Mohamed Khairy

Pingping Jiang

Pascal Boulet

Marie-Christine Record
email: m-c.record@univ-amu.fr

Electron Density and Optoelectronic Properties of Copper Antimony Sulphur Ternary Compounds for Photovoltaic Applications

Keywords: Copper-based chalcogenides, DFT, optoelectronic properties, electron density topology, solarenergy conversion

Design of efficient solar energy-conversion materials has attracted much interest in the last decades. Among these materials, copper-based semiconducting chalcogenides have been employed as alternatives for copper indium gallium selenide (CIGS) thin-film solar cells due to their low toxicity and earth-abundant absorber components. In the present manuscript, structural, electronic, topological, and optical properties of ternary chalcogenide CuSbS2, Cu3SbS3, and Cu3SbS4 have been investigated using the full potential linear augmented plane wave (FP-LAPW) method. An indirect bandgap is observed for CuSbS2 with Eg = 1.178 eV and a direct bandgap is found for Cu3SbS3, and Cu3SbS4 with Eg = 1.283 and 1.0 eV, respectively. The valence band maximum (VBM) of CuSbS2, Cu3SbS3, and Cu3SbS4 are mainly predominated by a strong Cu-3d and S-3p orbitals hybridization. The conduction band of CuSbS2 and Cu3SbS3 are mainly characterized by Sb-5p orbital and S-3p orbital mixing. However, conduction band of Cu3SbS4 is dominated by the mixing of Sb-5s and S-3p orbitals. It is found that the Cu-S and Sb-S bonds lie in the transit closed-shell zone, between the typical ionic and covalent bonds. The optical properties of CuSbS2, Cu3SbS3, and Cu3SbS4 in terms of absorption coefficient, extinction coefficient, refractive index, and reflectivity have been investigated. The results show that the CuSbS2, Cu3SbS3, and Cu3SbS4 compounds have real potential to be used for solar-energy conversion.

Introduction

The search for and design of efficient solar energy-conversion materials have attracted much interest in the last decades in order to overcome the global energy shortage and CO2 emission in the inevitable future expansion [START_REF] Sun | Chalcogenide Perovskites for Photovoltaics[END_REF]. In 2019, the producing capacity of solar photovoltaic (PV) reached about 633 GW, with a 24 % growth yearon-year, and might foresee reaching 4.7 terawatts by 2050 as proposed by the International Energy Agency (IEA). More than 90% of world production capacity is held by crystalline silicon modules, which are being very effective. The cheaper thin-film compound semiconductors might be alternatives and strong competitors to silicon PV. Recently, transition metal chalcogenides have enabled a breakthrough in the development of thinfilm photovoltaic solar cells because of their optoelectronic properties in terms of photo-stability and highsurface-area visible-light absorber [START_REF] Yang | CuSbS2 as a Promising Earth-Abundant Photovoltaic Absorber Material: A Combined Theoretical and Experimental Study[END_REF]. For example, the copper indium gallium selenide (CIGS) and cadmium telluride (CdTe) solar cells revealed a spectroscopic limited limited maximum efficiency (SLME) of about 20.8% and 19.6%, respectively. Although these thin-film photovoltaic cells are commercially available, their elemental components are toxic and relatively rare, which limits their terawatt scale productions [START_REF] Ramasamy | Selective Nanocrystal Synthesis and Calculated Electronic Structure of All Four Phases of Copper-Antimony-Sulfide[END_REF]. The copperzinc tin sulfoselenide (CZTSSe) was explored as a promising alternative material because it might fulfill the prerequisites for sufficient solar irradiation but still, the efficiency of PV devices is relatively low, despite more than a decade of painstaking researches [START_REF] Todorov | Beyond 11% Efficiency: Characteristics of State-of-the-Art Cu2ZnSn(S,Se)4 Solar Cells[END_REF]. The copper-based chalcogenide systems including CuSbS2 (Chalcostibite), Cu3SbS4 (Famatinite), Cu12Sb4S13 (Tetrahedrite), and Cu3SbS3 (Skinnerite) phases have been explored as they are interesting alternatives for CIGS thin-film solar cells due to their low-toxicity and earthabundant absorber components [START_REF] Ramasamy | Selective Nanocrystal Synthesis and Calculated Electronic Structure of All Four Phases of Copper-Antimony-Sulfide[END_REF][START_REF] Mohamadkhani | Sb2S3 and Cu3SbS4 nanocrystals as inorganic hole transporting materials in perovskite solar cells[END_REF][START_REF] Lin | Antimony loss and composition-dependent phase evolution of CuSbS2 absorber using oxides nanoparticles ink[END_REF][START_REF] Chlibi | Touch sensor and photovoltaic characteristics of CuSbS2 thin films[END_REF][START_REF] Zaki | Solar cell fabrication from semiconducting Cu3SbS3 on n-Si: Parameters evolution[END_REF][START_REF] Gupta | Simulation studies on photovoltaic response of ultrathin CuSb(S/Se)2 ternary compound semiconductors absorber-based single junction solar cells[END_REF][START_REF] Kumar | Effect of substrate temperature on properties of co-evaporated copper antimony sulfide thin films[END_REF][START_REF] Wan | Spray pyrolysis deposited CuSbS2 absorber layers for thin-film solar cells[END_REF][START_REF] Banu | Phase transition behavior and defect analysis of CuSbS2 thin films for photovoltaic application prepared by hybrid inks[END_REF][START_REF] Han | Fabrication and Characterization of Cu3SbS4 Solar Cell with Cd-free Buffer[END_REF]. The Cu-Sb-S system compounds are p-type semiconductors with optical band gap (Eg) ranging between 0.5 and 2.0 eV and a large absorption coefficient over 10 4 cm -1 at visible wavelengths, which shows a comparable efficiency (i.e., 22.9%) to that of CIGS and CZTSSe [START_REF] Yu | Inverse Design of High Absorption Thin-Film Photovoltaic Materials[END_REF]. Yet, due to a lack of knowledge in the fundamental physical properties comprehension these compounds have not reached the stage of being integrated into devices. Therefore, further developments in PV technology based on these compounds call for a deep understanding of the electronic and optical properties of these materials and of their structure-properties relationships, which is the topic of the present work.

