Audrey Cayron

Christophe Viallon

Ayad Ghannam

Alessandro Magnani

Thierry Parra

Compact and wideband 3-D IPD butler matrix for millimeter-wave communications

Keywords: Integrated Passive Devices (IPD), 3-D technology, Solenoid, Transformer, Metal-Insulator-Metal (MIM) capacitor, Millimeter waves, 5G, Quadrature hybrid Coupler, Phase Shifter, Crossover, Butler matrix. keyword one, keyword two

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Introduction

Using large bandwidths in the millimeter-wave spectrum may significantly increase data rates of the next generation of wireless communication applications. However, short wavelengths bring about new challenges to radio architectures that have to overcome high propagation losses and fast fading effects. One of these challenges is the integration of high gain antennas with adaptive spatial filtering to mitigate high path losses and to provide cost-effective and reliable coverage. Among strategies available for beamforming, the most versatile is the phased array system [START_REF] Roh | Millimeter-wave beamforming as an enabling technology for 5G cellular communications: Theoretical feasibility and prototype results[END_REF]. While this approach is well-suited to base stations, it is hardly compliant with mobile handsets which face additional constraints in terms of cost, energy efficiency and size limitations [START_REF] Huo | 5G Cellular User Equipment: From Theory to Practical Hardware Design[END_REF]. For the latter handset, the implementation of phase-switched networks using passive circuits, such as Rothman lenses and Blass or Butler matrices, is more relevant [START_REF] Ojaroudiparchin | A Switchable 3-D-Coverage-Phased Array Antenna Package for 5G Mobile Terminals[END_REF][START_REF] Bang | A SAR Reduced mm-Wave Beam-Steerable Array Antenna With Dual-Mode Operation for Fully Metal-Covered 5G Cellular Handsets[END_REF]. Compared to phased-array systems, such a solution dissipates much less DC power but features less discrete beam directions.

Among these passive networks, the Butler matrix has been extensively researched owing to its low complexity. A n × n Butler matrix produces n phase-shifted replicas with equal magnitude of a single signal applied to one of its n inputs. The phase relationship between outputs is set from the selected input. Connecting outputs to an antenna array makes it easy to create a switched multi-beam system. In the targeted frequency range of 24 to 29 GHz, the literature reports very different ideas and technologies. The most compact circuits are based on CMOS back end of line (BEOL) [START_REF] Chin | A 24-GHz CMOS Butler Matrix MMIC for multi-beam smart antenna systems[END_REF][START_REF] Park | A 28 GHz CMOS Butler matrix for 5G mm-wave beamforming systems[END_REF]. However, this technology is not really suitable because of the complexity and cost of manufacturing, and the average performances achieved.

On the other hand, low-cost and low-complexity printed circuit board (PCB) technologies support the implementation of very different design techniques such as microstrip lines [START_REF] Trinh-Van | A Sidelobe-Reduced, Four-Beam Array Antenna Fed by a Modified 4x4 Butler Matrix for 5G Applications[END_REF][START_REF] Ashraf | PMC Packaged Single-Substrate 4 × 4 Butler Matrix and Double-Ridge Gap Waveguide Horn Antenna Array for Multibeam Applications[END_REF][START_REF] Lee | A 28-GHz Switched-Beam Antenna with Integrated Butler Matrix and Switch for 5G Applications[END_REF], substrate integrated waveguides (SIW) [START_REF] Yang | SIW Multibeam Array for 5G Mobile Devices[END_REF][START_REF] Yang | SIW Butler Matrix with Modified Hybrid Coupler for Slot Antenna Array[END_REF][START_REF] Sun | Millimeter-Wave Multibeam Antenna Based on Folded C-Type SIW[END_REF][START_REF] Pezhman | A compact 4 × 4 SIW beamforming network for 5G applications[END_REF] or suspended lines (SISL) [START_REF] Wang | A Low-Loss Butler Matrix Using Patch Element and Honeycomb Concept on SISL Platform[END_REF]. The resulting dimensions are quite large, but SIW butler matrices offer by far the best performance today. Finally, integrated passive device technologies (IPD) provide intermediate dimensions, low manufacturing costs and complexity [START_REF] Haroun | A Compact 24-26 GHz IPD-Based 4x4 Butler Matrix for Beam Forming Antenna Systems[END_REF][START_REF] Lee | A compact switched beam-forming network using silicon IPD technology for low-cost 5G communication[END_REF]. Conventional IPD technologies are suitable for the integration of semi-distributed planar devices, as in [START_REF] Haroun | A Compact 24-26 GHz IPD-Based 4x4 Butler Matrix for Beam Forming Antenna Systems[END_REF][START_REF] Lee | A compact switched beam-forming network using silicon IPD technology for low-cost 5G communication[END_REF], using MIM capacitors and spiral inductors with improved Q-factors compared to CMOS technology [START_REF] Carchon | Wafer-level packaging technology for high-Q on-chip inductors and transmission lines[END_REF][START_REF] Cayron | High-Performance Compact 3-D Solenoids for RF Applications[END_REF]. In order to increase integration densities of IPD circuits without compromising losses and overcoming the previous apparent trade-off, the use of the third dimension is proposed in this paper. Based on a dedicated and innovative 3-D technology process, a family of compact, high-performance devices derived from solenoids is designed and used for the integration of a 4×4 Butler matrix.

The paper is organized as follows. Section 2 discusses the design of each component of the Butler Matrix. The technological process for the fabrication of 3-D circuits is described in Section 3. Section 4 deals with Butler matrix measurements and a comparison is made with simulated data. Finally, these results are assessed in relation to other works published at similar frequencies in Section 5.

Butler Matrix Design

The 4 × 4 Butler matrix presented consists of four quadrature hybrid couplers, one crossover and two phase shifters (Fig- ure 1). The main contribution of this work lies in the design of each of the components constituting the Butler matrix. The hybrid coupler and the phase shifter generalize the use of solenoids to take full advantage of the technological process employed, to maximize the compactness and minimize the losses while the crossover is simply the intersection of two lines.

As seen in Figure 1, the phase shift value ϕ introduced by each phase shifter is adjusted in order to obtain a phase difference of -45°between transmissions of the phase shifter and the crossover. In this configuration, the phase difference observed between the adjacent outputs 5 to 8 of the Butler Matrix is -45°, 135°, -135°and 45°when excitation is applied from port 1 to 4, respectively. The signal applied to one of the inputs 1 to 4 is distributed equally between the four outputs 5 to 8, and a transmission coefficient theoretically equal to -6 dB is then expected whatever the excited input.

The following sections present the design of the hybrid quadrature coupler, the crossover and the phase shifter. The latter two components make up the middle network (Figure 1). These are optimized simultaneously, as it is essential to keep the phase shift observed constant between their respective transmissions over a widest frequency range.

Quadrature Hybrid Coupler

Branch-line, Lange and basic coupled-line couplers are used extensively in microwave and millimeter-wave circuits to create 90°phase shifts. All these circuits occupy large chip area due to the long transmission line sections required for their implementation, but this problem can be mitigated by adopting a semi-distributed or lumped element design approach. The basic coupled-line coupler topology is of particular interest here because the coupled lines can be replaced by an ultra-compact 3-D transformer made by combining two solenoids. It is formed by winding two turns of two parallel strips around an insulating core of SU8 resin, as illustrated in Figure 2a.

The design of a 50 Ω-matched quadrature hybrid coupler from a transformer requires to match the even and odd mode ABCD matrices of its lumped equivalent model (see black parts of Figure 2b) with those of an ideal coupled-line hybrid coupler. Each element of the model is then expressed according to the characteristics of the coupled-line coupler: Z 0o = 20.7 Ω, Z 0e = 120.7 Ω, θ = 90°, k = 0.707 [START_REF] Pozar | Microwave Engineering[END_REF], Z 0o , Z 0e , θ and k being the odd and even mode characteristic impedances, the electrical length and the coupling factor, respectively. To achieve a quadrature hybrid coupler operating at 27 GHz, the following values are calculated [START_REF] Hogerheiden | Improved planar spiral transformer theory applied to a miniature lumped element quadrature hybrid[END_REF]: L = 417 pH, k = 0.71, C g = 49 fF and C c = 118 fF. These values define a starting point for the circuit design. The inductance value L is determined by adjusting the number of turns and the aspect ratio of the vertical section of the 3-D transformer's dielectric core. As its aspect ratio must remain close the square shape to minimize the proximity induced losses in the conductors, the best compromise leads to an inductance of 460 pH. The coupling factor k is technology limited as it depends on the spacing between turns. By reducing it to the minimum possible, a value close to 0.6 is obtained. Finally, two external capacitors C m and C c (in gray in Figure 2b) are added to provide an extra degree of freedom and bring the equivalent characteristic impedances Z 0o and Z 0e and the coupling factor k of the circuit in Figure 2 In practice, solenoids are integrated around a 110 µm-thick SU8 resist core and the area of the coupler is 340 µm×280 µm (0.095 mm 2 ). The concept and design of this coupler was first described in [START_REF] Cayron | Wideband and Compact 3-D Quadrature Coupler for 5G Applications[END_REF]. However, in this version, capacitors C c and C m have been rearranged and placed under the lower metallization of the solenoids to improve compactness. Values of capacitors C c and C m are set to 55 fF and 325 fF for a performance alignment on the targeted center frequency of 27 GHz. To minimize imbalances and achieve a good electrical symmetry, ports are designed such the ports h1 and h3 (ports h2 and h4 respectively) are kept in close proximity.

Results of the coupler's S -parameter simulation along with magnitude imbalance and phase difference between transmissions are shown in Figure 3. At 27 GHz, insertion losses extracted from S h21 or S h31 (Figure 3a) come to approximately 0.3 dB. Reflection S h11 and isolation S h41 coefficients remain below -17 dB over the 24 GHz to 29 GHz range. From Figure 3b, it can be noticed that the phase difference between outputs h2 and h3 is 90°and the magnitude imbalance is -0.22 dB at 27 GHz. Within the 24 GHz to 29 GHz frequency band, coupling imbalances are maintained below 0.4 dB and ±1.5°a round 90°.

