Jun-Hui Lin

Guo-Jie Chen

Nafees Ahmad

Muhammad Ishaq

Shuo Chen

Zheng-Hua Su

Ping Fan

Xiang-Hua Zhang

Yi Zhang

Guang-Xing Liang

Back contact interfacial modification mechanism in highly-efficient antimony selenide thin-film solar cells

Keywords: Sb 2 Se 3 solar cells, MoO 2 intermediate layer, Back contact, Defects

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

Introduction

Solar energy holds the promise of carbon-free energy that can be used to meet our energy demands. Si-based solar cells have the highest power conversion efficiency (PCE); it contributes significantly to photovoltaic (PV) devices with a PCE of more than 26.8% [1].

However, the low absorption coefficient and high processing cost of Si are major issues that limit its future application for the development of highly efficient and low-cost PVs.

Compound-based solar cells, such as perovskites, copper-indium-gallium-selenide (Cu(In,Ga)Se 2 ), and cadmium telluride (CdTe), have attracted huge attention and have attained PCE values higher than 21% [1]. However, the instability of perovskites, the toxic nature of Cd, and the low natural abundances of In and Ga are important issues in scaling up this technology. Therefore, research is being conducted on stable and environment-friendly PV semiconductor materials. Among various photoactive materials, antimony selenide (Sb 2 Se 3 ) thin films have an appropriate band gap, suitable absorption coefficient, and good conductivity [2][3][4][5]. Furthermore, their high theoretically attainable PCE (more than 30%) makes them potential candidates for the future generation of PVs [6]. Sb 2 Se 3 solar cells have drawn huge interest, and their performances have gradually improved. The reported PCE of Sb 2 Se 3 solar cells have increased promptly from 1.9% to 10.57% [2,3,[7][8][9][10][11][12][13][14][15]. The series-connected antimony selenosulfide monolithic integrated PV minimodules have achieved PCE of 7.15% [16]. Tang's group prepared Sb 2 Se 3 photo-absorber film by thermal evaporation method and obtained 2.1% efficiency [17]. Afterward, the rapid thermal evaporation method was used to tune the crystal orientation of Sb 2 Se 3 , which raised the PCE up to 5.6% [18]. In 2018, the same research group prepared a high-quality Sb 2 Se 3 absorber layer by vapor transporting deposition, and the defect concentration of the Sb 2 Se 3 absorber layer was reduced [3]. The Sb 2 Se 3 device exhibited a PCE of 7.6%. Mai et al. fabricated Sb 2 Se 3 nanorod array by close space sublimation process and gained a much-improved PCE of 9.2% [2]. Chen's group fabricated Sb 2 (S, Se) 3 solar cells with a PCE of 10% by hydrothermal method [19]. However, the PCE values were still considerably lower than the theoretical limits (PCE = 30%) of the Sb 2 Se 3 device. Sb 2 Se 3 PVs have shown exceptional performances with the device configuration of Mo/Sb 2 Se 3 /CdS/indium tin oxide (ITO)/Ag, similar to CZTS and CdTe solar cells [20,21]. Back contact engineering is one of the best strategies for improving the PV parameters (V OC , J SC , and fill factor (FF)) of chalcogenide thin-film solar cells [22]. The characteristics of Mo/Sb 2 Se 3 back contact play a significant role in photo-generated carrier transport in Sb 2 Se 3 devices, where the low barrier of Mo/Sb 2 Se 3 back contact is important to achieve a high PCE. In addition, a MoSe 2 layer was observed between Sb 2 Se 3 and Mo electrode [23]. A thick MoSe 2 interface layer may be harmful to the transport of carriers at the Mo/Sb 2 Se 3 back contact, which reduces the PCE of Sb 2 Se 3 solar cells. In our previous work, (211)-oriented Mo not only induced the growth of (hk1)-oriented Sb 2 Se 3 but also improved the ohmic contact at the Mo/Sb 2 Se 3 back interface due to the existence of MoSe 2 layer [24]. The ohmic contact of Mo/Sb 2 Se 3 interface can be improved by further reducing the thickness of MoSe 2 interface appropriately. Thus, further optimization of the back contact of Sb 2 Se 3 may lead to the auxiliary promotion of PCE. Relatively, less attention has been given to the modification of back contact (Mo/Sb 2 Se 3 ) of the device structure of Mo/Sb 2 Se 3 /CdS/ITO/Ag. Mo selenization was used to prepare the MoSe 2 intermediate layer (IL) at the back contact to boost the PCE of Sb 2 Se 3 solar cells, but the PCE of Sb 2 Se 3 solar cells was limited to 5% [25]. Thus, a better back contact modification of Sb 2 Se 3 solar cells is needed for detailed investigation. In this study, we adopted an ambient pre-annealing process to prepare the MoO 2 layer between Sb 2 Se 3 absorber layer and Mo substrate in Sb 2 Se 3 solar cells. The MoO 2 layer suppressed the formation of MoSe 2 interface layer, and the Mo/Sb 2 Se 3 back contact barrier was abridged. Compared with Sb 2 Se 3 solar cells (without MoO 2 IL), the V OC of Sb 2 Se 3 solar cells increased from 0.481 V to 0.487 V, the J SC increased from 23.81 mA/cm 2 to 29.29 mA/cm 2 , and FFFF increased from 50.28% to 57.10%, which led to a final PCE of 8.14% with the MoO 2 IL. Afterward, the effect of MoO 2 IL on the Sb 2 Se 3 properties, interface properties, carrier diffusion length, and defect properties of devices were explored. In addition, the influence of annealing temperature on the thickness of MoO 2 layer was thoroughly investigated.

Experimental

Preparation of MoO 2 intermediate layer

First, substrates (Mo-coated glass) were washed with ethanol, detergent, and distilled water by ultrasonication. The cleaned Mo substrates were annealed in the furnace under the air flow to grow the MoO 2 IL. Here, the annealing temperatures of samples were kept at 300 ℃ and 400 ℃.

The annealing duration of samples was 15 min. The unannealed sample was labeled as Mo1, and the samples annealed at 300 ℃ and 400 ℃ were respectively labeled as Mo2 and Mo3.

Preparation of Sb 2 Se 3 thin films

The Sb precursors were prepared on Mo1, Mo2, and Mo3 substrates by radio frequency magnetron sputtering at very low pressure (below 5.0×10 -4 Pa). The flow rate of Ar was 40 sccm, the sputtering power of Sb was kept at 34 W, the sputtering time of Sb metal precursor was 40 min, and the sputtering pressure for deposition of Sb was 1 Pa. Subsequently, Sb 2 Se 3 was fabricated by post-selenization of the Sb layer. The Se (0.4 g) and Sb metal precursors were kept in the compartment. The evacuation process was conducted, and argon was introduced into the furnace prior to selenization. The selenization pressure for all samples was 7×10 4 Pa. The selenization temperature of Sb 2 Se 3 on Mo1, Mo2, and Mo3 substrates was 410 ℃. The ramping rate for all selenized samples was 20 ℃/min, and the selenization time of all samples was 15 min. Three samples were labeled as S Mo1 , S Mo2 , and S Mo3 .

Fabrication of Sb 2 Se 3 solar cells

Cadmium sulfide (CdS) as a buffer layer was deposited onto the S Mo1 , S Mo2 , and S Mo3 samples by a chemical bath deposition method. The mixed solution was prepared by mixing cadmium sulfate (0.015 M), NH 3 OH aqueous solution, water, and thiourea (0.75 M). The Sb 2 Se 3 absorber was vertically dipped in the solution at 85 ℃ with continuous stirring for at least 9 min. The CdS films were put into the oven for 30 min to remove excess solution from the surface. The Sb 2 Se 3 /CdS heterojunction was heated at 325 ℃ in a vacuum, and the annealing time of all samples was 5 min. Afterward, the ITO layers were sputtered on the top surface of CdS buffer layers. Sputtering pressure (0.4 Pa), sputtering time (25 min), and sputtering power (120 W) were kept the same for all devices. Finally, the Ag electrodes were deposited by thermal evaporation. The device area measured 0.09 cm 2 after scabbing. The three devices were labeled as S Mo1 , S Mo2, and S Mo3 .

Characterizations

The crystal phases of MoO 2 ILs and Sb 2 Se 3 thin films were analyzed by X-ray diffraction (XRD, Ultima-iv) with Cu K α radiation. To further investigate the crystal phases of MoO 2 thin films, we analyzed the samples by Raman spectroscopy (HORIBA Jobin Yvon, LabRAM HR Evolution) with an excitation wavelength of 532 nm. Film morphologies of samples were obtained by the scanning electron microscopy (SEM, Zeiss SUPRA 55). Energy dispersive Xray spectroscopy (EDS, BRUKER QUANTAX 200) was utilized for the characterization of sample elemental compositions. The transmission electron microscopy (TEM) images of sample cross-sectional morphologies were obtained by FEI Titan Cubed ThemisG2 300 microscope. The samples for TEM imaging were fabricated by a focused ion beam (FEI Scios).

The elemental depth distribution of devices was obtained by TEM coupled with EDS. The ohmic contact properties of Mo/Sb 2 Se 3 back contact were tested by a multi-meter (Keithley, 2400 Series). The work functions of samples were analyzed by ultraviolet-photoelectron spectroscopy (UPS, Thermo Scientific ESCALAB 250Xi). The current density-voltage (J-V) of solar cells was measured by a multi-meter (Keithley, 2400 Series) under standard test conditions (100 mW/cm 2 , AM 1.5 G). The dark J-V curves of solar cells were also measured by a multi-meter (Keithley, 2400 Series). A Keithley 2400 source meter and Zolix SCS101 system were used to test the external quantum efficiency (EQE) of solar cells. Temperaturedependent dark J-V measurements were characterized by Lakeshore 325 temperature controller, and the temperatures were swept from 300 K to 230 K in a step of 10 K. The capacitancevoltage (C-V) measurements and drive level capacitance (DLCP) measurements were characterized by a Keithley 4200A-SCS system with JANIS cryogenic platform. The measurement of temperature-dependent V OC was utilized by the Lakeshore 325 temperature controller. The electrochemical impedance spectroscopy (EIS) of devices was characterized by the CHI600E electrochemical workstation. Temperature-dependent capacitance frequency (Cf-T) measurements were carried out within the frequency range of 100 Hz to 10 MHz using the same cryostat and cooling system as mentioned above.

