Model of SAM-based molecular diodes made of ferrocenylalkanethiols

David Duche 1, a) , Ujwol Planchoke 1 , Florian-Xuan Dang 2 , Judikael Le Rouzo 1 , MarcBescond 1 , Jean-Jacques Simon 1 ,TeodorSilviu Balaban 2 , and Ludovic Escoubas 1 1 Aix Marseille Universite, CNRS, Universite de Toulon, IM2NP UMR 7334, 13397, Marseille, France 2 Aix-Marseille Universite, CNRS UMR 7313, Institut des Sciences Moleculaires de Marseille, Chirosciences, Service 442, Avenue Escadrille Normandie-Niemen, F-13013 Marseille, France. * david.duche@im2np.fr There has been significant work investigating the use of self assembled monolayers (SAM) made of ferrocenyl terminated alkanethiols for realizing molecular diodes leading to remarkably large forward-to-reverse current rectification ratios. In this study, we use a multi band barrier tunneling model to examine the electrical properties of SAM-based molecular diodes made of HSC 9 Fc, HSC 11 Fc and HSC i FcC 13-i (0 ≤ i ≤ 13). Using our simple physical model, we reproduce the experimental data of charge transport across various ferrocenyl substituted alkanethiols performed by Nijhuis, Reus and Whitesides (J. AM. CHEM. SOC. 2010, 132, 18386-184016) and L. Yuan and al. (Nature Communication 2015, 6:6324). Especially, the model allows predicting the rectification direction in HSC i FcC 13-i (0 ≤ i ≤ 13) based molecular diodes depending on the position of the ferrocenyl (Fc) moiety within the molecules. We show that the asymmetry of barrier length at both sides of the Highest Occupied Molecular Orbital (HOMO) of the ferrocenyl moiety strongly contributes to the rectifying properties of ferrocenyl-alkanethiol based molecular junctions. Furthermore, our results reveal that bound and quasi-bound states play an important role in the charge transport.

I. Introduction

In 1974, A. Aviram and M. A. Ratner 1 proposed the concept of a molecular diode. It is based on the idea that a molecule composed of a donor (D) group and an acceptor (A) group linked together by a σ bridge (a D-σ-A compound) would exhibit a natural rectification behavior. Since these first works, numerous researches related to molecular electronics have been carried out as this field promises the development of new nanoscale electronic components [2][3][4] .

Molecular diodes functionalized with thiol linkers provide strong advantages due to their ability to form self assembled monolayers (SAMs) covalently bound at the surface of noble metals (Ag, Au). It allows heterometallicnanogaps to be associated with organic molecules exhibiting diode behavior 5 . Furthermore, self-assembled molecular diodes can be coated at the surface of arrays of metallic nanostructures (nano-particles or nano-antennas) aiming at obtaining opto-electronic devices such as sensors 6 , selective filters 7 or nano-rectennas 8,[START_REF] Nunzi | proc of SPIE[END_REF] .

Molecular diodes made of ferrocenyl-containing alkanethiols are of great interest since they exhibit strong asymmetries leading to remarkably large forward-to-reverse current rectification ratios. The forward-to-reverse current rectification ratios (RR) can be used as a figure of merit to evaluate the rectifying properties of the molecular diodes. In our study, RR is defined as the ratio between the current at -1V and at 1V:

(1)
Where |J(±1V )| is the absolute value of the current density (A/cm 2 ). Nijhuis, Reus and Whitesides 10 and L. Yuan et al. 11 obtained RR greater than 100 using ferrocenyl-alkanethiols based molecular diodes in which both electrodes exhibited similar work functions. In this case, the rectification process was not governed by the work function difference between the electrodes but was due to the intrinsic rectifying properties of ferrocenyl-alkanethiols. Furthermore, L. Yuan et al. 11 experimentally showed very recently that a control of the direction of rectification is possible by placing the Fc units of ferrocenyl-alkanethiols (HSC i FcC 13-i ) at different positions within the alkyl chain.

In this study, we develop a multiband quantum transport model based on a matrix formulation 12 in which we consider both the HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital) levels, and examine the electrical properties of the molecular junctions made of ferrocenyl-alkanethiols. The image potential in the potential barriers is also included in our model. We compare the computed current versus bias voltage I(Va) of the diodes under darkness with experimental measurements obtained by Nijhuis, Reus and Whitesides [START_REF] Nijhuis | [END_REF] and we give an insight into the physical phenomena occurring in ferrocenylalkanethiols based molecular diodes. Especially, we investigate through simulation how bound and quasi-bound states of the electronic levels of the molecules can participate to the charge transport. After this introduction, the second section of the paper is devoted to the description of the model developed to study the electrical properties of the molecular diodes. The third section is dedicated to the simulation of the electrical properties of HSC 9 Fc and HSC 11 Fc based molecular diodes. We investigate the influence of the HOMO and the LUMO energy bands of the ferrocen moiety and the alkyl chain length on the electrical properties of the diodes. In the forth section, we discuss the rectifying properties of HSC i FcC 13-i (0 ≤ i ≤ 13) based molecular diodes depending of the position of the ferrocene (Fc) moiety within the molecules.

II. Model

In order to help the understanding, we consider the specific case of a 11-(ferrocenyl)-1undecane-thiol (HSC 11 Fc) based molecular diode. As it is depicted in figure 1(a 13 . For this reason, the HOMO of the alkyl chain does not participate to the charge transportation and only the LUMO will be considered in the following. The ferrocenyl moieties are considered to be semiconductive exhibiting HOMO and LUMO levels quite close to the Fermi level of each electrode. The exact position of the energy levels and their broadening will be discussed in detail in the section III.

We used a quantum transport model to examine the electrical properties of the molecular junctions. An electron is emitted from one of the two electrodes with a total energy E and is transferred through the potential barriers to the other electrode. The wave functions of the electron (Ψ) are given by the solutions of the time-independent Schrodinger equation. In the lack of an experimental estimate, the effective mass of the electron in the tunneling junction is assumed to be equal to the free electron mass (m 0 ).

A. Calculation of the barrier potential within the tunneling junction:

The potential in the tunnel junction was considered to be invariant along both the transverse y and z axes. We assume the Fermi level of the left electrode to be 10 eV but, as we will see in the following, the electrical properties of the diodes essentially depend on the energy relative to the vacuum level 14 . The potential variation (V (x)) within the junctions has been expressed as follows:

(2) where x is the distance of the electron from the left electrode, q is the elementary charge, d is the distance separating the two electrodes, W L =W Ag and W R =W Ga2O3-EgGaIn are the work functions of the left silver electrode and the right Ga 2 O 3 -EgGaInelectrode respectively. Va is the applied voltage (cf. figure 1). The Va parameter is required in order to compute the I(Va) characteristics of the diodes and to examine their rectifying properties. In our model, we consider that a positive bias induces a decrease of the Fermi level of the right electrode and results in an additional potential within the junction. ∆Φ is the energy difference between the work function of the left Ag electrode and the molecular orbital (HOMO or LUMO) of the functional groups located within the molecular junction. Within the Van der Waals' contacting, ∆Φ is defined as the energy difference between the work function of the left electrode and the vacuum level. Because the relative dielectric constant of organic materials is low (∼ 2), the image potential screening is weak within the molecular junctions 15,16 . Thus, an electron in the vicinity of an electrode "feels" an additional image potential, which results in barrier lowering. The solution of the image force problem results in an expression for the image potential V image (x) which is an infinite serie 17 :

(

Where ε 0 and ε r are the dielectric constant of the vacuum and the relative dielectric constant of the organic material within the junctions, respectively. The relative dielectric constant of the ferrocenyl-alkanethiols has been considered to be equal to the dielectric constant of the alkyl chains (ε r = 2.1) 15 . This expression can be accurately expressed by an hyperbolic function as follows 17,18 :

(4)

B. Calculation of the current density through the tunnel junction:

Assuming an isotropic distribution of electron velocities in the metal electrodes, the tunneling current density through the junction can be calculated from the tunneling probability T 14,17,19 :

(5

)
Where T is calculated using a matrix formalism 12 . The Fermi-Dirac distribution functions under bias in the left (f L ) and in the right (f R ) electrode are given by the following formula 17 : (6) (7) Due to the semi-conducting character of the ferrocenyl moiety, both the HOMO and the LUMO have to be considered. In our model, the contributions of the two levels are calculated separately.