Crossover

The crossover enables a signal transmission from port x1 to port x2 (resp. x3 to x4) while the other two ports remain isolated (Figure 1). This function is carried out via a bridge that allows the crossing of two transmission lines, when the required number of metal layers is technologically available [START_REF] Chin | A 24-GHz CMOS Butler Matrix MMIC for multi-beam smart antenna systems[END_REF][START_REF] Haroun | A Compact 24-26 GHz IPD-Based 4x4 Butler Matrix for Beam Forming Antenna Systems[END_REF][START_REF] Lee | A compact switched beam-forming network using silicon IPD technology for low-cost 5G communication[END_REF]. Otherwise, it can be obtained by cascading two 90°hybrid couplers [START_REF] Yang | SIW Multibeam Array for 5G Mobile Devices[END_REF][START_REF] Yang | SIW Butler Matrix with Modified Hybrid Coupler for Slot Antenna Array[END_REF][START_REF] Sun | Millimeter-Wave Multibeam Antenna Based on Folded C-Type SIW[END_REF]. Here, the first solution is preferred owing to better compactness and a broader frequency bandwidth.

The top view and the 3-D model of the designed crossover are presented in Figure 4. Despite the lack of geometric symmetry, the two paths are drawn to exhibit the same electrical length. In addition to the bridge, two long parallel strips are drawn to connect the input couplers to the output couplers. Such a design is prone to radiation losses, but not desirable. A third strip integrated on top of 110 µm-thick SU8 pillars and connected to ground mitigates these effects as much as possible. The whole creates a slightly frequency dispersive high-impedance grounded coplanar strips waveguide (CPS). Four identical capacitors, named C x , are added in series with the ends of the lines to improve the impedance matching of the crossover with the couplers it connects to. The first design steps are performed using multi-level microstrip line models usually available in RF CAD software to define the main line dimensions (length, width and spacing). Circuit dimensions are then refined by using electromagnetic simulation. The final simulated characteristics are shown in Figure 5. The insertion losses are comprised between 0.6 dB and 0.9 dB in the 24 GHz to 29 GHz range, and the S x31 and S x41 isolations are under 10 dB and 26 dB, respectively. The electrical symmetry of the crossover is estimated by measuring the imbalances between S x21 and S x43 parameters, on magnitudes and phases (Figure 6). Values less than 0.05 dB and 0.2°, respectively, are reported in the same frequency band.

Phase Shifter

The phase shifter presented in Fig. 7 consists of a 3-D coil wrapped around the 110 µm-thick SU8 core in association with input/output series capacitors C p . This circuit acts as a section of transmission line whose phase slope and attenuation are matched to those of the crossover. The 3D coil consists of two turns of 50 µm-wide strips. The inductance/capacitance ratio of this structure is initially too high due to the strong inter-turn mutual positive coupling and the low capacitance to ground. This problem is solved by interposing a 30 µm-wide grounded line with 15 µm line spacing. The C p capacitor is used to fine-tune the phase difference observed with the crossover. It also adjusts the transmission's phase slope in the lower frequency range. As for the crossover, the first design steps rely on electrical simulations using models of coupled microstrip lines. Electromagnetic simulations are then used to determine the final dimensions. The footprint of the circuit shown in Fig. 7 is 635 µm×330 µm (0.21 mm 2 ). Simulated data of the device (Figure 8) exhibit a broadband behavior. Return losses remain less than -24 dB and insertion losses are better than 0.35 dB in the frequency range 24 GHz to 29 GHz.

Bandwidth Optimization of the Middle Network

Several conditions must be met to achieve broadband operation of the middle network. First, a phase difference of -45°between phase shifter and crossover transmissions must be reached at the center frequency. Second, this difference must be kept for the largest possible frequency band, while both magnitudes are kept as close as possible to each other. As the crossover introduces a phase shift of -45°at the center frequency of 27 GHz, ϕ has to be adjusted to -90°to reach the phase difference of -45°between phase shifter and crossover transmission parameters, as highlighted in Figure 1. ϕ depends on the width w c of the SU8 core of phase shifter (Figure 7a). Therefore, phase adjustment is very easily carried out by choosing the optimal width w c at 27 GHz. Here, the result is a w c set to 84 µm.

Once w c is set, capacitors C x and C p are tuned to keep this phase difference close to -45°at 27 GHz but also within the whole frequency range, by matching the slopes of phase variations versus frequency between transmissions of both the phase sifter and the crossover. This optimization has almost no effect on transmission magnitudes as long as components remain impedance-matched. The transmission angles of the crossover (S x21 ) and phase shifter (S p21 ) are shown in Figure 9 for several C x and C p values and for w c set to 84 µm. The best trade-off with respect to the aforementioned requirements is obtained for capacitors C x and C p of 300 fF and 1.6 pF, respectively.

The resulting magnitude and phase differences observed between the transmission parameters of the phase shifter and the crossover are given in Figure 10. From 24 GHz to 29 GHz, the magnitude difference is kept within the range 0.3 dB to 0.5 dB while phase difference varies from -44.1°to -46°.

3-D IPD Fabrication Process

3-D IPD processes have emerged with the potential to enhance performance and integration densities when compared to conventional planar IPD technologies [START_REF] Liu | Investigation of integrated passive device with through-silicon via[END_REF][START_REF] Letz | Glass in Electronic Packaging and Integration: High Q Inductances for 2.35 GHz Impedance Matching in 0[END_REF][START_REF] Kim | Ultrathin High-Q 2-D and 3-D RF Inductors in Glass Packages[END_REF][START_REF] Li | Fully Symmetric 3-D Transformers With Through-Silicon via IPD Technology for RF Applications[END_REF][START_REF] Ma | A Low-Loss Bandpass Filter With Stacked Double-Layer Structure Using Glass-Based Integrated Passive Device Technology[END_REF].

The key innovation lies in leveraging the third dimension to design 3-D structures, including 3-D solenoid inductors rather than planar spiral inductors, resulting in improved Q-factors. These processes typically involve metalizing both sides of a silicon or glass substrate ranging from 50 to 250 µm in thickness. Unlike silicon [START_REF] Liu | Investigation of integrated passive device with through-silicon via[END_REF][START_REF] Li | Fully Symmetric 3-D Transformers With Through-Silicon via IPD Technology for RF Applications[END_REF], glass offers the advantage of producing solenoids with notably high Q-factors. Inductance densities have, however, remained in the range of 3 to 17 nH/mm 2 , comparable to those achieved by conventional planar IPD technologies using spiral inductors. This is due to the manufacturing of Through Glass Via (TGV), which require large diameters and pitches, limiting device scalability and adaptability to increasing operational frequencies. These technologies are also complex to implement and involve numerous technological steps.

The proposed 3-D IPD technology aims to address these limitations in achieving significantly higher inductance densities, up to 60 nH/mm 2 [START_REF] Cayron | High-Performance Compact 3-D Solenoids for RF Applications[END_REF], along with high Q-factors and resonant frequencies. This makes it a strong candidate to accommodate millimeter-wave frequencies, distinguishing it from other 3-D IPD technologies. The technology detailed in [START_REF] Cayron | High-Performance Compact 3-D Solenoids for RF Applications[END_REF] for the integration of the solenoids is supplemented by additional steps for the implementation of MIM capacitors. The overall process flow is depicted in Figure 11.

MIM capacitors are manufactured first. The bottom electrode, referred to as M1 in Figure 11, is obtained from the evaporation of a 0.5 µm-thick aluminum layer on a resist mold (Figure 11a). This resist is removed using a lift-off process (Figure 11b). The insulating layer INS is made up of a 440 nm thin layer of silicon nitride Si x N y , deposited by an Inductively Coupled Plasma Chemical Vapor Deposition (ICPCVD) process at a temperature under 100 °C (Figure 11c). The top electrode is formed along with the first level of the solenoid in a single copper electroplating step named M2 (Figure 11d). The copper thickness is set to 15 µm. A photoresist (P-resist) is added to protect M2 layer against oxidation and etching that can occur during the following steps and vias are opened for further electrical connections to M2 (Figure 11e).

All steps required for the manufacture of 3-D metallization are described below. A 110 µm-thick SU8 photoresist layer is deposited and patterned to form the cores of solenoids and the stands for strips required within the upper metal (Figure 11f). A thick P-resist layer is applied and openings are made to create the mold for the upper metallization M3 growth (Figure 11g). Both vertical and upper sections of the M3 layer are electroplated simultaneously using a single 3-D seed layer, and a copper thickness of 15 µm is processed for this M3 level (Figure 11h). The latter step can also be used for the manufacture of metal bridges if required for line crossovers or coplanar waveguides (CPW). In this case, the P-resist layer located under the metal strip is not removed.

The whole manufacturing process requires six masks, which is comparable to conventional IPD technology. The maximum temperature of 100 °C reached during fabrication makes this process compliant with a large variety of substrate materials, both mineral and polymer-based. For the application considered here, the process is developed on a glass substrate.

Butler Matrix Simulation and Measurement

The fabricated Butler Matrix is shown in Figure 12. The four hybrid couplers, the two phase shifters on each branch, the grounded upper structure, all CPW and pads of matrix ports can be seen on this picture. Thanks to the grounded lines in and around the components of the Butler matrix, a very low degradation of their individual performance can be observed when close to each other. Thus, a very compact Butler matrix is obtained. Except for measurement pads and CPW accesses, the circuit footprint is 700 µm × 1200 µm (0.84 mm 2 ) for a height of 145 µm. The characterization of the 4 × 4 Butler matrix ideally requires an 8-port Vector Network Analyser (VNA). To circumvent this need, which is quite difficult to achieve given the number of ports and the high frequencies involved, a 4-port VNA is used in conjunction with matched loads placed on unused ports. This approach requires six partial measurements which are processed to recover the 8×8 scattering matrix of the Butler matrix. Two additional CPW transmission lines of different lengths, with the same geometry as the CPW access lines, are also used to calculate and de-embed the contribution of the access pads and CPWs. The method used for this operation is described in [START_REF] Cayron | Measurement and Deembedding Technique for the on-wafer Characterization of Multiport Devices[END_REF]. The on-wafer characterization has been performed on a PM-8 Suss Microtec probe station and a Keysight N5247A PNA-X 4-port VNA. Four Cascade Infinity RF probes are used, as well, with a GSGSG configuration (G for Ground and S for Signal) and a pitch of 150 µm.

