| Rahmani

| Chadli

| Patrick Hermet

| Mejía-López

Mourad Boutahir
email: mourad.boutahir@fis.puc.cl

Charge Transfer Evidence in Donor-Acceptor Single-Walled Carbon Nanotubes filled with Sexithiophene Oligomers: Nanotube Diameter Dependence

Encapsulation of photo-active organic molecules inside single-walled carbon nanotubes (SWNTs), appears to be of great interest in terms of high power conversion effciency, and long-term stability for a commercial application of organic solar cells (OSCs). In this paper, we report a charge transfer (CT) evidence in Donor-Acceptor SWNTs filled with Sexithiophene oligomers (6T) by Raman spectroscopy. To compute the optimal diameter and demonstrate the most stable structure of the hybrid systems with either a single 6T molecule encapsulated into SWNTs (6T@SWNTs), or two 6T chains encapsulated (6T-6T@SWNTs), we have performed structural geometry optimization on the hybrid encapsulated systems using a convenient Lennard-Jones (LJ) expression of the van der Waals (vdW) intermolecular potential. Combining the density functional theory (DFT), molecular mechanics, bond polarizability model and the spectral moment method (SMM), we computed the polarized nonresonant Raman spectra of 6T molecule and SWNTs (metallic and semiconducting) before and after encapsulation. The influence of the encapsulation on the Raman-active modes of the 6T molecule and those of the nanotube (radial breathing modes and tangential modes) are analyzed. In particular, significant changes observed in the G-band frequency. The possibility (or not) of an eventual CT between the 6T oligomer and the nanotube in both hybrid systems (6T@SWNTs and 6T-6T@SWNTs) is discussed. We show that there is a dependence of the CT with respect to the diameter of SWNTs, the CT vanish with increasing diameter of the nanotubes. Our finding of CT behavior in the the filled SWNTs with respect to SWNT diameter will provide a useful guidance for enhancing the performance of OSCs by SWNTs.

| INTRODUCTION

One of the most effective and practical ways to reduce the current energy crisis and strengthen environmental protection is the exploitation of clean and sustainable solar energy. In this context, photovoltaic (PV) devices, which directly convert solar radiation into electricity, have received more research attention 1 . The conversion and optimisation of sunlight to electricity PCE present the main challenge for PV cell designers.

The theoretical upper limit to PCE from a Shockley-Queisser analysis for a single junction solar cell (SC) was reported to be about 30% 2 .

Currently, silicon-based SCs technology (with a band gap of 1.1 eV) is by far the dominant PV technology retaining a mature manufacturing and an excellent PV performance with about 25% efficiency 3 . However, such systems suffer from the high cost of manufacturing and installation, and it is still not cheap enough to globally compete with fossil fuels 4 . Among all the alternative technologies to silicon-based SCs, organic PV have attracted significant attention because of their low costs, simple preparation, large area, mechanical flexibility, and lightweight ability 5 , but the most critical challenges for OSCs are their low efficiency and lifetime 6;7 . Their energy efficiency and durability need to be enhanced for making them practically viable.

Most of the research on OSCs has focused on bulkheterojunction (BHJ) architectures, and one of the most widely examined material systems consisted of conjugated polymer as the electron donor and fullerene derivatives as the electron acceptor [START_REF] Ganesamoorthy | [END_REF] . The simple design of these devices typically consist of an active layer comprises an intimate blend of two organic molecular structure, one electron donating strongly light absorbing, and another electron acceptor materials usually a fullerene derivative with electron accepting properties, placed between two electrodes utilized to generate power. In these cells, when light is incident on the device, electron-hole pairs called excitons are formed on the light absorber materials, and then, PV conversion is based on the dissociation of these photo-generated charges into electrons and holes at the donor-acceptor interfaces [START_REF]Tress in Organic Solar Cells[END_REF] .

Significant progress has been made for conjugated polymer/fullerene based BHJ OSCs and these typical combinations has afford to PCE close to or exceeding 11% [START_REF] Green | [END_REF] . Never-theless, the performance of this kind of devices is ultimately limited by the intrinsic defficiencies of fullerene family, including weak absorption in the solar spectrum range, limited optoelectronic tunabilitty, small charge mobility and thermal instability 11 . Thus, alternatives to fullerenes as electron acceptors materials would bring more potential. In this regards, the scientific communities has proposed carbon nanotubes, and in particular, SWNTs as promising alternatives to the fullerenes, because of their several unique structural, excellent photo-chemical stability, mechanical strength, thermal, optical and electronic properties 12;13;14;15 . In comparison with fullerene acceptors, SWNTs possess distinct advantages that are not found in fullerenes, in terms of optical absorption and tunability of bandgaps, it offers distinctive properties such as the very broad spectral coverage with band-gap electronic transitions well into the near-IR spectral region 16;17;18;19 .

Hence, in recent years, SWNTs are considered as attractive candidates and import element in OSCs, and recent trends suggest that a successful utilization of SWNTs, in particular, the direct integration of SWNTs inside the BHJ photo-active layers could potentially overcome many of the handicap and lead to the realization of high efficiency and low-cost OSCs 20 .

Indeed, SWNTs offer a wide range of band gaps to match the solar spectrum and enhanced absorption in the IR range (0.48-1.37 eV) 21;22 . They also exhibit excellent charge-carrier mobility (up to 10 5 cm 2 /V.s) at room temperature 23 , and enormous current carrying capability (up to 10 9 A. -2 ) 24 . The use of SWNTs as a light harvester and charge transporter in the active layer of OSCs provides an opportunity to avoiding carrier recombination and permits efficient exciton quenching at the interfaces and charge carrier transport [START_REF] Hermes | Green Nanoparticles[END_REF] .

In fact, the PCE of OSCs utilizing blends of conjugated polymers and SWNTs as two integrative parts of the photoactive layer is limited to a few percent [START_REF] Green | [END_REF] , and they are still far behind other solar cell technologies, in particular, the fullerene based devices. The limiting factors for SWNTs are several, including the noncomplete exciton-dissociation for the low amounts of SWNTs, and on the other hand, the increased recombination pathways for the high amounts of SWNTs percentage in the polymer matrix 14;13 . Moreover, SWNTs are typically a mixture of metallic and semiconducting as produced nanotubes. This electronic variety may affect the device PCE, and several authors indicate semiconducting nanotubes as the only desirable ones for OSCs 26;27 . Furthermore, although the PCE of OSCs is an important issue for practical applications, the inferior device stability is also necessary in moving these devices toward commercialization, and still remains a great challenge. Many external or intrinsic factors limit OSC stability such as irradiation, heat, mechanical stress, oxygen and humidity 7;28;29 An elegant solution and powerful technic that can overcomes those several limits consist in encapsulating of photoactive molecules inside SWNTs to form new nanohybrid systems with adjustable optoelectronic properties. These nanohybrid systems are particularly attractive when the preservation of intrinsic SWNTs electronic and charge transport properties is desired, while overcoming the degradation problem of conjugated molecules. Actually, the organic molecules inside SWNTs will be protected from any external reactive species by the surrounding nanotube wall as proposed by Takenobu et al 30 . In addition, insertion into SWNTs can suppress the light irradiation degradation of the molecules as reported by Yanagi et al 31 , and thus, the degradation of conjugated molecules might be overcome by encapsulating them inside SWNTs.