First, the tunneling current density J HOMO is calculated by considering only the HOMO of the ferrocenyl moiety. In the same manner, the tunneling current density J LUMO is calculated by considering only the LUMO of the ferrocenyl moiety. Finally both tunneling current densities are added to obtain the total tunneling current density: (8) We have then implemented a ballistic transport model in which the energy E of an electron injected from the electrode remains constant along the active region of the system. Inelastic scattering phenomena, like interactions of electrons with phonons, are neglected. The simplicity of our physical model is an asset to give an insight into the physical phenomena occurring in molecular diodes. Furthermore, such a simple model does not require high computation resources and could be used for the optimization of the electrical properties of molecular diodes 20 .

III. HSC11Fc and HSC9Fc based molecular diodes

We consider now an HSC 11 Fc based self-assembled molecular diode in the following configuration: Ag/SAM/Ga 2 O 3 -EGaIn. The shape of the potential barrier depends on the workfunctions of the electrodes, the HOMO and LUMO of the different functional groups within the ferrocenylalkanethiol and the applied voltage. Figure 1b shows the energy band diagram of the diode. In accordance with the Nijhuis, Reus and Whitesides' experimental work [START_REF] Nijhuis | [END_REF] , we consider metallic Ag and Ga 2 O 3 -EGaIn electrodes with work functions of W Ag = 4.67 eV and W Ga2O3-EGaIn = 4.23 eV respectively. The LUMO level of the alkyl chains is set to -0.67 eV. This value is in accordance with experimental measurements 21 and with values obtained through numerical simulations 13,15 . The energy position of the HOMO and the LUMO of the ferrocen moieties are -3.27 eV and -4.97 eV respectively while their broadenings (Γ) is varied between 0.1 eV and 0.7 eV. These values arein accordance with numerical simulations performed using the density functional theory(DFT) for an HSC 11 Fc based molecular diode in which both electrodes are made of gold (Au) 13 . In the present work, starting from values extracted from ref 13, we adjust the energy position and the broadening of the HOMO and the LUMO to fit the data of Nijhuis, Reus and Whitesides' experimental work [START_REF] Nijhuis | [END_REF] . This adjustment is necessary because the electrical properties of the molecules are strongly influenced by the electrodes. Especially, the energy levels can be broadened within the molecular diode depending on the coupling strength between the electrons in the electrodes and those in the molecules 11,22 . The contacts at theAg

A. Influence of the Γ broadening

We first investigate the influence of the energy level broadening Γ on the electrical properties of HSC 11 Fc based diodes. The broadening of both the LUMO and the HOMO is varied independently. The other parameters are kept unchanged.

The HOMO level broadening (Γ HOMO ) is varied from 0.1 eV to 0.7 eV while the LUMO level broadening is kept constant (Γ LUMO = 0.6 eV). The resulting calculated I(Va) characteristics are presented in figure 2(a). The HOMO level broadening mainly influences the diode electrical properties for negative applied voltages. A strong increase of the current is observed for applied voltages lower than -0.8 V when Γ HOMO is upper than 0.57eV. Thus, the I(Va) characteristics are highly asymmetric. This current increase is stable for broadenings varying between 0.57 eV and 0.7 eV. On the contrary, this current increase is becoming less and less pronounced when the broadening is decreasing from 0.57 eV to 0.1 eV and the I(Va) characteristics become more and more symmetric. The figure 2(b) shows the I(Va) characteristics of the diode for different values of the LUMO level broadening (0.1 eV ≤ Γ LUMO ≤ 0.7 eV). The LUMO level broadening mainly influences the slope of the I(Va) curves for positive applied voltages but a smaller increase of current can be observed. Thus, these calculations show that the rectification ratio is mainly influenced by the HOMO. In the following, we investigate the strong current increase occurring at negative applied voltage for the high values of the HOMO broadening. For these investigations, the LUMO broadening is fixed (Γ LUMO =0.6 eV) while two different values of the HOMO broadening have been considered (Γ HOMO = 0.6 eV and Γ HOMO = 0.5 eV). 3(a) reveals a sharp increase of the tunneling probability for energies ranging between 9.2 eV and 11 eV and for voltages ranging between 0 and -2 V. This region is surrounded by a dashed line in figure 3(a). It corresponds to the presence of a resonant state in the HOMO of the ferrocenyl moiety. This resonance is shifted to higher energy values when the applied voltage is decreasing from 0 V to -2 V. It crosses the Fermi level of the left Ag electrode for Va = -1.06V. When Va is decreasing from 0 V to -2 V, this resonance is approaching more and more the Fermi level of the left Ag electrode[the black line in figure 3(a)]. Thus, the resonance participates more and more to the charge transportation.

When the resonance is close enough to the Ag Fermi level (Va = -0.8 V) the current of the diode strongly increases [cf. figure 2(a)]. The current continues to sharply increase until the resonance rises into the window between the Fermi levels of the two electrodes. This resonance corresponds to a bound state in the HOMO, which becomes a quasi-bound state when its energy position is higher than the Fermi level of the left electrode 12 . The inset of the figure 3(a The figure 4(a) shows the calculated tunneling probability for Γ HOMO = 0.5 eV. As previously, these computations are performed by only considering the HOMO of the ferrocenyl moiety. In contrast to the previous results, the figure 4(a) does not reveal a sharp increase of the tunneling probability for energies ranging between 9.2 eV and 11 eV and for voltages ranging between 0 and -2 V. Thus, the resonant state coupling within the HOMO previously observed for Γ HOMO = 0.6 eV is less pronounced for Γ HOMO = 0.5 eV. The inset of the figure 4(a) shows the transmission probability versus energy for an applied voltage of -1.06 eV. The transmission probability at 10 eV is less sharp than previously. We explain these results by the fact that the resonant state cannot be coupled efficiently within the HOMO. The figure 4(b) gives the potential inside the HSC 11 Fc based junction at Va = -1.06 V and for Γ HOMO = 0.5eV and Γ LUMO = 0.6 eV. The blue dashed line is located at the Fermi level of the left electrode, which corresponds to the energy level at which the bound state should be coupled. These results reveal that the bound state is not located within the HOMO. The figure 4(b) shows that the HOMO is located between the Fermi level of both electrodes at Va = -1.06 V. Thus, because the HOMO rises between the Fermi levels of both electrodes, we can observe a slight increase of current for applied voltages lower than -0.8 V (cf. figure 2(a)). Nevertheless, our results reveal that the HOMO is not large enough to allow a bound state appearing. It may explain why the asymmetry of the I(Va) characteristics is weakly pronounced for Γ HOMO = 0.5 eV (cf. figure 2(a)).