The deembedded experimental S -parameter magnitudes of the Butler matrix when the input signal is applied to port 1 are shown in Figure 13, and compared with simulated ones. Input reflection magnitudes (S 11 , S 22 ) and magnitudes of isolations with other inputs (S 21 , S 31 and S 41 ) are plotted in Figure 13a while transmission magnitudes toward ports 5 to 8 (S 51 , S 61 , S 71 and S 81 ) are given in Figure 13b. Phase differences between outputs are reported in Figure 14. Simulations and measurements are in fairly good agreement knowing that two sources of uncertainty affect the experimental data: mismatchinduced errors due to impedances connected to unused DUT ports that changes from one partial measurement to another [START_REF] Cayron | Measurement and Deembedding Technique for the on-wafer Characterization of Multiport Devices[END_REF][START_REF] Tippet | A Rigorous Technique for Measuring the Scattering Matrix of a Multiport Device with a 2-Port Network Analyzer[END_REF], and the access de-embedding process. In Figure 13a, the -10 dB bandwidth, extracted from S 11 and S 22 parameters, is from 20 GHz to 30.1 GHz. Within this range, isolations are less than -17 dB after 22.4 GHz except for S 41 which is limited by S x31 crossover isolation. Alleviating the crossover's compactness constraints should easily improve this. With respect to transmissions (Figure 13b), average losses resulting from the Butler matrix are less than 2 dB between 21 GHz and 30.3 GHz. The observed inter-channel dispersion is primarily caused by over-coupling in the input couplers of the Butler matrix, implemented from initial version [START_REF] Cayron | Wideband and Compact 3-D Quadrature Coupler for 5G Applications[END_REF] while the output couplers benefit from the improvements discussed in section 2.1. For the phases plotted in Figure 14, a good agreement is also obtained between simulations and measurements. Phase errors are minimal (7°) around 25 GHz and remain below 8°b etween 23.3 GHz and 26.5 GHz and below 10°from 22.1 GHz to 27.5 GHz. At the highest frequencies, the discrepancies observed between simulation and measurements could be the result of the aforementioned measurement errors but also of the post-layout electromagnetic model of the circuit which considers rectangular sections for the metallization whereas these are more complex in practice.

Comparison and Discussion

The measured performances of the butler matrix are summarized in Table 1 and compared to similar works reported in the literature operating in the same frequency bands. The discussion focuses on the electrical performances obtained with respect to the dimensions obtained using different technologies. To be able to compare this work with other reported Butler matrices, the available data have been re-processed on the basis of common criteria. For example, to highlight the phase shift optimization work done between the components of the proposed butler matrix, we have chosen to define a bandwidth based on a maximum phase error arbitrarily fixed at 10°.Worst-case data are also extracted within this band for the isolation (Iso.), the return-loss (RL) and the average insertion losses (aIL), when available. The averaged insertion losses enable an assessment of the inherent loss associated with each technology without being disturbed by inter-channel dispersion of transmissions.

The best insertion losses, around 0.5 dB, are obtained from SIW technologies that benefit from the absence of radiative losses, copper metallization and very low loss angle substrates [START_REF] Yang | SIW Multibeam Array for 5G Mobile Devices[END_REF][START_REF] Sun | Millimeter-Wave Multibeam Antenna Based on Folded C-Type SIW[END_REF]. Unsurprisingly, these matrices present the largest dimensions of this comparison. IPD and particularly CMOS technologies offer a much better compactness but this advantage comes at a performance cost, with insertion losses around 2 dB for CMOS [START_REF] Chin | A 24-GHz CMOS Butler Matrix MMIC for multi-beam smart antenna systems[END_REF] and 3 dB for IPD [START_REF] Haroun | A Compact 24-26 GHz IPD-Based 4x4 Butler Matrix for Beam Forming Antenna Systems[END_REF]. In [START_REF] Haroun | A Compact 24-26 GHz IPD-Based 4x4 Butler Matrix for Beam Forming Antenna Systems[END_REF], the authors favored compactness by using very narrow (3 µm-width strips) high-impedance transmission lines at the expense of insertion losses. However, IPD technologies usually improve Q-factors compared to their CMOS silicon-based counterparts thanks to their much thicker and better conducing materials Frequency (GHz)

Phase differences (°)

∠S 6i -∠S 5i ∠S 7i -∠S 6i ∠S 8i -∠S 7i
Figure 14: Simulated ( ) and measured ( ) phase differences between adjacent outputs for excitation successively applied to port i, with i from 1 to 4.

used for metal layers (Cu vs. Al) placed on insulating substrates (i.e. glass) [START_REF] Cayron | High-Performance Compact 3-D Solenoids for RF Applications[END_REF][START_REF] Haroun | Compact 60-GHz IPD-Based Branch-Line Coupler for System-on-Package V-Band Radios[END_REF]. But these characteristics make the circuits manufactured in IPD technologies more bulky than their CMOS counterparts. By offering thick and wide metallizations, the 3-D technology presented in this paper reduces resistive losses compared to conventional IPD technologies while offering a much better integration density thanks to the exploitation of the third dimension. These features help to significantly improve performance and reduce manufacturing costs compared to traditional IPD technology, without increasing manufacturing complexity. The proposed 3-D Butler matrix combines relatively low insertion losses of at best 1.3 dB, thus coming close to the performance achieved by SIW technologies, with a footprint only twice as large as that of CMOS integrated matrices and five to ten times lower than IPD.

For applications where bandwidth is of great importance, SIW technology does not appear to be the best option. With a waveguide height and length driven by technology and crossover respectively, the few remaining degrees of freedom lead to a difficult trade-off between phase shifter return loss, bandwidth and phase difference with respect to the crossover [START_REF] Trinh-Van | A Sidelobe-Reduced, Four-Beam Array Antenna Fed by a Modified 4x4 Butler Matrix for 5G Applications[END_REF][START_REF] Ashraf | PMC Packaged Single-Substrate 4 × 4 Butler Matrix and Double-Ridge Gap Waveguide Horn Antenna Array for Multibeam Applications[END_REF]. In addition, as the antennas are connected directly to the output of the Butler matrix, practical routing constraints require the addition of a crossover and a pair of phase shifters to cross the signals from ports 6 and 7 in Figure 1 and properly feed the antenna array. IPD technologies enable larger bandwidths but the design remains limited given the small number of metal layers most often available. The highest relative bandwidth of Table 1 (23 %) is achieved by the CMOS Butler matrix in [START_REF] Chin | A 24-GHz CMOS Butler Matrix MMIC for multi-beam smart antenna systems[END_REF] which takes advantage of the high number of metal layers to miniaturize each component and to adjust their characteristics relative to each other. The 3-D implementation of the Butler matrix, as proposed in this paper, relies on a large number of geometrical parameters that allowed us to reach the best performance trade-off and a 22 %-large bandwidth (Table 1).

Finally, when the Butler matrix operates in transmission, power handling must be considered. Qualitatively, when comparing metallization characteristics, it can be stated that the proposed 3-D Butler matrix can handle more power than CMOS solutions, but less than SIW technology.

Conclusion

A 4 × 4 Butler matrix is presented which meets requirements of beamforming for millimeter-wave 5G or other communication systems. The circuit has been implemented with a 3-D IPD technology based on three metallic levels, a thin Si x N y dielectric deposited at a low temperature for MIM capacitors, and a 110 µm-thick SU8 photoresist for the shaping of solenoids. The surface area of the fabricated matrix is less than 1 mm 2 , while performances tend to peak as in the case of transmission losses at almost 1.3 dB. So, the trade-off between size and performances is much better compared to other published solutions. Also, the relative bandwidth of 22 % ranks this Butler matrix among the best published works in the 20-30 GHz frequency band. To summarize, this 3-D Butler matrix comes close to the compactness offered by solutions using the BEOL of CMOS technologies with performances close to SIW solutions.

Figure 1 :

 1 Figure 1: Block diagram of the proposed 4×4 Butler matrix.

  close to the target values. C m compensates the excess impedance brought by the inductance L while C c increases the coupling factor. The performance tuning is performed using an electrical simulator (Keysight ADS) based on the 3-D electromagnetic model of the transformer (ANSYS HFSS).

Figure 2 :

 2 Figure 2: (a) 3-D model of the 90°hybrid coupler and (b) equivalent network highlighting fabricated transformer in black and added MIM capacitors in gray.

Figure 3 :

 3 Figure 3: 90°hybrid coupler simulated characteristics, (a) S -parameters and (b) amplitude imbalances and phase difference.

Figure 4 :

 4 Figure 4: (a) Top view and (b) 3-D model of the crossover. Signal lines are drawn in green and blue. Orange parts are connected to ground.

Figure 5 :

 5 Figure 5: Crossover simulated S -parameters from port 1 and with C x = 300 fF.

Figure 6 :

 6 Figure 6: Simulated magnitude ( ) and phase ( ) imbalances between crossover paths, with C x = 300 fF.

Figure 7 :Figure 8 :

 78 Figure 7: (a) Top view and (b) 3-D model of the phase shifter. The signal strip is in blue and orange parts are connected to ground.

Figure 9 :

 9 Figure 9: Crossover S x21 angle versus C x ( ) and phase shifter S p21 angle versus C p ( ) for phase difference and phase slope adjustments over frequency of the middle network. w c is set to 84 µm.

Figure 10 :

 10 Figure 10: Simulated magnitude ( ) and phase differences ( ) observed between S p21 (phase shifter) and S x21 (crossover) transmissions of the middle network.

Figure 11 :

 11 Figure 11: Sectional view of the main steps for the integration of a capacitor, a solenoid and a bridge (from left to right) using the 3-D IPD process.