Generally, in comparison with conventional fullerene devices, SWNTs filled with organic molecules will possess distinct advantages in terms of high PCEs, and long-term stability for commercial application of OSCs.

In order to complete our study about the encapsulation of a series of oligothiophenes in SWNTs 32;33 , we propose here a comparative investigation on the structural and vibrational properties of nanohybrids formed through SWNTs filled with one of the most important classes of conjugated oligomers that can be applied as photo-active material in OSCs, sexithiophene (6T) 34;35 . It is well-known that SWNTs behave not only as electron acceptors but as light-harvesting electron donors as well depending on the electronic nature of the molecule used for their functionalization. Since 6T are electron-donor in nature, SWNTs can act as an acceptor in their donor-acceptor complexes. Indeed, there are several reports on the structure, stability and properties of the filled SWNTs with 6T molecules investigated by using aberration-corrected high-resolution transmission electron microscopy, Raman spectroscopy, and optical spectroscopy 36;37;38;39 . Despite the excellent experimental work in this research field 40;41;42 , leading recently to encapsulate efficiently 6T in SWNT at low temperature 43 , computational approaches are indispensable for obtaining atomistic information of 6T inside nanotubes, especially, the close proximity between 6T and SWNTs may also result in charge transfer (CT) in the hybrid systems. In the present paper, we theoretically study the CT in the filled SWNTs with 6T molecules using Raman spectroscopy. Firstly, to compute the optimal diameter and demonstrate the most stable structure of the hybrid systems with either one 6T molecule (6T@SWNTs) and two 6T chains encapsulated (6T-6T@SWNTs)(see figure 1), we have performed structural geometry optimization on the hybrids using a convenient LJ expression of the vdW intermolecular potential. Then, we present calculations of the Raman spectra of 6T molecules and SWNTs before and after encapsulation. The polarized nonresonant Raman spectra are calculated in the framework of the force constants model combined with the spectral moments method (SMM) 44 . Finally, discussion and conclusions in the last section.

| MODEL AND METHODOLOGY

Calculation of Raman spectra necessitates the knowledge of the dynamical matrix (DM) and the polarizability tensor of the system. In our previous works 32;33 , we developed a hybrid approach to compute the nonresonant Raman spectra of bi-thiophene (2T) and quater-thiophene (4T) molecules encapsulated into metallic and semiconducting SWNTs, combining the DFT, molecular mechanics, bond polarizability model and SMM. The DM of the hybrid system has a 3Nx3N dimension (N is the number of atoms in the primitive unit cell). Exploiting the symmetry of the system may be reduced considerably the number of the DM elements to be determined. However, other than the hermitian (lower or upper triangular) character of the DM, in the case of our hybrids, except the trivial identity operation, no symmetry elements exist. Consequently, all the diagonal and off-diagonal elements of the DM have to be calculated.

First principles-based methods are very accurate to compute the DM (frozen phonon or density functional perturbation theory) but their computational cost is very high for large systems, like 6T@SWNTs, and especially without any symmetry. Molecular mechanics could be an excellent alternative to build the 6T@SWNTs DM but such a force field still remains unknown. Thus, taking advantage of DFT and molecular mechanics, we adopted a three-step methodology.

The idea consists to decompose the 6T@SWNT hybrid system into two independent subsystems (6T and SWNT), which will be coupled with an adequate empirical intermolecular potential. The DM of the 6T@SWNTs hybrids is built block by block from the DM of each subsystem, where the DM of the SWNT and 6T form the bidiagonal block of the DM of the 6T@SWNTs, while the DM associated with the 6T and SWNT interactions forms the off-diagonal block.

In the first step, the DM of the oligomers molecules will be calculated under DFT at the local density approximation (LDA) level of theory, as implemented inside the Spanish Initiative for Electronic Simulations with Thousands of Atoms (SIESTA) package 45 . In the second step, the DM of SWNT will then be computed from the force constant model introduced by Saito et al [START_REF] Dresselhaus | Physical properties of carbon nanotubes[END_REF] . Lastly, the vdW interactions (longranged dispersive forces) are the binding mechanism in the hybrid systems under investigation. LJ potential is adopted for an adequate description of these interactions between 6T-SWNTs:

( ) = 4 12 - 6 (1)
where :

= 2.964 meV and = 0.3407 nm, = 10.7 meV and = 0.3560 nm, and ℎ = 0.67 meV and ℎ = 0.1069 nm are the LJ parameters of carbon, sulfur, and hydrogen atoms respectively. We calculated the LJ parameters of carbon-sulfur and carbon-hydrogen using the combining rules of Lorentz-Berthelot:

= √ and = ( + )∕2.
The DFT calculations on 6T molecules have been carried out using LDA exchange-correlation functional. The valence electrons were described by a double-singly polarized basis set. The localization of the basis is controlled by an energy shift of 50 meV and the real space integration was performed on a regular grid corresponding to a plane wave cuto around 360 Ry. We considered a vacuum size of 12Å to avoid interactions between adjacent systems.

The Raman susceptibility tensor is computed using the bond polarizability model of SWNTs 47 combined with one of the free 6T molecules 48 . This approach has been successfully used to predict the nonresonant Raman spectra of SWNTs and double-walled carbon nanotubes (DWNTs) as a function of their lengths 49;50;51;52 . For more details on the Raman equations and the computational details to derive the Raman susceptibility from the bond polarizability model, see ref 48 .

Finally, Computation of Raman spectra of the investigated hybrids are based on the SMM. Indeed, the usual method to calculate the Raman response requires a direct diagonalization of the DM of the system. However, when the system under investigation contains a large number of atoms (like 6T@SWNT), the DM is very large and its diagonalization demands a very long computing time or break down. In such cases, the SMM appears as a unique and very powerful method as it allows us to compute directly the Raman spectra without any diagonalization of the DM. For more details on this hermetic method, see Ref 44;49 .