Result and discussion

XRD analysis was performed to study the effect of air on the annealing of Mo. The XRD results (Fig. S1a) showed the presence of MoO 2 crystal phases (JCPDS#32-0671) at Mo back electrodes. Furthermore, the Raman spectra (Fig. S1b with a thickness of 80 nm can be observed at Sb 2 Se 3 /Mo back electrode. This finding demonstrates that the selenization process has no effect on the thickness of MoO 2 layer. In contrast to the SEM image (Fig. S3) of the S Mo1 device, the MoSe 2 interface layer was not visible at the Mo/Sb 2 Se 3 back contact in the S Mo2 device. Thus, the MoO 2 layer suppressed the formation of MoSe 2 layer. The (211)-oriented Sb 2 Se 3 has large grains penetrating through the full absorber layer in the S Mo2 device. On the other hand, a comparatively more dominant (221) oriented Sb 2 Se 3 absorber layer can be observed in the SEM image of S Mo1 devices (Fig. S3), consistent with the XRD results. According to the literature, the PCE of the Sb 2 Se 3 device with (211)-oriented Sb 2 Se 3 is more dominant than the (221)-oriented Sb 2 Se 3 [26]. In addition to the favored orientation, the back contact of the S Mo2 device featured a compact and void-free interface (Fig. 1a) in comparison with that of the S Mo1 device (Fig. S3). These findings demonstrate that the morphology of the Mo/Sb 2 Se 3 back contact was enhanced by the MoO 2 IL. Fig. 1(b) illustrates the J-V characteristic of S Mo1 , S Mo2 , and S Mo3 devices. The S Mo1 device had a V OC of 0.481 V, a J SC of 23.81 mA/cm 2 , a FF of 50.28%, and a PCE of 5.75%. When the MoO 2 IL with a thickness of 80 nm was introduced at the back contact of S Mo2 device, all the PV parameters of S Mo2 device increased. The S Mo2 device delivered a V OC of 0.487 V, J SC of 29.29 mA/cm 2 , and FF of 57.10%, thus achieving a PCE of 8.14%. The V OC-deficit decreased from 829 mV in S Mo1 device to 793 mV in S Mo2 device indicating the better performance due to the MoO 2 introduction. In addition, the MoO 2 layer with a thickness of 800 nm resulted in PV performance degradation. The S Mo3 device obtained a low PCE of 4.18% with a V OC , J SC , and FF of 0.424 V, 21.52 mA/cm 2 , and 45.76%, respectively. The resistances of MoO 2 IL increased as the thickness further increased. The Mo/Sb 2 Se 3 back contact with the high resistance limited the transport of photo-generated carrier, which led to performance degradation. All photovoltaic parameters were shown in Table 1. Fig. S4 summarizes the statistical distribution performances of the device parameters. Fig. 1(c) presents the J-V parameters of S Mo1 and S Mo2 devices under light and dark conditions. The existence of a back contact barrier led to the crossover behavior among the light and dark J-V curves besides the double diode performance [27]. Compared with S Mo2 device with MoO 2 IL, the crossover points occurred at a lower current in the S Mo1 device. According to the literature, the crossover behavior at a low current is attributed to the high back contact barrier in solar cells [28]. Thus, the high back contact barrier height may be present in S Mo1 devices. In addition, the collection of photogenerated holes mainly depends on the Mo/MoSe 2 interface. Thus, we further investigated the barrier of Mo/MoSe 2 in the S Mo1 device. Fig. S5 shows the UPS spectra of MoSe 2 , Sb 2 Se 3 , MoO 2 , and Mo. The barrier heights of Mo/MoSe 2 , Mo/MoO 2 , and MoO 2 /Sb 2 Se 3 were 0.55, 0.02, and 0.03 eV, respectively. Fig. 1(d ande) presents the band diagrams of S Mo1 and S Mo2 devices. Fig. S6 reveals the effects of the MoO 2 layer on the EQE of solar cells, band gap, and Urbach energy of the absorber. Figs. S6(a andb) show the EQE of S Mo1 and S Mo2 devices, respectively. The EQE results demonstrate that the S Mo2 device had a higher J SC than the S Mo1 device due to its superior carrier collection efficiency. Better crystal orientation improved crystalline quality, and a reduced MoSe 2 interface layer all contributed to the improved J SC , which also resulted in a higher FF [28]. The band gaps of Sb 2 Se 3 in S Mo1 and S Mo2 devices measured 1.31 and 1.28 eV, respectively (Fig. S6c). Thus, the MoO 2 IL can change the band gap of the Sb 2 Se 3 absorber layer. Fig. S6(d) shows the Urbach energy (E u ) of Sb 2 Se 3 attained from EQE. The E u parameter is used to evaluate the band tail states because of impurities, defects, and disorders in photo-absorber materials [24]. An E u of 22. ratio from 1.28 to 0.87. Thus, an overly thick MoO 2 layer limits the growth of (hk1)-oriented Sb 2 Se 3 . These findings were further authenticated by evaluating the texture coefficient (TC) of Sb 2 Se 3 peaks (Fig. 2b), which can be calculated by Equation (1) [29] (1)

           N i l k h l k h hkl hkl hkl i i i i i i I I N I I TC 1 ) ( 0 ) ( ) ( 0 ) ( 1
where the peak intensities of planes hkl are I 0(hkl) and I (hkl) in the standard and measured XRD patterns of Sb 2 Se 3 thin films, respectively. A large TC value indicates the preferred orientation along a specific direction [30]. Compared with S Mo1 and S Mo3 samples, the TC value of S Mo2 sample's (211) peak was higher. When the thickness (MoO 2 ) increased from 0 nm to 80 nm, the TC value of S Mo2 sample's (211) peak increased and then declined with the further increase in thickness. Fig. 2(c-e) displays the images of surface morphologies of S Mo1 , S Mo2 , and S Mo3 samples. Alongside the preferred orientation, the S Mo2 sample also showed compact, flat, and large-grained surface morphology, whereas the other two samples comprised comparatively smaller grains and several voids (Fig. 2c-e). Fig. 2(f) shows the plotted porosity and average crystal size of Sb 2 Se 3 , which indicates that the S Mo2 sample had larger crystal sizes and fewer pin holes. These results demonstrated that the MoO 2 IL with 80 nm-thickness was obliged to the growth of (211)-oriented Sb 2 Se 3 with large grains. The champion S Mo2 sample was Sb-poor and Se-rich as listed in Table S1.

To further study the interface morphologies of Mo/Sb 2 Se 3 in S Mo2 solar cells, we captured the TEM images of S Mo2 devices (Fig. 3). ITO, window layer, a buffer layer (CdS), Sb 2 Se 3 absorber layer, MoO 2 IL, and Mo back electrode of S Mo2 device were observed from the top to the bottom in Fig. 3(a). High-angle annular dark field scanning-transmission electron microscopy) was performed at the heterojunction interface of Sb 2 Se 3 /CdS in Fig. 3(b). The interface of Sb 2 Se 3 /CdS was indistinct, which implies less lattice mismatch between Sb 2 Se 3 and CdS. Fig. MoO 2 /Sb 2 Se 3 interfaces is expected to be applied to establish efficient charge carrier generation and transport. Fig. 3(d-f) displays the high-resolution TEM images of Sb 2 Se 3 absorber layer, MoO 2 IL, and Mo electrode in the device. To further examine the preferred orientation of each layer, we examined the electron diffraction patterns of Sb 2 Se 3 , MoO 2 , and Mo using Fourier transform (Fig. 3g-i). In Fig. 3(g), the (221), (211), and (002) planes of Sb 2 Se 3 can be observed. Their corresponding resistances were 14.08, 9.90, and 25.64 Ω. The S Mo2 device exhibited the largest slope indicating the lowest resistivity and it can improve the ohmic behavior at the Mo/MoO 2 /Sb 2 Se 3 back contact which is favorable for the efficient transport of photogenerated holes [24]. J-V-T curves of devices were also characterized at the temperature range of 230-300 K in a dark environment (Fig. 4a andb). R s and barrier heights of the back contact diode were obtained from the result of dark J-V-T [31,32]. Fig. 4(c) shows the temperature-dependent R s . The R s of the S Mo1 device increased 20 times from 300 K to 230 K, compared with the 4 times increased observed for the S Mo2 device. The contact barrier (Φ B ) at the Mo/Sb 2 Se 3 led to a high R s value at low temperatures. The transport of photogenerated carriers was suppressed by hindering the contact barrier. At low temperatures, the back contact diode term is dominated by fitting the corresponding linear region of ln (R s T) versus 1/T plot in Fig. 4(d). The Φ B of S Mo1 and S Mo2 devices were 217 and 73.9 meV, respectively. The smaller barrier existed at the back contact of S Mo2 device. In addition, the J-V-T analysis was a useful method used to determine a dominant recombination path present in Sb 2 Se 3 solar cells by plotting Aln(J 0 ) against 1/kT (Fig. 4e). The Aln(J 0 ) versus 1/kT data should yield a straight line and extrapolate to the activation energy E A /q at T=0 K. The activation energy (E A ) of recombination for the S Mo1 device was 0.71 eV, and that for S Mo2 device was 1.18 eV. The bandgap of Sb 2 Se 3 thin films can be obtained from EQE, and the calculated bandgaps of S Mo1 and S Mo2 were 1.31 and 1.28 eV, respectively (Fig. S6). The E A for the S Mo1 device was considerably lower than the band gap of Sb 2 Se 3 in S Mo1 device, which suggests that the recombination mechanism of S Mo1 device was mainly influenced by interface recombination. The E A for the S Mo2 device was relatively close to the band gap of Sb 2 Se 3 in S Mo2 device, which signified the passivation of recombination at the interface. Fig. 4(f) presents a model of the back contact junction of Sb 2 Se 3 solar cell as a Schottky diode. The circuit model includes two diodes: the main solar cell diode (D SC ) and back contact diode (D BC ) [31]. When the solar cell is forward-biased, the back contact diode is in reverse bias. The reversed biased D BC is detrimental to the output of photo-generated current.

Therefore, MoO 2 IL reduces the back contact barrier value, which significantly mitigates the depraved effect of reversed biased D BC on the output of photo-generated current.

The interfacial defects and bulk defects of S Mo1 and S Mo2 devices were also investigated by C-V and DLCP measurements (Fig. 5a). The DLCP (N DLCP ) is solely sensitive to responses from bulk defects and free carriers, whereas the C-V (N C-V ) theoretically incorporates responses from interfacial defects, bulk defects, and free carriers [6,10]. Thus, the interfacial defects of Sb 2 Se 3 /CdS were calculated from N C-V -N DLCP at zero V. The plots of N C-V and N DLCP for S Mo1 and S Mo2 devices can be obtained from Equation 2[33]:

(2) r,n D C-V 2 2 0 r,n r,p D r,p 3 0 DLCP 2 0 r,p 1 0 r,p 0 2 (1/ ) 2 2 / N N d C qA N dV C N q A C x A C                                
where A is the area of solar cells, is the carrier concentration of CdS, is the permittivity To further study the effect of MoO 2 IL on the bulk defect of Sb 2 Se 3 , we used admittance spectroscopy measurement to examine the energy levels of defects in the bandgap and defect density in the device. Fig. 5(c andd) shows the capacitance-frequency (C-f) results of S Mo1 and S Mo2 devices measured at different temperatures from 300 K to 180 K with an increment of 5

K. One defect level was witnessed in S Mo1 and S Mo2 devices. The inflection point corresponding to the admittance spectrum was determined by the Arrhenius plot. Its frequency value (ω 0 ) was obtained from the angular frequency point ω at the maximum of the ωdC/dω plot. The defect activation energies (E a ) were calculated from the slopes of Arrhenius plots that were linearly fitted based on Equation 3 [34 _ 36].

(3) device with an E a of 311 meV can be both referred to as Se vacancy (V Se ) (Fig. 5e) [37,38]. To further gain insights, we Gaussian fitted the distribution of each defect type using the Kimerling model based on the following equations [39].

2 a 0 0 2 exp( ) E T kT    
(4)

  2 0 2 ln( ) T E kT     ( 5
) d t ( ( )) V dC N E q d kT      
where built-in potential, angular frequency, and defect density are denoted as , and , and d V 

, respectively. The defect densities of values are given in Fig. 5

(f). The ( ( ))

t N E  a E calculated defect densities of S Mo1 and S Mo2 devices were 1.91×10 16 and 6.64×10 15 cm -3 , respectively. The MoO 2 IL reduced the device's defect density, resulting in less recombination at the interfacial and photo-absorber layers (Table 2). Furthermore, carrier properties were obtained from temperature-dependent V OC measurement. and S Mo2 devices. Shunt conductance (G), diode ideality factor (A), series resistance (R), and reverse-saturation current density (J 0 ) were obtained from Equation ( 6) [40]. against (J+J SC ) -1 (Fig. 6e). The R of S Mo1 and S Mo2 devices were 5.05 and 2.89 Ω . cm 2 , respectively. The resulting value of R in S Mo2 device was smaller than that of S Mo1 device. In addition, the A of S Mo1 and S Mo2 devices were 2.34 and 1.79, respectively, implying the less interface recombination in S Mo2 device. By plotting ln(J+J SC -GV) versus V-RJ (Fig. 6f), the J 0 values of 1.1×10 -3 and 8.94×10 -4 mA/cm 2 were observed for S Mo1 and S Mo2 devices, respectively. Compared with the S Mo1 device, the S Mo2 device with MoO 2 IL had lower G, R, and A, which confirmed the improved Sb 2 Se 3 /CdS heterojunction quality.