Figure 12 :

 12 Figure 12: Scanning Electron Microscopy (SEM) picture of the fabricated 4×4 Butler matrix.

Figure 13 :

 13 Figure 13: Simulated ( ) and measured ( ) S -parameters magnitudes of the Butler matrix with excitation at port 1. (a) return loss and isolations and (b) transmissions from input 1 toward outputs 5 to 8.

Table 1 :

 1 Performance comparison between Butler Matrices in K and KA bands.

	Reference	[5]	[15]	[16]	[10]	[12]	[14]	This work
	Technology	CMOS IPD	IPD	SIW	SIW	SISL	3-D IPD
	Area (mm 2 )	0.41	4	7.5	1520	684	1190	0.84
	BW (GHz)	21-26.5	25.9-29.9	29.7-29.9	29.5-31.7	29.1-31	24.5-26.4	22.1-27.5
	BW (%)	23	14.3	0.7	7.3	6.3	7.5	22
	Iso. (dB)	n.c	n.c.	n.c.	-18	-21	-14	-12
	RL (dB)	n.c	n.c.	n.c.	-18	-21	-11	-17.5
	aIL (dB)	2.1-2.3	2.9-3.2	n.c.	0.3-1.1	0.3-0.42	1.1-2.1	1.3-1.7

Acknowledgment

The authors would like to thank David Bourrier, Alexandre Rumeau and Damien Saugnon from the Laboratory of Analysis and Architecture of Systems (LAAS) in Toulouse, for their technical support.

This work was supported by LAAS-CNRS micro and nano technologies platform, member of the French RENATECH network and by 3DiS Technologies.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


William Jouanneau
email: w.jouanneau@gmail.com

Don-Jean Léandri-Breton

Dorte Herzke

Børge Moe

Vladimir A Nikiforov

Marie Pallud

Charline Parenteau

Geir W Gabrielsen

Olivier Chastel

Does contaminant exposure disrupt maternal hormones deposition? A study on per-and polyfluoroalkyl substances in an Arctic seabird

Keywords: Black-legged kittiwake, PFAS, Maternal effect, Corticosterone, Testosterone, Thyroid hormones

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Introduction

Freshly laid avian eggs contain, in addition to basic resources, substantial levels of maternal hormones [START_REF] Groothuis | Maternal hormones as a tool to adjust offspring phenotype in avian species[END_REF][START_REF] Schwabl | Yolk is a source of maternal testosterone for developing birds[END_REF]). The amount of maternal hormones deposited in the egg yolk is known to be influenced by environmental factors (e.g., abiotic conditions [START_REF] Lessells | Yolk steroids in great tit Parus major eggs: variation and covariation between hormones and with environmental and parental factors[END_REF], food availability [START_REF] Verboven | Maternal condition, yolk androgens and offspring performance: a supplemental feeding experiment in the lesser black-backed gull (Larus fuscus)[END_REF] and social interactions [START_REF] Pilz | Egg yolk androgen levels increase with breeding density in the European Starling, Sturnus vulgaris[END_REF])), the offspring characteristics (e.g., sex of the embryo [START_REF] Müller | Sex Differences in Yolk Hormones Depend on Maternal Social Status in Leghorn Chickens (Gallus gallus domesticus)[END_REF], laying date [START_REF] Tomita | Within-and Among-Clutch Variation in Maternal Yolk Testosterone Level in the Black-Tailed Gulls Larus crassirostris[END_REF], position of the egg in the laying order [START_REF] Schwabl | Yolk is a source of maternal testosterone for developing birds[END_REF], composition of the egg [START_REF] Groothuis | Multiple pathways of maternal effects in black-headed gull eggs: constraint and adaptive compensatory adjustment[END_REF]) and the state of the mother bird [START_REF] Tschirren | Heritable variation in maternal yolk hormone transfer in a wild bird population[END_REF]e.g., her age, physical condition, past experience, genetic background) or the male quality [START_REF] Rutkowska | Mapping the past, present and future research landscape of paternal effects[END_REF]. Although mainly explored for steroids, experimental prenatal exposure to maternal hormones in ovo have shown to impact hatching date and offspring growth [START_REF] Von Engelhardt | Sex-specific effects of yolk testosterone on survival, begging and growth of zebra finches[END_REF], metabolism [START_REF] Tobler | Costly steroids: egg testosterone modulates nestling metabolic rate in the zebra finch[END_REF], immune system [START_REF] Navara | Variable effects of yolk androgens on growth, survival, and immunity in eastern bluebird nestlings[END_REF], sex-ratio [START_REF] Rubolini | Effects of elevated yolk testosterone levels on survival, growth and immunity of male and female yellow-legged gull chicks[END_REF], behavior [START_REF] Possenti | Effect of yolk corticosterone on begging in the yellow-legged gull[END_REF]) and survival [START_REF] Saino | Stressed mothers lay eggs with high corticosterone levels which produce low-quality offspring[END_REF]. Maternal hormones, in interaction with the offspring and maternal genotype, are believed to behave as messengers enabling adaptive maternal effects to prepare the offspring to prevailing environmental conditions [START_REF] Mousseau | The adaptive significance of maternal effects[END_REF][START_REF] Von Engelhardt | Maternal hormones in avian eggs[END_REF]. Independent regulation between circulating and transferred maternal hormones is an essential prerequisite for hormones to be adaptive regulators of offspring development.

Although very little is known about transfer mechanisms, the literature suggests that such a separate control over deposition and response may at least be possible (Della [START_REF] Costa | Yolk immunoreactive corticosterone does not relate with maternal fecal glucocorticoids in a captive population of Greater Rheas (Rhea americana)[END_REF][START_REF] Groothuis | Hormone-mediated maternal effects in birds: mechanisms matter but what do we know of them?[END_REF][START_REF] Kumar | Steroid receptors and their regulation in avian extraembryonic membranes provide a novel substrate for hormone mediated maternal effects[END_REF][START_REF] Okuliarova | Egg deposition of maternal testosterone is primarily controlled by the preovulatory peak of luteinizing hormone in Japanese quail[END_REF]. Being the results of a coevolutionary process between maternal transfer and offspring responses to these substances, such intergenerational effects may either have beneficial or even detrimental outcomes for the mother and/or the offspring (Hsu et al. 2020a;[START_REF] Marshall | When is a maternal effect adaptive?[END_REF]. Indeed, maternal effects may increase offspring fitness, but also reduce it to increase maternal survival in unprofitable conditions. Maternal hormones and the offspring's response should therefore match an optimal trade-off for a given situation.

In this context, any disruption to the transfer of maternal hormones may be detrimental not only to the offspring but also to the siblings and the parents [START_REF] Bebbington | Who listens to mother? A whole-family perspective on the evolution of maternal hormone allocation[END_REF][START_REF] Groothuis | Revisiting mechanisms and functions of prenatal hormone-mediated maternal effects using avian species as a model[END_REF]. In birds, endocrine pathways are known to be affected by various environmental contaminants (e.g., trace elements, organic compounds; [START_REF] Metcalfe | An introduction to the sources, fate, occurrence and effects of endocrine disrupting chemicals released into the environment[END_REF][START_REF] Tan | The endocrine effects of mercury in humans and wildlife[END_REF][START_REF] Tyler | Endocrine Disruption in Wildlife: A Critical Review of the Evidence[END_REF]. These contaminants are transferred to the yolk [START_REF] Ackerman | Maternal transfer of mercury to songbird eggs[END_REF][START_REF] Verreault | Maternal transfer of organohalogen contaminants and metabolites to eggs of Arctic-breeding glaucous gulls[END_REF]) and may therefore potentially disrupt maternal hormone deposition. The effects of contaminants on maternal hormone deposition has nonetheless been seldom investigated: legacy persistent organic pollutants (POPs: organochlorines, brominated flame retardants) altered maternal steroids deposition in eggs of glaucous gulls (Larus hyperboreus; [START_REF] Verboven | Maternally derived testosterone and 17beta-estradiol in the eggs of Arctic-breeding glaucous gulls in relation to persistent organic pollutants[END_REF], but not in common terns (Sterna hirundo; [START_REF] French | Maternal steroids and contaminants in common tern eggs: a mechanism of endocrine disruption?[END_REF]) and great tits (Parus major; [START_REF] Ruuskanen | Transgenerational endocrine disruption: Does elemental pollution affect egg or nestling thyroid hormone levels in a wild songbird?[END_REF].

