary from 20 to 115 µm. Gap between the Si3N4 micro-ring and the ridge is in between 160 and 680 nm. Figure 1 gives a better understanding of the various parameters mentioned for coupling to a micro-ring. Q-factors are up to 7x 10 6 . Cornell University have obtained a good Q-factor with a propagation loss within the ring equal to 4.2 dB/m and we estimate the absorption loss to be 71%. These performances are interesting. However, it is clear that the micro-rings quality factors are not as high as are those obtained with crystalline resonators. We concretely have selected two different materials for the sensitivity analysis. The first one is Magnesium Fluoride (MgF2). It is characterized by it is refractive index. For the ordinary and extraordinary ray between (No, Ne), it is respectively equal to 1.37 and 1.38 with a transmission in the range 0.12 -8.5 µm. Density of MgF2 is 3.148g/cm 3 . The second chosen material is Calcium fluoride (CaF2). Its refractive index for the ordinary and extraordinary ray between (No, Ne) is respectively equal to 1.42 and 1.44. Its transmission is in the range 0.2 -9 µm. Its density is 3.18g/cm 3 .

MODELLING OF THE COUPLED DEVICES

We look at the coupling between a thin fiber and a resonator. One can refer for the coupling of resonators to a paper, which concerns another type of resonator, the micro-spheres [START_REF] Salzenstein | Coupling of high quality factor optical resonators[END_REF]. We can make some analogies between the propagation of an optical signal and that of a microprobe signal along a coplanar line [START_REF] Salzenstein | Coplanar waveguides on dielectric membranes micromachined on GaAs substrate[END_REF]. The design problem that has been studied in order to maximize the factor (Q) is described in the figure 2. The value d1 refer to the gap between the fiber and resonator (which should be less that the λ in the center of the fiber), d2 is the optical fiber diameter, d3 is the inner diameter of the resonator, and d4 is the external diameter. Modelling is based on the following references [20 -24]. Because of the optical symmetry and the Gallery mode in the resonator, we assume that the main phenomena will take place at the close circumferential structure of the resonator disc. For the Final element modelling, we reduce the study at the circumference area of the resonator. In the following simulation, we have included the discontinuity at the boundary between the straight waveguide and the ring waveguide. This integration of the phase discontinuity and thereby the discontinuity in the field envelope, E1, a Field Continuity boundary condition is used at the boundary between the straight waveguide and the ring waveguide. Parameters are given on Fig. 3. Tangential components of the electric and the magnetic fields are then continuous at the boundary, despite the phase jump. Incident and transmitted/coupled fields are obtained in the equation [Eq.1] :

(

Following the above equation, it describe the relation between the incident fields (Ei1 and Ei2) and the transmitted/coupled fields (Et1 and Et2), the transmission with the coupling coefficients t and k, as well as the round-trip loss L. In the Matrix, we assume that the total input power equals the total output power and the summation of the coupler' transmission and coupling coefficients are equal to one. The propagation around the ring waveguide is in function of the loss coefficient L and the accumulated phase ϕ is described in equation [Eq.2]:

Where /t/ refers to the transmission loss and the ϕt refers to the corresponding phase. The difference between the two phase (ϕt and ϕ) is integer value and promotional to 2 at the resonance frequency. At the critical coupling when |t| = L, transmission field is supposed to be equal to zero. Objective function is the improvement of the quality factor Q that is evaluated in term of λo central resonance wavelength, Q = λo/Δλ. The ranges of the parameters variation are chosen so as the coupling between the resonator and the optical fiber are always active. Finite element results at the resonance is described below. The optimal quality factor Q obtained is quite similar to the one obtained by experimental. This should consolidate our finite element simulation and the coupled strategy for further optimizations. Fig. 4 indicates a result of simulation. The field continuity boundary condition between the straight waveguide and the ring waveguide allowed us to ensure that the tangential components of the electric and the magnetic fields are continuous at the boundary, despite the phase jump.

CONCLUSION

At this first step of the multi-physic optimization, we have demonstrated that we can simulate and find an optimal design. We can be extended this process to other application using coupled devices. Our sensitivity analysis shows a good correlation between Q-factor obtained with experiment and with finite element simulation. This optimization process may integrate later some constraints related to the manufacturing process, thermal analysis of the resonator so we can represent better at actual stage it can bring a great support to define better performances in several applications of these resonators in achieving high performances devices. Optimization of the model should bring a help to define better performances in several other applications of these resonators in achieving high performances devices [25 -28] or sensors.

Fig. 1 :

 1 Fig. 1: Photograph of an optical resonator coupled to a tapered optical fiber.

Fig. 2 :Fig. 3 :

 23 Fig. 2: 3D & 2D views of the design parameters used for the optimization process. The contour represent the boundary condition as we need to model the gap in the air.

Fig. 4 :

 4 Fig. 4: Modeling and meshing of the waveguide (a, b & c) with Finite element simulation of the coupled resonator based on the following assumption of optical symmetry and the Gallery mode in the resonator (d &e).

Table 1 :

 1 Table

	References	e	L	g	D	Q-factor
	Colombia University & University of California, Si3N4	750nm	N-C	N-C	N-C	6.6x 10 6
	[14]
	Cornell University, Si3N4 [15]	644nm	900nm	N-C	20µm	3x 10 6
	Cornell University, Si3N4 [13]	910 nm	1.8 µm	680nm	115µm	7x 10 6
	Femto-st Institute, Si3N4 [17]	1µm	3µm	600nm	90µm	1x 10 5
	Guangxi University, Silicon [16]	320nm	500nm	160nm	40µm	N-C

of the main parameters for silicon nitride microrings and their coupling to a ridge realized on a chip.