| RESULTS AND DISCUSSION

| Stability of 6T confined into SWNTs

Aiming to gain insight into the formation of the filled nanotubes in terms of bonding, geometry, and stability, we focus here on the structural arrangements of such nanohybrids which are prerequisites for comprehension of their properties. In our calculations, we respectively considered two con figurations: the 6T@SWNTs where only one 6T molecule is placed inside the nanotube, and the 6T-6T@SWNTs where two molecules are placed inside the nanotube cavity. We determined the range of nanotube diameters in which the encapsulated systems are stable for the two encapsulated systems (6T@SWNTs and 6T-6T@SWNTs). Such a study could lead the experimentalists to provide effective estimates about reasonable and suitable SWNT sizes and the steric hindrance of the 6T in the inner space of the nanotube. In our calculations, we adopt that the sizes of the oligothiophenes are sorely reduced under nanoconfinement by aligning all the 6T rings to form a planar structure. For a single 6T molecule placed inside SWNT, the optimized arrangements correspond to an isolated chain inserted inside SWNTs cavity and centered along the nanotube axis. On the other hand, concerning the optimized configuration for two 6T molecules, we have first adopted an initial position of 6T molecules according to the minimum energy calculations using LJ potential. The interchain distance found for two free-standing 6T molecules in a parallel configuration is d=0.508nm (see figure 1). In practice, the structure relaxation is performed by minimizing the distance between atoms associated with LJ poten-tial. Figure 2 shows the LJ potential as a function of SWNT diameter varying from 0.8 to 2.5 nm and from 1.1 to 2.9 nm for 6T@SWNTs and 6T-6T@SWNTs hybrid systems respectively. First, for 6T@SWNT hybrid system, we observe a minimum at 0.93 nm corresponding to the equilibrium distance between the SWNT and 6T molecule.

Thus, the insertion of a single 6T molecule, located aligned at the SWNT center, is particularly suitable for SWNTs with a diameter around 0.93 nm. Good agreement acquired between this diameter value obtained from the minimization of the LJ energy and the experimental observations of Alvarez et al 53 for a single oligothiophene molecule. For 6T-6T@SWNTs hybrid systems, figure 2 gives clear evidence that encapsulating two 6T molecules is favorable for tubes with diameter close to 1.24 nm. This optimal diameter agrees well with Loi et al 37 (correspond to mean diameters of 1.21 nm according to the relationship proposed in ref 54 ).

Beside that, total energy calculations suggest that the vdW interactions between the 6T and the tube is stronger than the intermolecular interaction 37 . Coherently, such behavior is reported by yumura et al. 55 in their investigation on the optimized geometries for terthiophene inside SWNTs armchair, which demonstrate a good correlation to our findings in term of SWNT size and structural arrangement of thiophene oligomers inside SWNT, where the optimal distance of the 6T chain to the tube wall is distinctly smaller than the interchain distance (see figure1). Therefore, the vdW bond between the 6T and the tube turns out to be stronger than the intermolecular interaction, and the internal 6T prefer to be located near the walls of the nanotubes rather than close to the axis.

| Raman spectra of isolated 6T

The calculated Raman spectrum of 6T molecule in the 0-1680 -1 range is ilustrated in figure 3. The spectrum shows various lines. The analyzis of the corresponding eigenvectors allowed to their assignements, which are in good agreement with the experimental ones 56;57;58 , except for the lowest frequencies between 0 and 90 -1 that are not experimentally available. While this line is calculated at 1502 -1 with small intensity, which it can be explained necessarily as a coupling between the C-C bonds motions and the in-plane bending (C-H) whither the hydrogen atoms recoil with a large vibrational displacement which opposes that of the carbon atoms, leading thus to a losing of its intensity.

| Raman spectra of 6T molecules confined into SWNTs

A Raman spectrum of pristine SWNTs comprises two main characteristic bands: the lower frequency radial breathing modes (RBM) (100-400 -1 ), which corresponds to coherent vibrations of the all carbon atoms in the radial direction, and the heigher frequency tangential modes (TM) or G-band (above 1500 -1 ), which belongs to longitudinal and transversal vibrations of carbon atoms 59 . The investigation of Raman spectra changes induced by the filling of SWNTs with 6T molecules is of special interest in the nanotube community. Indeed, changes in the Raman spectra allow monitoring structural modifications of the nanotube sidewalls due to CT effects 60 . This CT effect resulting from the 6T molecules encapsulated inside SWNT can be probed through the downshifts and (or) up-shifts observed in the Raman modes, and a survey of this phenomenon (The possibility (or not) of a CT) constitutes the main goal of the present investigation. F I G U R E 4 Raman spectra of the empty (black curves) and encapsulated metallic SWNTs (red curves).(top) (12,0) and 6T@(12,0). (bottom) (7,7) and 6T@(7,7).

For this purpose, first, we considered four 6T@SWNT hybrids with different nanotube chirality (n, m),possessing a similar diameter to one another, around the optimal value (0.93nm) found in section 3.

R a m a n I n t e n s i t y R a m a n I n t e n s i t y

F I G U R E 5 Raman spectra of the empty (black curves) and encapsulated semiconducting SWNTs (red curves).(top) (10,3) and 6T@(10,3). (bottom) (8,6) and 6T@(8,6).

| Raman spectra of 6T@SWNTs

F I G U R E 6

Raman spectra of the empty (black curves) and encapsulated metallic SWNTs (red curves).(top) (12,6) and 6T-6T@ (12,6). (bottom) (9,9) and 6T-6T@(9,9).

Concerning the main modes of 6T oligomer, Raman spectra of 6T@SWNTs hybrid systems with metallic (figure 4) or semiconducting (figure 5) nanotubes show an up-shift due to vdW interactions, as well as the disappearance of the other lines. Indeed, the lines located in the lower frequency range are very sensitive to the confinement of 6T into SWNT.

It is visible that the libration modes (8 and 25 -1 ) of 6T molecule appear in figure 3 vanish in the Raman spectra of 6T@SWNTs hybrids shown in figures 4 and 5. This absence of libration clarify a stability of 6T in the SWNT cavity. The free 6T with its fixed orientation repeatedly rotates slightly back and forth, then this reciprocating motion is deactivated after encapsulation, and consequently cause the absence of libration modes. Besides, for the different SWNTs considered, an up-shift associated to vdW interaction of all Raman features between 1 and 23 -1 is spotted on the 6T@SWNTs spectra after encapsulation with respect to corresponding ones in the free 6T molecule, which constitutes another hint of a sig-nificant interaction between the subsystems (6T and SWNT) in the hybrids.