There is a clear need for further investigations on the effects of contaminants on the transfer of maternal hormones in eggs. Especially since most of the work has focussed on steroids, and not on other deposited hormones (e.g., glucocorticoids and thyroid hormones; von Engelhardt and Groothuis 2011). More specifically, seabirds are exposed to a large variety of deleterious substances [START_REF] Bianchini | Why do we monitor? Using seabird eggs to track trends in Arctic environmental contamination[END_REF], but some of them receive little attention. Among them are per-and polyfluoroalkyl substances (PFAS), a family of synthetic compounds used as surface-active agents in a multitude of manufactured products: firefighting foams, waterproof clothing, non-stick cookware, coatings, food packaging; [START_REF] Buck | Perfluoroalkyl and polyfluoroalkyl substances in the environment: terminology, classification, and origins[END_REF]. Despite the known PFAS endocrine disrupting capabilities [START_REF] Chen | Perfluorobutanesulfonate Exposure Skews Sex Ratio in Fish and Transgenerationally Impairs Reproduction[END_REF][START_REF] Coperchini | Thyroid Disrupting Effects of Old and New Generation PFAS[END_REF][START_REF] Di Nisio | Endocrine disruption of vitamin D activity by perfluoro-octanoic acid (PFOA)[END_REF][START_REF] Di Nisio | Endocrine Disruption of Androgenic Activity by Perfluoroalkyl Substances: Clinical and Experimental Evidence[END_REF][START_REF] Jensen | Emerging endocrine disrupters: perfluoroalkylated substances[END_REF][START_REF] Rickard | Per-and poly-fluoroalkyl substances (PFAS) and female reproductive outcomes: PFAS elimination, endocrine-mediated effects, and disease[END_REF][START_REF] Shi | Accumulation, Biotransformation, and Endocrine Disruption Effects of Fluorotelomer Surfactant Mixtures on Zebrafish[END_REF], to date our knowledge on that matter remains extremely limited in wildlife. Indeed, a few correlative studies on birds suggests that PFAS may affect concentrations of thyroid hormones, corticosterone and prolactin, potentially leading to effects on physiology, parental investment and incubation behaviours [START_REF] Ask | Per-and Polyfluoroalkyl Substances Are Positively Associated with Thyroid Hormones in an Arctic Seabird[END_REF][START_REF] Blévin | Contaminants, prolactin and parental care in an Arctic seabird: Contrasted associations of perfluoroalkyl substances and organochlorine compounds with egg-turning behavior[END_REF][START_REF] Mortensen | Homology modeling to screen for potential binding of contaminants to thyroid hormone receptor and transthyretin in glaucous gull (Larus hyperboreus) and herring gull (Larus argentatus)[END_REF][START_REF] Nøst | Halogenated organic contaminants and their correlations with circulating thyroid hormones in developing Arctic seabirds[END_REF]Sebastiano et al. 2020b;[START_REF] Tartu | Endocrine and fitness correlates of long-chain perfluorinated carboxylates exposure in Arctic breeding black-legged kittiwakes[END_REF]. The disrupting mechanisms are not well identified, but like other endocrine-disrupting compounds, PFAS may cause an alteration of the synthesis and breakdown, the release, transport and binding or elimination of endogenous hormones [START_REF] Metcalfe | An introduction to the sources, fate, occurrence and effects of endocrine disrupting chemicals released into the environment[END_REF]. Specifically, some studies have shown that some PFAS are, for example, particularly prone to bind to hormone transport proteins [START_REF] Jones | Binding of perfluorinated fatty acids to serum proteins[END_REF][START_REF] Kar | Endocrine-disrupting activity of per-and polyfluoroalkyl substances: Exploring combined approaches of ligand and structure based modeling[END_REF][START_REF] Mortensen | Homology modeling to screen for potential binding of contaminants to thyroid hormone receptor and transthyretin in glaucous gull (Larus hyperboreus) and herring gull (Larus argentatus)[END_REF]. Previous investigations have shown that PFAS may exhibit a dissimilar relationship with circulating hormones than the more widely studied chlorinated POPs [START_REF] Melnes | Dissimilar effects of organohalogenated compounds on thyroid hormones in glaucous gulls[END_REF][START_REF] Tartu | Endocrine and fitness correlates of long-chain perfluorinated carboxylates exposure in Arctic breeding black-legged kittiwakes[END_REF], which urge for additional studies regarding PFAS endocrine disrupting activities. PFAS can be transferred to the yolk [START_REF] Bertolero | Accumulation and maternal transfer of perfluorooctane sulphonic acid in yellow-legged (Larus michahellis) and Audouin's gull (Larus audouinii) from the Ebro Delta Natural Park[END_REF][START_REF] Gebbink | Comparative tissue and body compartment accumulation and maternal transfer to eggs of perfluoroalkyl sulfonates and carboxylates in Great Lakes herring gulls[END_REF][START_REF] Jouanneau | A Bad Start in Life? Maternal Transfer of Legacy and Emerging Poly-and Perfluoroalkyl Substances to Eggs in an Arctic Seabird[END_REF]), but their impact on maternal hormone deposition have not been investigated yet. Nonetheless, any disruption of the formation of maternal hormones or competitive binding by PFAS to transport proteins may lead to the deterioration of maternal hormones transfer and consequently to the transmission of maladaptive information to the offspring.

In this context, the aim of the present study is to investigate maternal hormone deposition in eggs of the Arctic-breeding black-legged kittiwake (Rissa tridactyla; hereafter "kittiwake"), known to be dietary exposed to PFAS in the wild (Blévin et al. 2017a;[START_REF] Jouanneau | A Bad Start in Life? Maternal Transfer of Legacy and Emerging Poly-and Perfluoroalkyl Substances to Eggs in an Arctic Seabird[END_REF][START_REF] Tartu | Endocrine and fitness correlates of long-chain perfluorinated carboxylates exposure in Arctic breeding black-legged kittiwakes[END_REF]. Specifically, we studied the relationship between female PFAS burden, and yolk maternal glucocorticoids (corticosterone), steroids (testosterone, dihydrotestosterone and androstenedione), and thyroid hormones (triiodothyronine and thyroxine), all known to be transferred to the eggs and to play a key role in embryo development [START_REF] Groothuis | Maternal hormones as a tool to adjust offspring phenotype in avian species[END_REF][START_REF] Groothuis | Determinants of within-and among-clutch variation in levels of maternal hormones in Black-Headed Gull eggs[END_REF]2008;[START_REF] Ruuskanen | Effects of experimentally manipulated yolk thyroid hormone levels on offspring development in a wild bird species[END_REF]Sarraude et al. 2020a;Sarraude et al. 2020c). By sampling females during the pre-laying stage (i.e., during egg formation), and their eggs as soon as they were laid, we provide valuable insights into the relationship between maternal circulating and maternally deposited hormones, and shed light on the potential impacts of maternal PFAS on maternal transfer. Given the established endocrine disrupting properties of PFAS, we hypothesized a possible alteration of the maternal hormone's deposition, via a disrupted transfer of some hormones in eggs in the most PFAS-contaminated females.

Methods

Study area and sample collection

We carried out the field study between May and June 2019 in a kittiwake colony in Kongsfjorden, Svalbard (see [START_REF] Jouanneau | A Bad Start in Life? Maternal Transfer of Legacy and Emerging Poly-and Perfluoroalkyl Substances to Eggs in an Arctic Seabird[END_REF] for further information on the field operations). Briefly, adults from 14 nests were captured using a noose at the end of a fishing rod, during the pre-laying period (i.e., at the time of egg formation), and immediately sampled for 2 mL of blood from the alar vein. Skull length (head + bill) was measured with an accuracy of 0.1 mm using a calliper and birds were weighted to the nearest 2 g with a Pesola spring balance. The sex of individuals were identified by molecular sexing from red blood cells following [START_REF] Fridolfsson | A Simple and Universal Method for Molecular Sexing of Non-Ratite Birds[END_REF] and only females (n = 14) were kept for further analyses. At the end of each day, we separated plasma and red blood cells via centrifugation and kept both samples frozen (-20 °C) until analyses. In this species, females usually lay a twoegg clutch [START_REF] Moe | Climate change and phenological responses of two seabird species breeding in the high-Arctic[END_REF]. We monitored those nests daily and collected first-(n = 14) and second-laid eggs (n = 11) less than 24h after laying. Hormones measured in freshly laid eggs, as we did in the present study, are entirely synthesised by the female before being transferred to the eggs (von Engelhardt and Groothuis 2011). We weighted the eggs in the laboratory to the nearest 0.01 g, then separated yolk and albumen into microtubes and kept both samples frozen until analyses. Field operations were approved by the Governor of Svalbard and by the Norwegian Animal Research Authority (NARA, permit number 19970).

Per-and polyfluoroalkyl substances analysis

We adapted a method from [START_REF] Powley | Matrix effect-free analytical methods for determination of perfluorinated carboxylic acids in environmental matrixes[END_REF], contaminants analysis method and concentrations have been extensively described in a previous study on PFAS maternal transfer [START_REF] Jouanneau | A Bad Start in Life? Maternal Transfer of Legacy and Emerging Poly-and Perfluoroalkyl Substances to Eggs in an Arctic Seabird[END_REF]. Only compounds detected in more than 70 % of the females were kept for further investigations (see supporting information (SI), Table S1 for a list of all measured compounds and detection percentages). Consequently, only the following compounds were kept for statistical analyses: perfluorohexanesulfonic acid (PFHxS), branched perfluorooctanesulfonic acid (brPFOS), linear perfluorooctanesulfonic acid (linPFOS), perfluorooctanoic acid (PFOA), perfluorononanoic acid (PFNA), perfluorodecanoic acid (PFDcA), perfluoroundecanoic acid (PFUnA), perfluorododecanoic acid (PFDoA), perfluorotridecanoic acid (PFTriA) and perfluorotetradecanoic acid (PFTeA). For all included PFAS, values lower than the limit of detection (LOD) were set to half of the LOD of the specific compound. We provided all concentrations in ng g -1 wet weight (ww).

Hormone analyses

We measured the following steroid and thyroid hormones in female plasma and egg yolk: dihydrotestosterone (DHT), androstenedione (AND), testosterone (T), corticosterone (CORT), triiodothyronine (T3) and thyroxine (T4). Extraction of the plasma and yolk samples is detailed for all hormones in the SI.

Steroid hormones (DHT, AND, T and CORT)

The four hormones were assayed with similar procedures: Radio-immunoassay (RIA)

Thyroid hormones (T3 and T4)

Total T3 and T4 were measured with RIA method, 25 μL of yolk extract or plasma were incubated overnight at 4 o C with 10 000 cpm of the appropriate I 125 -steroid (Perkin Elmer, US) and polyclonal rabbit antiserum (Sigma Aldrich, France). The bound fraction was then separated from free fraction by addition of a polyclonal sheep antiserum against rabbit antiserum and the activity was counted on a Gamma Wizard 2470 counter (Perkin Elmer, US).

We also calculated the T3/T4 ratio, often used when investigating thyroid hormones.

Quality control

We previously validated RIA and ELISA hormones assays on the kittiwake plasma and yolk. We diluted all extracts in the appropriate assay buffer, their displacement regression lines were all parallel to the standard ones. To guarantee the quality and control for reproducibility and precision of the RIA, hormone standards, blanks, total activity and non-specific activity were concurrently analysed. We ran all samples in duplicate in one or two runs. Additional information on the hormone analyses quality control can be found in SI, minimal detectable and intra-assay variation for plasma and yolk can be found in SI, Table S2. Samples below the LOD (n = 6) were replaced with a value equal to half of the LOD of the specific hormone. We provided all plasma concentrations in ng mL -1 , and yolk concentrations in ng g -1 ww. Bleeding time was kept as short as possible (mean ± SD: 02 min 09 sec ± 36 sec) and was not related to baseline CORT levels in plasma (linear model: F1, 12 = 0.15, p = 0.70).