These results are in accordance with the mechanism proposed by Nijhuis, Reus and Whitesides [START_REF] Nijhuis | [END_REF] and by Cui et al. 13 for the current rectification by HSC 11 Fc SAM based molecular junctions.

They suggested that the large rectification observed for HC 11 Fc molecular junctions originates from the accessible HOMO of the Fc moiety, which is asymmetrically positioned in the junction and electronically coupled to one electrode through non-uniform potential drops. According to recent theoretical works 16 , our computations show that the molecular orbital width Γ HOMO is an important parameter influencing the rectification ratio of the diodes. Furthermore, our results reveal that bound or quasi-bound states may play a crucial role in the charge transportation within HSC 11 Fc based molecular junctions.

B. Influence of the energy position

We investigate the influence of the energy position of the HOMO and LUMO on the electrical properties of HSC 11 Fc based diodes. For this purpose, the broadening of both the HOMO and LUMO levels are fixed (Γ HOMO = Γ LUM O = 0.6 eV). The energy position of the HOMO is first varied between -4.64 eV and -5.17 eV while the energy position of the LUMO is kept constant at -3.27 eV. The figure 5(a) shows that the strong current increase in the junction is shifted to lower negative applied voltages (Va) when the energy position of the HOMO is decreasing. In other words, when the energy position of the HOMO is decreasing, a stronger negative applied voltage is required to raise the HOMO between the Fermi levels of both electrodes. Then, the energy position of the LUMO is varied between -3.47 eV and -3.07eV while the energy position of the HOMO is kept at -4.97 eV. The results are shown in figure 5(b) and reveal that the energy position of the LUMO mainly influences the slope of the I(Va) curve at positive bias. Thus, the closer is the LUMO to the Fermi level of the right electrode, the lower is the resistivity of the junction at positive bias. These results show that the HOMO electrode work function offset strongly influences the diode rectification ratios.

C. Influence of the alkyl chain length

Finally, the energy level positions and the level broadenings are adjusted to fit the experimental I(Va) characteristics obtained by Nijhuis, Reus and Whitesides [START_REF] Nijhuis | [END_REF] . For the HOMO, the obtained energy position and broadening are -4.955 eV and 0.57 eV, respectively. For the LUMO, the obtained energy position and broadening are -3.27 eV and 0.57eV, respectively. The distance between the end of the molecule and the right electrode is adjusted at 0.27 nm. The figure 6(a) shows that the computed I(Va) characteristic of the HSC 11 Fc based junction agrees quite well with experimental measurements. The calculated RR (from equation 1) between Va=-1 V and Va=1 V is 109 while Nijhuis, Reus and Whitesides experimentally obtained a RR of 100 [START_REF] Nijhuis | [END_REF]

IV. Influence of the ferrocenyl position within the molecular junction

In this section, we investigate the influence of the ferrocenyl position within the molecular junction on the rectifying properties of the molecular diodes. The figure 1(d) gives the theoretical band diagram of HSCiFcC13-i based molecular diodes having Ag and Ga 2 O 3 -EgGaIn electrodes. Both the CH 3 and Fc end groups form Van der Waals interactions with the Ga 2 O 3 -EgGaIn electrode and the sulfur forms a covalent bounding with the Ag electrode. Our model does not take into account the fact that the broadening of the HOMO level may increase exponentially when the Fc moiety is very close to the Ag electrode 16 . Nevertheless, as it will be presented in the following, this model is able to reproduce the main electrical behavior of the HSCiFcC13-i based molecular diodes which tends to prove that the asymmetry of barrier lengths at both sides of the HOMO also strongly contributes to the rectifying properties of the junctions. As previously, the HOMO energy position and broadening are fixed at -4.955 eV and 0.57 eV, respectively. These values are in strong accordance with the values obtained from experimental UPS measurements. Indeed, a HOMO energy position around -5eV and a HOMO broadening between 0.5eV and 0.75eV have been obtained from UPS measurements 11,16 bound state within the HOMO of the Fc moiety for negative and positive bias. This resonant states does not cross any electrode Fermi level in the considered range of applied voltages. Thus, they do not participate actively to the charge transportation either at positive voltages or at negative voltages which nicely explains why the I(Va) curveis symmetric. In other words, the accessible HOMO of the Fc moiety is symmetrically positioned in the junction, which results in a symmetric electronic coupling to both electrodes. The potential drop within the junction is too low to ensure that the bound state enters in the window between the Fermi levels of the electrodes.

  ) and 1(b), we consider a self assembled monolayer (SAM) of SC 11 Fc sandwiched between two electrodes and forming a Metal-SAM-Metal diode. The first electrode is made of silver (Ag). The SAM is bound to the Ag electrode by covalent bounds between the sulfur and the Ag atoms (Ag-S). The second Ga 2 O 3 -EGaIn electrode is an eutectic liquid electrode usually used to fabricate molecular diodes. It is generally assumed that the terminated Fc moities of the SAM form a Van der Walls contact with the Ga 2 O 3 -EGaIn electrode 10,11 . The figure 1(b) gives the theoretical band diagram (with respect to vacuum) of the resulting Ag-SC 11 Fc-Ga 2 O 3 -EgGaIn molecular junction before the alignment of the Fermi levels. Both electrodes are defined by their work functions allowing us to determine the Fermi level of the electrons in the metals. The alkyl chain of the molecule exhibits a large band gap with an HOMO well below the Fermi level of each electrode

FIG. 1 .

 1 FIG.1. (a) Schematic representation of molecular diodes made of ferrocenyl-containing alkanethiols. It Consists in Ag bottom electrodes, SAM of SC 9 Fc, SC 11 Fc or SC i FcC 13i and Ga2O3-EGaIn electrodes. Theoretical energy band diagram of molecular diodes made of (b) HSC 11 Fc, (c) HSC 9 FC and (d) HSC i FcC 13i .

  FIG.2. Influence of the the energy level broadening (a) Γ HOMO and (b) Γ LUMO on the calculated I(Va) characteristics of a HSC11Fc molecular diode.

FIG. 3 .

 3 FIG. 3. The figures (a) and (b) present computed color maps of the tunneling probability for the HSC 11 FC based junction (by considering Γ HOMO =Γ LUMO =0.6eV). The computations are performed considering (a) only the HOMO and (b) only the LUMO of the ferrocenyl moiety. The resonant states are surrounded by dashed lines. (c) Potential inside the HSC 11 Fc based molecular diode at Va=-1.06V (Γ HOMO =Γ LUMO =0.6eV). The inset of the figure (a) shows the transmission probability versus energy for Va=-1.06 eV.