In the low-frequency range (100-400 -1 ), encapsulation of 6T into SWNT is expected to induce a certain shift in the RBM band positions of 6T@SWNT, since encapsulated oligomers should affect the motion of carbon atoms in the nanotube along its radius, mainly the RBM shifts induced under the nanoconfinement effect can originate from dispersive interactions (vdW) and CT. Indeed, for the fullerenes-filled SWNTs 61;62;63;64;65;66 . the dispersive interactions (vdW) induce a small down-shift in RBM band of SWNTs of 2 or 3 -1 . Bandow et al 67 experimentally showed that fullerenes encapsulated into SWNTs caused a down-shift in the RBM of nanotubes by encapsulation, the authors explain this downshift in RBM band by softening of the C-C bonds of the SWNT sidewall, corresponding to exothermic fullerene encapsulation. Nevertheless, Okada and co-workers 68 predicted a frequency shift of RBM phonon for the C60 molecules inserted into metallic armchair SWNTs depending on the tube diameter where the encapsulation of C60 molecules gave a higher frequency shift for (10,10) SWNT but a lower shift for (11,11) and (12,12) SWNTs with greater diameters. This diameter dependence of the frequency shift is ascribed to the charge redistribution induced by weak hybridization between -electron states and nearly free electron states. In addition, the small shift of the RBM band to a higher frequency indicates that, energetically, the SWNT diameter is favorable for the molecules encapsulated 68 . On the other hand, CT to and from SWNT can modify the C-C bonds in the nanotube and therefore the SWNT electronic properties. Doping SWNTs with strong electron-donor or acceptor constitutes a direct way to observe the CT effect. The insertion of alkali metals (electron-donors) species into SWNTs, rubidium 69 for example, no shift in the RBM is observed, and a small down-shift for lithium 70 . By contrast, Chen et al. 71 reported that doping of SWNTs with caesium gives rise to an upshift in RBM by about 2 -1 . This behavior is observed also when electron acceptor molecules are encapsulated into bundles of SWNTs 72 . However, the CT (positive or negative) onto individual metallic nanotubes 73 has been reported to induce a small RBM upshift of about 2 -1 . Such behavior is observed when oligothiophene derivatives 37;74;75 are inserted into bundles of carbon nanotubes. It was surprising that the same direction of RBM shift is seen for SWNTs doped with electron-donor and acceptor, making RBM shifts as a measure of charge transfer ambiguous without prior knowledge of the ionization potential of the molecule or electron affinity.

Generally, the RBM shifts are at most -3 -1 for dispersive interactions 68;72;76 and 2 -1 or CT 71;73 . Thus, for semiconducting 6T@SWNTs, the peak positions in empty SWNTs are downshifted by 2 -1 and 1 -1 for 6T@(10,3) and 6T@(8,6) respectively (figure 5). As well, the peak positions in the empty armchair (7,7) metallic tube is down-shifted by about 1 -1 in 6T@(7,7) spectrum, whereas for 6T@(12,0) hybrid, the RBM clearly exhibits a frequency up-shift after encapsulation by 1 -1 (figure 4). However, the physical interactions between 6T oligomers and the SWNTs are presumably dispersive and combined to a CT as suggested by Alvarez et al 53 for the oligothiophene derivatives filled carbon nanotubes, where both effects may compensate each other, and the shift of the RBM is expected to be smaller or close to zero.

Concerning the high-frequencies region where the TM are observed, the G-band feature for pristine SWNTs is fitted with two main components. The lower frequency peak ( -) is assigned to the transverse optical (TO) phonon modes, and the other peaked at a higher frequency ( + ) belongs to the longitudinal optical (LO) phonon modes, independently of whether SWNT is metallic or semiconducting. The chirality dependence of TM where the -peak (resp. + ) is dominant at the armchair chiral angle ( =30 ) (resp. zigzag chiral angle ( =0 )), and the appearance of two peaks ( -and + ) when increasing from 0 to 30 was discussed in detail in Ref 49 .

Another point to mention is the electron-phonon coupling which gives rise to the Breit Wigner-Fano lineshape observed in metallic SWNT 77 , does not considered in the present approach. Consequently, the spectra exhibit only Lorentzian lineshapes. The splitting of the -and + Raman peaks (two narrow Lorentzian peaks), and their assignment to the TO and LO phonons, respectively, was discussed in our previous work 33 .

For the G-band of metallic SWNTs (right-hand part of figure 4), the calculated Raman spectra are featured by an only peak affected to 1 (ZZ) TM, peaked at 1591 -1 in the (12,0) zigzag SWNT, and at 1582 -1 in the (7,7) armchair SWNT. It is visible that the G-band spectra of the filled SWNTs as compared to the pristine SWNTs demonstrate a down-shift of the -peak (TO mode) by 1 -1 in the 6T@(7,7), as well as a significant up-shift of the + peak (LO mode) by 4 -1 in the 6T@(12,0) spectrum. For the G-band of semiconducting SWNTs (right-hand part of figure 5), the two inspected tubes (10,3) and (8,6) are chiral with ≃ 13 , and 25 , respectively, and both the -and + peaks appear in the Raman spectra of empty SWNTs. Under confinement effect, the spectra of the filled SWNTs show a down-shift of the -peaks (TO modes) by 1 -1 At the opposite, the + peaks (LO modes) demonstrates a considerable up-shift by 3 -1 for the 6T@(10,3) and 6T@(8,6) hybrids.

On the basis of these observations, and as previously was reported for the 2T@SWNTs 32 and 4T@SWNTs 33 hybrid systems, the G-band behavior under the confinement effect for both metallic and semiconducting 6T@SWNTs hybrids shows also similar trends. The -peaks (TO) of SWNTs show a slight down-shift of about 1 -1 whereas the + peaks (LO) exhibit a larger up-shift by about 3 and 4 -1 . Indeed, the + feature associated with axial carbon atom vibrations (LO) of the SWNT (see figure 8) is sensitive to CT from dopant additions to SWNTs 78;79 . It was discussed that the up-shift of the G-band lines corresponded to the CT from the SWNTs to the encapsulated molecules (p-doping) 30;80;81 and the down-shift of the G-band lines testified to the CT from the incorporated molecules to the SWNT walls (ndoping) 30;80;82 . Further, it was reported that p-doping leads to the contraction of bonds and phonon stiffening, consequently, this change of the C-C bond length under CT leads to an upshift of the + band 83 . However, Kalbac et al 84 showed that applying the positive potentials to the SWNTs (analogous to n-doping) may also induce the hardening of the G-band. That is why conclusions about the direction of CT in our hybrid systems cannot be drawn exclusively from Raman spectra.

Fortunately at all events, we can conclude that these up-shifts of the + lines proved a CT takes place between the SWNTs and 6T molecules.

On the other hand, for the insignificant shift of the - peaks associated with circumferential carbon atoms vibrations (TO) of the SWNT (see figure 8) toward lower frequencies, there is possibly a concurrence between dispersive interactions of 6T oligomers with SWNTs which give rise to phonon softening and the shift of the -peaks toward lower frequen-cies, and the effect of a CT which results in the up-shift of the -peaks. Consequently, due to the compensation of the both effects, it is expected that the shifts of the -peaks should be smaller or even to have the opposite sign than for p-doping.

| Raman spectra of 6T-6T@SWNTs

Our discussion up to now referred to a single 6T molecule encapsulated into a SWNTs. In this section, we want to explore the Raman responses of carbon nanotubes filled with more than one molecule. The configuration inspected in this case consists in two molecular chains inserted in the same SWNT. Thus, we considered four 6T-6T@SWNT hybrids with different tube chirality (n,m) and whose the diameters are around 1.24 nm (the optimal value found in section 3.1 to encapsulate two 6T). The Raman spectra of the 6T-6T@SWNTs hybrid systems (red curves) in comparison with the spectra of the empty SWNTs (black curves) are displayed on figures 6 and 7 respectively. Likewise, all spectra of the 6T-6T@SWNTs hybrids show a superposition of the 6T and SWNTs spectra whatever the electronic charateristic of the nanotube (semiconducting or metallic). However, the detailed analysis of RBM and G-bands modes, as well as the Raman modes of the oligomers allows obtaining further report about the CT in the encapsulated SWNTs. F I G U R E 7 Raman spectra of the empty (black curves) and encapsulated semiconducting SWNTs (red curves).(top) (16,0) and 6T-6T@(16,0). (bottom) (13,5) and 6T-6T@ (13,5).