Statistical analyses

Preliminary analyses

All statistical analyses were performed using R (v. 4.0.0; R Core Team, 2020). We tested the normality of residuals and visually inspected diagnostic plots for each models, to check whether the data met the linear model assumptions [START_REF] Zuur | Mixed effects models and extensions in ecology with R[END_REF]. First, we investigated the relationship between each hormone or PFAS in females' plasma and the sampling date using linear models (LMs). If the relationship was significant (p < 0.05) we used the residuals of the LM instead of the specific hormone or PFAS in the following analyses. This enabled us to obtain comparable individuals by minimizing the variance due to the sampling time. T3 and PFTeA were significantly decreasing with time in females (LM: F1, 12 = 7.06, p = 0.02 and F1, 12 = 6.56, p = 0.03 respectively) and residuals of the LM were consequently used in subsequent analyses.

Factors influencing the maternal transfer of hormones

We used linear mixed-effect models (LMMs, package "nlme" ) to investigate the effect of female and egg characteristics on the concentrations of each transferred hormone independently (i.e., one model per hormone). The full models included the maternal circulating concentration for the specific hormone, the female's scaled mass index (a proxy of the body condition of the female calculated following [START_REF] Peig | New perspectives for estimating body condition from mass/length data: the scaled mass index as an alternative method[END_REF]), the egg mass (used as a proxy of egg quality), the rank of the egg in the clutch by laying order (egg rank: 1 or 2) and the laying date of the first-laid eggs as fixed factors (see models formula in the SI). For all full LMMs, we built a set of models ranging from the full to the null model with all possible combination of predictors and we selected the best model according to the Akaik ̈e's Information

Criterion for small sample size (AICc; i.e., the most parsimonious one among those with a ΔAICc < 2; package "AICcmodavg"). In all LMMs, the nest ID was used as a random variable to account for the relation between both eggs of a clutch and therefore avoid pseudo-replication.

Relationship between PFAS concentration in females and the maternal hormones in their eggs

We assessed the effect of each maternal circulating PFAS on the transfer of each maternal hormone in eggs using LMs. As females were sampled before they laid their first egg, and since females may excrete a significant amount of PFAS during the laying process, we only included first-laid eggs in these analyses to avoid biased results. We built one model per hormone. For each PFAS independently, the full model included the specific PFAS as fixed factor as well as any variables identified as having a significant impact on the specific maternal hormone concentrations in the yolk in section 2.4.2 (except "egg rank" since only first-laid eggs were used here; see models formula in the SI). AICc selection was also performed on the full models, although only two models were compared: the full model and the full model without the PFAS variable.

Results

We provide the descriptive statistics for hormone concentration in females' plasma and egg yolk as well as PFAS concentrations in females' plasma in Table 1 &Table 2.

Factors influencing the maternal transfer of hormones

Egg yolk hormone levels were unrelated to female hormone plasma levels (SI Table S3).

First-laid eggs had significantly lower AND concentrations than second-laid eggs (SI Table S3 & Table S4; mean of first-and second-laid eggs respectively: 855 and 1030 ng g -1 ; confidence interval (CI) of the difference: [93. 1 -218]). We also found decreasing T3 and T3/T4 ratio with egg mass (CI of the slope: [-0.021 --0.001] and [-0.282 -0.079] respectively; SI Table S4 & Figure 1), but increasing T3 and T3/T4 ratio with female's scaled mass index (CI of the slope:

[0.000 -0.002] and [0.001 -0.019] respectively; SI Table S4 & Figure 1). No other investigated egg or female characteristics affected maternal hormones deposition (SI Table S4).

Female PFAS contamination and maternal hormone deposition

Yolk concentration of CORT, AND, DHT, T3 and T4, as well as T3/T4 ratios were not related to maternal PFAS burden in first-laid eggs (SI Table S5). The model selection showed that T was the only maternally transferred hormone related to certain female PFAS, PFNA, PFDcA and PFUnA (SI Table S5). Specifically, we found increasing T in eggs with increasing plasma circulating maternal concentrations of these three compounds with comparable strength even with different range of concentration found (PFNA: F1, 12 = 5.88; p = 0.032; CI of the slope:

[0.41 -7.75], PFDcA: F1, 12 = 5.87; p = 0.032; CI of the slope: [0.28 -5.27], and PFUnA: F1, 12 = 6.27; p = 0.028; CI of the slope: [0.10 -1.47]; SI Table S6 and Figure 2).

Discussion

We investigated maternally deposited concentrations of androgens, glucocorticoids and thyroid hormones in egg yolk of black-legged kittiwake in relation with the female's and eggs characteristics, and the potential disrupting effect of PFAS on maternal hormone deposition.

We found that egg yolk hormone levels were unrelated to female hormone plasma levels at the time of sampling, but that laying order, egg mass and the female's scaled mass index appeared to influence yolk concentration of some of the studied hormones. We observed an increased maternal T deposition in the first-laid egg in females bearing high levels of PFNA, PFDcA or PFUnA.

Factors influencing the maternal transfer of hormones

Differential deposition of androgens along the laying sequence -as observed for AND in the present study -have been described as a mean to influence the outcome of sibling rivalry in various avian species implementing brood reduction, ultimately maximising females' reproductive outputs [START_REF] Eising | Maternal androgens in black-headed gull (Larus ridibundus) eggs: consequences for chick development[END_REF][START_REF] Muriel | Age-related patterns of yolk androgen deposition are consistent with adaptive brood reduction in spotless starlings[END_REF][START_REF] Pinheiro | Yolk androgen deposition in rockhopper penguins, a species with reversed hatching asynchrony[END_REF]. Studies on black-legged kittiwakes have reported higher T and AND in second-laid eggs, the amount deposited likely being determined by a complex trade-off between offspring and mother fitness and the outcomes of such a differential deposition largely depends on females and environmental conditions [START_REF] Benowitz-Fredericks | Effects of food availability on yolk androgen deposition in the black-legged kittiwake (Rissa tridactyla), a seabird with facultative brood reduction[END_REF][START_REF] Gasparini | Food availability affects the maternal transfer of androgens and antibodies into eggs of a colonial seabird[END_REF][START_REF] Müller | Maternal androgens increase sibling aggression, dominance, and competitive ability in the siblicidal black-legged kittiwake (Rissa tridactyla)[END_REF][START_REF] Vallarino | Egg components vary independently of each other in the facultative siblicidal Black-legged Kittiwake Rissa tridactyla[END_REF]. Higher androgen concentrations enhance embryo growth and therefore reduce the detrimental effect of hatching asynchrony for the junior egg, however, at the expense of potential long-term costs for the offspring [START_REF] Groothuis | Maternal hormones as a tool to adjust offspring phenotype in avian species[END_REF]. Interestingly, contrary to AND, we did not observe any difference in the deposition of T, DHT or CORT in first-and second-laid eggs in the present study, despite the fact that they are all products of the same metabolic pathway.

Recent studies showed that maternal deposited thyroid hormones were associated with environmental factors including food availability and temperature experienced during the prelaying stage [START_REF] Hsu | Maternally transferred thyroid hormones and life-history variation in birds[END_REF][START_REF] Ruuskanen | Maternal Thyroid Hormones: An Unexplored Mechanism Underlying Maternal Effects in an Ecological Framework[END_REF]. Their effects are still unclear but seem to occur mainly during the embryological development period and largely act on offspring growth and positively impact hatching success and telomere length during early postnatal period [START_REF] Hsu | Transient growth-enhancing effects of elevated maternal thyroid hormones at no apparent oxidative cost during early postnatal period[END_REF][START_REF] Ruuskanen | Effects of experimentally manipulated yolk thyroid hormone levels on offspring development in a wild bird species[END_REF]Sarraude et al. 2020a;Sarraude et al. 2020b;Sarraude et al. 2020c;[START_REF] Stier | Born to be young? Prenatal thyroid hormones increase early-life telomere length in wild collared flycatchers[END_REF]. The increasing concentration of maternal T3 (but not T4) deposited with increasing females scaled mass index found in the present study may illustrate that females in good condition can invest more in their offspring than those in lower condition. However, heavier eggs -which have been identified in many species as eggs of higher quality, leading to a higher survival probability of the offspring [START_REF] Williams | Intraspecific variation in egg size and egg composition in birds: effects on offspring fitness[END_REF])received lower T3 concentrations (but not T4) than lighter eggs, although we investigated concentrations and not total deposited amount in eggs. Data on yolk thyroid hormones are very limited for birds at the moment and the factors driving thyroid hormone deposition in eggs are still unclear and need further clarifications (Hsu et al. 2020b).

Other factors including adult features (e.g., age, past experience, phenotype and genetic [START_REF] Tschirren | Heritable variation in maternal yolk hormone transfer in a wild bird population[END_REF][START_REF] Von Engelhardt | Maternal hormones in avian eggs[END_REF])), and the environment experienced before or during egg laying by females (e.g., food quality and availability [START_REF] Gasparini | Food availability affects the maternal transfer of androgens and antibodies into eggs of a colonial seabird[END_REF][START_REF] Verboven | Maternal condition, yolk androgens and offspring performance: a supplemental feeding experiment in the lesser black-backed gull (Larus fuscus)[END_REF] or social interactions [START_REF] Bentz | Evolutionary implications of interspecific variation in a maternal effect: a meta-analysis of yolk testosterone response to competition[END_REF])) were also proven important predictors of maternal hormones deposition in eggs. These data were not available in the present study and would be interesting to include in further integrative studies. That being said, breeding occurred extremely late in 2019 (laying date median in the whole colony in 2019: 25 th of June, 10 days later than usual average median laying date for the same population; [START_REF] Keogan | Variation and correlation in the timing of breeding of North Atlantic seabirds across multiple scales[END_REF]. It is likely that this late breeding was a consequence of delayed food supply which may have affected hormone levels (e.g., corticosterone; [START_REF] Goutte | Annual variation in the timing of breeding, pre-breeding foraging areas and corticosterone levels in an Arctic population of black-legged kittiwakes[END_REF][START_REF] Riechert | Predicting reproductive success from hormone concentrations in the common tern (Sterna hirundo) while considering food abundance[END_REF]. The maternal hormones deposition may thus have been largely impacted by these particular conditions. Therefore, we do recommend additional investigations in various environmental conditions, as well as experimental studies, to better identify the drivers of maternal hormone deposition in eggs.