  ) shows the transmission probability versus energy for an applied voltage of -1.06 eV. It clearly shows that a bound state, whose the energy position corresponds to the Fermi level of the left Ag electrode (10eV), exists. The figure 3(c) presents the potential inside the junction for HSC 11 Fc based diodes at Va = -1.06 V and for Γ HOMO = Γ LUMO = 0.6 eV. The dashed red line shows the energy position of the bound state within the HOMO, which is equal to the Fermi level of the left electrode at Va = -1.06 eV. The figure 3(b) shows the calculated tunneling probability map by considering only the LUMO of the ferrocenyl moiety (Γ LUM O = 0.6 eV) and allows to computethe current density J LUMO . It reveals the presence of a quasi-bound state (red line) at high energy (12 to 13 eV) and for negative applied voltage (0 to -2V). Because this resonance never falls within the window between the Fermi levels of both electrodes, it does not strongly participate to the charge transportation.

FIG. 4 .

 4 FIG.4. (a) Computed color map of the tunneling probability for the HSC 11 FC based junction by considering Γ HOMO =Γ LUMO =0.5 eV. The computations are performed considering only the HOMO of the ferrocene moiety. (b) Potential inside the HSC 11 Fc based molecular diode at Va = -1.06 V (Γ HOMO =Γ LUMO =0.5 eV).

FIG. 5 .

 5 FIG. 5. Influence of the (a) HOMO and (b) LUMO energy positions on the I(Va) characteristic of the HSC 11 Fc based molecular junction.

FIG. 6 .

 6 figure 6(b) depicts the computed I(Va) characteristic of a HSC 9 FC based molecular diodes. As shown in figure 1(b) and 1(c), while the whole length of HSC 11 including the covalent bond (S-Ag) is 1.55 nm, the length of HSC 9 is reduced to 1.35 nm 10 . The other parameters are identical to those used for the HSC 11 Fc based molecular diode. The computed I(Va) curve reproduces quite well the Nijhuis, Reus and Whiteside's experimental data 23 and reveals a strong increase of

FIG. 7 .

 7 FIG. 7. Computed (a) I(Va) characteristics, (b) color map of the tunneling probability and (c) potential inside the molecular junction for a HSC 13 Fc based diode. Computed (d) I(Va) characteristics, (e) color map of the tunneling probability and (f) potential inside the molecular junction for a HSFcC 13 based diode.

  FIG.8. Computed (a) I(Va) characteristics and (b) color map of the tunneling probability of a HSC 6 FcC 7 based diode.

Acknowledgements:

This work has been carried out thanks to the support of the A*MIDEX project (n° ANR-11-IDEX-0001-02) funded by the "Investissements d'Avenir" French Government program, managed by the French National Research Agency (ANR).

V. Conclusion

We have developed a simple but efficient and reliable 1D multiband quantum transport model considering both the HOMO and LUMO levels to investigate the electrical properties of molecular diodes made of ferrocenyl-alkanethiols. Our results suggest that the large rectification ratio observed for HC11Fc molecular junctions originates from the accessible HOMO of the Fc moiety which is asymmetrically positioned in the junction and electronically coupled to one electrode through non-uniform potential drops. Our results reveal that bound or quasi-bound states play an important role in the charge transportationin the molecular diodes. The computed I(Va) characteristics of HSC11Fc and HSC9Fc based junctions agree well with experimental measurements obtained by Nijhuis, Reus and Whitesides [START_REF] Nijhuis | [END_REF] . The calculated RR between Va = -1 V and Va = 1 V are 109 and 26 for HSC11Fc and HSC9Fc based junctions respectively while Whiteside et al. experimentally obtained RR of 100 and 10 for HSC11Fc and HSC9Fc based junctions, respectively [START_REF] Nijhuis | [END_REF] . We show that our model allows explaining and predicting the electrical properties of molecular diodes made of HSCiFcC13-i. In accordance with the experimental results obtained by L. Yuan et al. 11 , we show that the direction of rectification depends on the position of the Fc units within the alkyl chain of ferrocenyl-alkanethiol. Finally, our model allows extracting electronic properties of the ferrocenylalkanethiol such as the orbital energy positions and the orbital widths. Furthermore, this model has the advantage that it does not require DFT or TD-DFT time consuming computations.


Marcel Pasquinelli
email: marcel.pasquinelli@univ-amu.fr

Jean-Jacques Simon

Judikaël Le Rouzo

François Flory

Ludovic Escoubas

Judikael Le Rouzo

Normalized area solar cell and potential applications

Keywords: Photovoltaic, Solar Cell, Efficiency, Serial resistance, Shunt resistance. Methodology

published or not. The documents may come

Normalized area solar cell and potential applications

Single diode model for illuminated solar cell could be used here [START_REF] Charles | Mialhe A practical method of analysis of the current-voltage characteristics of solar cells[END_REF][START_REF] Kaminsky | I-V methods to extract junction parameters with special emphasis on low series resistance Solid State Electronics[END_REF][START_REF] Chegaar | Langueur Determination of Solar Cells Parameters under Illuminated Conditions[END_REF], this model take in account the shunt across the junction (rsh), the lumped resistance (rs).

In this model, the output (I-V) characteristic is given by the equation 1 .

. 1 ) ) . ( exp( Rsh

I Rs V akT I Rs V q I Iph I I Iph I o Rsh D                (1)
Equation 1: (I-V) analytical expression for one exponential model solar cell

The difficulty in equation 1is that two kinds of parameters coexists, intensive parameter such as voltage (V), temperature (T),… and extensive ones such as current (I), resistances (Rs and Rsh). If we want a quantitative comparison between solar cells with different surface areas (S), it is necessary to give the current density, J, versus voltage, V, equation. This expression is simply derived from (1) with the assumption:

S I J  (2) S Rsh J S Rs V akT J S Rs V q J Jph J J Jph J o Rsh D . . . 1 ) ) . . ( exp(                (3)
We can now introduce a normalized area solar cell (S = 1cm 2 for instance) with resistance specifications given in .cm 2 units.

S Rs rs

.  [START_REF] Charles | Mialhe A practical method of analysis of the current-voltage characteristics of solar cells[END_REF] And

S Rsh rsh .  (5) rsh J rs V akT J rs V q J Jph J J Jph J o Rsh D . 1 ) ) . ( exp(                (6)
It is now obvious that for a given solar cell (material and process) the serial and shunt resistance decrease if the area increases. To highlight this, for two solar cells with S and S' area respectively and if S' > S, equations 4, 5 and 6 imply that: Applications and results

-Surface area effect on photovoltaic properties in one sun application

Thanks to this model, it is relatively easy to extrapolate photovoltaic parameters computed for a unit size solar cell to another size, just by calculating Rs and Rsh for the size S. The formula used in this case is:

For size S: S rs Rs  and S rsh Rsh 

In order to verify this assumption, PC1D and SPICE codes are used, we have modelized a unit solar cell with parameters generally used in conventional p-type silicon solar cells. Table 2 shows values obtained for three surface areas, it is clear that these results are in good agreement with the previous assumption.

Area (cm

-Serial resistance loss in concentrated photovoltaic CPV solar cells

Concentrated photovoltaic is very attractive due to the fact that for the same solar cell size, the photovoltaic properties are increased with X, when the device is illuminated under X sun.

A current question is whether conventional solar cells can be used for low concentration applications, typically X<10.

With our model, it is evident that it is not possible, because of the high serial resistance value. In fact, figures 2a and 2b show the drastic effect of the serial resistance. If solar flux is concentrated on conventional solar cells (rs = 1.5 .cm 2 ), Jsc increases linearly if X < 10 and saturates after this value, but and most importantly, there is a decrease in conversion efficiency.