First, concerning the modes of encapsulated oligothiophene molecules, Raman spectra of 6T-6T@SWNTs hybrids with metallic (figure 6) or semiconducting (figure 7) nanotubes show an up-shift due to vdW interactions, as well as the vanishing of other modes. The libration modes located in the lower frequency region (8 and 25 -1 ) disappear in the Raman spectra of 6T-6T@SWNTs hybrids (figures 6 and 7). The vanishing of the librations explicates the stability of confined 6T-6T inside the SWNTs cavity as discussed for nanotubes filled with only a single molecule. Further, an up-shift of the 6T mode frequencies (from 1 to 7 -1 ) in 6T-6T@SWNTs spectra as compared to the corresponding positions in the isolated 6T molecule (figure 3), indicates a considerable interaction between 6T-6T and the nanotubes under confinement effect.

Next, in the RBM frequency region (100-400 -1 ), all filled nanotubes exhibit an up-shift in the RBM frequency after encapsulation as shown in figures 6 and 7. Indeed, for 6T-6T@SWNTs with metallic nanotubes, the RBM observed in empty tubes is up-shifted by about 5 -1 or 6T-6T@ (12,6) and by about 9 -1 for 6T-6T@(9,9) (figure 6). Likewise, in the case of semiconducting nanotubes, the RBM observed in empty SWNTs is up-shifted by 5 -1 for 6T6T-@(16,0), and by 3 -1 for 6T-6T@(13,5) (figure 7). Actually, experimental observation of Water filling of thin SWNT down to chiral index (5,3) and theoretical studies on encapsulation of sexithiophene in SWNTs suggesting that the RBM behaviors can be associated to the amount of confined molecules into SWNTs and their supramolecular organization 85 . However, the encapsulation of Zn-diphenylporphyrin (electron donor) inside SWNTs leads to an RBM up-shift of 3 to 5 -1 and intensity reduction, which was interpreted by Kataura et al 86 as a sidewall deformation due to the large size of the molecule (about 1.0 nm).

A comparison with the detailed study reported by Almadori et al 74 about the RBM shift behaviour with a nanotube diameter dependence for the encapsulation of different kinds of oligothiophenes (quaterthiophene, dimethylquaterthiophene, and sexithiophene), revealed an agreeable similarity on the behavior of the RBM shifts observed in both our hybrid systems (6T@SWNTs and 6T-6T@SWNTs). Indeed, for small diameter SWNTs (between 0.68 and 1.1 nm)

where only one single molecule can fit in the tube, the shifts of the RBM mode are almost constant (around a value of 2 -1 ). Then, for nanotube diameters between 1.10 and 1.45 nm, which can accommodate two molecules, a linear behavior of the RBM up-shits is observed (from 4 to 8 -1 ). These RBM behavior suggests that the physical interactions of thiophene molecules with the largest diameter nanotubes (larger than 1.1 nm), cannot be simply understood as a superposition of dispersive interactions and CT, but it can be understood as a mechanical strain on SWNTs induced by the confined 6T-6T molecules (as evidenced in ref. 74 ). of the SWNT and 6T molecules was described by molecular mechanics and DFT respectively, whereas the 6T-SWNTs coupling between the subsystems was described by an LJ potential. First, we determined the range of SWNT diameters in which the hybrids are stable for the two encapsulated systems 6T@SWNTs and 6T-6T@SWNTs. We found that the configurations suitable in terms of the energetics for the insertion of a single 6T molecular chain (resp. two 6T molecules) corresponding to the optimal SWNT diameter around 0.93 nm (resp. 1.24 nm). Then, for the obtained configurations of 6T@SWNTs and 6T-6T@SWNTs hybrid systems with metallic and semiconducting nanotubes, the nonresonant Raman spectra have been calculated using the bond-polarizability model combined with the spectral moment method. The CT in the 6T@SWNTs and 6T-6T@SWNTs has been investigated by analyzing the Raman-active modes of the 6T molecule, as the RBM and G-band modes of SWNTs, before and after encapsulation. The RBM and G-band shift behaviour with a nanotube diameter dependence revealed an agreeable agreement with the reported experimental results. Our calculations testify to the presence of the CT in the 6T@SWNTs encapsulated systems without specifying their direction. It may occur from or to SWNTs, namely, whether SWNTs work as donor or acceptor in 6T@SWNTs hybrids. The identification of the CT and its direction in hybrid systems by electronic and optical calculations is the goal of our future works. Alternatively, we predict that CT does not occur in 6T-6T@SWNTs hybrid systems, since there is no change in the peak positions of the G-band after encapsulation. The G-band of 6T-6T@SWNTs nanostructure is unchanged in comparison with the one of pristine SWNTs. One may therefore assume that incorporation of the 6T molecules into SWNTs cavities with diameters above 1.2 nm does not lead to a modification of nanotube electronic properties. Thus, only the nanotubes with diameters below 1.2 nm are interesting for OSCs.

Finally, SWNTs with a diameter distribution of 0.9-1nm, appropriate to S1 optical band-gaps in the energy range 1-

  . Concerning the extreme environmental external factors, like oxygen and water, encapsulation strategy for a protection from the ambient could give them a longer stability. As for the internal degradation factors, like irradiation and heating are closely related to the stability of active layer materials. Indeed, intrinsic molecular structure of active layer materials is one of the most important factors that affect the OSCs stability. Furthermore, the degradation of conjugated polymers under illumination is the most challenging handicap to realize long-term OSCs stability. In fact, degradation occurring in OSCs gets accelerated in the presence of UV light and produces the decomposition of organic molecules, and thus results in formation of new molecules with inferior properties, causing degradation in PV performances of the devices. Ensuring, therefore, the stability of the conjugated polymer under continuous light irradiation is critical for achieving practical use of OSCs, and insist on the development of innovative technics allowing to overcome degradation issues.