Female PFAS contamination and maternal hormone deposition

Very few studies explored the relationship between endocrine-disrupting chemicals (EDCs) and maternal transferred hormones in avian or non-avian oviparous species, and to the best of our knowledge, only two studies found a correlation [START_REF] Hamlin | Environmental influence on yolk steroids in American alligators (Alligator mississippiensis)[END_REF][START_REF] Verboven | Maternally derived testosterone and 17beta-estradiol in the eggs of Arctic-breeding glaucous gulls in relation to persistent organic pollutants[END_REF], when others could not demonstrate any clear tendency [START_REF] French | Maternal steroids and contaminants in common tern eggs: a mechanism of endocrine disruption?[END_REF][START_REF] Johnston | Effects of maternally transferred organochlorine contaminants on early life survival in a freshwater fish[END_REF][START_REF] Ruuskanen | Transgenerational endocrine disruption: Does elemental pollution affect egg or nestling thyroid hormone levels in a wild songbird?[END_REF]. Several emerging and legacy PFAS are suspected or identified EDCs [START_REF] Coperchini | Thyroid Disrupting Effects of Old and New Generation PFAS[END_REF][START_REF] Johnson | Understanding Risk to Wildlife from Exposures to Per-and Polyfluorinated Alkyl Substances[END_REF], and recent studies on seabirds and raptors have reported association between glucocorticoids, thyroid hormones and some long-chain perfluoroalkyl acids [START_REF] Ask | Per-and Polyfluoroalkyl Substances Are Positively Associated with Thyroid Hormones in an Arctic Seabird[END_REF][START_REF] Choy | Potential disruption of thyroid hormones by perfluoroalkyl acids in an Arctic seabird during reproduction[END_REF][START_REF] Melnes | Dissimilar effects of organohalogenated compounds on thyroid hormones in glaucous gulls[END_REF]Sebastiano et al. 2020a;[START_REF] Sun | Influence of perfluoroalkyl acids and other parameters on circulating thyroid hormones and immune-related microRNA expression in free-ranging nestling peregrine falcons[END_REF][START_REF] Tartu | Endocrine and fitness correlates of long-chain perfluorinated carboxylates exposure in Arctic breeding black-legged kittiwakes[END_REF]. Regarding maternal hormones transfer to the eggs, our study shows that PFNA (C9), PFDcA (C10) and PFUnA (C11) concentrations in females are positively correlated with maternal T concentration in eggs. No significant correlations could be found for the perfluoroalkyl carboxylic acids (PFCAs) with longer carbon chains (C12 -C14), even though they were present at comparable concentrations.

Long-chain PFCAs (≥C8) have very similar physico-chemical characteristics [START_REF] Thackray | A global atmospheric chemistry model for the fate and transport of PFCAs and their precursors[END_REF], we could therefore expect a similar mode of action for them, and so, an additive effect when adding up the concentrations. However, no correlation was found between the sum of long-chain PFCAs (C8 -C14) and T (LM: F1, 12 = 3.24; p = 0.097; CI of the slope: [-0.05 -0.50]). There was also no significant relationship between maternal T deposited in eggs and females PFOS (brPFOS or linPFOS) although it is the predominant compound in females' plasma (Table 2). Perfluoroalkyl sulfonic acids (PFSAs) including PFHxS and PFOS have different physicochemical properties than PFCAs. Despite high PFOS concentrations and that this compound was previously found to downregulate the production of T in humans and rats [START_REF] Tarapore | Perfluoroalkyl Chemicals and Male Reproductive Health: Do PFOA and PFOS Increase Risk for Male Infertility?[END_REF], PFOS may be less prone to affect T transfer than long-chain

PFCAs. Although we cannot exclude that the observed relationships for C9 -C11 PFCAs may have been induced by unidentified, correlated factors, our results suggest that at least some long-chain PFCAs may cause a disruption of the maternal hormones concentrations in eggs.

A hypothesis behind this relationship may include disturbance of T biosynthesis or breakdown mechanisms by PFAS. Among hormones, if androgens are mainly formed in the theca interna cells of the follicles wall, thyroid hormones and corticosterone are synthesized by distant glands (thyroid and adrenal glands, respectively) of the mother bird [START_REF] Groothuis | Hormone-mediated maternal effects in birds: mechanisms matter but what do we know of them?[END_REF]. All hormones are then transferred to the oocyte via blood, although the mechanisms are still largely unexplored (von Engelhardt and Groothuis 2011). For instance, a disrupting effect of PFAS on the steroidogenesis may happen as steroids are produced from cholesterol, whose concentration in blood is known to be affected by PFAS in vertebrates [START_REF] Geiger | The association between PFOA, PFOS and serum lipid levels in adolescents[END_REF][START_REF] Geng | Effect of perfluorooctanesulfonic acid (PFOS) on the liver lipid metabolism of the developing chicken embryo[END_REF][START_REF] Jacobsen | Effects of perfluorooctane sulfonate on genes controlling hepatic fatty acid metabolism in livers of chicken embryos[END_REF][START_REF] Lin | Per-and polyfluoroalkyl substances and blood lipid levels in prediabetic adults-longitudinal analysis of the diabetes prevention program outcomes study[END_REF][START_REF] Roth | Exposure to a mixture of legacy, alternative, and replacement per-and polyfluoroalkyl substances (PFAS) results in sex-dependent modulation of cholesterol metabolism and liver injury[END_REF].

However, we would expect a similar disruption in females' plasma, which was not the case (LM for PFNA: F1, 12 = 1.79; p = 0.206; CI of the slope: [-0.67 -0.16], PFDcA: F1, 12 = 1.17; p = 0.30; CI of the slope: [-0.43 -0.15], and PFUnA: F1, 12 = 0.73; p = 0.41; CI of the slope: [-0.11 -0.05]). A disruption of the steroidogenesis may also happen at the enzymatic level. AND is metabolized to T by the 17β-hydroxysteroid dehydrogenase (17β-HSD) which is known to be inhibited by PFAS in humans and rats [START_REF] Zhu | Perfluoroalkyl substances cause Leydig cell dysfunction as endocrine disruptors[END_REF]. However, this reduced the production of T and thus cannot explain the higher levels of T observed in eggs of females with higher PFAS concentration. Another hypothesis could involve gonadotrophic hormones such as luteinizing hormone (LH). PFAS are known to affect LH in humans [START_REF] Raymer | Concentrations of perfluorooctane sulfonate (PFOS) and perfluorooctanoate (PFOA) and their associations with human semen quality measurements[END_REF], but this hormone was found essential to control T deposition in Japanese quails (Coturnix japonica; [START_REF] Okuliarova | Egg deposition of maternal testosterone is primarily controlled by the preovulatory peak of luteinizing hormone in Japanese quail[END_REF]). We did not measure LH in females and thus cannot explore this assumption, but this may be a valuable lead to explore in further studies.

Maternal hormone transfer mechanisms may also be affected. Unlike other vertebrates, birds do not produce any transport protein with high affinity to steroids as the sex hormone-binding globulin [START_REF] Wingfield | Physiologic properties of steroid hormone-binding proteins in avian blood[END_REF]. Instead, the corticosteroid-binding globulin which has a high affinity for CORT, may also transport androgens [START_REF] Lin | Avian corticosteroid-binding globulin: biological function and regulatory mechanisms in physiological stress responses[END_REF][START_REF] Vashchenko | Identification of Avian Corticosteroid-binding Globulin (SerpinA6) Reveals the Molecular Basis of Evolutionary Adaptations in SerpinA6 Structure and Function as a Steroid-binding Protein[END_REF]. Lipoproteins and albumin may bind to all steroids as well, with a low affinity [START_REF] Malisch | Steroid-binding proteins and free steroids in birds[END_REF][START_REF] Mcnabb | Thyroid Hormone Deposition in Avian Eggs and Effects on Embryonic Development[END_REF]. PFAS in blood are bound to albumin, fatty-acid binding proteins and organic anion transporters [START_REF] Ng | Bioaccumulation of perfluorinated alkyl acids: observations and models[END_REF]. Therefore, a competition for blood transporters, including albumin, between PFAS and maternal T during the process of maternal transfer to egg should result in a negative relationship between PFAS in females and deposited T in eggs, but we observe an opposite trend. Also, a displacement of hormones fixed to albumin by PFAS have previously been described as unlikely at environmental concentrations [START_REF] Jones | Binding of perfluorinated fatty acids to serum proteins[END_REF]). An alternative explanation can be offered on the basis of the molecular structure of the observed PFCAs. In kittiwakes, PFAS are linearly positively correlated between females and their eggs for most compounds, with the transfer efficiency depending on their physico-chemical characteristics caused by the increasing perfluorinated carbon chain length [START_REF] Jouanneau | A Bad Start in Life? Maternal Transfer of Legacy and Emerging Poly-and Perfluoroalkyl Substances to Eggs in an Arctic Seabird[END_REF]. Therefore, we can predict that the disrupting activity of PFAS in general and PFCAs with medium long chain length (C9 -C11) on T will vary according to the PFAS carbon chain length. In our study, the sample size was relatively low, which may limit the relationship between T and some of the PFAS. Further studies with a larger sample size would be essential to investigate the aforementioned hypotheses.