In this work, we have investigated the structural, electronic, and optical properties of ternary chalcogenide CuSbS2, Cu3SbS3, and Cu3SbS4 using density functional theory (DFT) calculations with the full-potential linearized augmented plane-wave (FP-LAPW) method that was suggested to be one of the most efficient methods to solve many-electron problems in the solid crystal. In order to try to understand the relationship between bond interactions and optoelectronic properties, the electron density topology has been investigated as well using Bader's quantum theory of atoms in molecules (QTAIM) [START_REF] Bader | Atoms in Molecules[END_REF]. Cu12Sb4S13 has not been considered in the present work as it shows a semi-metallic behaviour [START_REF] Ramasamy | Selective Nanocrystal Synthesis and Calculated Electronic Structure of All Four Phases of Copper-Antimony-Sulfide[END_REF]. The investigation of the structure-properties relationship in the Cu-Sb-S compounds has never been done to date. Although the optical properties have already been published for CuSbS2 [START_REF] Ramasamy | Selective Nanocrystal Synthesis and Calculated Electronic Structure of All Four Phases of Copper-Antimony-Sulfide[END_REF][START_REF] Kumar | CuSbS2 and CuBiS2 as potential absorber materials for thin-film solar cells[END_REF][START_REF] Maeda | First-principles study of electronic structure of CuSbS2 and CuSbSe2 photovoltaic semiconductors[END_REF], Cu3SbS3 [START_REF] Ramasamy | Selective Nanocrystal Synthesis and Calculated Electronic Structure of All Four Phases of Copper-Antimony-Sulfide[END_REF] and Cu3SbS4 [START_REF] Ramasamy | Selective Nanocrystal Synthesis and Calculated Electronic Structure of All Four Phases of Copper-Antimony-Sulfide[END_REF][START_REF] Li | Structural, electronic and optical properties of famatinite and enargite Cu3SbS4 under pressure: A theoretical investigation[END_REF], we have re-investigated these properties for the three compounds with the same procedure, as our aim is to study the relation between the electronic densities and the optical properties.

Computational details

First principle density functional theory calculations using the FP-LAPW method based on Kohn-Sham equations have been carried out using the WIEN2k package [START_REF] Blaha | WIEN2k, an augmented plane wave + local orbitals program for calculating crystal properties Karlheinz Schwarz[END_REF]. The structural optimizations have been performed using the generalized gradient approximation (GGA) with the Perdew, Burke, and Ernzerhof (PBE) functionals [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] as implemented in the WIEN2k package. As the modified Becke-Johnson (mBJ) potential allows for estimating bandgap energies more accurately it has been used to calculate electron band structures and density of states [START_REF] Koller | Merits and limits of the modified Becke-Johnson exchange potential[END_REF][START_REF] Khan | Optoelectronic and thermoelectric properties of KAuX5 (X = S, Se): a first principles study[END_REF][START_REF] Tran | Accurate Band Gaps of Semiconductors and Insulators with a Semilocal Exchange-Correlation Potential[END_REF]. Unfortunately, since the mBJ functional gave wrong bandgap energy for Cu3SbS4, the hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE06) has been utilized for this compound [START_REF] Heyd | Hybrid functionals based on a screened Coulomb potential[END_REF]. The corevalence electron separation has been defined as follows: Cu [Ar] 3d 10 4s 1 , Sb [Kr] 4d 10 5s 2 5p 3 , and S [Ne] 3s 2 4p 4 . The structure optimization has been performed by calculating the total energy (in Ry) with respect to crystal volume, b/a, and c/a ratio in proper sequence and full structure relaxation has been carried out until the total residual forces on all atoms were less than 2 mRy per Bohr. The optimized volumes and cell parameters have been obtained from fitting curves against the Birch-Murnaghan equation of state:

𝑬(𝑽) = 𝑬 𝒐 + ( 𝟗𝑽 𝒐 𝟏𝟔 )( 𝑩 𝟒𝟕𝟎𝟑.𝟔 )(𝜼 𝟐 -𝟏) 𝟑 𝑩 𝒑 + (𝜼 𝟐 -𝟏) 𝟐 (𝟔 -𝟒𝜼 𝟐 ) , (1)

𝜼 = (

𝑽 𝒐 𝑽 ) 𝟏 𝟑 , (2)
where, V0, and V are the initial and distorted volumes, B is the bulk modulus, and BP is the derivative of bulk modulus with respect to pressure.

The convergence parameter RMTKmax has been set to 7, where Rmt is the radius of the smallest sphere and Kmax is a maximum wave vector. The charge density has been obtained up to Gmax=14 (a.u.) -1 . For the mBJ calculations, the Brillouin zone has been sampled with a mesh of 1000 k-points. For hybrid calculations, a 6×6×6 grid of 30 k-points has been used. A 16×16×16 k-points grid (4096 k-points in the full Brillouin zone) has been used for optical calculations.

The optical properties of the Cu-Sb-S compounds have been calculated based on their response to electromagnetic perturbations as implemented in Wien2k [START_REF] Ambrosch-Draxl | Linear optical properties of solids within the full-potential linearized augmented planewave method[END_REF]. The frequency-dependent complex dielectric function has been determined as ε(ω) = ε1(ω)+ iε2(ω), where ω is the photon frequency. The imaginary (absorptive) part of dielectric function ε2(ω) is calculated using the following momentum matrix elements between the valence and conduction wave functions:

𝜺 𝟐 (𝝎) = 𝒆 𝟐 ℏ 𝝅𝒎 𝟐 𝝎 𝟐 ∑ ∫ |𝑴 𝒄𝒗 𝑩𝒁 𝒗,𝒄 (𝒌)| 𝟐 𝜹{𝝎 𝒄𝒗 (𝒌)𝝎}𝒅 𝟑 𝒌 . (3)
The real (dispersive) part of the dielectric function ε1(ω) and the absorption coefficient α(ω) have been calculated by Kramers-Kronig transformation as:

𝜺 𝟏 (𝝎) = 𝟏 + 𝟐 𝝅 𝑷 ∫ 𝝎 , 𝜺 𝟐 (𝝎 , ) 𝝎 ,𝟐 ;𝝎 𝟐 < 𝟎 𝒅𝝎 , , (4)
𝜶(𝝎) = √𝟐 𝝎 >?𝜺 𝟏 (𝝎) 𝟐 + 𝜺 𝟐 (𝝎) 𝟐 -𝜺 𝟏 (𝝎)@ 𝟏 𝟐 , ( 5
)
where P is the momentum operator. The extinction coefficient k(ω), energy loss L(ω), and refractive index n(ω) have been calculated using real and imaginary parts of dielectric function as:

𝒌(𝝎) = A =𝜺 𝟏 𝟐 (𝝎)>𝜺 𝟐 𝟐 (𝝎) 𝟐 - 𝜺 𝟏 (𝝎) 𝟐 B 𝟏 𝟐 , (6)

𝑳(𝝎) =

𝜺 𝟐 (𝝎)

𝜺 𝟏 (𝝎) 𝟐 &𝜺 𝟐 (𝝎) 𝟐 , ( 7)

𝒏(𝝎) = A 𝜺 𝟏 (𝝎) 𝟐 + =𝜺 𝟏 𝟐 (𝝎)>𝜺 𝟐 𝟐 (𝝎) 𝟐 B 𝟏 𝟐 , (8)
The reflectivity has been calculated by the following equation:

𝑹(𝝎) = (𝒏(𝝎);𝟏) 𝟐 >𝒌(𝝎) 𝟐 (𝒏(𝝎)>𝟏) 𝟐 >𝒌(𝝎) 𝟐 . (9)
The real-space analysis of the quantum chemical interactions has been carried out using Critic2 program [START_REF] Otero-De-La-Roza | Critic2: A program for real-space analysis of quantum chemical interactions in solids[END_REF].