1

 1 Schematic of the encapsulation of 6T molecule in SWNTs and characteristic distances after energy minimization. (a) 6T, (b) 6T@(7,7) and (c) 6T-6T@(16.0). The highlighted distances are given in nm. Atom colors: grey-carbon, yellow-sulfur and white-hydrogen.

  experimental observations for two parallel oligothiophene molecules placed inside SWNTs, and the fact that the RBM position in Raman spectra of the SWNTs is at 196 -1

F 3

 3 I G U R E 2 Lennard Jones potential as a function of the tube diameter for hybrid systems with one (6T) and two (6T-6T) chains encapsulated in SWNTs. Raman spectrum of isolated 6T.Let us first consider the lower-frequency range 0-400 -1 . This frequency range is dominated by three features centered at 50, 130 and 382 -1 , two weak lines centered at 8 and 25 -1 , and one doublet around 295 -1 . For Raman frequencies below 90 -1 , no experimental data has found in the literature. Though, three Raman modes are predicted from DFT simulations (two modes centered at 8 and 25 -1 and one mode centered at 50 -1 ).The couple of lines at 8 and 25 -1 are libration modes, whereas the feature located at 50 -1 is associated to in-plan bending (C-S-C) and in-plan bending (C-H) modes. For the other features at 130, 295 and 382 -1 are assigned respectively to the in-plane bending (S-C=C) modes, the scissor (S-C-C-S), and in-plane bending (S-C=C) with the contribution of in-plan bending (C-H) modes. Next, the intermediate-frequency range (400-1100 -1 ) is dominated by two lines centered at 490, 615 and one doublet around 850 -1 , three weak features centered at 670, 727, and one doublet around 1048 -1 . These lines are assigned respectively to the in-plane torsional (S-C) modes, the in-plane bending (C-S-C), the stretchings (C-S) with the contribution of the in-plane bending (C-H), the in-plane bending (C-S-C) combined to the out-of-plane bending (C-H) modes, a combination of the streachings (C-S) and the in-plane bending (C=C-C), and the stretching (C-C) modes along with the inplane bendings (C-C-H ). Now, in the heigher-frequency range (1100-1680 -1 ), four strong lines were observed, centered at 1199, 1288, 1323 and 1633 -1 , and three weak features located at 1377, 1502, and 1610 -1 . The modes at 1199 -1 along with those at 1288 and 1323 -1 are assigned to a progression of the in-plane bendings (C-C=C) and the in-plane bendings (C-H), whereas a combination of the stretchings (C-C) and the in-plane bendings (C=C-S) give rise to the feature located at 1377 -1 Finally,the stretching (C=C) along with the inplane beniding (C-S-C) vibrations contribute to the lines centered at frequencies higher than 1400 -1 .Finally, the stretching (C=C) along with the in plane bending (C-S-C) vibrations contribute to the lines centered at frequencies higher than 1400 -1 . It is worth mentioning that the line around 1500 -1 which is a common feature of the Raman spectra of aromatic and heteroaromatic systems, where both the C=C and C-C stretching vibrations are active, is always very strong and dominates the whole Raman spectrum.

Figures 4 (

 4 Figures 4 ( metallicSWNTs) and 5 (semiconducting SWNTs)demonstrate the Raman spectra of the 6T@SWNTs hybrid systems (red curves) in comparison with the spectra of the empty SWNTs (black curves). It is visible that all spectra of the 6T@SWNTs hybrids apear as the superposition of the 6T and SWNTs spectra whatever the electronic charateristic of the

1 F I G U R E 8

 18 Calculated eigen displacement vectors for the TM in(7,7) and 6T@(7,7) (left), and (12,0) and 6T@(12,0) (right).Concerning the high-frequency region of achiral SWNTs where the TM are observed (figures 6 and 7), the calculated ZZ-polarized Raman spectra are featured by a single peak assigned to A 1 (ZZ) TM, centered at 1590 -1 in the (16,0) zigzag SWNT, and at 1585 -1 in the (9,9) armchair SWNT.The + peak (resp. -) is dominant at the zigzag chiral angle ( =0 ) (resp. armchair chiral angle ( = 30 ) as discussed in the previous section. For chiral SWNTs, the two considered tubes are(13,5) and(12,6), with ≃ 15 • , and 19 • , respectively.Both the + (LO) and -(TO) peaks appear in the Raman spectra of empty SWNTs.As we can see in figures 6 and 7, the encapsulation of two molecules does not affect the peaks position of the G-band in the both metallic and semiconducting nanotubes spectra. However, CT between the encapsulated molecules and the SWNTs causes shifts of the G-band peaks30 . Thus, since there is no change in the peak positions of the G-band after encapsulation, we conclude that CT does not occur in 6T-6T@SWNTs hybrid systems. Indeed, according to Ref31 , the encapsulation of -carotene inside SWNTs (with a diameter of about 1.4 nm) leads to an RBM up-shift of 3 -1 , and none change in the peak position of the G-band could be observed.Besides, Loi et al37 have reported an experimental work on the encapsulation of 6T inside SWNTs whom diameters are between 1.2 and 1.5 nm. The encapsulation of 6T gave an RBM up-shift of 5 -1 and the G-band frequencies was found to be the same for SWNTs and 6T@SWNTs samples.4 | DISCUSSION AND CONCLU-SIONSOverall, the outstanding optoelectronic properties of semiconducting SWNTs make them highly attractive absorbers integrated in the active layer of OSCs. Their optical band gap can be tuned to optimize absorption of different spectral ranges by tailoring the distribution of their diameters. An efficient absorption of the solar spectrum can be achieved by tuning a distribution of SWNTs ranging from 0.8 to 1.2 nm in diameter resulting in optical band-gaps ranging from 1.0 to 1.3 eV, close to the Shockley-Queisser optimum for a single junction PV device. In this paper, we use an original approach to study the encapsulation of only one 6T molecule and two 6T molecules inside the SWNTs cavity. The dynamical model

1. 2

 2 eV, could be harness for photon capturing with energies above 1 eV, which constitute practically the same spectral band trapped by a silicon-based SCs 18;87;15 . Indeed, following light absorption by either SWNTs or 6T molecules (under the concept of BHJs), the excitation of 6T accompanied by electron (resp. hole) transfer or the excitation of SWNTs accompanied by hole (resp. electron) transfer, produce the same charge separation state, consequently, the spectral coverage achieved by a certain mixture of SWNTs with average diameters of 0.93 nm (the optimal value found to encapsulate only one 6T) could be exploited to optimize light-harvesting and, by extension, the PCE of OSCs. In this context, we believe that the encapsulation of photo-active organic molecules inside SWNTs, thus creating a new hybrid system, appear to be of great interest in terms of high PCEs, and long-term stability for commercial application of OSCs.

Funding information (CONICYT)-Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) Posdoctodado 2020 Nº 3200046

AC K N OW L E D G M E N T

The work was supported by Moulay Ismail University Research Support (13-16)

C O N F L I C T O F I N T E R E S T

The authors declare no conflict of interest.