(6) 0 L exp ( ) q J J V RJ GV J AkT          

Conclusions

In summary, we systematically improved the PV properties of Sb

  ) indicated the formation of MoO 2 phases on the surfaces of Mo substrates. The presence and thickness of MoO 2 ILs are depicted in Fig, S2, where Mo1 represents the sample without air annealing, Mo2 denotes the sample annealed at 300 ℃, and the sample annealed at 400 ℃ was labeled as Mo3. Samples Mo2 and Mo3 exhibited compact and smooth layers of MoO 2 having a thickness of 80 and 800 nm, respectively. Fig. 1(a) shows the cross-sectional morphology of the full device (Mo/Sb 2 Se 3 /CdS/ITO/Ag) fabricated on the sample Mo2, which is labeled as S Mo2. MoO 2 layer

  3 meV indicated the reduction of defect states due to the introduction of MoO 2 IL. The roles of MoO 2 IL include obtaining the ideal orientation of Sb 2 Se 3 , limiting the growth of MoSe 2 interface layer, lowering the back contact barrier, promoting grain growth, and increasing minority carrier diffusion length. These functions of MoO 2 IL in the device need to be investigated in detail.

Fig. 2 (

 2 Fig. 2(a) shows the XRD data of the Sb 2 Se 3 film on Mo1, Mo2, and Mo3 substrates. All the

3

  (c) shows the TEM image of back contact (Mo/MoO 2 /Sb 2 Se 3 ). A distinct interface with flattened and tacky contact can be observed at the Mo/MoO 2 and MoO 2 /Sb 2 Se 3 interfaces. The absence of dislocation, amorphous layer, or crystal lattice distortion at the Mo/MoO 2 and

Fig. 3 (

 3 Fig. 3(h) illustrates the (011), (-211), and (022) planes of MoO 2 , whereas Fig. 3(i) illustrates

D N 0  1 C

 01 of free space, and and are the relative permittivities of CdS and Sb 2 Se 3 respectively. parameters attained from the C-V data. The low discrepancy 0 C between the results of DLCP and the C-V of S Mo2 indicated minor interfacial defect concentration and less interface recombination than S Mo1 at the Sb 2 Se 3 /CdS interface. The concentrations of interfacial defect for S Mo1 and S Mo2 devices were 1.91×10 16 and 5.50×10 15 cm -3 , respectively. Moreover, the S Mo2 device possessed a larger depletion width (W d ) as compared with S Mo1 which was reasonable to occur since it varied positively with built-in voltage (V bi ), indicating the improved carrier transport in this high built-in electrical field, which improves the carrier transports. To further analyze the depletion region information and the mechanism behind the enhanced device performance, we performed C-V measurements. Fig. 5(b) shows the 1/C 2 -V curves. The V bi extracted from the extended slope of the curves to the xaxis intercept for S Mo1 and S Mo2 devices were 533 and 582 mV, respectively. The MoO 2 IL improved the growth quality of Sb 2 Se 3 absorber layer, which optimized the Sb 2 Se 3 /CdS heterojunction interface qualities. Thus, the MoO 2 IL increased the built-in voltage (V bi ) of Sb 2 Se 3 solar cells, which led to the increased V OC , J SC , and FF of S Mo2.

  Boltzmann constant, and is the defect activation energy representing the average defect a E energy level relative to the valence band maximum or conduction band minimum. According to the literature, the defect in the S Mo1 device with an E a of 321 meV and the fault in the S Mo2

Fig. 6 (

 6 Fig.6(a) illustrates the E a of the main recombination in the solar cell. E a of S Mo1 and S Mo2

Fig. 6 (

 6 Fig. 6(d) shows the dJ/dV versus V plot. The G values of S Mo1 and S Mo2 devices were 11.05 and

Fig. 1 .

 1 Fig. 1. (a) Cross-sectional SEM image of S Mo2 device. (b) J-V curves of S Mo1, S Mo2 and S Mo3

Fig. 2 .

 2 Fig. 2. (a) XRD patterns of Sb 2 Se 3 thin films. (b) Texture coefficients of the diffraction peaks

Fig. 3 .

 3 Fig. 3. (a) Cross-sectional TEM image of S Mo2 device. (b) Sb 2 Se 3 /CdS interface TEM image.

Fig. 4 .

 4 Fig. 4. (a and b) Temperature-dependent dark current density vs voltage characteristics for a

Fig. 5 .

 5 Fig. 5. (a) C-V and DLCP profiles of the S Mo1 and S Mo2 devices. (b) 1/C 2 -V plots of the S Mo1 and

Fig. 6 .

 6 Fig. 6. (a) Temperature-dependent V OC measurements . (b) Nyquist plots of S Mo1 and S Mo2

Fig. S1 .

 S1 Fig. S1. (a) XRD patterns of Mo1, Mo2, and Mo3 substrates, and (b) Raman spectra of the

Fig. S2 .

 S2 Fig. S2. (a-b) Surface SEM images of Mo substrates, and (d-f) cross-sectional SEM images of

Fig. S6 .

 S6 Fig. S6. (a) EQE and integarated J SC of S Mo1 device, (b) EQE and integarated J SC of S Mo2 device,

Fig. S7 .

 S7 Fig. S7. EDS element depth profiles of Mo, O, Sb and Se elements in S Mo2 device.

Table 1 .

 1 2 Se 3 solar cells by introducing MoO 2 IL to optimize Sb 2 Se 3 crystal growth and back contact properties. MoO 2 IL successfully reduced the thickness of the MoSe 2 interface layer, and less void can be observed at the Mo/Sb 2 Se 3 interface. The back contact barrier of Mo/Sb 2 Se 3 was lowered by the MoO 2 IL, which significantly increased the FF of the solar cell. The growth of (211)-oriented Sb 2 Se 3 with large grains was induced by the MoO 2 IL. In addition, the introduction of MoO 2 IL not only improved the minority carrier diffusion length but also reduced the bulk defects of Sb 2 Se 3 and interface defects at Sb 2 Se 3 /CdS, which inhibited the recombination of devices and improved the carrier transport. Thus, compared with that of S Mo1 solar cells without MoO 2 IL, the V OC of the S Mo2 with MoO 2 layer increased from 0.481 V to 0.487 V and J SC from 23.81 mA/cm 2 to 29.29 mA/cm 2 and attained a champion PCE of 8.14%. Our work provides an effective method to regulate Sb 2 Se 3 crystal growth and back interface properties by introducing MoO 2 IL for highly efficient Sb 2 Se 3 devices. The photovoltaic parameters of S Mo1 , S Mo2 and S Mo3 devices.

	Devices	V OC (V)	J SC (mA/cm 2 )	FF (%)	PCE (%)
	S Mo1	0.481	23.81	50.28	5.75
	S Mo2	0.487	29.29	57.10	8.14
	S Mo3	0.424	21.52	45.76	4.18

Table 2 .

 2 Summary of the results derived from CV, DLCP and AS measurement.

				Interface defect
	Devices	N CV (cm -3 ) N DLCP (cm -3 )		V bi (mV)	W d (nm)
				density (cm -3 )
	S Mo1	8.11×10 16	6.20×10 16	1.91×10 16	533	0.281
	S Mo2	6.71×10 16	6.16×10 16	5.50×10 15	582	0.290

Table S1 .

 S1 EDS results for Sb 2 Se 3 thin films with different Mo substrates.

	Sample	Sb (at. %)	Se (at. %)	Sb/Se ratio
	S Mo1	35.54	64.46	0.55
	S Mo2	38.09	61.91	0.62
	S Mo3	40.68	59.32	0.69

Acknowledgements

This work was supported by the National Natural Science Foundation of China (62074102), the Guangdong Basic and Applied Basic Research Foundation (2022A1515010979), the Key Project of Department of Education of Guangdong Province (2018KZDXM059), the Science and Technology plan project of Shenzhen (20220808165025003). The authors wish to acknowledge the assistance on HAADF-STEM observation received from the Electron Microscope Center of the Shenzhen University.

Supporting Information

Back contact interfacial modification mechanism in highyefficient antimony selenide thin-film solar cells

Jun-Hui Lin 1 , Guo-Jie Chen 1 , Nafees Ahmad 1 , Muhammad Ishaq 2 , Shuo Chen 1 , Zheng-Hua Su 1 , Ping Fan 1 , Xiang-Hua Zhang 3 , Yi Zhang 4 , Guang-Xing Liang Highlights  MoO2 layer induces the growth of (211) oriented Sb2Se3 with large grains.  Low back contact barrier can be achieved by introducing the MoO2 layer.  The carrier recombination, bulk and interfacial defects can be passivated.  Highly efficiency of 8.14% obtained by back contact optimization.

Declaration of interests

☒ 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.

☐ The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:


Stéphane Drouet

Sébastien Chevrot

Fabrice Cotton

Annie Souriau

Simultaneous Inversion of Source Spectra, Attenuation Parameters, and Site Responses: Application to the Data of the French Accelerometric Network

Displacement spectra of earthquakes recorded by the French accelerometric network at regional scale are modeled as the product of source, propagation (including geometric and anelastic attenuation), and site effects. We use an iterative Gauss-Newton inversion to solve the nonlinear problem and retrieve these different terms. This method is easy to implement because the partial derivatives of the amplitude spectrum with respect to the different parameters have simple analytic forms. After convergence, we linearize the problem around the solution to compute the correlation matrix, which allows us to identify the parameters which are poorly resolved. We analyze data from two tectonically active regions: the Alps and the Pyrenees. Eighty-three earthquakes with local magnitudes between 3.0 and 5.3 are analyzed, with epicentral distances in the range 15-200 km. S-wave displacement spectra are computed using a fast Fourier transform and integration in the 0.5-15-Hz frequency domain. We assume a Brune-type source, with a geometric attenuation of the form R γ , γ being constant, and a frequency-dependent quality factor of the form Q Q 0 × f α . The results reveal that the attenuation parameters are correlated to each other and to the seismic moments. The two regions have different attenuation patterns. The geometrical spreading factor is equal to 1 for the Alps and 1.2 for the Pyrenees. The anelastic attenuation exhibits low Q 0 values (322 and 376 for the Alps and the Pyrenees, respectively) with regional variations for α (0.21 in the Alps and 0.46 in the Pyrenees). Computed moment magnitudes are generally 0.5 unit smaller than local magnitudes, and the logarithms of the corner frequencies decrease linearly with magnitude according to log 10 f c 1:72 0:32 × M w . Stress drops range from 10 5 to 10 7 Pa (i.e., 1-100 bars), with a slight dependence to magnitude (large stress drops for large magnitudes). Finally, robust site responses relative to an average rock-site response are derived, allowing us to identify good reference rock sites.

Introduction

In regions of low to moderate seismicity, as is the case in France, strong motion prediction is generally based upon extrapolation of weak-motion modeling, with extrapolations implying nonlinear processes [START_REF] Bay | Predictive ground motion scaling in Switzerland: best estimates and uncertainties[END_REF]. Attenuation and site responses are crucial parameters to perform such a prediction. Another important parameter that requires careful determination is the seismic moment. For historical and practical reasons, several magnitude scales are used to characterize small events, based on either record duration, S-wave amplitude, or on the coda decay. Moment magnitudes are now widely used for large events, but their determination for small events still leads to variable results.