Results and discussion

Crystal structures of the Cu-Sb-S system compounds

The crystal structure of Cu I Sb III S -II (CuSbS2, Chalcostibite) is composed of square pyramidal SbS5 units, which share their edges to form continuous SbS2 units aligned with the b axis. The SbS2 units are regularly separated by CuS4 tetrahedra. Thus, the bases of the square pyramidal units are lined up to face one another and the Sb electron lone pair points towards the void separating the SbS5 units (Fig. 1a). The Cu I Sb III S -II (Cu3SbS3) has a Skinnerite structure and derives from the Wittichenite structure. The Cu atoms are in nearly trigonal planar coordination with S atoms, the Sb atom is trigonally coordinated by S, and S is tetrahedrally coordinated by three Cu atoms and one Sb atom. As can be seen in Figure 1b, there are different crystallographic positions for both

Cu and Sb atoms. The crystal structure of Cu I Sb V S -II (Cu3SbS4, Famatinite) derives from the zinc blende structure, which is characterized by S atoms laying at the nodes of a face-centred cubic lattice and Cu or Sb atoms located in the tetrahedral sites and forming MS5 units. The Cu atoms are classified as Cu1 and Cu2, which occupy Wyckoff 2b and 4d positions, while Sb and S atoms occupy 2a and 8i ones, respectively (Fig. 1c). Thus, two types of Cu-S bond and one type of Sb-S bond can be distinguished.

Band structure of Cu-Sb-S system compounds

To understand the electronic properties of the Cu-Sb-S compounds, the band structures and the density of states (DOS) have been calculated using the PBE and mBJ functionals, as well as the HSE06 functional in the particular case of the Cu3SbS4 compound. At first, the band structures of CuSbS2, Cu3SbS3, and Cu3SbS4 have been calculated with the PBE functional along the high symmetry directions in the Brillouin zone (BZ) (Fig. S1).

As the modified mBJ potential allows for estimating bandgap energies more accurately, the band structures of the Cu-Sb-S compounds have been estimated with this potential, the results of which are illustrated in Fig. 2 and II). Interestingly, the difference between the lowest direct bandgap and fundamental indirect bandgap is about 0.1 eV, thus, a strong optical absorption might occur at such energy [START_REF] Jiang | A DFT study of the electronic, optical and topological properties of free and biaxially strained CuIn1-xAlxSe2[END_REF]. The band structure of Cu3SbS3 shows that the valence band bears two maxima located at the Γ-point and X-point and that the conduction band bears two minima located at the Γ-point and X-point, too. A direct bandgap is observed with a value of 1.283 eV, which is 0.12 eV to 0.59 eV lower than the experimental values (Table II). Furthermore, a flat conduction band bottom is observed. Thus, a strong optical absorption is expected in the Cu3SbS3 compound.

The band structure of Cu3SbS4 exhibits VBM and CBM at Γ-point leading to a direct bandgap with a value of 1.0 eV as estimated by the HSE06 functional, which agrees well with both the direct and indirect energy bandgap values determined by experiments. The energetic distributions of the electronic states for CuSbS2 and Cu3SbS3 compounds have been investigated by calculating the density of states with the mBJ potential functional, and for the Cu3SbS4 compound by the hybrid HSE06 functional. Fig. 3 shows the atom-projected and orbital-projected density of states (aDOS and oDOS) for Cu-Sb-S compounds in the energy range from -7 to 7 eV. The aDOS contains different energy regions and is contributed by each atom of the crystal system (Fig. have weak interaction with S-3p and become chemically inert as lone-pair electrons. As it was observed in PbS [START_REF] Walsh | The origin of the stereochemically active Pb(II) lone pair: DFT calculations on PbO and PbS[END_REF], the crystal systems in which CuSbS2, and Cu3SbS3 crystallize, namely orthorhombic and monoclinic, are dictated by this electron lone pair, which necessitates a distortion of the crystal lattice to be energetically stable.

W L L G D X Z W K E F
Despite having an inert effect on chemical bonds, this electron lone pair has a stereochemical effect on the crystal structure and is only involved in van der Waals interactions. By contrast, in the case of Cu3SbS4, (Cu I Sb V S -II ) there is no pure Sb-5s orbital accommodating electrons, and the atoms are connected via covalent bonds to form Chalcopyrite tetrahedral structure. Therefore, the Cu-Sb-S compounds offer various bonding properties that deserve investigation through the topological analysis of the electron density.

Electron density topological properties of the Cu-Sb-S system compounds

Since the knowledge on structure-property relationship is still limited, investigating quantum-mechanical atomic and molecular interactions in solid crystals is relevant in view of material design for the targeted application. In this context, the investigation of electron density in real space within solids has been studied by the quantum theory of atoms in molecules (QTAIM) using Critic2 program. The calculated electron density Laplacians in the (-110) plane of CuSbS2, Cu3SbS3, and Cu3SbS4 are depicted in Fig. 4a, Fig. 4b, and Fig. 4c, respectively. The symbols b, r, and c represent bond, ring, and cage critical points, respectively, as described in the QTAIM theory. Bond length, bond angle, electron density (ρBCP), electron density Laplacian (𝛁 𝟐 ρBCP), ellipticity, and local electron kinetic (VBCP), potential (GBCP), and total energy (HBCP) densities at bond critical points (BCP) extracted from Critic2 program outputs are gathered in Table S1. The relation between electron density Laplacian, kinetic energy GBCP, and potential energy VBCP densities at BCP is given by:

ℏ 𝟐 𝟒𝒎 𝛁 𝟐 𝝆 𝑩𝑪𝑷 = 𝟐𝑮 𝑩𝑪𝑷 + 𝑽 𝑩𝑪𝑷 , (10)
and the variation of bond degree (BD = HBCP/ρBCP) versus |VBCP|/GBCP ratio can be used to distinguish bonding types [START_REF] Yang | A rapid method for analyzing the chemical bond from energy densities calculations at the bond critical point[END_REF]. Figure 4d shows these characteristics for CuSbS2, Cu3SbS3, and Cu3SbS4. A linear evolution is observed with a correlation coefficient R 2 of 0.904, 0.993, and 0.867, respectively. Three and seventeen different Cu-S bonds can be evidenced in CuSbS2 and Cu3SbS3, respectively (see Table S1). The longest Cu-S bond in Laplacian (Figure 4a-c) for Cu-S bonds differs from one structure to another, the kinetic energies per electron at the bond critical point (GBCP/ρBCP), which are related to the polarizability of the charge distribution [START_REF] Yang | A rapid method for analyzing the chemical bond from energy densities calculations at the bond critical point[END_REF], are almost the same (comprised between 0.82 and 0.87, see Table S1). The best concordance is observed between CuSbS2 and Cu3SbS3 (Fig. 4d). Moreover, the local energy densities for CuSbS2 and Cu3SbS3 are all very close to one another on the graph. All these results suggest that the Cu-S bonds in CuSbS2, Cu3SbS3, and Cu3SbS4

have close bonding characteristics, though not strictly the same due to the difference in atoms environment. In agreement with Ref. [START_REF] Yang | A rapid method for analyzing the chemical bond from energy densities calculations at the bond critical point[END_REF], for similar GBCP/ρBCP the interatomic distances increase with the absolute value of the bond degree. This is exemplified for the Cu-S bonds in Fig. 4e, though this holds for the Sb-S bonds, too. or Sb-5s/S-3p, respectively. The Sb-S with a large bond degree revealed a high absorption coefficient (> 10 4

cm -1 ) of Cu-Sb-S materials near the Fermi level. These results should lead to a lower bandgap of CuSbS2 compared to that of Cu3SbS4. However, the presence of empty Sb-5s orbital in the conduction band causes a Sb-5s/S-3p hybridization in the case of Cu3SbS4, which confers it a lower bandgap than expected, leading to a reversed bandgap order between CuSbS2 and Cu3SbS4 as shown in Fig. 2 and Fig. 3.

Optical properties of Cu-Sb-S system compounds

Further, the valence band maximum (VBM) of Cu-Sb-S structures is mainly due to the mixing of Cu-3d and S-3p, which can stabilize the holes and provides high mobility Cu/S framework paths. The optical properties of CuSbS2 and Cu3SbS3 have been calculated using the mBJ potential functional, while those of Cu3SbS4 have been calculated using the HSE06 functional one. The refractive index, extinction coefficient, absorption coefficient, and reflectivity have been determined by utilizing the calculated dielectric function as described in the computational section. For Cu3SbS4 with a tetragonal structure, the optical functions are analysed along with two directions, namely xx and zz, while for CuSbS2 and Cu3SbS3 with orthorhombic and monoclinic structures the optical properties are analysed according to the three diagonal components xx, yy, and zz. The dielectric function ε(ω) characterizes the collective excitations close to the Fermi-level and depends strongly on the band structure [START_REF] Amin | Opto-electronic response of spinels MgAl2O4 and MgGa2O4 through modified Becke-Johnson exchange potential[END_REF]. The calculated dielectric functions for CuSbS2, Cu3SbS3, and Cu3SbS4 are depicted in Fig. 5, the real parts ε1(ω) of which being shown in Fig. 5a, 5c and 5e and the imaginary parts ε2(ω) of which being shown in Fig. 5b, 5d and 5f. The maximum peak values of ε1(ω) for CuSbS2 (Fig. 5a), Cu3SbS3 (Fig. 5c), and Cu3SbS4 (Fig. 5e) are fair agreement with those reported in literature (Ref [START_REF] Gassoumi | The investigation of crystal structure, elastic and optoelectronic properties of CuSbS2 and CuBiS2 compounds for photovoltaic applications[END_REF] for CuSbS2 and Ref [START_REF] Li | Structural, electronic and optical properties of famatinite and enargite Cu3SbS4 under pressure: A theoretical investigation[END_REF] for Cu3SbS4). ε1(ω) becomes negative above a certain photon energy: about 6 eV for the CuSbS2 and Cu3SbS3 compounds, and about 8 eV for Cu3SbS4. This indicates that the Cu-Sb-S materials have a metallic character above these photon energy thresholds [START_REF] Gassoumi | The investigation of crystal structure, elastic and optoelectronic properties of CuSbS2 and CuBiS2 compounds for photovoltaic applications[END_REF]. At zero frequency limit (ω = 0), ε1(ω) gives the static dielectric permittivity. Higher static dielectric permittivity values have been obtained for Cu3SbS4 indicating higher polarizability for this compound. This result agrees with the GBCP/rBCP values (Table S1) since lower GBCP/rBCP corresponds to higher polarizability [START_REF] Yang | A rapid method for analyzing the chemical bond from energy densities calculations at the bond critical point[END_REF]. According to the Penn model [START_REF] Penn | Wave-Number-Dependent Dielectric Function of Semiconductors[END_REF] ε1(0) is defined as ε1(0) ≈ 1+ (ℏω/Eg) 5f). Along the series CuSbS2, Cu3SbS3, Cu3SbS4 the decreasing tendency of ε2(ω) values and the shift of the peak maximum towards higher incident energies indicate a decrease of the ability of the Cu-Sb-S compounds to absorb light. Thus, CuSbS2 compound has the highest ability to absorb the incident light although it has indirect bandgap [START_REF] Jiang | A DFT study of the electronic, optical and topological properties of free and biaxially strained CuIn1-xAlxSe2[END_REF]. Compared with theoretical data reported in the literature [START_REF] Gassoumi | The investigation of crystal structure, elastic and optoelectronic properties of CuSbS2 and CuBiS2 compounds for photovoltaic applications[END_REF][START_REF] Li | Structural, electronic and optical properties of famatinite and enargite Cu3SbS4 under pressure: A theoretical investigation[END_REF] for CuSbS2 and Cu3SbS4, the following comments can be made. For CuSbS2 the maximum values of ε2(ω) are in fair agreement with ours, the peak being slightly shifted towards lower photon energies in our case. The agreement is worse for Cu3SbS4 as the peak reported by Li et al. [START_REF] Li | Structural, electronic and optical properties of famatinite and enargite Cu3SbS4 under pressure: A theoretical investigation[END_REF] is significantly shifted toward lower photon energies. This might be explained by their band gap for Cu3SbS4 that they found much smaller than ourselves. The difference in the energy gaps can also explain the differences observed in the absorption results between our results and those of Ramasamy et al. [START_REF] Ramasamy | Selective Nanocrystal Synthesis and Calculated Electronic Structure of All Four Phases of Copper-Antimony-Sulfide[END_REF] for Cu3SbS4.