R E F E R E N C E S


M De Santis

V Langlais

K Schneider

X Torrelles

Growth-mode and interface structure of epitaxial ultrathin MgO/Ag(001) films

Keywords: magnesium oxide films, epitaxial growth, ultrathin films structure, surface x-ray diffraction

MgO ultrathin films are of great technological importance as electron tunneling barrier in electronics and spintronics, and as template for metallic clusters in catalysis and for molecular networks for 2D electronics. The wide band-gap of MgO allows for a very effective decoupling from the substrate. The films morphology and the detailed structure of the interface are crucial for applications, controlling the electronic transfer. Using surface x-ray diffraction, we studied the growth-mode and the structure of MgO/Ag(001) ultrathin films elaborated by reactive molecular beam epitaxy as function of the substrate temperature. We observed that deposition of about 1 monolayer results in an MgO(001) film in coherent epitaxy, with the oxygen atoms on top of silver as predicted by DFT calculations, and an interlayer distance at the interface of about 270 pm. Under well-defined conditions, a sharp MgO bilayer is formed covering a fraction of the substrate surface.

Introduction

Oxide surfaces and surface oxides play a fundamental role for a large number of important processes. All metals are generally covered by a thin native oxide film, and it is this oxide skin that governs their surface reactivity rather than the surface properties of the metal itself. In addition, oxides themselves are also used as catalysts and as supports for metallic cluster catalysts. The metal/oxide interfacial interactions that occur in the latter structures can have significative effects on catalyst performances.

The use of thin-films growth techniques to prepare model oxide surfaces is a field of fundamental science that has attracted more and more attention in the past decades [1]. The epitaxy of oxides on metals allows to synthetize crystalline films that in some cases can reach a high degree of perfection. The ability to engineer nearly perfect ultrathin oxide layers is a key issue for nanotechnological applications. From a fundamental point of view, their crystal structure allows to model and to reach a better understanding of the oxide and interfaces properties. In ultrathin films, the conductivity achieved through tunneling permits the use of electron-based techniques to investigate the structural and electronic properties of the films, interfaces and adatoms. Ultrathin insulating films provide also a precise electrostatic coupling and electron tunneling from a conducting substrate to a second electrode or to adsorbed nanostructures [2], which can be tuned choosing accurately the number of dielectric spacer layers [3].

Here we will discuss the growth of a well-defined and structurally ordered magnesium oxide (MgO) layer on top of the silver (001) surface. MgO is the insulating material of choice in spintronic and is important in catalysis as template for metallic clusters. Growth of non-polar (001) oriented MgO films results in general in a high crystalline quality and in high performances e.g. as tunneling barrier [4]. MgO thin films on Ag(001) surface is a prototypical model system for the understanding of the metal-oxide interface due to the small lattice mismatch between the oxide and the metal, which results in a coherent growth for ultrathin films [5,6]. Defect-free MgO (001) single crystal surface is practically inert, but low coordinated atoms at edge, step, corner, and kink sites can act as electrons donors. Moreover, reactivity can originate from the presence of trapped electrons in surface defect sites [7]. Electron transfer can be observed when molecules, metal atoms or clusters are deposited on the surface of an ultrathin film, even in the absence of defects. This is the result of electron tunneling through the thin oxide layer rending possible STM experiments [3]. It was shown both experimentally [8] and by DFT calculations [9] that Au atoms deposited on MgO(001) "thick" films are essentially neutral and keep their atomic character. On the contrary Au atoms adsorbed on a MgO ultrathin film are negatively charged [10,11]. Ultrathin MgO films themselves exhibit improved properties as catalyst for chemical reactions compared to bulk MgO, e. g. for water dissociation [12]. Charge transfer through the MgO layer not only promotes the catalytic activity, but also control the properties of hybrid inorganic/organic interfaces of interest for optoelectronic [13].

Moreover, ultrathin insulating layers inserted between a metallic substrate and deposited atoms or molecules are employed to improve their magnetic properties. Magnetic remanence was recently observed up to a temperature of 30 kelvin in individual holmium atoms adsorbed on ultrathin MgO(001) layers on Ag(001) [14]. This extraordinary stability was achieved thanks to the decoupling of the Ho spin from the underlying metal by the MgO tunnel barrier, and is function of its thickness. In a similar manner, giant hysteresis was observed for single-molecule magnets adsorbed on MgO/Ag(001) [15] Tailoring magnetic and catalytic properties and comparing experiments with theory require a precise control of the film growth and morphology down to the monolayer (ML) thickness and the realization of almost defect free layers. The electronic structure and morphology of ultrathin MgO films grown on Ag(001) under different conditions were studied by several groups using mainly XPS, STM or other scanning probe microscopy techniques [3,16,17,18,19,20]. Island formation was observed in a large temperature interval, spanning from 373 K to 673 K [21]. A decreasing of the island density and an increasing of their size was found up to 573 K. At this temperature, the flattest and largest MgO islands were reported. This represents a compromise between a sufficiently high mobility of Mg and MgO molecules and a not too high one of Ag adatoms. Further increasing the temperature at 673 K, MgO dendrites formation was observed. Pal et al. have shown that MgO films morphology depends not only on the growth parameters values (crystal temperature, metal flux, and oxygen partial pressure), but also on aftergrowth treatments [19]. They observed a bilayer growth for films elaborated at 773 K followed by usual cooling conditions, which switches to monolayer growth if the film is submitted to a slow cooling.

Here we use surface x-ray diffraction (SXRD) to study the structure and morphology of about 1 ML thick MgO films grown on Ag(001) in the 620-720 K temperature range. SXRD is a unique tool to investigate in particular the interface structure. This last one impacts various electronic properties, like e.g. the work function of the system, which is