In a previous study [START_REF] Drouet | Attenuation, seismic moment, and site effects for weak-motion events: application to the Pyrenees[END_REF], we used a twostep linear inversion adapted from [START_REF] Scherbaum | Distribution of attenuation in the Kaoiki, Hawaii, source volume estimated by inversion of P wave spectra[END_REF] to retrieve the source, propagation, and site terms. This method was applied to accelerometric data collected by the Réseau Accélérométrique Permanent (i.e., French Accelerometric Network, RAP) in the French Pyrenees. However, the linearization process required several simplifications in the formalization of the problem, in particular an anelastic attenuation that is not frequency dependent. In addition, this method did not resolve some parameters that are strongly correlated, such as attenuation parameters and corner frequencies, or attenuation parameters and seismic moments.

Several other studies deal with such inversion of source, propagation, and site terms. Some authors used information from one particular frequency to linearize the inversion [START_REF] Bonilla | Site amplification in the San Fernando Valley, California: variability of site-effect estimation using the S-wave, coda and H/V methods[END_REF][START_REF] Malagnini | Ground-motion scaling in the region of the 1997 Umbria-Marche earthquake (Italy)[END_REF]. [START_REF] Frankel | Site response for Seattle and source parameters of earthquakes in the Puget Sound region[END_REF] used a nonlinear inversion to retrieve source and site terms after correcting for attenuation using a body-wave geometrical decay and a quality factor adapted to the region under study.

Here, we propose to use a similar Gauss-Newton method to invert simultaneously the different parameters describing propagation, sources, and sites. The problem is nonlinear because of the form of the source excitation and of the frequency-dependent quality factor. Following the classical approach, the amplitude spectra are expressed as a product of source, propagation, and site terms. The Gauss-Newton method starts from an a priori model and explores iteratively the model space, using the partial derivatives of the amplitude spectrum with respect to the different parameters that are computed at each step. In addition, we can compute the correlation matrix, which allows us to estimate the trade-off between the parameters and to identify those that are poorly resolved. We have applied this method to the accelerometric data for two tectonically active regions: the Alps and the Pyrenees. The application to the Pyrenean data will allow us to compare our results with those obtained with the linear method previously used [START_REF] Drouet | Attenuation, seismic moment, and site effects for weak-motion events: application to the Pyrenees[END_REF].

The French Context

France is a country of low to moderate seismicity. The strongest earthquakes occur principally in the Rhine Graben, the Alps, the Pyrenees, and the western part of France where only two accelerometers are currently installed. The other regions are characterized by a lower level of activity. Figure 1 shows the seismic activity in the French national territory for the period 1984-2004 as given by the Bureau Central Sismologique Français (BCSF). The deformation rates within France are low, of the order of a few millimeters per year, as inferred by Global Positioning System (GPS) measurements [START_REF] Nocquet | Crustal velocity field of western Europe from permanent GPS array solutions, 1996-2001[END_REF]. However, evidence of strong earthquakes (M ∼6) with large recurrence times is found in the historical seismicity [START_REF] Lambert | Mille Ans de Séismes en France[END_REF], and the two regions analyzed in this study were struck by such events in the past. The RAP accelerometric network has been operating in France since 1996. It is managed by several institutions, and the data are freely accessible at www-rap.obs.ujf-grenoble.fr. There are 109 stations now deployed in the French metropolitan territory and another 20 in the Lesser Antilles (Martinique and Guadeloupe). The number of stations has increased since 2000, and a large database of moderate earthquakes is now available.

Several magnitude scales are currently used to characterize the seismicity in France. At the national level, the Réseau National de Surveillance Sismique (RéNaSS) at Strasbourg uses a magnitude scale (M R eNaSS ) based on the maximum amplitude of the vertical component with a specific amplitude decay of the form aΔ b , with Δ the epicentral distance and a, b constants, compatible with Richter's M L scale. The Laboratoire de Détection Géophysique (LDG) of the Atomic Energy Commission has defined another magnitude scale (M LDG ) based on the amplitude of the Lg wave at distances between 100 and 500 km, with a distance correction defined for the whole national territory. Defining an appropriate amplitude decay in order to determine a momentbased magnitude scale is one of the goals of this study.

Numerous studies of crustal attenuation have been conducted in France. [START_REF] Modiano | Experimental study of the spectral content for shallow earthquakes[END_REF] used the high frequency part of Fourier spectra, assuming a source decay as f 2 , to estimate a constant quality factor. [START_REF] Thouvenot | Frequency dependence of the quality factor in the upper crust: a deep seismic sounding approach[END_REF] used ray integrals and a depth-dependent quality factor to compute anelastic attenuation for compressional waves. Other authors used the decay of Lg waves at large distance in order to estimate a frequency-dependent quality factor [START_REF] Nicolas | Attenuation of regional phases in western Europe[END_REF][START_REF] Campillo | Frequency-dependent attenuation in the crust beneath central France from Lg waves: data analysis and numerical modelling[END_REF][START_REF] Campillo | Frequency dependence and spatial distribution of seismic attenuation in France: experimental results and possible interpretations[END_REF], or the decay of coda waves [START_REF] Herráiz | Application of coda wave analysis to microearthquake analog data[END_REF][START_REF] Gagnepain-Beyneix | Evidence of spatial variations of attenuation in the western Pyrenean range[END_REF][START_REF] Eva | Regional coda Q variations in the western Alps (northern Italy)[END_REF], where the single scattering model is used. The different attenuation models obtained for France are summarized in Table 1. These different studies found Q-values between 100 and 1000, but large values of Q 0 were generally associated with low values for α, suggesting a strong trade-off between these two parameters. Quantifying these correlations between attenuations parameters is also a goal of the present study.

One of the critical factors in the accurate determination of earthquake source parameters and estimation of seismic hazard is detailed information on site response. The actual site classification of the French accelerometric stations is based on geological maps and visual description of sites. According to [START_REF] Steidl | What is a reference site?[END_REF], instruments located on apparently competent bedrock may not be good reference sites with a flat amplitude response in the frequencies of engineering interest. One of the goals of our study is to determine site effects of each individual French accelerometric station and to identify reference stations having a transfer function similar to that expected for a rock site. Reference sites where accelerometric stations are now installed have been used to evaluate local site effects in large cities (Grenoble, Nice) with site-to-reference spectral ratio methods [START_REF] Semblat | Numerical analysis of seismic wave amplification in Nice (France) and comparisons with experiments[END_REF][START_REF] Le Brun | Site effect study in urban area: experimental results in Grenoble (France)[END_REF] or to assess rock ground motion models [START_REF] Scherbaum | On the use of response spectral-reference data for the selection and ranking of ground-motion models for seismic-hazard analysis in regions of moderate seismicity: The case of rock motion[END_REF]. The critical assumption in these studies is that the surface-rock-site record (reference) at these stations is equivalent to the input motion at the base of the soil layers, and that these particular rock sites have a flat transfer function. We will assess the validity of this assumption.

Data Selection and Spectrum Computation

Two data sets have been constructed for two regions of France: the Alps and the Pyrenees. For these two regions, the data sets consist of earthquakes with local magnitudes larger than 3 and recorded by at least three RAP stations. This selection results in 55 earthquakes in the Alps and 28 earthquakes in the Pyrenees. Records corresponding to distances between 15 and 200 km are kept. Figure 2 presents the location of the two regions with earthquake epicenters, stations, and paths. In Figure 3, we plot the recording distances for each station for the two areas. One can see that each station records earthquakes at various distances and that there is no obvious bias of recording distance with magnitude (open triangles are earthquakes with M R eNaSS lower than or equal to 3.5, and black triangles are earthquakes with M R eNaSS greater than 3.5). Table 2 lists the stations and Tables 3 and4 list the earthquakes that are used in this study.

We compute the Fourier spectrum of each record after removing the linear trend. The spectra are then divided by ω 2 (where ω 2πf, with f the frequency) in order to obtain displacement spectra. The spectra are finally smoothed between 0.5 and 30 Hz. The smoothing is performed by computing the mean value over frequency bands with a constant width in a logarithmic scale in order to lower the level of high-frequency fluctuations in the spectra. The east-west and north-south components are combined in the Fourier domain to obtain a single horizontal component:

SH SE 2 SN 2 q (1)
In some studies, the root mean square of the two components is used. Depending on the correlation between the eastwest and north-south components, the difference between the two approaches may lead to a systematic difference in the moment magnitude or in the logarithms of the site effect by a factor that does not exceed log 10 2 p .

Noise spectra are computed in the same way as signal spectra, from the beginning of the record to the P-wave arrival time. A minimum signal-to-noise ratio of 3 is imposed at any frequency used in the inversion.

Acceleration waveforms for the east-west and northsouth components of the 8 November 1997 earthquake (number 5 in Table 3) at stations SAOF, CALF, and OGCA are shown in Figure 4, as well as the raw and smoothed displacement spectra for S waves and noise. The displacement spectra of S waves reveal a rather flat level for frequencies greater than approximately 0.4 Hz followed by a decay at high frequency. A strong increase is also observed at very low frequency, owing to division by ω 2 or instrumental noise. However, it is hard to define the high and low frequency asymptotes that define the corner frequency and the seismic moment of the event.

It is important to note that the S-wave spectra depend significantly on the window length that is used to extract the S waves. Authors concerned with attenuation select generally narrow windows around the S arrival (e.g., [START_REF] Castro | Attenuation and site effects in the region of Guadeloupe, Lesser Antilles[END_REF], whereas those concerned with site effects use longer windows in order to catch more energy [START_REF] Seekins | Site amplification at five locations in San Fransisco, California: a comparison of S waves, codas, and microtremors[END_REF][START_REF] Castro | Site response of strong ground motion stations in the Umbria, central Italy, region[END_REF]. We choose to use time windows beginning 1 sec before the Sg arrival with a duration of 5 sec, which seemed to be a good compromise between the need to select mostly Sg waves and exclude the other phases and the need to get enough energy to compute the The number of accelerometric stations that recorded the event is indicated in the column entitled Number, and the distance range Δ min , Δ max is in the last column. Magnitudes LDG and RéNaSS are the two local magnitudes used on the French territory. spectra down to 0.5 Hz. For comparison, the spectra computed with 10-sec time windows are plotted in Figure 4. Note that the difference in amplitude is due to the normalization by the window length. For the smallest distances, for which almost all the energy is present below 5 sec, a longest window will lead to smallest amplitudes because of the normalization, and this is true at least up to 100 km (see Fig. 4). For the largest distances, the difference in amplitude is less pronounced, and we decided to keep the 5-sec window because we do not want to include other phases than the direct S waves in the analysis.

In what follows, we limit the inversion to frequencies lower than Hz in order to avoid the strong attenuation at high frequency due to the shallow subsurface known as the f max effect [START_REF] Hanks | f max[END_REF]. The final data sets consist in 352 spectra for 55 earthquakes and 31 stations for the Alps data set, and 156 spectra for 28 earthquakes and 18 stations for the Pyrenees data set.