As they mentioned in their article, the calculated gap is highly overestimated. By contrast for Cu3SbS3, both the energy gap and the absorption spectrum calculated in [START_REF] Ramasamy | Selective Nanocrystal Synthesis and Calculated Electronic Structure of All Four Phases of Copper-Antimony-Sulfide[END_REF] are close to ours. Fig. 7 shows the variation of the extinction coefficient k(ω) with photon energy for CuSbS2, Cu3SbS3, and Cu3SbS4. The maximum values of the extinction coefficient along the xx, yy and zz directions are: 2.022, 2.169, and 2.245 at 5.834, 5.528, and 3.315 eV for CuSbS2; 1.948, 2.175, and 2.107 at 6.508, 6.680, and 3.433 eV for Cu3SbS3; and 1.75, 1.75, and 1.98 at 8.02, 8.02 and 8.12 eV for Cu3SbS4. These results indicate high efficiency of the Cu-Sb-S system compounds for photovoltaic applications due to absorption of the most intense part of the sun radiation. The calculated energy loss L(ω) for CuSbS2, Cu3SbS3, and Cu3SbS4 are shown in Fig. 8a, 8b, and 8c, respectively. The highest peak values along the xx, yy and zz directions are: 0.201, 0.313, and 0.332 at 12.769, 11.656, and 8.471 eV for CuSbS2; 0.334, 0.329, and 0.348 at 12.825, 12.568, and 12.710 eV for Cu3SbS3; 0.375, 0.375, and 0.403 at 12.825, 12.825, and 12.865 eV for Cu3SbS4. These maximum peaks are associated to bulk plasmon, which gives information about strain in solid materials [START_REF] Palisaitis | Effect of strain on low-loss electron energy loss spectra of group-III nitrides[END_REF]. Thus, Cu3SbS3 and Cu3SbS4 compounds offer better relative stability for photovoltaic applications compared to CuSbS2.

Conclusions

The electronic, QTAIM topological, and optical characteristics of CuSbS2, Cu3SbS3, and Cu3SbS4 compounds have been theoretically explored by utilizing WIEN2k package to provide fundamental insights and understand their relevance applicability for photovoltaics. The CuSbS2, Cu3SbS3, and Cu3SbS4 exhibit bandgap energy of Eg = 1.178, 1.283, and 1.0 eV, respectively, which are mainly attributed to a strong Cu-3d and S-3p orbitals hybridization in VBM and Sb-5p/Sb-5s orbitals and S-3p orbital mixing in CBM. The three Cu-Sb-S compounds exhibit high absorption coefficient (> 10 4 cm -1 ) with relative stability in visible light region. The electron density topological studies revealed that the Cu-S bonds in CuSbS2, Cu3SbS3, and Cu3SbS4 have close bonding characteristics, though not strictly the same due to the difference in atoms environment. In addition, nonlocalized interactions prevail in Sb-Sb and Cu-Cu bonds in CuSbS2 and Cu3SbS3, respectively. This study brings new results on electronic and optical properties of CuSbS2, Cu3SbS3, and Cu3SbS4 as well as original ones on their bonding characteristics. In the electronic and optical properties investigations already published, though the authors used HSE06 functional, the band gap was either under-or overestimated in comparison with experimental data, which could impact negatively the optical properties. Our work evidences that the HSE06 functional yields good electronic gaps and properties, provided that well converged technical parameters (planewave cutoff energy and k-point grid) are employed. The setting of these parameters is a limiting feature for DFT investigations. In future work this study will be extended by combining macroscopic properties with microscopic ones into a quantitative structure-property relationship model that will allow for the design of efficient materials.

Fig. 1 .

 1 Fig. 1. Optimized crystal of Cu-Sb-S structures. (a) CuSbS2, (b) Cu3SbS3 and (c) Cu3SbS4.

Fig. S2 .

 S2 Fig. S2. However, the mBJ functional fails to estimate properly the band structure of Cu3SbS4 compound (wrong bandgap). Thus, the HSE06 functional has been used (Fig. 2c). The dashed horizontal line represents the position of the Fermi energy level (EF). The values of the band gaps Eg have been estimated from the energy difference between the conduction band minimum (CBM) and the valence band maximum (VBM) and the data are gathered in TableII. It is found that the value of band gaps calculated using PBE is underestimated in

Fig. 2 .

 2 Fig. 2. Band structures of CuSbS2 (a) and Cu3SbS3 (b) crystals calculated with the mBJ functional, and Cu3SbS4 (c) calculated with the hybrid HSE06 functional.

  3 a, c, and e), while the oDOS represents the contribution of different orbital states of the interconnected atoms (Fig.3 b, d, and f). The fully occupied d orbitals of Sb are not considered in our study. For CuSbS2, the region [-6.0; -1.7] eV is mainly contributed by Cu and S atoms and slightly by Sb ones. These contributions correspond to Cu-3d and S-3p, and to a lesser extent by Sb-5p/5s, particularly in the region [-2.9; -1.97] eV. The regions [-1.7; 0.0] eV and[1.0; 3.8] eV are mainly contributed by Cu and S with a predominance of Cu-3d orbitals and S-3p orbitals hybridization, and by Sb and S atoms corresponding to mixing of Sb-5p and S-3p orbitals, respectively. The region[4.35; 7.0] eV mainly contains the Cu, Sb, and S atoms contributions, which correspond to Cu-4s, S-3p, and Sb-5p orbitals interactions. For Cu3SbS3, four regions can be observed, namely [-6.16; -2.52] eV contributed by Cu, Sb and S atoms (Cu-3d, S-3p and small contribution of Sb-5p/5s), [-2.52; 0.0] eV mainly contributed by Cu atom and very small contribution of S atom (Cu-3d and S-3p),[1.18; 4.0] eV mainly contributed by Sb and S atoms (Sb-5p and S-3p orbitals) and [4.0; 7.0] eV contributed by Cu, Sb and S atoms (Cu-4s, S-3p and Sb-5p orbitals). The DOS of Cu3SbS4 compound can be divided into five regions separated by energy gaps. These regions are [-7.32; -4.34] eV, which is contributed by Cu, S and to a lesser extent by Sb (Cu-3d, S-3p, and Sb-5p orbital at higher energy (> -5. 98 eV)), [-3.47; -0.56] eV, which is mainly contributed by Cu and to a lesser extent by S (Cu-3d and S-3p orbitals interactions), [0.7; 1.65] eV, which is composed of Cu, Sb and S atoms (Sb-5s and S-3p and small contribution of Cu-3d orbitals), [2.2; 4.03] eV, which is mainly assigned to Sb and a small contribution of S atoms (Sb-5p and S-3p orbitals) and [4.2; 7.0] eV, which is attributed to Cu, Sb and S atoms (Cu-4s, Sb-5p, and S-3p orbitals interactions). It is found that the DOS peaks located at the vicinity of the valence band maximum of CuSbS2, Cu3SbS3, and Cu3SbS4 are predominated by a strong Cu-3d and S-3p orbitals hybridization. The conduction band of both CuSbS2 and Cu3SbS3 is mainly contributed by mixing of Sb-5p and S-3p orbital, while the conduction band of Cu3SbS4 is dominated by mixing of Sb-5s and S-3p orbitals. As the oxidation state of copper is +I in all the Cu-Sb-S compounds (Cu + , 3d 10 ), the 3d 10 orbitals in the valence band are fully occupied, therefore, a very small contribution of Cu-3d orbital states occurs in the conduction band. The contribution of Sb-5s orbital is very small in the VBM region of CuSbS2 and Cu3SbS3, thus the Sb 5s electrons