If you want to optimise this possible utilisation for conventional solar cells, the rs value must be divided by a factor of ten (rs = 0.15 .cm 2 ), which is not easy with today's technology.

-Solar cell modelized by N unit solar cells

In a solar cell, global performances are largely relative to local ones, specifically in heterogeneous material such as multi-crystalline silicon.

To evaluate local properties it is useful to divide a large size into N unit solar cells, in figure 3 in order to illustrate this method, we have chosen N = 4, the USCs are connected in parallel. Evidently, the performances for the final solar cell are conserved, but this ideal case could be attributed to an homogeneous solar cell, in terms of materiel, for instance monocrystalline wafer and uniform processes. Generally, especially for multicrystalline ingots, heterogeneous properties govern final solar cell performances. In a rapid approach we can evaluate the effects of local defects at the scale of individual USC on global performance, such as local shunt (rsh), local bad electrical contact (rs) and local bad photon collection or conversion (Jph) Now, to evaluate the impact of unit solar cells on the final device, we have chosen to see the influence of rs, rsh and Jph after a 50% variation of their initial value.

Application 2: Serial resistance discrepancy

In the electrical model figure 1, serial resistance rs is a lumped value that takes into account contact resistance on the emitter and the base, grid line contact and semiconductor resistivity. This final value depends greatly on the process and also on possible degradation during the solar cell's lifetime. In this case, illustrated by figure 5a, b and c, we have just increased the rs value for one cell, this modified value is equal to 2,25 ohms, which represents also 50% variation. We can see in figure 5c, that only conversion efficiency of the solar cell is affected and decreases to 14,81 %.

Application 3: Shunt resistance discrepancy

For this case, we have taken into account a 50% decrease of the shunt resistance in the unit solar cell (figure 6a, b, andc). Especially in multicristalline wafers, shunt leakage must be attributed to crystallographic defects decorated with metallic impurities crossing the junction. During the solar cell fabrication, shunt resistance degradation must appear at the aperture of the junction process. We can see that for this local variation, the total properties of the cell are not greatly affected, but evidently if the shunt leakage increases the impact will be more important. This case must be attributed to an accidental partial shadowing of the cell, or more problematically to a local area with poor electronic quality due to the presence of electrical recombining impurities for instance. We have also kept with the same total variation (50%) of the unit Jsc value, 17.5 mA/cm 2 instead of 35 mA/cm 2 , and the results are described in figure 7a, b andc. It is obvious that this situation is the worst case, because of the degradation of all photovoltaic parameters (V oc , J sc and )

U.S.C rsh

Conclusion:

We have proposed a method seeking to explain properties of solar cell by local analysis thanks to a normalized area solar cell concept. Most of actual solar cells technologies are based on multicristaline materials (Si, CIGS, CdTe,) and for each category as we have done for silicon, parameters for each unit solar cell must be defined.

As we have described in this article, several applications could be concerned with this analysis and for further studies, it will be such interesting to implement and compare this model with local photoelectrical characterizations as Light Beam Induced Current (LBIC), Photoluminescence and Electroluminescence Imaging.

U.S.C Jsc

Figure 1 :

 1 Figure 1: One diode electrical model of illuminated solar cell

Figure 2a :Figure 2b :

 2a2b Figure 2a: Short circuit current density evolution with concentration factor for two serial resistances values.( rs =1.5 .cm 2 and 0.15 .cm 2 )

Figure 3 :Application 1 :Figure 4 :

 314 Figure 3: Homogeneous solar cell composed by four parallel Unit Solar Cells

Figure 5 :

 5 Figure 5: Serial resistance discrepancy 5a: U.S.C parameters; 5b: Solar cell made by four distributed U.S.C: and 5 c: Final solar cell parameters.

Figure 6 :

 6 Figure 6: Shunt resistance discrepancy 6a: U.S.C parameters; 6b: Solar cell made by four distributed U.S.C: and 6c: Final solar cell parameters.

Application 4 :

 4 Local photocurrent generation discrepancy

Figure 7 :

 7 Figure 7: Local photocurrent generation/recombination discrepancy 7a: U.S.C parameters; 7b: Solar cell made by four distributed U.S.C: and 7 c: Final solar cell parameters.

Best values for parameters used in equation

	Obscurity current		Diode ideality					Serial resistance	Shunt resistance	Photocurrent
	density (mA/cm 2 )		factor							()	()	density (mA/cm 2 )
																						( one sun)
				10 -7									1,2							1.5	1500	33
	rs		Rs	. S		R	'	. S s	'	(7)	and		rsh		Rsh	. S		R	'	. S sh	'	(8)
	For instance, if	S	'	S . 2	,	' R  s	2 Rs	and	R	'	sh		2 Rsh

[START_REF] Chegaar | Langueur Determination of Solar Cells Parameters under Illuminated Conditions[END_REF]

To estimate Jo, Jph, a, rs and rsh values, we have made some statistical measurements on elaborated solar cells characterized under standard one sun test condition (AM1,5G) (Table

1 )

Table 1 :

 1 Electrical and photovoltaic parameters average values for p-type multi-crystalline silicon solar cells (surface area size = 1 cm 2 )

Table 2 :

 2 Evolution of photovoltaic parameters with the surface areas of the cells

	2 )	Voc (mV)	Jsc (mA/cm	2 )	Isc(mA)	Efficiency (%)	Rs (ohm)	Rsh (ohm)
	1	602,2	32,8		32,8	14,80	1,5	1500
	10	602,2	32,8		328	14,78	0,15	150
	100	602,2	32,8		3280	14,77	0,015	15


N Malavasi

S Arnouts

D Vibert

S De La Torre

T Moutard

C Pichon

I Davidzon

K Kraljic

M Bolzonella

L Guzzo

B Garilli

M Scodeggio

B R Granett

U Abbas

C Adami

D Bottini

A Cappi

O Cucciati

P Franzetti

A Fritz

A Iovino

J Krywult

V Le Brun

O Le Fèvre

D Maccagni

K Ma Lek

F Marulli

M Polletta

A Pollo

L Tasca

R Tojeiro

D Vergani

A Zanichelli

J Bel

E Branchini

J Coupon

G De Lucia

Y Dubois

A Hawken

O Ilbert

C Laigle

L Moscardini

T Sousbie

M Treyer

G Zamorani

The VIMOS Public Extragalactic Redshift Survey

Keywords: Cosmology, observations -Cosmology, large-scale structure of Universe -Galaxies, evolution -Galaxies, high-redshift -Galaxies, statistics

INTRODUCTION

A major success of the ΛCDM model is its ability to reproduce the wealth of large-scale structures (LSS) observed in the galaxy distribution (e.g. Springel et al. 2006). These structures arise from the growth of primordial, nearly Gaussian, matter density fluctuations under the effect of gravity. In this process, matter departs from underdense regions and flows through dense sheets that wind up, forming filaments along which matter drifts and progressively gets accreted onto high-density peaks. This leads to a cosmic web (CW) where dense nodes are connected by filaments, framing walls separated by large voids (Bond et al. 1996). The baryonic gas follows the gravitational potential gradients imposed by the dark matter distribution, then is shocked, forming (among other structures) tenuous ionised hydrogen filaments, the intergalactic medium (IGM), in which galaxies can form. These filaments are regions where gas, momentum, and energy are exchanged through the complex processes of infall and outflow. While it has long been established that the local density environment on typical scales below a few Mpc plays a role in shaping galaxy properties (see e.g. Dressler 1980;Zehavi et al. 2005), the extent to which large-scale anisotropic structures and the tidal field of the CW influence the evolution of galaxies (and subsequently properties such as morphology, accretion mode, and merging rate) still remains an open issue.