Inversion Method

The S-wave displacement spectrum A ij r ij ; f can be written as the product of a source, a propagation, and a station term:

A ijk r ij ; f k Ω i f k D ij r ij ; f k S j f k ;
(2) where r ij is the hypocentral distance from earthquake i to station j, and f k is the frequency. We use the far-field displacement spectrum given by Brune's model [START_REF] Brune | Tectonic stress and the spectra of seismic shear waves from earthquakes[END_REF][START_REF] Brune | Correction[END_REF]:

Ω i f k ∼ M 0 i 1 f k =f c i 2 ;
(3)

where M 0 i is the seismic moment, and f c i is the corner frequency of event i. As a minimum distance of a few wavelengths is required for the far-field approximation to be valid (e.g., [START_REF] Aki | Quantitative Seismology, Second Ed[END_REF], the use of frequencies down to 0.5 Hz (i.e., wavelengths up to 5 km) imposes a minimum hypocentral distance of about 15 km. Attenuation involves anelastic decay and geometrical spreading:

D ij r ij ; f k exp πr ij f k Qf k v S × 1 r γ ij ; (4)
where v S is the average S-wave velocity along the path, and Qf k Q 0 × f α k is the quality factor at frequency f k . Note that the geometrical spreading is allowed to differ from the classical r 1 ij form. S j f k is the site effect at the station j. This term is equal to unity at each frequency in the absence of site effect (rock site conditions). Equation ( 2) may thus be written as

y ijk m 0 i log 10 1 f k f c i 2 γ log 10 r ij πr ij f k log e 10Q 0 f α k v S s jk ;
(5)

where

y ijk log 10 A ijk r ij ; f k ; (6)
m 0 i log 10 M 0 i × 2R θϕ 4πρv 3 S ; (7)
s jk log 10 S j f k ;

(8) with R θϕ , the source radiation pattern, assumed to be constant (R θϕ 0:55 for S waves; [START_REF] Boore | Average body-wave radiation coefficients[END_REF], and ρ and β the density and the S-wave velocity of the medium at the source, respectively (we assume β v S 3:5 km= sec 1 and ρ 2800 kg=m 3 ). The factor 2 in equation ( 7) accounts for the free surface reflection at the station assuming a quasi-vertical incidence. This is exact for SH and a reasonable approximation for SV [START_REF] Aki | Quantitative Seismology, Second Ed[END_REF].

We have to solve a system of equations where the unknowns are the m 0 i values (related to seismic moment) and the corner frequency f c i for each event i, the site term s jk for each station j and each frequency f k , and the attenuation parameters Q 0 , α, and γ. We use an iterative Gauss-Newton method. Following [START_REF] Tarantola | Inverse Problem Theory and Methods for Model Parameters Estimation[END_REF], the perturbation of the model parameters at each iteration is given by

Δm m n1 m n G t n C 1 D G n C 1 M 1 fG t n C 1 D gm n d obs C 1 M m n m prior g; (9)
where m n is the vector composed of the parameters at iteration n and G n is the matrix composed of the partial derivatives of y ijk with respect to the current values of the parameters ∂y ijk ∂m 0 i 1;

(10)

∂y ijk ∂f c i 2f 2 k log e 10f c i f 2 c i f 2 k ; ( 11
)
∂y ijk ∂γ log 10 r ij ;

(12)

∂y ijk ∂Q 0 πr ij f 1 α k log e 10v S Q 2 0 ;
(13)

∂y ijk ∂α πr ij f 1 α k logf k log e 10v S Q 0 ;
(14)

∂y ijk ∂s jk 1: (15)
C D and C M are the data and model covariance matrices, respectively, with C D ij σ D 2 i 0:2 2 , where i 1; …; number of data, and C M ij σ M 2 i , where i 1; …; number of parameters and the σ M i are defined at the end of this paragraph, gm n is the vector composed of the y ijk calculated in the current model m n , d obs is the data vector, and finally, m prior is the vector composed of the starting values for the parameters.

Assuming that the parameters follow a Gaussian statistics and that the problem is not strongly nonlinear, we define the a posteriori covariance matrix [START_REF] Tarantola | Inverse Problem Theory and Methods for Model Parameters Estimation[END_REF]:

C M 0 G t C 1 D G C 1 M 1 (16)
from which the correlation matrix is simply deduced by

Corr ij C M 0 ij C M 0 ii C M 0 jj : (17)
In addition, we need to remove a degree of freedom by imposing a constraint on the site responses [START_REF] Boatwright | A general inversion scheme for source, site, and propagation characteristics using multiply recorded sets of moderate-sized earthquakes[END_REF][START_REF] Field | A comparison and test of various siteresponse estimation techniques, including three that are not referencesite dependent[END_REF]. As shown by [START_REF] Bonilla | Site amplification in the San Fernando Valley, California: variability of site-effect estimation using the S-wave, coda and H/V methods[END_REF], the mean response of a set of stations located on rock sites is a good reference. Because the stations under study have not been investigated yet, and because the geological map information is heterogeneous, the following method has been used to define our reference condition. A first inversion has been performed assuming that the mean of the whole set of stations is free of site effect at each frequency. We decided then to remove from the set of reference stations those showing amplification peaks or troughs compared to the mean. Then a second inversion was performed using this reference condition. We finally checked on the final results that the stations used in the reference still have a flat transfer function not too far from a theoretical rock-site response.

We define the starting model as follows. We compute m 0 i from the RéNaSS magnitudes using the [START_REF] Hanks | A moment magnitude scale[END_REF] relationship

m 0 i 1:5 × M R eNaSS 9:1 log 10 2R θϕ 4πρv 3 S 0:5 (18)
and assume f c i 6:5 6, which covers the whole range of corner frequencies considering the magnitude range of the events analyzed, s jk 0 1, and γ 1 0:5. The anelastic attenuation parameters are estimated for each region from Table 1 and from [START_REF] Drouet | Analyse des données accélérométriques pour la caractérisation de l'aléa sismique en France métropolitaine[END_REF] as Q 0 300 300 and α 0:5 0:5. Thus, we explore a broad model space, but still the starting values must not be too far from the real values for the linearized inversion to be valid. We checked that the results of the inversion were not dependent on the starting model.

Results

Correlation

Correlation matrices are computed by linearizing the problem around the solution and are shown for the two data sets in Figure 5. The matrices are symmetric and organized from left to right and from bottom to top as follows: logarithm of seismic moments (columns 1-28 for the Pyrenees and 1-55 for the Alps), logarithm of corner frequencies (columns 29-56 for the Pyrenees and 56-111 for the Alps), attenuation parameters (γ, Q 0 , and α) (columns 57-59 for the Pyrenees and 112-114 for the Alps), and site effects (columns 60-383 for the Pyrenees, 18 stations times 18 frequencies, and columns 115-671 for the Alps, 31 stations times 18 frequencies). The matrices at the bottom of Figure 5 correspond to a zoom on the logarithms of seismic moments, corner frequencies, and attenuation parameters. One can see that the correlation matrix is more complicated for the Pyrenees than for the Alps, but the general conclusions are the same. The attenuation parameters are strongly correlated to each other and are also correlated to the logarithms of seismic moments, which are also correlated to each other. As predicted from the source model, the logarithms of the seismic moments and the corner frequencies are negatively correlated (e.g., [START_REF] Brune | Tectonic stress and the spectra of seismic shear waves from earthquakes[END_REF][START_REF] Brune | Correction[END_REF]; M 0 ∝ f 3 c ). The logarithms of the site effects are only weakly correlated to the other parameters, especially for the Alps, and are correlated to each other in the case of the Pyrenees. We have also computed the model resolution matrices, which are shown for the two data sets on Figure 6. The trace of the matrix is equal to the number of parameters in both cases, and the offdiagonal elements are small, indicating that the parameters are resolved.

Attenuation

The results for the attenuation parameters are summarized in Table 1 and compared to the results from previous studies. Attenuation in the two regions is relatively different. The geometric attenuation seems to be higher in the Pyrenees (γ 1:2) than in the Alps (γ 1:0), while the anelastic attenuation is higher in the Alps, where the quality factor varies slowly with the frequency according to Qf 322 × f 0:21 , compared to Qf 376 × f 0:46 for the Pyrenees.

The value of γ 1:2 retrieved for the Pyrenees differs slightly from the usual value γ 1 obtained at teleseismic distances, but is comparable to values reported in other regional studies [START_REF] Atkinson | The shape of ground motion attenuation curves in southeastern Canada[END_REF][START_REF] Malagnini | Ground-motion scaling in the region of the 1997 Umbria-Marche earthquake (Italy)[END_REF][START_REF] Bay | Spectral shear-wave ground-motion scaling in Switzerland[END_REF][START_REF] Atkinson | Empirical attenuation of ground-motion spectral amplitudes in southeastern Canada and the northeastern United States[END_REF]. This difference is probably due to the attenuation by scattering, which is strong in the Pyrenees (e.g., [START_REF] Gagnepain-Beyneix | Evidence of spatial variations of attenuation in the western Pyrenean range[END_REF], leading to a geometrical expansion slightly different than the one expected for body waves.

The a posteriori covariance matrix gives a very small standard deviation for attenuation parameters. Tests using different starting models give a more reliable estimation of standard deviation for the inverted parameters that are less than about 5% for γ, and less than 15% for Q 0 and α. The values of Q 0 and α are compatible with previous results for France as shown in Table 1. The similarity of anelastic attenuation for Lg and Sg waves suggests that the quality factor obtained in both cases is related to shear waves [START_REF] Campillo | Frequency-dependent attenuation in the crust beneath central France from Lg waves: data analysis and numerical modelling[END_REF].

Source Parameters

In order to convert seismic moments into moment magnitudes, we use the relationship given by [START_REF] Hanks | A moment magnitude scale[END_REF]:

M w log 10 M 0 9:1 1:5 ; ( 19
)
with M 0 in N m. Figure 7 shows moment magnitudes as a function of local magnitudes for all the events, with different symbols for the two regions. The moment magnitudes are compared to the local magnitudes M LDG and M R eNaSS .

The results for the two regions are compatible, and we can define the following relationships:

M w 0:270:19 0:950:05 × M LDG ;

(20)

M w 0:020:17 0:930:05 × M R eNaSS : (21)

The corner frequencies are plotted as a function of the different magnitudes in Figure 8. We find the following linear relationships between log 10 f c and the magnitudes M LDG , M R eNaSS , and M w : log 10 f c 1:740:03 0:280:01 × M LDG ; (22) log 10 f c 1:590:03 0:260:01 × M R eNaSS ;

(23) log 10 f c 1:720:03 0:320:01 × M w : (24)

From a theoretical point of view, [START_REF] Deichmann | Local magnitude, a moment revisited[END_REF] shows that there should exist a one-to-one relationship between local magnitudes and moment magnitudes, or equivalently that the logarithms of the seismic moment should be proportional to 1.5 times the local magnitudes. However, observed relationships between the logarithms of the seismic moment and the local magnitudes give a slope lower than 1.5 [START_REF] Deichmann | Local magnitude, a moment revisited[END_REF]. In this study, we find a slope of 1.45 (or 1.42) for the relationship between log 10 M 0 and M LDG (or M R eNaSS ). Concerning the relationship between the logarithms of the corner frequency and the moment magnitudes, theory predicts [START_REF] Brune | Tectonic stress and the spectra of seismic shear waves from earthquakes[END_REF] log 10 f c ∝ 0:5 × M w ;

(25) while we find a lower slope of 0:32. This result can be compared to the relation of [START_REF] Drouet | Attenuation, seismic moment, and site effects for weak-motion events: application to the Pyrenees[END_REF], and [START_REF] Chevrot | Source spectra and site-response estimates using the coda of Lg waves in western Europe[END_REF] (Fig. 8), who find values of 0.25 and 0.35, respectively.

Figure 9 shows the relationship between seismic moment and stress drop, which is computed from [START_REF] Brune | Tectonic stress and the spectra of seismic shear waves from earthquakes[END_REF]:

Δσ 7 16 M 0 f c 0:37β 3 : (26)
The stress drops are scattered, but most of the values lie between 10 5 and 10 7 Pa (i.e., 1 and 100 bars). One can observe a slight tendency to higher stress drops for higher moments, but as suggested by [START_REF] Ide | Does apparent stress vary with earthquake size?[END_REF], this can be an effect of the finite-frequency bandwidth that we analyze.