Fig. 3 .

 3 Fig. 3. Atom-projected density of states (aDOS) and orbital-projected density of states (oDOS) for CuSbS2 (a, and b) and Cu3SbS3 (c, and d) calculated with the mBJ functional, and Cu3SbS4 (e, and f) calculated with the HSE06 functional.

  Sb-S structure is distinguished with an asterisk sign (*) in Figure4d. Although the electron density

  Espinosa et al. classified the bonds into three categories based on the |VBCP|/GBCP ratio and bond degree (BD) HBCP/ρBCP[START_REF] Espinosa | From weak to strong interactions: A comprehensive analysis of the topological and energetic properties of the electron density distribution involving X-H….F-Y systems[END_REF]: Pure closed-shell (CS) including ionic bond, hydrogen bond, and van der Waals interactions (|VBCP|/GBCP <1), pure shared-shell (SS) including covalent and polar bonds (|VBCP|/GBCP > 2), and bonds belonging to the transit region with positive Laplacian and negative total energy density (1< |VBCP|/GBCP < 2). It has been found that the Cu-S and Sb-S bonds for Cu-Sb-S structures lie in the transit zone, between the typical ionic and covalent bonds. The Sb-Sb and Cu-Cu bonds for CuSbS2 and Cu3SbS3, respectively, lie close to the point (|VBCP|/GBCP=1, HBCP/ρBCP=0), which correspond to non-localized interactions. The accumulation of electron density at BCP is generally increased along bond path as the bond length decreases. This means large overlapping of electron clouds and increased refractive index of the materials. The optical properties of the semiconductor materials under incident photons depend on the electron transition from valence band maximum to empty conduction band minimum, attributed in the compounds of interest to mixing of Cu-3d/S-3p and Sb-5p

Fig. 4 .

 4 Fig. 4. Electron density Laplacian of CuSbS2 (a), Cu3SbS3 (b) and Cu3SbS4 (c). (d) Bond degree vs. |VBCP|/GBCP. (*) represents the longest bond length for each pairwise. (e) Relation between bond length and bond degree at BCPs for Cu-Sb-S system compounds.

  36 -0.34 -0.32 -0.30 -0.28 -0

Fig. 5 .Fig. 6 .

 56 Fig. 5. Real and imaginary dielectric functions of Cu-Sb-S materials: (a, and b) CuSbS2; (c, and d) Cu3SbS3; (e, and f) Cu3SbS4.

Fig. 7 .

 7 Fig. 7. Extinction coefficient of Cu-Sb-S materials: (a) CuSbS2, (b) Cu3SbS3 and (c) Cu3SbS4.

Fig. 8 .

 8 Fig. 8. Energy loss of Cu-Sb-S materials: (a) CuSbS2, (b) Cu3SbS3 and (c) Cu3SbS4.

Fig. 9 .

 9 Fig. 9. Reflectivity of Cu-Sb-S materials: (a) CuSbS2, (b) Cu3SbS3 and (c) Cu3SbS4.

Fig. 10 .

 10 Fig. 10. Refractive index of Cu-Sb-S materials: (a) CuSbS2, (b) Cu3SbS3 and (c) Cu3SbS4.

Fig. 9

 9 Fig.9shows the reflectivity R(ω) of CuSbS2, Cu3SbS3, and Cu3SbS4 with respect to photon energy. Due to the presence of collective plasma resonance[START_REF] Murtazaa | Structural, electronic, optical and thermodynamic properties of cubic REGa3 (RE = Sc or Lu) compounds: Ab initio study[END_REF], a sudden reduction is observed at 4.13 and 8.54 eV for CuSbS2, 4.6 eV for Cu3SbS3 and 2.679, 6.869, and 9.271 eV for Cu3SbS4. The refractive index values n(ω) of CuSbS2, Cu3SbS3 and Cu3SbS4 are depicted in Fig. 10a, 10b, and 10c, respectively. At zero frequency limit (ω = 0), the static refractive indices n(0) are nxx = 3.326, nyy = 3.403 , and nzz = 3.479 for CuSbS2, nxx = 3.108, nyy = 3.452, and nzz = 3.357 for Cu3SbS3, nxx = nyy = 2.258, and nzz = 2.449 for Cu3SbS4. The maximum values of n(ω) along the xx, yy and zz components are: 4.189, 4.269, and 4.381 at 1.766, 1.861, and 1.748 eV for CuSbS2; 3.684, 4.144, and 4.120 at 1.923, 1.998, and 1.899 eV for Cu3SbS3; 1.762, 1.762 and 2.116 at 2.645, 2.645, and 2.714 eV for Cu3SbS4. According to these values, since the speed of light passing through the materials depends on their refractive index, the speed of light should decrease along the sequence Cu3SbS3, Cu3SbS4 and CuSbS2.

  TableIgathers the lattice constants calculated in this work with the PBE functional for CuSbS2, Cu3SbS3, and Cu3SbS4 together with the experimental ones reported in the literature. There is a slight overestimation of the lattice parameters (< 2 %) for CuSbS2 and Cu3SbS3 compounds, which is quite reasonable for structural results. Further, the Cu3SbS4 structure has been optimized with the HSE06 hybrid functional, which leads to better agreement with experimental cell parameters than the PBE functional.