Overall, our study provides further evidence that certain long-chain PFCAs are the most associated with effects in this kittiwakes' population (Blévin et al. 2017a;[START_REF] Blévin | Contaminants, prolactin and parental care in an Arctic seabird: Contrasted associations of perfluoroalkyl substances and organochlorine compounds with egg-turning behavior[END_REF]Blévin et al. 2017b;[START_REF] Costantini | Higher plasma oxidative damage and lower plasma antioxidant defences in an Arctic seabird exposed to longer perfluoroalkyl acids[END_REF][START_REF] Tartu | Endocrine and fitness correlates of long-chain perfluorinated carboxylates exposure in Arctic breeding black-legged kittiwakes[END_REF], and that it is essential to investigate how single compounds affect physiological markers, in addition to how they act together (Sebastiano et al. 2020a). However, correlative studies in wild populations need to be interpreted with caution as the observed relationship between C9 to C11 PFCAs and T may be the consequence of alternative and unknown correlated contextual cues. Maternal yolk hormone concentrations are related to egg quality in some species, therefore in this wild population, females feeding on higher trophic level could accumulate more PFAS and invest more in reproduction by laying eggs with higher T concentrations.

A large body of literature describes the consequences of high T concentrations in eggs.

In semi-precocial seabirds, elevated yolk T was related to various development factors on offspring of seabirds from the same family (impaired sex-ratio [START_REF] Rubolini | Effects of elevated yolk testosterone levels on survival, growth and immunity of male and female yellow-legged gull chicks[END_REF], growth and body mass [START_REF] Eising | Maternal androgens in black-headed gull (Larus ridibundus) eggs: consequences for chick development[END_REF][START_REF] Parolini | Contrasting effects of increased yolk testosterone content on development and oxidative status in gull embryos[END_REF][START_REF] Rubolini | Effects of elevated yolk testosterone levels on survival, growth and immunity of male and female yellow-legged gull chicks[END_REF], increased begging [START_REF] Boncoraglio | Effects of elevated yolk androgens on perinatal begging behavior in yellow-legged gull (Larus michahellis) chicks[END_REF], competitiveness [START_REF] Müller | Maternal yolk androgens stimulate territorial behaviour in black-headed gull chicks[END_REF]) and survival [START_REF] Eising | Yolk androgens and begging behaviour in black-headed gull chicks: an experimental field study[END_REF], decreased hatching time [START_REF] Eising | Maternal androgens in black-headed gull (Larus ridibundus) eggs: consequences for chick development[END_REF], immune response [START_REF] Muller | Prenatal androgen exposure modulates cellular and humoral immune function of black-headed gull chicks[END_REF]) and telomere length [START_REF] Parolini | Egg Testosterone Differentially Affects Telomere Length in Somatic Tissues of Yellow-Legged Gull Embryos[END_REF]). In kittiwakes more specifically, experimentally elevated T in eggs led to an increased aggressiveness and dominance in the clutch [START_REF] Müller | Testosterone increases siblicidal aggression in black-legged kittiwake chicks (Rissa tridactyla)[END_REF][START_REF] Müller | Maternal androgens increase sibling aggression, dominance, and competitive ability in the siblicidal black-legged kittiwake (Rissa tridactyla)[END_REF]. Most of the studies cited above investigate the effects of experimentally elevated T, which often exceed T concentrations observed in wild populations. Embryos in natura may buffer maternal T through inactivation pathways, which could at least reduce the impact of an elevated deposition of maternal T [START_REF] Campbell | Characterizing the timing of yolk testosterone metabolism and the effects of etiocholanolone on development in avian eggs[END_REF].

A disruption of maternal deposited T may impact the embryo at different levels, inducing a mismatch between the environment experienced early and later in life by the offspring and its phenotype, which may ultimately affect its survival and fitness. Moreover, in kittiwakes, the most PFAS contaminated females laid the most contaminated eggs [START_REF] Jouanneau | A Bad Start in Life? Maternal Transfer of Legacy and Emerging Poly-and Perfluoroalkyl Substances to Eggs in an Arctic Seabird[END_REF], therefore the disrupted deposition of maternal T and the high concentrations of PFAS in females and eggs may have additive consequences on the embryo (known to be particularly sensitive to EDCs; Hamlin and Guillette 2011) through disruptions of the maternal adaptive effect, of embryo development and of the female's behavior during incubation and chick-rearing periods.

In the present study, we found no effect of PFAS on CORT and thyroid hormones (THs) deposition in eggs, despite these contaminants being known to negatively correlate with circulating CORT, and positively correlate with circulating THs in seabirds including kittiwakes and some birds of prey [START_REF] Ask | Per-and Polyfluoroalkyl Substances Are Positively Associated with Thyroid Hormones in an Arctic Seabird[END_REF][START_REF] Choy | Potential disruption of thyroid hormones by perfluoroalkyl acids in an Arctic seabird during reproduction[END_REF]Sebastiano et al. 2020b;[START_REF] Sun | Influence of perfluoroalkyl acids and other parameters on circulating thyroid hormones and immune-related microRNA expression in free-ranging nestling peregrine falcons[END_REF][START_REF] Tartu | Endocrine and fitness correlates of long-chain perfluorinated carboxylates exposure in Arctic breeding black-legged kittiwakes[END_REF]. CORT is known to be affected by food availability [START_REF] Goutte | Annual variation in the timing of breeding, pre-breeding foraging areas and corticosterone levels in an Arctic population of black-legged kittiwakes[END_REF][START_REF] Riechert | Predicting reproductive success from hormone concentrations in the common tern (Sterna hirundo) while considering food abundance[END_REF]. It is likely that the late breeding in 2019 was a consequence of delayed food supply which may have affected CORT levels. This may have, in turn, affected the maternal deposition of CORT in the yolk and possibly affected the relationship between PFAS and CORT deposition. Investigating of this relationship in different environmental contexts ("good" and "poor" conditions), may help in concluding on how PFAS may affect the maternal transfer of CORT. Concerning THs disruption by PFAS, mechanisms affected were explored in humans and birds and may include interaction with THs receptors and binding proteins, with the thyroid peroxidase enzyme activity or with thyroid-stimulating hormone [START_REF] Fenton | Per-and Polyfluoroalkyl Substance Toxicity and Human Health Review: Current State of Knowledge and Strategies for Informing Future Research[END_REF][START_REF] Kar | Endocrine-disrupting activity of per-and polyfluoroalkyl substances: Exploring combined approaches of ligand and structure based modeling[END_REF][START_REF] Mortensen | Homology modeling to screen for potential binding of contaminants to thyroid hormone receptor and transthyretin in glaucous gull (Larus hyperboreus) and herring gull (Larus argentatus)[END_REF]. In birds, maternal THs were found to impact several parameters in embryogenesis development and in post-hatch performance and fitness [START_REF] Darras | The Role of Maternal Thyroid Hormones in Avian Embryonic Development[END_REF][START_REF] Hsu | Transient growth-enhancing effects of elevated maternal thyroid hormones at no apparent oxidative cost during early postnatal period[END_REF]Sarraude et al. 2020a;Sarraude et al. 2020c;[START_REF] Stier | Born to be young? Prenatal thyroid hormones increase early-life telomere length in wild collared flycatchers[END_REF].

Therefore, the impact of PFAS may be limited on these endpoints during kittiwake embryo development, at least at the concentrations we measured in the present study.

Conclusion

This study identified some of the main factors driving the deposition of several major maternal hormones in eggs of the black-legged kittiwake. It also produced a first insight into the relationship between females PFAS burden in plasma and maternal transferred hormones in egg yolk. None of the investigated thyroid (T3 and T4) and glucocorticoid (CORT) hormones deposition seemed to be affected by female contamination. Similar results were observed for steroid hormones including AND and DHT, but we observed a positive relationship between some long-chain PFAS and T deposited in eggs. Although our results do not provide evidence for a causal relationship between PFAS contamination in females and maternal T in eggs, we suggested that the transfer mechanism may be similar for some PFAS and T, which may eventually affect maternal adaptive effects driven by T deposition.

Nonetheless, maternal hormones deposition depends on a complex combination of various intrinsic and extrinsic factors, including environmental conditions. The specific context in 2019, leading to a very late breeding may thus have affected maternal hormones transfer in a specific manner. We strongly recommend additional investigations among species and time, as well as experimental studies to draw strong conclusions on the main effects of PFAS on hormone deposition in avian eggs.

  °C with 4000 cpm of the appropriate H 3 -steroid (Perkin Elmer, US) and polyclonal antiserum (Ab). Anti-testosterone Ab was provided by Dr. Picaper (Nuclear medicine, CHU La Source, Orléans, France). The two anti-corticosterone Ab (one for plasma and one for yolk) were supplied by Merck, Sigma Aldrich, France. The bound fraction was then separated from the free fraction by addition of dextran-coated charcoal and the activity was counted on a Tri-Carb 2810TR scintillation counter (Perkin Elmer, US). AND and DHT were assayed with commercial ELISA kits supplied by IBL International(AND and DHT in yolk, ref. DB 52161 and DB 52021, respectively),

or Enzyme Linked ImmunoSorbent Assay (ELISA) methods. CORT and T were measured with RIA method, 100 μL of extract were incubated overnight at 4 Abnova

(AND in plasma, ref. KA 1898) and Demeditec (DHT in plasma, ref. DE 2330)

.

Acknowledgements

This project was supported by IPEV [prog. 330 to O. Chastel], the ANR ILETOP [ANR-16-CE34-0005] and ANR ToxSeaBird [ANR-21-CE34-0019]. W. Jouanneau was funded by a PhD grant from the University of La Rochelle, France. D.-J. Léandri-Breton was funded by the Natural Sciences and Engineering Research Council of Canada, the Fonds de Recherche du Québec -Nature et Technologies and the Northern Scientific Training Program. We acknowledge the French Polar Institute (IPEV) and the Alfred Wegener Institute (AWI) wintering staff in Ny-Ålesund as well as the Norwegian Polar Institute (NPI) and A. Corbeau from the Université de Rennes for their help and logistic support during the field season. We are also thankful to E. Grimaud and C. Ribout from the Centre d'Etudes Biologiques de Chizé

(CEBC) for hormonal analysis and for sexing the birds as well as for multiple advices they provided. The author wish to thank Yonina Eizenberg for kindly improving the English of the manuscript and two anonymous reviewers for their constructive feedbacks.