Site Effects

The site effects are the most robust results as indicated by their weak correlations to the other parameters. After a first inversion for which the mean logarithm of the site amplification factors over the whole set of stations was constrained to zero, we identify the stations showing site responses that are not flat and affected by large site effects described above and below the average (stations CALF, ESCA, ISOL, MENA, NROC, OGAG, OGAP, OGBL, OGCU, OGDH, OGFB, OGGM, OGMA, OGSR, OGTB, and SAOF in the Alps). A new closure condition was thus defined without those stations. The stations used in the reference are indicated by gray boxes in Figures 10 and11. Note that most of these stations are located on rock, according to geological maps, and only four of them are actually classified as sediment: OGPC for the Alps, and PYAS, PYFO, and PYLU for the Pyrenees; those stations are actually investigated. On the other hand, some stations classified as rock sites after geological maps show moderate to high amplifications (CALF, ESCA, ISOL, MENA, OGAG, OGGM, OGMA, and SAOF for the Alps) and thus were not used in the reference. With this new reference condition, the corner frequencies determined for the Alps are found systematically higher than before, while the other parameters are almost unchanged, except the site effects. We checked the influence of removing the stations with the highest and lowest amplitudes for the Pyrenees, but the results were unchanged between the different inversions indicating that there is no bias in the reference condition for this data set.

Site transfer functions for the stations under study are given in Figures 10 and11. For the Pyrenees, [START_REF] Drouet | Attenuation, seismic moment, and site effects for weak-motion events: application to the Pyrenees[END_REF] used a linear two-step inversion, assuming a constant quality factor and a grid search for the corner frequency, for computing the site response for the same stations. Their results are superimposed in Figure 11, showing a good agreement between the two methods. Figure 10 shows that strong site amplifications are found in sediment filled valleys as in Grenoble or Nice (stations OGCU, OGDH, and OGSR for Grenoble, and NROC for Nice, in Fig. 10). Significant amplifications can also affect stations identified as rock sites from geological maps and visual description of the sites (see Table 2,and Figs. 10 and 11). As shown by [START_REF] Steidl | What is a reference site?[END_REF], near-surface weathering and cracking affect the recorded ground motion. Even stations located on rock sites may have significant site effects. Station OGFB has been considered to located on the free surface, while it is actually located in a 500-m-deep borehole. Thus, OGFB site response must be multiplied by a factor of 2 to compensate for this effect.

Following [START_REF] Field | A comparison and test of various siteresponse estimation techniques, including three that are not referencesite dependent[END_REF] and [START_REF] Chávez-García | Lateral propagation effects observed at Parkway, New Zealand. A case history to compare 1D versus 2D site effects[END_REF], it is interesting to compare site effects derived from the inversion with those from other methods. Site effects derived from noise horizontal-to-vertical (H/V) [START_REF] Nakamura | A method for dynamic characteristics estimations of subsurface using microtremors on the ground surface Q[END_REF], earthquake H/V [START_REF] Lermo | Site effect evaluation using spectral ratios with only one station[END_REF], or spectral ratios with respect to a reference station, are available for some sites. Figure 12 presents this comparison for station PYLO in the Pyrenees and OGDH in the Alps. For better comparison, we have also inverted vertical component data. The results for the attenuation parameters and the source parameters are very close to those obtained from the horizontal component, but the site effects are different.

At the PYLO site, spectral ratios with reference station as well as H/V ratios were computed for a velocimetric station (CHA) located a few meters away from PYLO by [START_REF] Dubos | Etudes des effets de sites dans la ville de Lourdes (Pyrénées, France) par la méthode des rapports spectraux[END_REF]. The duration of the time windows they used to compute noise spectra was 30 sec, while for earthquake signals, windows begin at the S-wave arrival time and have a length dependent on magnitude and distance (a few seconds to 40-sec wide). At the OGDH site, the same methods were applied by P. Gueguen (personal comm., 2007), using also 30-sec time windows to compute noise spectra, and for earthquake data, a window beginning with the S waves and ending when the signal-to-noise ratio was too small. For the PYLO station, we plot on Figure 12 the horizontal site transfer function as well as the ratio between the horizontal and vertical transfer functions determined in this study. For the OGDH station, we plot the ratio between the horizontal transfer functions of stations OGDH and OGMU to be com-pared to the classical spectral ratio with reference station, and here again the ratio between the horizontal and vertical transfer functions for comparison with H/V methods.

For PYLO, all the methods give similar results with a small increase in amplitude from 1 to 4 Hz followed by a sharp decrease up to 7 Hz. This effect is probably due to topography because station PYLO is installed on the slope of a small hill of outcropping hard rock. At station OGDH, a strong amplification is observed at 2 Hz, except with the H/V noise method. Note the good agreement between the ratios OGDH/OGMU for the resonant frequency of the site effect, and the very good agreement between H/V with earthquake data and the ratio between the horizontal and vertical site responses from our nonlinear inversion. The Grenoble basin is known to have a natural frequency of 0.3 Hz [START_REF] Le Brun | Site effect study in urban area: experimental results in Grenoble (France)[END_REF], which is outside the frequency range we investigated, and the observed resonant frequencies are probably multiples of this frequency or resonance inside superficial layers of sediments. The discrepancy between the results from noise measurement and earthquake data may be due to the fact that earthquake-generated waves produce resonance of the whole basin. Concerning the spectral ratios with reference station, the difference in amplitude can be explained by the longer windows used by P. Gueguen (personal comm., 2007), which probably include surface waves and therefore more energy.

In light of these results, we can identify stations with a flat response close to 1 and located with no ambiguity on rock according to geological maps (OGCA, OGLE, and OGSI for the Alps; PYAT, PYBE, and PYFE for the Pyrenees). We suggest that those stations are to be used as reference sites for the classical spectral ratio method. horizontal site response from nonlinear inversion, solid black line; H/V of noise at PYLO, dashed black line; ratio between horizontal and vertical site responses obtained in this study, dashed-dotted line; a station located a few meters away from PYLO, gray curves. (Spectral ratio with reference station, solid curves; H/V of noise, dashed curves; H/V of earthquake data, dotted curves; from [START_REF] Dubos | Etudes des effets de sites dans la ville de Lourdes (Pyrénées, France) par la méthode des rapports spectraux[END_REF]. Right-hand side: ratio between OGDH and OGMU site responses from nonlinear inversion, solid black line; ratio between horizontal and vertical site responses from nonlinear inversion for station OGDH, dashed-dotted line; spectral ratios with OGMU as a reference, dotted and dashed black lines for east-west and north-south components, respectively; H/Vof noise, dashed gray line; and H/Vof earthquake data, dotted gray line. The last four results are from P. Gueguen (personal comm., 2007).

Discussion and Conclusions

In order to check the results of the inversion, Figure 13a shows the histogram of the logarithms of amplitudes residuals (difference between the logarithms of observed and modeled amplitudes) for the two data sets. This distribution is close to a Gaussian with a small variance of about 0.2. Our model is thus fitting the data rather well. Figure 13b shows the same residuals but as a function of hypocentral distance. There is no apparent bias with distance in the results, suggesting that assuming a constant γ is a reasonable assumption. Figure 14 shows the acceleration spectra after correction of attenuation and site effects for three events in each region, with different magnitudes, recorded over a wide range of distances, as well as the theoretical acceleration Brune spectra computed using the inverted seismic moments and corner frequencies for each event. The source spectra determined from the different stations are in good agreement, indicating that the Brune's model is adapted and that there is no obvious influence, in this frequency band, of the f max effect [START_REF] Hanks | f max[END_REF] in our data. Path and site effects can thus be used to invert directly for the source parameters, providing a convenient way to compute moment magnitudes, at least for the small to moderate events with sources that are described by the Brune's model.

The a posteriori correlation matrix suggests that (1) there is a strong trade-off between attenuation parameters, (2) this trade-off also affects seismic moments determination, and (3) on the other hand, the site effects are weakly correlated to the other parameters. In order to check the validity of the attenuation models that we derived for the Alps and the Pyrenees, we plot on Figure 15, for one earthquake in each region and three frequencies, the peak-ground acceleration computed from the filtered waveforms (butterworth filter of order 4), corrected for site effects (black and gray dots for east-west and north-south components, respectively). The black curves show the predicted attenuation using the inverted attenuation parameters γ, Q 0 , and α (see Table 1). One has to note that there is no amplitude scaling and that only the shape of the curves is relevant. There is a reasonable agreement between observed and modeled attenuation at each frequency.

The obtained Q-values (Q 0 and α) are compatible with other independent results for France (see Table 1). However, a low Q 0 is always counterbalanced by a high α (see, e.g., [START_REF] Gagnepain-Beyneix | Evidence of spatial variations of attenuation in the western Pyrenean range[END_REF]. This illustrates the trade-off between these parameters revealed by the correlation matrix. The shape of the spectra is also influenced by site effects, in particular the f max frequency [START_REF] Hanks | f max[END_REF]. Its effect is limited here because we cut the high-frequency part of the spectra at 15 Hz, but this also probably decreases our ability to resolve Q.

The frequency-independent attenuation (geometrical spreading) is represented by the R γ term. We obtain a value for γ close to one for the Alps, and slightly larger (1.2) for the Pyrenean data. Some weak-motion studies report similar results [START_REF] Atkinson | The shape of ground motion attenuation curves in southeastern Canada[END_REF][START_REF] Malagnini | Ground-motion scaling in the region of the 1997 Umbria-Marche earthquake (Italy)[END_REF][START_REF] Bay | Spectral shear-wave ground-motion scaling in Switzerland[END_REF][START_REF] Atkinson | Empirical attenuation of ground-motion spectral amplitudes in southeastern Canada and the northeastern United States[END_REF]. In these studies, the exponent of the geometrical decay is distance dependent to account for the different types of waves present in the signal. In our study, no distance dependence is observed, but our distance range is limited to 15-200 km, and the window used to compute the spectra is such that it mostly includes Sg waves.

Another related problem concerns the influence of the scattering in the regions under study. [START_REF] Gagnepain-Beyneix | Evidence of spatial variations of attenuation in the western Pyrenean range[END_REF] analyzed coda waves in the Pyrenees and showed that scattering is the prevailing mechanism of attenuation below 10 Hz. Moreover, the Alps and the Pyrenees seem to show strong spatial dependence of attenuation as indicated by the extinction of Lg waves for trans-Pyrenean and trans-Alpine paths [START_REF] Campillo | Attenuation of crustal waves across the Alpine range[END_REF][START_REF] Chazalon | Crustal wave propagation anomaly across the Pyrenean range. Comparison between observations and numerical simulations[END_REF].

Crustal attenuation and amplification have not been taken into account in this study. As shown by Boore and Joy- ner (1997) a velocity gradient from a value of 3500 m=sec in the vicinity of the source-to-rock velocity at the surface produces amplifications. For reasonable values of kappa, and a surface rock velocity of 620 m=sec, the combined effect of both attenuation and amplification peaks between about 2 and 5 Hz with a maximum level of less than 1.8, according to [START_REF] Boore | Site amplifications for generic rock sites[END_REF]. The surface velocities of rock stations in the Alps and the Pyrenees are still under investigation. Preliminary array measurements performed on some of these stations (e.g., OGMU) indicate a velocity between 1000 and 1500 m=sec (P. Gueguen, personal comm., 2007). The combined effect of both crustal attenuation and amplification is then difficult to quantify but is probably less than 1.5. The source spectrum obtained in this study are the product of the Brune model and this neglected factor. Because high-frequency level scales with stress drop to the 2=3 power, our obtained corner frequencies and stress drops are then higher than they would be if we had included this factor.