Table I .

 I Calculated lattice constants compared with experimental literature data.

	Compound	Crystal	Space		Lattice constants			Method	Ref.
		structure	group
				a (pm)	b (pm)	c (pm) α (°) β (°)	γ
									(°)
	CuSbS2	Orthorhombic	Pnma	611.8	385.3	1457.3	90	90	90	PBE	This
	chalcostibite		(62)								work
		Orthorhombic	Pnma	602.4	378.6	1470.1	90	90	90	Exp.	[2]
			(62)
		Orthorhombic	Pnma	601.6	379.7	1449.9	90	90	90	Exp.	[28]
			(62)
		Orthorhombic	Pnma	602.0	379.0	1449.0	90	90	90	Exp.	[29]
			(62)
	Cu3SbS3	monoclinic	P121/c	804.5	1034.1	1340.1	90	90.4	90	PBE	This
	skinnerite		(14)								work
		monoclinic	P121/c	780.8	1023.3	1326.8	90	90.4	90	Exp.	[29]
			(14)
		monoclinic	P121/c	784.6	1024.7	1325.3	90	90.4	90	Exp.	[30]
			(14)
	Cu3SbS4	Tetragonal	I-42m	549.2	549.2	1085.7	90	90	90	PBE	This
	famatinite		(121)								work
			I-42m	544.7	544.7	1081.7	90	90	90	HSE06	This
			(121)								work
		Tetragonal	I-42m	539.1	539.1	1087.0	90	90	90	Exp.	[31]
			(121)
		Tetragonal	I-42m	539.0	539.0	1075.0	90	90	90	Exp.	[32]
			(121)

Table II .

 II Calculated band gaps of the Cu-Sb-S compounds compared with the literature data.

	Chemical compound Transition type Eg (eV)	Method	Ref
	CuSbS2 (Chalcostibite)	Direct	1.4	Exp. (Transmission)	[2]
		Indirect	1.1	Exp. (Absorbance)	[3]
		Indirect	1.6	Calc. (DFT, HSE06)	[3]
		Indirect	1.69	Calc. (DFT, HSE06)	[28]
		Indirect	0.9	Calc. (DFT, PBE)	[28]
		Direct	1.2	Exp. (Reflectance)	[29]
		Indirect	1.0	Exp. (Reflectance)	[29]
		N/A	1.53	Exp. (Absorbance)	[34]
		Direct	1.58	Exp. (Absorbance)	[35]
		Indirect	1.28	Calc. (DFT, mBJ)	[16]
		Indirect	1.72	Calc. (DFT, HSE06)	[17]
		Indirect	0.79	Calc. (DFT, PBE)	[17]
		Indirect	1.16	Calc. (DFT, HSE06)	[18]
		Indirect	0.77	Calc. (DFT, PBE)	[18]
		Indirect	0.885	Calc. (DFT, PBE)	This work
		Indirect	1.178	Calc. (DFT, mBJ)	This work
	Cu3SbS3 (Skinnerite)	Direct	1.4	Exp. (Absorbance)	[3]
		Direct	1.5	Calc. (DFT, HSE06)	[3]
		Direct	1.85	Exp. (Reflectance)	[29]
		Indirect	1.52	Exp. (Reflectance)	[29]
		Direct	1.46	Exp. (Reflectance)	[30]
		N/A	0.93	Exp. (Absorbance)	[34]
		Direct	1.6	Exp. (Reflectance)	[36]
		Direct	1.87	Exp. (Absorbance)	[37]
		Indirect	1.072	Calc. (DFT, PBE)	This work
		Direct	1.283	Calc. (DFT, mBJ)	This work
	Cu3SbS4 (Famatinite)	Indirect	1.2	Exp. (Absorbance)	[3]
		Indirect	2.5	Calc. (DFT, HSE06)	[3]
			0.85	Calc. (DFT, HSE06)	[32]
			0.58	Calc. (quasi-particle self-consistent GW)	[17]
		Direct	0.9	Exp. (Absorbance)	[38]
		N/A	1.72	Exp (Absorbance)	[34]
		Direct	0.82	Exp. (Reflectance)	[39]
			0.47	Exp. (Absorbance)	[40]
		Indirect	1.0	Exp. (Absorbance)	[41]
		Direct	0.89	Exp. (Ultraviolet photoelectron spectroscopy)	[42]
		Direct	0.39	Calc. (DFT, HSE06)	[19]
			0.0	Calc. (DFT, PBE)	This work
			0.0	Calc. (DFT, mBJ)	This work
		Direct	1.0	Calc. (DFT, HSE06)	This work

  2 , where ℏω is the plasma energy. Hence, the band gap of the Cu-Sb-S materials should increase when going from Cu3SbS4 to CuSbS2 and to Cu3SbS3. This is supported by our band gap calculations (see section 3.2). The maximum peak values of ε2(ω) for the xx, yy and zz components are: 12.05, 13.117, and 14.061 at 2.19, 2.325, and 2.326 eV for

	CuSbS2 (Figure 5b); 9.79, 13.483, and 13.257 at 2.918, 3.012, and 3.012 eV for Cu3SbS3 (Figure 5d); 6.815,
	6.815 and 7.974 at 7.855, 7.855, and 7.797 eV for Cu3SbS4 (Fig.

Acknowledgments

The authors acknowledge the Egyptian-French cooperation program provided by the French Institute and the Science and Technology Fund (STDF-IFE) in Egypt, Grant No. 31127 for the financial support. This work was granted access to the HPC resources of the Centre Informatique National de l'Enseignement Supérieur (CINES), Montpellier, France under allocation A0090806881 made by the Grand Equipement National de Calcul Intensif (GENCI). It was also granted access to the HPC resources of Aix-Marseille University financed by the project Equip@Meso (ANR-10-EQPX-29-01) of the program "Investissements d'Avenir" supervised by the Agence Nationale de la Recherche.

Supplementary data

 S1: Electron density topological properties of Cu-Sb-S materials.

Conflict of interest:

The authors declare that they have no conflict of interest.


Jean-Lynce Gnanago

Tony Gerges

Laura Chastagnier

Emma Petiot

Vincent Semet

Philippe Lombard

Christophe Marquette

Michel Cabrera

Simon Lambert

Compact MRI bioreactor for real-time monitoring 3D printed tissue-engineered constructs.