There is significant numerical evidence that large-scale environment has an impact on the formation and evolution of galaxies. In particular, N-body dark matter simulations have shown that the spin and the shape of dark matter haloes depend on the large-scale environment in which they reside (Aragón-Calvo et al. 2007;Hahn et al. 2007;Sousbie et al. 2009). Moreover, using hydrodynamical simulations, Kereš et al. (2005) found that at high redshift cold streams can penetrate deep inside haloes and feed galaxies with fresh gas to sustain intense star formation (SF) activity (see also Dekel et al. 2009;Dekel & Birnboim 2006). Pichon et al. (2011) proposed that the filamentary flows advect angular momentum onto the disks of galaxies and that the spin of newly formed galaxies tends preferentially to be parallel to the axis of their closest filament. Codis et al. (2012) quantified a mass transition, with the most massive haloes ending up with a spin perpendicular to the filaments as a result of successive mergers along the filaments. These results have been extended to galaxies by Dubois et al. (2014) with the state-of-the-art hydrodynamical simulation Horizon-AGN (see also Codis et al. 2015, for a theoretical motivation for this transition based on constrained tidal torque theory). On the side of observations, the correlation between the spin of galaxies and their filaments or sheets has been recently detected in the Sloan Digital Sky Survey (Tempel et al. 2013;Zhang et al. 2013;Trujillo et al. 2006). This remarkable result confirms the role played by the large scale dynamical environment in the evolution of galaxies1 , which is usually neglected in galaxy formation models (e.g. Zehavi et al. 2005;Guo et al. 2011).

In the local Universe (z ≤ 0.3) the large galaxy redshift surveys 2dF (Colless et al. 2001), SDSS (York et al. 2000), and GAMA (Driver et al. 2011) have captured the CW in great detail and led to several analyses showing variations of individual (Beygu et al. 2013;Alpaslan et al. 2015Alpaslan et al. , 2016) ) and statistical (Eardley et al. 2015;Martínez et al. 2016) galaxy properties as a function of their CW environment. At higher redshifts, because of the small volumes probed and the low sampling rates achieved by redshift surveys, this kind of analysis has not been possible until recently. The state-of-the-art redshift survey VIPERS (Guzzo et al. 2014) overcomes these limitations by probing a volume equivalent to the local 2dF survey with a dense spectroscopic sampling of galaxies. It allowed the first measurement of the growth rate of the LSS at 0.5 ≤ z ≤ 1.2 (de la Torre et al. 2013) and the fine mapping of the CW at an epoch when the Universe was about half its current age.

In this paper, we exploit the final, complete sample of the VIPERS survey to detect the filamentary structure of the CW at high redshift and to study the correlation between galaxy properties and their distance to the closest filament. After describing the data in Sect. 2, we illustrate in Sect. 3 the filament reconstruction with the Discrete Persistent Structure Extractor (DisPerSE, Sousbie 2011) on mock samples of the VIPERS survey and its fidelity. We present the application to the VIPERS data in Sect. 4, where we also report a significative mass and type segregation within filaments. Finally, we discuss in Sect. 5 our results within the current paradigm of galaxy assembly. Unless stated otherwise, we assume the Planck Collaboration et al. (2015) cosmology with H 0 = 67.51 km s -1 Mpc -1 , h = H 0 /100, Ω m = 0.3121, and Ω Λ = 0.6879.

DATA

The VIMOS Public Extragalactic Redshift Survey (VIPERS) is a magnitude-limited spectroscopic galaxy survey to i AB ≤ 22.5. It covers an overall footprint of about 16 deg 2 and 8 deg 2 in the W1 and W4 fields of the CFHTLS-Wide imaging survey, respectively. VIPERS spectra were collected in low resolution mode, R = 230, leading to a radial velocity error of σ v = 175(1 + z spec ) km s -1 . The spectroscopic targets were pre-selected in a colour-colour space to remove galaxies below z = 0.5, which coupled with an optimized observing strategy, provides an average effective sampling rate of about 40%. We refer the reader to the survey description papers by Guzzo et al. (2014) and Garilli et al. (2014) and to the parallel paper by Scodeggio et al. (2016) for more details.

In this work we use the final galaxy sample, described in the latter paper (the so-called PDR-2). We consider only the most secure redshifts, corresponding to quality flag ≥ 2 in the VIPERS grading scheme (confidence level, CL > 97%). The mean number density of galaxies, n(z), varies significantly at the redshift boundaries of the survey, due to the magnitude limit, the target sampling rate, and the colour selection (see de la Torre et al. 2013;Guzzo et al. 2014, for details). For this reason we limit this analysis to the 50 980 galaxies in the range 0.5 ≤ z ≤ 0.85, where the typical spatial resolution in terms of mean inter-galaxy separation, D z ∼ n(z) -1/3 , is the highest (7.7 < D z /Mpc < 10). These values are comparable with those of the GAMA survey (Driver et al. 2011, with 4. 6 < D z /Mpc < 8.8 for 0.1 < z < 0.3 andr ≤ 19.8), and make VIPERS the first galaxy redshift survey well suited for studying the CW at high redshift. The stellar masses for the objects in our sample and the classification between active and passive populations were derived according to Moutard et al. (2016b), on the basis of the SED-fitting analysis of the multi-wavelength data collected in the VIPERS regions 2 (Moutard et al. 2016a).

DETECTING FILAMENTS IN THE VIPERS SURVEY

The DisPerSE code. In order to trace the CW in VIPERS, we rely on the Discrete Persistent Structure Extractor (DisPerSE, see Sousbie 2011;Sousbie et al. 2011, for a complete description). DisPerSE identifies filaments as ridges in the density field (calculated using the Delaunay Tessellation Field Estimator, DTFE). DisPerSE uses the discrete Morse theory to extract critical points, where the gradient of the density field vanishes (e.g. maxima and saddle points), and the field lines connecting them. It then pairs the critical points in topological features, called "critical pairs", using the persistent homology theory. The robustness of each feature (including the filaments) is assessed by the relative density contrast of its critical pair, the so-called persistence, which is chosen to pass a certain signal-to-noise (S/N) threshold. The noise level is defined relative to the variance of persistence values obtained from random sets of points. Because DisPerSE is based on a topologicallymotivated algorithm, it is both very robust and flexible through the choice of the persistence threshold. Since it filters out the sampling noise, it enables an unsmoothed density field, more noisy but less biased, to be analysed. By construction it is also multi-scale: it builds a network which adapts naturally to the uneven sampling of observed catalogues. The persistence threshold is calibrated on mocks to account for the specific design of VIPERS. (2016). The parent catalogues include all the galaxies down to the magnitude limit i AB = 22.5 together with the correct selection function at 0.4 < z < 0.6 due to the VIPERS colour pre-selection. The VIPERS-like catalogues are built from the parent ones with all the observational effects applied (i.e. pointing strategy, target sampling rate, gaps between VI-MOS quadrants, photometric mask and random errors on redshift).