Another important result concerns the source characteristics. The Brune-type source model, which assumes a single corner frequency and a f 2 , fall-off seems realistic for the small earthquakes analyzed here. Our moment magnitudes scale with local magnitudes but are systematically lower (Fig. 7). Table 5 compares different moment magnitude estimations for the larger earthquakes of our data set. They are very close, although the methods used are different. The Eidgenössische Technische Hochschule Zürich (ETHZ), the U.S. Geological Survey, and [START_REF] Rueda | Near-real-time seismic moment-tensor determination in Spain[END_REF][START_REF] Rueda | Near-real-time seismic moment-tensor determination in Spain[END_REF]B. Delouis (personal comm., 2007) use a waveform inversion technique and thus low frequencies compared to our 0.5-15-Hz band.

Finally, we computed stress drops between 10 5 and 10 7 Pa (i.e., 1 and 100 bars), which seem to be slightly dependent on seismic moment, a dependence that has also been observed by several authors [START_REF] Atkinson | Earthquake source spectra in eastern North America[END_REF][START_REF] Kanamori | Determination of earthquake energy release and M L using Terrascope[END_REF][START_REF] Abercrombie | Earthquake source scaling relationships from 1 to 5 M L using seismograms recorded at 2.5 km depth[END_REF][START_REF] Prejean | Observations of earthquake source parameters at 2 km depth in the Long Valley caldera, eastern California[END_REF]. Considering the dispersion in our data and recent studies on the influence of limiting the frequency bandwidth [START_REF] Ide | Does apparent stress vary with earthquake size?[END_REF], and of correlations between source, site, and propagation parameters in stress-drops estimates [START_REF] Ide | Apparent break in earthquake scaling due to path and site effects on deep borehole recordings[END_REF], this dependence could be an artifact. Moreover, recent studies have found that large earthquakes have a different behavior, which is probably related to the difference between earthquakes that do affect, and those that do not affect, the whole seismogenic zone [START_REF] Mai | Source scaling properties from finitefault-rupture models[END_REF]. However, studies using weak-motion attenuation models to predict moderate events use a scaling of stress drop with magnitude in order to explain the high frequency part of the earthquake spectra [START_REF] Malagnini | Characteristics of the ground motion in northeastern Italy[END_REF][START_REF] Bay | Predictive ground motion scaling in Switzerland: best estimates and uncertainties[END_REF]. Thus, the question of stress-drop scaling with magnitude still needs to be addressed. Our approach also gives us site responses, and is an interesting alternative to other methods, such as the H/V 3, and number 5, Table 4, respectively). East-west component, black dots; north-south component, gray dots. The black lines correspond to our models of attenuation using the parameters γ, Q 0 , and α from Table 1, the solid one for the region considered, and the dashed line stands for the other region. Note that only the shape of the curves is relevant because there is no scaling in amplitude. method and the spectral ratio with a reference station. Site classifications for the building codes are generally based on the average first 30-m S-wave velocity, but as noted by [START_REF] Luzi | Geotechnical site characterisation in the Umbria-Marche area and evaluation of earthquake site response[END_REF], this is probably a rough approximation, and other information is required such as geomorphological conditions or depth of bedrock. The results presented here can probably help to refine the site classification of the French accelerometric stations based on the amplitude or the frequency of amplification observed in the transfer functions. Moreover, [START_REF] Luzi | Geotechnical site characterisation in the Umbria-Marche area and evaluation of earthquake site response[END_REF] also show that the transfer functions obtained by generalized inversion contain information on 2D and 3D site effects and thus provide better results than the H/V method in the context of sedimentary basins.

Figure 1 .

 1 Figure 1. Seismic activity in France given by the BCSF for the period 1984-2004.

Figure 2 .

 2 Figure 2. Maps of the two regions under study with earthquakes (circles), stations (squares), and paths (gray lines) analyzed. Alps, 1; Pyrenees, 2.

Figure 3 .

 3 Figure 3. Recording distances as a function of station for earthquakes with RéNaSS magnitude ≤ 3:5 (open triangles), and earthquakes with RéNaSS magnitude > 3:5 (black triangles).

Figure 4 .

 4 Figure 4. (a) Records of the acceleration for the east-west and north-south components of the 8 November 1997 earthquake (number 5 inTable3) at the SAOF, CALF, and OGCA stations. The gray box shows the 5-sec time window used to compute the spectra. (b) Raw and smoothed Fourier spectra of the displacement for signal (H) and noise (n) for this event with 5-sec time window. The smoothed Fourier spectra computed using a 10-sec time window are also shown (red lines).

Figure 5 .

 5 Figure 5. (a) Correlation matrix obtained for the inversion of the Pyrenean data. From left to right and bottom to top: log 10 M 0 (28 parameters), log 10 f c (28 parameters), attenuation parameters γ; Q 0 ; α, and site effects (342 parameters). (b) Zoom on the lower left corner of (a). (c) Correlation matrix obtained for the inversion of the Alpine data. From left to right and bottom to top: log 10 M 0 (55 parameters), log 10 f c (55 parameters), attenuation parameters γ; Q 0 ; α, and site effects (558 parameters). (b) Zoom on the lower left corner of (c).

Figure 6 .

 6 Figure 6. Same as Figure 5 but for the model resolution matrix.

Figure 7 .

 7 Figure 7. Comparison between moment magnitudes and local magnitudes. Pyrenees, black circles; Alps, gray triangles; One-to-one relationship, thin line; regression for the two data sets, solid line. Error bars are 1σ confidence level.

Figure 9 .

 9 Figure 9. Comparison between seismic moments and stress drops. Pyrenean data, black circles; Alpine data, gray triangles. Dotted lines correspond to constant stress drops of 10 5 and 10 7 Pa (i.e., 1 and 100 bars).

Figure 8 .Figure 10 .Figure 11 .

 81011 Figure 8. (a) Comparison between local LDG magnitudes and corner frequencies. Pyrenean data, black circles; Alpine data, gray triangles; regression of the two data sets, solid line. Dashed line is from Chevrot and Cansi (1996), and dotted line is from Drouet et al. (2005). (b) Same as (a) for local RéNaSS magnitudes. (c) Same as (a) for moment magnitudes. Error bars are 1σ confidence level.

Figure 12 .

 12 Figure 12. Site effects for the stations PYLO (Pyrenees) and OGDH (Alps) obtained with different methods. Left-hand side: PYLO

Figure 13 .

 13 Figure 13. (a) Histogram of the residuals of the logarithms of amplitude spectra. (b) Residuals as a function of hypocentral distance, black dots; mean residual over distance bins, gray dots.

Figure 14 .

 14 Figure14. Acceleration spectra after correction of site and path effects (gray lines) for three events in each region(numbers 41, 48, and

Figure 15 .

 15 Figure15. Peak ground acceleration from filtered time series around the central frequency indicated, divided by the corresponding site effect determined in this study for each station, for two earthquakes in the Alps and the Pyrenees (number 41, Table3, and number 5, Table4, respectively). East-west component, black dots; north-south component, gray dots. The black lines correspond to our models of attenuation using the parameters γ, Q 0 , and α from Table1, the solid one for the region considered, and the dashed line stands for the other region. Note that only the shape of the curves is relevant because there is no scaling in amplitude.

Table

  Summary of the Major Results on Anelastic Attenuation in France(Qf Q 0 f α )

	Authors	Q 0	α	Frequency band (Hz)	Wave Type	Region
	Herráiz and Mezcua (1984)	557		1.4-2.8	Coda	Pyrenees
	Modiano and Hatzfeld (1982)	180-350		15-50	Sg	Pyrenees
	Nicolas et al. (1982)	100 to 1000 depending on f	0.8	0.5-16	Pn, SnPg, Sg	France
	Thouvenot (1983)	180 to 1600 depending on depth	0.25	20 for Q 0 10 to 20 for α	Pn	Alps
	Gagnepain-Beyneix (1987)	30-142	0.7-1.1	2-40	Coda	Pyrenees
	Eva et al. (1991)	100 to 1000 depending on f		2-16	Coda	Alps
	Campillo et al. (1985)	290	0.5	0.5-10	Lg	France
	Campillo and Plantet (1991)	320	0.5	0.5-10	Lg	France
	This study	322	0.21	0.5-15	Sg	Alps
	γ 1:0
	This study	376	0.46	0.5-15	Sg	Pyrenees
	γ 1:2

Table 2 Accelerometric

 2 Stations from the RAP Used in This Study

	Name	Latitude (°N)	Longitude (°E)	Altitude (m)	Geological Site Classification	Installation Date (DD/MM/YYYY)
				RAP Stations in the Alps
	CALF	43.751	6.919	1242	rock	30/10/1995
	ESCA	43.820	7.368	550	rock	30/10/2003
	ISOL	44.184	7.050	910	rock	17/09/2003
	MENA	43.784	7.485	210	rock	09/02/1999
	NBOR	43.686	7.301	191	rock	07/05/1998
	NROC	43.706	7.287	22	sediment	07/05/1998
	OGAG	44.788	6.540	1307	rock	09/06/1995
	OGAN	45.892	6.136	468	rock	18/02/1997
	OGAP	45.904	6.133	467	sediment	05/02/1998
	OGBL	45.621	5.871	192	sediment	01/09/1998
	OGCA	43.718	5.654	400	rock	13/06/1996
	OGCH	45.585	5.919	525	rock	01/07/1997
	OGCU	45.200	5.770	212	sediment	18/06/1997
	OGDH	45.172	5.734	212	sediment	17/04/1996
	OGDI	44.089	6.218	770	rock	21/04/1996
	OGEP	45.934	6.084	490	sediment	21/03/2002
	OGFB	45.203	5.818	220	sol	15/12/2000
	OGFH	45.203	5.818	220	sediment	19/12/2000
	OGGM	45.200	6.104	1575	rock	11/05/1995
	OGLE	45.521	6.468	639	rock	05/12/1997
	OGMA	45.769	5.534	670	rock	21/04/1999
	OGMB	44.971	6.500	1460	rock	25/09/1998
	OGMO	45.200	6.671	1200	rock	07/10/1996
	OGMU	45.188	5.720	250	rock	23/01/1997
	OGPC	45.135	5.689	215	sediment	08/01/1998
	OGSI	46.054	6.754	750	rock	03/05/1996
	OGSR	45.187	5.736	212	sediment	10/07/1996
	OGTB	46.318	6.602	860	sol	08/02/1999
	OGTI	45.487	6.919	1796	rock	21/01/1998
	SAOF	43.984	7.551	595	rock	27/04/1995
	STET	44.253	6.921	1200	rock	27/11/1996
				RAP Stations in the Pyrenees
	PYAD	43.097	0:426	450	rock	02/02/2001
	PYAS	43.012	0.797	430	sediment	19/06/2002
	PYAT	43.095	0:711	340	rock	24/04/2001
	PYBA	42.469	3.117	70	rock	15/04/2002
	PYBE	42.820	1.952	1080	rock	04/10/2001
	PYCA	43.024	0.182	701	rock	20/08/2003
	PYFE	42.814	2.502	275	rock	22/12/2000
	PYFO	42.967	1.602	380	sediment	21/12/2000
	PYLI	43.001	1.134	424	rock	16/04/2002
	PYLO	43.098	0:048	410	rock	24/07/2001
	PYLS	42.854	0.003	770	rock	30/07/2001
	PYLU	42.791	0.601	630	sediment	14/08/2001
	PYOR	42.772	1.502	1030	rock	26/09/2002
	PYPE	42.669	2.871	100	rock	08/06/2001
	PYPM	42.406	2.435	920	rock	20/12/2000
	PYPP	43.163	1:232	230	rock	15/07/2002
	PYPR	42.614	2.429	410	rock	23/05/2001
	PYPT	43.003	3.023	60	rock	27/08/2001

Table 4

 4 Same as Table 3 for the Pyrenees Area

	Magnitudes

Table 5

 5 Comparison of Moment Magnitude Determination from Different Institutes for a Selection of Events Used in This Study

		ETHZ	Other	This Study
	Event 5 in Table 4	3.9	3.6 (B. Delouis, personal comm., 2007)	4.3
	Event 14 in Table 4	4.3	4.0 Rueda and Mezcua (2005)	4.3
	Event 27 in Table 4	4.5		4.5
	Event 55 in Table 3	4.5	4.3 (B. Delouis, personal comm., 2007)	4.1

S.Drouet, S. Chevrot, F. Cotton, and A. Souriau

Simultaneous Inversion of Source Spectra, Attenuation Parameters, and Site Responses

in Table 3, and numbers 5, 12, and 19 in Table4). The theoretical acceleration source spectra, according to the Brune's model, computed with the inverted seismic moments and corner frequencies for each event, are also shown (black lines).