Introduction

Tissue engineering and regenerative medecine have been developing for a few decades now and the number of applications is growing [START_REF] Shafiee | Tissue Engineering: Toward a New Era of Medicine[END_REF] . From cartilage to skin, a wide range of tissues are currently being studied and constructed. However, along with the increasing number of applications, comes an increasing number of different parameters of interest for tissue characterization depending on its application. With multiscale and multiparametric acquisitions, MRI is best suited for characterizing various types of key properties in tissue development. Recent advances 2 highlighted the interest of real-time monitoring of tissues during their growth. As a non-invasive and non-ionizing modality, MRI also qualifies as a potential candidate for this task. In this context, the development of dedicated MRI apparatus specifically designed for this field becomes mandatory. Here we study the feasibility of integrating an MRI sensor directly into the bioreactor to monitor in real time cell fate and tissue growth in 3D printed tissue-engineered constructs.

Method

Different MRI setups have been designed for small tissue samples over the years 3 , 4 . The present case is different as the tissue is living and growing while being probed, to our knowledge, only one group 5 tackled this issue. This implies the combined integration of a coil and a non-magnetic bioreactor within the bore of the scanner. Merging these two functions can be done by addition with a conventional FR4-based circular coil placed on top of an operating bioreactor. This method is simple to setup, on the downside, the loss in coil sensitivity due to the bioreactor being placed between the sample and the coil can be detrimental. In addition, this loss would be bioreactordependent, leading to poor setup transferability between applications. On the other side, another solution exists with the integration of the coil within the bioreactor itself. This integration has been made possible by the previous advances in plastronics techniques [START_REF] Gerges | 3D Plastronics for Smartly Integrated Magnetic Resonance Imaging Coils[END_REF] . Once the design of the bioreactor was conceived in SOLIDWORKS, simulations were conducted using CST MICROWAVE STUDIO. The purpose was to evaluate the influence of the dielectric environment of the coil on its sensitivity and field homogeneity compared to a conventional FR4 coil that would be considered as a reference (figure 2).

A 12mm reception circular coil was designed and integrated within a perfusion bioreactor based on a previous design [START_REF] Pourchet | LARGE 3D BIOPRINTED TISSUE_ HETEROGENEOUS[END_REF] . This type of bioreactor is commonly used in tissue engineering [START_REF] Gaspar | The role of perfusion bioreactors in bone tissue engineering[END_REF] and fits the scope of this work as it contains no active parts. The cell culture medium is flowing through to the sample via 2 inlets connected to external fluidic circulation pumps. The bioreactor was 3D printed using high temperature resin. The copper coil was then deposited on the surface of the bioreactor following the method described in [START_REF] Gerges | 3D Plastronics for Smartly Integrated Magnetic Resonance Imaging Coils[END_REF] . X-ray fluorescence measurements showed a copper thickness of 45µm and a 4-points method placed the resistivity around 1.75×10 -8 Ω.m. As illustrated in figure 1, the coil and its passive decoupling circuit were conceived in 3D using via through the wall of the bioreactor. The 300 MHz tuning/matching of the coil was done remotely with a tuning box with two trimmer capacitors, one in parallel (tuning) and one in series (matching). Finally, a mechanical support was built to allow the bioreactor to fit inside a 36mm radius birdcage transmission coil.

Bench characterization of the coil included unloaded/loaded quality factor measurements. For comparison purposes, bench characterization has also been conducted on a coil made with copper tapped on an FR4 plate. Additional characterization of the bioreactor coil has been conducted in imaging conditions with a 7T Bruker MRI scanner. SNR measurements were performed on an echographic gel using 3D Flash sequence with following parameters: matrix 128×128×64, a FOV 19.2×19.2×9.6 mm 3 i.e.150µm 3 isotropic resolution, TR 33.81ms, TE 15ms, 16 averages for a total acquisition time of 74min. As proof of concept for our bioreactor, a 2D turborare MRI acquisition was performed on a tissue engineering construct with following parameters: matrix 256×256×64, a FOV 19.2×19.2mm 2 i.e. 75µm 2 in-plane resolution, 12 slices of 500 µm thickness, TR 3000ms, TE 15ms, Rare factor 8, 4averages for a total acquisition time of 4min 48s

Results

For long TE sequences, an important image artifact appeared. Numerical simulations showed that this is due to the 3D structure of the bioreactor coil leading to a parasitic loop causing field extinction near its location (figure 4). This parasitic loop could explain that the SNR was 1.36 times lower than the SNR obtained with a larger commercial single loop coil available at the imaging facility (16 mm diameter). An in-plane 75 µm² resolution on the bioprinted sample was achieved with the bioreactor.

Conclusion

The 3D integration of the MRI coil to the bioreactor needs to be improved to open the way for the first real-time monitoring of a constructing tissue. A validation step for this integration would require a B1 mapping using recent methods [START_REF] Sacolick | B1 mapping by Bloch-Siegert shift[END_REF] . The integration of a piezoelectric vibrating membrane is also studied for elastography purposes. In conclusion, this work demonstrates the feasibility of an integrated coil inside a bioreactor and paves the way for a democratization of the MRI tool for biologists using tissue-tailored fully integrated MRI-bioreactors.

Figures

  Figures

Figure 1 :

 1 Figure 1: Design and conception of the bioreactor (A) 3D model of the bioreactor and its support (B) Detailed view of the bottom of the 3D coil circuit and its integration. (C) Detailed view of the top of 3D coil circuit and its integration.

Figure 2 :

 2 Figure 2 : Results of CST Microwave simulations of 1W-normalized B1-field. (A) In plane XZ view of the bioreactor. (B) In plane YZ view of the bioreactor. (C) In plane XZ view of the FR4 coil. (D) In plane YZ view of the FR4 coil.

Figure 3 :

 3 Figure 3 : (A) Picture of the bioprinted tissue after construction. (B) 2D Turborare image of the tissue using the bioreactor acquired on a 7T MRI scanner with a 75 µm in plane resolution.

Figure 4 :

 4 Figure 4 : (A) Image acquired on the 7T MRI scanner with a 3D flash sequence. (B) Image artifact underlining. (C) Superposition of the location of the image artifact on top of the bioreactor. (D) Location of the parasitic coil responsible for the heterogeneous field (E) B1-field simulated on the XZ plane at the center of the sample.

Acknowledgements

This work was supported by a grant from the Agence Nationale de la Recherche (ESTIMATE Project N°ANR-18-CE19-0009-01). The financial support provided by Ingénierie@Lyon, member of the Carnot Institute Network (Metafab 3D project) for the postdoctoral scholarship of Dr T. Gerges is also acknowledged. Moreover, the role of CERMEP -Imagerie du vivant and Radu Bolbos is acknowledged.