The impact of observational biases on the skeleton reconstruction can be assessed by comparing the skeletons obtained from the parent and the VIPERS-like mock catalogues. To quantify the differences between two skeletons 2 The VIPERS-MLS survey: http://cesam.lam.fr/vipers-mls/ we define a pseudo-distance between the two skeletons to be compared. In practice, a skeleton S a is composed by N a short straight segments, s i a . We define the pseudo-distance from a skeleton S a to a skeleton S b , D(S a , S b ), as the probability distribution function (PDF) of the distances between each segment of S a , s i a , and its closest segment in S b , s j b (Sousbie et al. 2009). The distributions D(S a , S b ) and D(S b , S a ) are composed by N a and N b distances respectively. There is no reason for the pseudo-distance D(S a , S b ) to be identical to D(S b , S a ). Indeed the discrepancy between the two PDFs is related to the differences between the two skeletons3 .

Fig. 1 presents the PDFs of the pseudo-distances obtained by comparing the skeletons S Par and S VIP measured from the Parent and VIPERS-like catalogues, respectively, in the redshift range 0.5 < z < 0.85. In the upper panel, DisPerSE is run with a persistence threshold of 3σ in both catalogues. This threshold guarantees that less than 1% of critical pairs are spurious, as tested on random field simulations (Sousbie 2011). S VIP is reconstructed with less accuracy and detail due to the lower sampling. An estimate of the uncertainty in the location of the filaments is given by the modes of the PDFs which do not peak at distance D ∼ 0 (corresponding to a perfect match between the segments of the two skeletons) but D ∼ 1.5 -2 Mpc (marked as vertical arrows). The asymmetry between D(S Par , S VIP ) and D(S VIP , S Par ) reflects the fact that S Par (full sampling) has much more details (i.e. the leaves of branches, or small branches) which have no counterpart in S VIP . On the other hand 90% of the segments of S VIP have a counterpart in S Par with distances D ≤ 10 Mpc, illustrating the small fraction of spurious filaments. We also report the average length of the VIPERS-like (L VIP ) and the Parent (L Par ) skeletons, defined as the total skeleton length divided by the survey volume (expressed in Mpc/Mpc 3 ). L VIP is shorter than L Par as expected for a skeleton with fewer details. In the lower panel, the persistence threshold on the Parent catalogue is increased to 5.5σ. The length, L Par , is shortened with only the most significant filaments still present. The two PDFs for D(S VIP , S Par ) and D(S Par , S VIP ) are now much closer in amplitude and shape. Most of the segments in S Par (75%) have a counterpart in S VIP with D ≤ 10 Mpc. The modes of the distributions are almost unchanged. Even if the two skeletons are more similar, the skeleton S VIP tends to oscillate around its true location (as reconstructed by S Par ), making the length L VIP longer than L Par .

In conclusion, the close match between the two PDFs indicates that the skeleton reconstructed at 3σ for the VIPERS-like catalogue is able to detect the most robust filaments (corresponding to a 5.5σ persistence threshold in a fully sampled dataset) and contains a small fraction of spurious filaments.

RESULTS

The filamentary structures of the Cosmic Web. We run DisPerSE on the VIPERS fields with a 3σ persistence threshold. Fig. 2 shows the filamentary network (green lines) for W1 (top panels) and W4 (bottom panels) fields, overplotted on a map of the density contrast δ = n DTFE /n(z) -1, where n DTFE is the local DTFE density estimate. Even in the 2D projections, we can see that filaments reveal the ridges of the 3D density field which, by construction, connect the density peaks between them via saddle points. The averaged length of the skeletons are similar with L ∼ 0.0013 and 0.0016 Mpc/Mpc 3 in W1 and W4 respectively. At low (z ≤ 0.5) and high redshift (z ≥ 0.85), the number of filaments drops as a consequence of the lower sampling and only the most secure filaments are detected, as expected with DisPerSE. Thanks to the large contiguous volume probed by VIPERS, large voids, partly delineated by the filaments, are visible in both fields with radii as large as R ∼ 30 Mpc (see Micheletti et al. 2014 and the parallel paper by Hawken et al. 2016 for void analysis in VIPERS).

Mass segregation inside filaments. We now investigate how different galaxy populations are distributed within this filamentary network in the redshift range 0.5 ≤ z ≤ 0.85. We measure the distance of each galaxy to the nearest filament, D skel (which, in the figure, we report normalised to D z to take care of the variations of the mean inter-galaxy separation across the redshift range considered). The normalised PDFs of the distances, in the W1 and W4 fields combined, are shown in Fig. 3 for three selections: low vs high mass galaxies, star-forming vs quiescent galaxies, and starforming galaxies in three mass bins. The errorbars are estimated with a block-wise (1 deg 2 ) jackknife resampling. The first two samples are limited to M * ≥ 10 10.5 M to be complete in stellar mass for both quiescent and star-forming galaxies (see Davidzon et al. 2016) while a mass cut of M * ∼ 10 10 M is used when only star-forming galaxies are considered.

A trend between distance and stellar mass is observed (left column), with more massive galaxies being closer to filaments as indicated by the shift in the median values of the two PDFs (downward arrows). Passive galaxies are also found to be closer to filaments (middle column). While a large fraction (47%) of our massive (M * ≥ 10 10.5 M ) galaxies are also passive, by looking at the star-forming population alone we observe a similar trend, albeit weaker, with the most massive star-forming galaxies being closer to filaments (right column). However, since we wish to evaluate the impact of the filaments on galaxy properties, we have to take into account the contribution of the nodes of the density field, usually related to galaxy groups and clusters, which are at the intersections of filaments and are known to be privileged regions where quenching is more efficient. This task is not easy, as there are partial overlaps between the local density and the CW environment (Aragón-Calvo et al. 2010). As proposed by Gay et al. (2010), to minimize the node contributions we weight each galaxy by the inverse of the density field smoothed using a Gaussian filter with σ = 3 Mpc. The weighted PDFs are shown in the middle row of Fig. 3. A shift in the medians of the PDFs to larger distances is observed but the trends remain. We also adopted alternative approaches by rejecting galaxies in high density regions (δ ≥ 4), located within groups, according to a parallel analysis (Iovino et al., in prep.), or by keeping only the filaments with a higher persistence threshold. They do not qualitatively change the results discussed in this section.

The significance of the observed trends is illustrated by the residuals between the weighted distributions expressed in units of σ (bottom row of Fig. 3). The deviations exceed 2σ in most of the bins except for star-forming samples alone (due to shot noise in the most massive bin). We also quantify the differences with the χ 2 test of independence and the probabilities of observing such a difference by chance which are negligible (listed in middle panels). This confirms the existence of a weak but statistically significant segregation effect inside the filaments and suggests that galaxy processing happens also during the drift of galaxies towards the nodes of the CW.

In Fig. 3 we also look at how the mass-density relation is hidden in the observed mass segregation. We split the sample in local density bins and reshuffle the stellar masses between the galaxies in each bin. The mean PDF distributions for 10 random reshufflings are shown as dashed lines on the middle left panel. The PDFs for the low and high mass bins are close to the original ones, which shows that the mass segregation exists even after reshuffling the masses, if the mass-density relation is preserved. Therefore the mass segregation inside the filaments emerges naturally from the mass-density relation and the anisotropic distribution of the density in the CW.