Acknowledgments

We would like to thank the RAP teams for managing the network and making the data available. This work was supported by the Centre National de la Recherche Scientifique with funding from the French Environment Ministry. The work of one of the coauthors (F. Cotton) has been funded by the Interreg IIIB Sismovalp Project. Associate Editor Gail Atkinson and the two reviewers, Karen Assatourians and one anonymous reviewer, are gratefully thanked for their comments.


Greqam

Dan Protopopescu
email: dan.protopopescu@univmed.fr

Qualitative Analysis of Fundamental Theoretical Tools Employed in Modelling Decision Making Problems

Keywords: JEL classification: C10, C51, C52, C53, P51 Active (passive) learning, Rational decision-maker, Closed-loop (open-loop) strategy, Stochastic (deterministic) control, Numerical (analytical) solutions, Reversible decisions, Increasing uncertainty, Risk-aversion Classification JEL: C10, C51, C52, C53, P51 Apprentissage actif (passif), décideur rationnel, Stratégie en boucle fermée (ouverte), Contrôle stochastic (déterministe), Solutions numériques (analytiques), Décisions réversibles, Incertitude croissante, Aversion

The objective of this paper is to analyze fundamental theoretical tools employed in modelling decision making problems which involve multivariate risks. By exploiting the richness of the literature, we highlight the qualities as well as the "weaknesses" specific to a wide class of decision models. These are not free from critiques, especially when real world problems are considered. A little effort has been spent on improving this type of models, often conceptually convenient but not always adequate. This study emphasizes the need for a consistent framework to cover a broad area of research on the strategic behavior of potentially risk-averter policy-makers in a controlled dynamic stochastic environment. Work remains to be done in this exciting area.

Introduction

We often ascertain in the decision making literature models which are not free from critiques, especially when real world problems are considered. An implication of an inappropriate modelling is the divergence between theoretical results and empirical findings. More general models could provide greater robustness being less restrictive but they have greater modelling difficulties. The advantage of allowing a much broader structure consists in more appropriate decisions taken by policy-makers. However, difficulties emerge when computational costs are taken into account. In this article we analyze and compare qualitative theoretical tools employed in the context of decision theory, providing a consistent review of the existing literature. In doing so, we focus on their advantages and limitations, the purpose being to emphasize the need for a consistent framework which better describe decision problems under risk and uncertainty. Section 2 presents the learning advantages in the context of a dynamic stochastic system and compares active learning with passive learning. Sections 3 discusses the concept of rationality and highlights its "weaknesses". Section 4 analyzes two types of strategies often employed in problems of decision and control, namely the closed-loop and respectively open-loop strategies. Section 5 examines the role of numerical solutions for dynamic programing models and compares these with analytical solutions generally obtained in more restrictive conditions. Section 6 treats several types of decisions employed in the context of stochastic optimization problems. Section 7 deals with several types of aversions encountered in the decision making process and points out important characteristics of environmental policy-making problems, given that in this area of research the development of specific formal tools is very awaited. Section 8 concludes and discusses possible future work.

Active Learning versus Passive Learning

Learning is one of the three aspects (beside the parametric uncertainty and stochasticity) of the economic agent's uncertainty problem and has many dimensions. This can take place at various levels of a policy problem, ranging from economic agents who are learning in order to adapt to changes in the environment to policy-makers who are trying to formulate the best policy (i.e., a rule for choosing an optimal action at each point in time) in an uncertain and changing world. An optimal behavior may arise from a process of learning. We recall here


Greqam

Boubou Cissé

Stéphane Luchini

Jean Paul

Moatti Fevrier

Jean Paul Moatti
email: moatti@marseille.inserm.fr

EQUITY IN HEALTH CARE FINANCE AND DELIVERY: WHAT ABOUT AFRICA ?

Keywords: Equity, Health care, progressivity, inequality, stochastic dominance. JEL Classication : : C14, D63, I19

This paper applies concentration curves and indices, that have been previously used to analyze progressivity in health care nance and horizontal equity in health care delivery in developed countries, to a 1998-1999 household survey about health care expenditures and utilization carried out in four francophone West African capitals (Abidjan, Bamako, Conakry and Dakar). The paper also uses statistical inference for testing stochastic dominance relationship between curves, a technique already applied in the literature about equity in taxation, as the criterion for making rigorous inequality comparisons. In all four capitals, the results strongly suggest a regressive pattern of payments for health care, with lower income groups bearing an higher burden of health expenditures as a proportion of their income than do the higher income segments of the population. As soon as dominance between concentrations curves is statistically tested, results appear less conclusive, notably for the groups of population aected by severe morbidity, on the issue of horizontal inequity in health care delivery, which requires that persons with similar medical need be treated equally. Some recommendations are made for the use of equity measurements in access to care for future evaluations of the impact of health care reforms in Africa.


F O Sefiloglu
email: f.o.sefiloglu@vu.nl

Cleo Ninja Stratmann

Martin Brits

Lorenzo Scibetta

Martin Van Velzen

Quinn Groenewoud

A Dick Vethaak

Rachid Dris

Johnny Gasperi

Bruno Tassin

Feride Öykü

Marja Lamoree

Microplastics in urban freshwater : a case study in the city of Amsterdam

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

Introduction

The contamination of freshwaters with microplastics (MPs) has been globally established. From macro to nano-sizes, plastics enter aquatic ecosystems via direct sources such as discharges from waster water treatment plants and drainage outlets and indirect sources such as atmospheric deposition, surface runoff, or human activities. In the environment, plastics undergo degradation and weathering processes depending on the physicochemical properties and environmental conditions [START_REF] Li | Assessment of microplastics in Freshwater Systems: A Review[END_REF]. Although the presence of MP in freshwater is an indubitable fact, the degree of MP pollution needs further investigation to understand the effects on the ecosystem scale and society. The aim of this study is to determine the MP abundances in the urban region of Amsterdam (The Netherlands) including a large network of canals and waterways, receiving treated wastewater from wastewater treatment plants, and an average annual rainfall of 844 mm. The sampling was done with a state-of-the-art in-situ volume-reduced sampling pump at 11 locations in the Amsterdam canal network in 2022. The qualification and quantification of the polymers for three size fractions (0.7-10 µm, 10-300 µm and 300µm-5mm) was accomplished in two laboratories at VUA (Amsterdam) and ENPC (Paris) with two complementary analysis methods using pyrolysis-gas chromatography-mass spectrometry (Py-GC-MS) and micro Fourier transform infrared (µ-FTIR) imaging.

Materials and Methods

Samples were collected in June and July 2022 at 11 locations in Amsterdam including the main canals in the city center and Amstel River, which flows through the city of Amsterdam and feeds the canals. Sampling was done at the water surface layer (0-0.5 m water depth) and samples were in-situ fractionated in size classes of 10-300 µm and 300-5000 μm using the Universal Filtering Object designed by Aalborg University (AAU-UFO) sampling device. From each sampling point, 2 sets of parallel samples were collected for the size fractionation of 10-300 µm for the complementary analysis by Py-GC-MS and µ-FTIR. In addition, 2 L of bulk water samples were collected from the water outlet of the AAU-UFO to analyze the micro and nano plastics (MNPs) in the range of 0.7-10 μm by Py-GC-MS. In addition, conventional water parameters such as conductivity, pH, turbidity, and total suspended solids (TSS) were measured for each sampling site. Samples (on metal filters with a mesh size of 10 and 300 µm) were first digested with H2O2 (10%) at 30 °C for 18-24 h and rinsed with filtered water. Then, the suspension was filtered through pre-muffled 10 µm stainless steel filters. For the particles remaining on the filter, density separation was applied by using NaI solution (d=1.6-1.7 g.cm -3 ). Finally, the floating particles were filtered through a 0.2 µm Anodisc filter and 0.7 µm glass filter for µFTIR imaging and Py-GC-MS analysis, respectively (Figure 1). The qualitative and quantitative analyses were performed using two complementary methodologies for MP analysis. One parallel set of samples per sampling site was analyzed by double-shot analysis on a multi-shot micro-furnace pyrolyzer EGA/PY-3030D (Frontier Laboratories, Saikon, Japan) coupled with GC/MS (Agilent 6890 GC and 5975C MS, Santa Clara CA, USA). The other set was scanned with the automated µ-FTIR mapping (Nicolet iN10 MX, Thermo Scientific). Measurements were processed by Agilent MassHunter and SiMPle software.

Results and Discussion

Samples collected from the canals of Amsterdam (n=11) showed a high variance in TSS within the range of 6.4-54 mg/L. Double-shot Py-GC-MS was optimized and applied to the samples for the analysis of the six major polymer types detected in freshwater systems (PE, PP,PS, PVC, PET, PMMA) [START_REF] Koelmans | Microplastics in freshwaters and drinking water: Critical review and assessment of data quality[END_REF]. Preliminary data analysis on the samples collected from Lekkanaal for MPs >700 nm showed the presence of all the target polymers in the Amsterdam-Rhine Canal network. The total MP concentrations were found between 4.7 and 103.5 mg/m 3 with PE and PVC as the most abundant polymers. These results will be extended further by the analysis of the canal samples including all the size fractions and µ-FTIR imaging. Results are foreseen to be completed in early 2023.

Conclusions and outlook

This study contributes to the knowledge of the occurrence of MPs in urbanized areas by using two complementary analysis methods providing information on both particle number and mass of MPs in different size fractionations. The findings of this study will provide an important basis to understand the extent of MP pollution and the data for the identification of sources of contamination.

Figure 1 :

 1 Figure 1: Sampling and analysis method for the freshwater samples

Microplastics in urban freshwater : a case study in the city of Amsterdam. SETAC Europe 33rd Annual Meeting : Data-driven environmental decision-making, SETAC, Apr 2023, Dublin (IE), Ireland. hal-


Greqam

Claude Gamel

Keywords: justice sociale, libéralisme, évolutionnisme, contractualisme, égalité des chances, revenu minimum social justice, liberalism, evolutionism, contractualism, equality of opportunity, minimum income B 25, D 63, I 38

HAYEK ET RAWLS SUR LA JUSTICE SOCIALE : Les différences sont-elles « plus verbales que substantielles » ?

Résumé : Dans la pensée libérale contemporaine, Hayek, économiste théoricien du « mirage de la justice sociale » et Rawls, philosophe auteur d'une « Théorie de la justice », semblent en opposition complète ; pourtant le premier a pu affirmer que les différences qui le séparaient du second étaient « plus verbales que substantielles ». En dépit d'une opposition frontale de paradigme (évolutionnisme versus contractualisme), le présent article cherche à repérer les éléments qui pourraient étayer une telle remarque : dans la gestation des normes, les étapes sont comparables (anti-utilitarisme, impartialité, expérimentation) et aboutissent à deux versions d'une même conception de la justice en société, tant au niveau des normes retenues que de leur hiérarchie (prééminence de la liberté, réelle augmentation des chances de chacun, amélioration du sort des plus démunis).