A similar approach is adopted for the galaxy type segregation. We randomly attribute a galaxy type (passive/starforming) to galaxies by conserving the type fraction observed in different stellar mass bins. The mean PDFs for 10 random reshufflings are shown as dashed lines (middle panel). In this case the segregation almost vanishes, with a difference between the two PDFs of less than 1σ. The observed type segregation therefore does not arise just from the mass-type fraction relation but could have its origin in the dynamic of the large scale anisotropic structures of the CW.

DISCUSSION AND CONCLUSIONS

We reported the first characterization of large scale filamentary structures at z ∼ 0.7, carried out in the cosmological volume probed by the VIPERS spectroscopic survey. The reconstruction is based on the DisPerSE code and the capability of VIPERS to capture such a CW's filamentary network is tested on simulations. We observe a small but significant trend for galaxies with different stellar masses and stellar activity to segregate near the filaments with the most massive and/or passive galaxies being closer to filaments. The signal persists even after down-weighting the contribution of nodes and high density regions.

The galaxy segregation quantified in this paper is a first step in support of a new paradigm in galaxy formation where large scale cosmic flows play a role in shaping galaxy properties. Beyond the observed anisotropy of the mass distribution (which follows naturally from the massdensity relation and the anisotropy of density in the CW), we expect that other physical parameters (e.g. stellar activity controlled in part by gas accretion or morphology and size controlled in part by angular momentum) will be impacted by this large scale environment. Indeed, our results are fully consistent with the ingredients of the spin alignment theory presented in Codis et al. (2015) which relies on these large-scale cosmic flows. The stellar activity segregation observed here can be interpreted inside this theory. Low mass or star-forming galaxies are preferentially located at the outskirts of filaments, a vorticity rich environment (Laigle et al. 2015), where galaxies acquire both their angular momentum (leading to a spin parallel to the filaments) and their stellar mass essentially via smooth accretion (Welker et al. 2015). The stellar-mass segregation observed here is the next step, where at higher mass, a transition is predicted in simulations, when more massive post-mergers drifting along filaments convert the orbital momentum of their progenitors into spin perpendicular to the axis of the filament, with increased efficiency for higher merger rate (Dubois et al. 2014;Welker et al. 2015). The most massive galaxies, dominated by the quiescent population, should preferentially complete their stellar mass assembly in the core of filaments by merging.

We plan to extend the characterization of the CW in VIPERS in a future paper. It will be of interest to extend our analysis to other physical quantities such as star-formation rate or specific star-formation rate, spin orientation and extent to different CW perspective: the distance to nodes within the filaments or, of particular interest, the distance from the saddle of the filaments, expected to be the region in the filament where galaxies have been the less affected by environmental effects. This will become within reach with the upcoming large and deep spectroscopic surveys such as PFS (Prime Focus Spectrograph). With its higher sampling and high-redshift extension (z ∼ 1.5 -2), PFS-deep survey will offer the opportunity to explore such dependencies near the peak of the cosmic star formation activity with an unprecedented accuracy.

Meanwhile, alternative approaches based on large multiband photometric surveys (e.g. COSMOS, J-PAS, Benitez et al. 2014) with accurate photometric redshifts allow us to analyze the projected 2D CW in narrow redshift slices. Preliminary results on the filamentary structures in the COS-MOS field yield consistent results for the mass segregation inside the filaments (Laigle et al., in prep.).

Figure 1 .

 1 Figure1. PDFs of the pseudo-distances (defined in Sect. 3) between the Parent and VIPERS-like skeletons. Blue lines and orange shaded areas refer to S VIP projected onto S Par while red lines and green shaded areas are the reverse. Solid lines correspond to the mean of 10 mocks and the shaded areas enclose the 1σ r.m.s. (please note that uncertainties are negligible). Arrows show the modes of the distributions. Top: The two skeletons are extracted with a 3σ persistence threshold. Bottom: S Par is extracted with a 5.5σ threshold.

Figure 2 .

 2 Figure 2. Projected distribution of the filaments reconstructed with DisPerSE (in dark green) in the VIPERS W1 (top panel) and W4 (bottom panel) fields between 0.4 ≤ z ≤ 1. The density contrast, log(1 + δ DTFE ), is averaged on cells of 5 × 5 Mpc 2 and colour-coded as indicated (white for empty cells). Top rows: projected distribution along the declination direction (∆δ = 2). Bottom rows: projected distribution along the right ascension direction (in the central regions with ∆α = 2). 3D movies are available on the VIPERS website.

Figure 3 .

 3 Figure3. Distributions of the unweighted (top row) and density-weighted (middle row) normalised distances (D skel / D z ), for three selections: low vs high mass galaxies (left column), quiescent vs star-forming galaxies (middle column) and star-forming galaxies in three mass bins (right column). Vertical arrows indicate the medians of the PDFs and errorbars represent the dispersions computed with block-wise jackknife resampling. The PDFs after reshuffling of the samples (see text) are shown with dashed lines. The differences between the weighted distributions are shown in the bottom row. For star-forming galaxies (right panel) only the differences between high-intermediate (green) and high-low (red) mass bins are shown. The values resulting from the χ 2 test of independence are reported in the middle panels.

  Tests on VIPERS mock galaxy catalogues. We test the performance of DisPerSE on an updated version of the VIPERS mock galaxy catalogues described in de la Torre et al. (2013) matching the VIPERS final geometry. The upgrades are described in the parallel paper by de la Torre et al.

To prevent the spurious detection of filaments near the edges of the survey, DisPerSE encloses each field in a larger volume. New particles are added by interpolating the density field measured at the boundary of the survey (see e.g.

Sousbie et al. 2011

).

This intrinsic alignment is also a source of systematics affecting the cosmic shear signal (e.g.Chisari et al.

2015).

MNRAS 000, 1-7 (2016)

Note that by construction the Delaunay tessellation provides a simple way to reconnect LSS features with smoothed variations in density such as filaments across large gaps(Aragon-Calvo et al. 2015). For this reason and based on the results on simulations discussed here, we do not apply any correction for the gaps in the VIPERS survey.MNRAS 000, 1-7 (2016)

This paper has been typeset from a T E X/L A T E X file prepared by the author.MNRAS 000, 1-7 (2016)

ACKNOWLEDGMENTS

This work is based on observations collected at the European Southern Observatory, Cerro Paranal, Chile, us-ing the Very Large Telescope under programmes 182.A-0886 and partly 070.A-9007. Also based on observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/DAPNIA, at the Canada-France-Hawaii Telescope (CFHT), which is operated by the National Research Council (NRC) of Canada, the Institut National des Sciences de l'Univers of the Centre National de la Recherche Scientifique (CNRS) of France, and the University of Hawaii. This work is based in part on data products produced at TER-APIX and the Canadian Astronomy Data Centre as part of the Canada-France-Hawaii Telescope Legacy Survey, a collaborative project of NRC and CNRS. The VIPERS web site is http://www.vipers.inaf.it. This research is carried out within the framework of the Spin(e) collaboration (ANR-13-BS05-0005, http://cosmicorigin.org). NM acknowledges the financial contributions by grants ASI/INAF I/023/12/0 and PRIN MIUR 2010-2011 "The dark Universe and the cosmic evolution of baryons: from current surveys to Euclid".