Experimental methods

The present experiment was performed at the European Synchrotron Radiation Facility (ESRF, Grenoble, France) using the dedicated In Situ Nanostructures and Surfaces (INS2) apparatus of the BM32 beamline. The x-ray source is a bending magnet and the monochromator is a Si(111) double crystal, with the second crystal bent to give sagittal focusing on the sample. The vertical focusing is provided by two mirrors, resulting in a spot size of about 0.2×0.3 mm 2 . The experimental station consists of an ultrahigh vacuum chamber with base pressure in the low 10 -10 mbar range and fully equipped for sample preparation, which is mounted on a Z-axis diffractometer. Further degrees of freedom are available to align the sample at the centre of the diffractometer and with the surface normal parallel to the sample azimuthal rotation axis. The measurements were performed at a photon energy of 19.8 keV, and at a grazing angle of 0.48° (except of course for the reflectivity). It corresponds to about three times the Ag critical angle for total reflection at this energy. The polished surface of an Ag(001) single crystal (MaTeck, Jülich, Germany), with a 10 mm diameter and a miscut of less than 0.1°, was cleaned through successive cycles of Ar + ion sputtering and annealing at 800 K. The substrate temperature was measured using an infrared pyrometer. Cleanliness was checked by Auger electron spectroscopy (AES), such that all contaminants were below the detection limit. MgO was grown by reactive molecular beam epitaxy. Metallic Mg was evaporated by a water-cooled Knudsen cell, with the chamber backfilled with molecular oxygen at a partial pressure of 10 -6 mbar. The magnesium flux had been previously calibrated by using a quartz crystal microbalance. The deposition rate was about 1 ML every 5 min, where we define 1 ML as the number of atoms in an Ag(001) plane. In these conditions the oxygen pressure largely exceeds the one needed for stoichiometric growth (see e.g. ref. [23]). Several samples were grown by evaporating the same amount of Mg, corresponding to a nominal thickness of 0.8 ML, at a substrate temperature Ts of 620 K, 670 K and 720 K, respectively. After deposition, the samples were cooled down below 450 K in less than 5 min, and O2 pressure was removed while starting to cool down. The coverage and composition were checked by AES measuring the Ag MNN, O KLL, and Mg KLL Auger peaks at 356 eV, 513 eV and 1200 eV, respectively. Within the error bar, the intensity ratio of Mg and O peaks was the same for all samples, showing that the films have roughly the same stoichiometry. The Auger peaks of films grown at 620 K and 670 K had also roughly the same amplitude with respect to the substrate ones. Instead, the Mg and O peaks of the sample elaborated at 720 K were much weaker, showing that in this case most of Mg deposited is desorbed from the surface before a stable MgO layer can form. In previous studies [3,21,15], large flat islands with a low defects' density were observed on samples grown in close Mg flux and O2 pressure conditions and at a temperature of about 500 K, 573 K, and 625 K, respectively. Other groups used higher deposition temperatures applying a higher local oxygen pressure thanks to a doser [19,37]. SXRD measurements were performed at room temperature to solve the structure of the samples elaborated at 620 K and 670 K. The data were collected using a 2D detector (MAXIPIX, ESRF). SXRD is a powerful probe of the structure of crystalline surfaces. The diffracted intensity from a truncated crystal shows, as function of the momentum transfer, a sharp scattering line-shape parallel to the surface at integer (HK) indexes of the surface mesh, and a continuous distribution in the out-of-plane direction in-between Bragg peaks. This outof-plane intensity distribution is known as (HK) crystal truncation rod (CTR) [24]. A film, grown in registry with the substrate, gives a scattering contribution which interferes with the substrate CTR. The film structure can then be solved by a fine analysis of these CTR intensities [25].

The Ag(001) surface unit-cell is defined by the three basis vectors of a tetragonal body centred cell related to the fcc one by , , and , with =408.5 pm. Data were collected using the standard method for SXRD quantitative analysis. The diffractometer axes were settled to define a (HKL) node of the sample's reciprocal space, and the diffracted intensity was integrated while rocking the sample around the surface normal, which results in a ∆L portion of the CTR crossing the detector area. The structure factor amplitudes |FHKL| were then extracted by applying standard correction factors [26].

Finally, the data were averaged according to the substrate's P4mm symmetry and the agreement factor between the structure factors of equivalent reflections was used as a systematic error estimation for the final experimental error calculation [START_REF] Robinson | Handbook of Synchrotron Radiation[END_REF]. A set of 140 reflections, 83 of which nonequivalents, distributed along the (10), (11), and (20) CTRs, were collected for each sample, with an average agreement between the structure factors of equivalents reflections of 1.7% and 2.5% for the sample grown at 620 K and 670 K, respectively. 15 additional reflections were measured on the first sample along the specular (00) CTR, rocking in this case the incidence angle. The average MgO island size parallel to the surface was estimated by the reciprocal space width of the (10) CTR close to the antiphase condition, measured by a rocking scan at L=0.2, corresponding to about 50 nm. The very good agreement between equivalent reflections allows for a reliable structural refinement, which is done comparing the calculated structure-factor amplitudes for trial models with the measured ones and using a χ 2 minimization to find the best model and fit parameters. The data analysis discussed in the next section was performed using the ROD program described in ref. [START_REF] Vlieg | [END_REF]. Herein, all equations used in our calculations of the structure factor amplitude are reported.

Results and discussion

Figure 1 shows a comparison between the (10), (11), and (20) CTRs of the samples grown at 620 K and 670 K. The two datasets differ in the region in-between Bragg peaks, suggesting a different growth mode. The data of the sample grown at lower temperature show a weak bump in the middle between two Bragg peaks (full black circles). In SXRD this behavior is characteristic of a bilayer growth mode [29,30]. The bilayer structure was confirmed by the quantitative analysis. Two trial models were tested, both consisting of a (001) MgO film with rock salt structure in epitaxy on top of the silver surface. This film is compressed in plane to match the Ag lattice constant. The first model consists of a monatomic thick MgO layer, and resulted in quite a bad agreement between simulated structure factors and data collected on the sample grown at 620 K. The χ 2 is of 22 at least in this case. The agreement improved drastically for the second model, consisting of a MgO atomic bilayer (χ 2 of 3.5). The two models are sketched in figure 2 and the best fit curves are displayed in the upper panels of figure 3. In both models the interlayer spacings dAg1-Ag2, dAg2-Ag3, and the Debye-Waller parameters BAg1, BAg2, of the two Ag atomic plane closest to the interface were optimized, together with the interface spacing dMgO-Ag1, and a unique Debye parameter BMgO for Mg and O. The last one incorporates the MgO thermal vibrations plus its structural desorder. For the bilayer, the film interlayer spacing dMgO was also fitted. Finally, for both models, a roughness parameter β of the substrate [24], and the MgO covered surface fraction SMgO were optimized.

The final best fit parameters are given in table 1, and will be discussed in details in the following. Let's determine the chemisorption site first. As explained, SXRD intensity is the result of the interference between the substrate and the deposited film scattering amplitudes and is therefore sensitive to their relative position. In the framework of the bilayer model, we simulated the structure factors for several chemisorption sites. The best fit discussed above, with a χ 2 of 3.5, was obtained for oxygen on top of silver and Mg on hollow sites, as shown in figure 2. This agrees with the results obtained already in early DFT calculations [31] and with photoemission experiments. In the last ones, the MgO/Ag(001) electronic structure is explained with the O 2p -Ag 5sp levels hybridization [32]. The refinement of the same film structure but with magnesium on top of Ag at the interface resulted in a relatively good qualitative agreement (dotted curve in figure 3, blue online) but in a definitively worst quantitative one with a χ 2 of 7.2. In the lower panels of figure 3 the structure factor differences ∆|F| between measured and calculated structure factors are plotted for each rod and for the three model considered. They are compared Table 1. Best fit parameter values for the films structure obtained by deposition of about 0.8 ML of Mg on Ag(001) in 10 -6 mbar O2, at a substrate temperature of 620 K and 670 K. The model is sketched on the right panel of figure 2 (2 MgO ML with O on top of Ag), a third layer was added to fit the sample grown at 670 K. These values are compared to bulk and to the clean Ag(001) surface ones. dAg1-Ag2 and d'Ag1-Ag2 refer to the first Ag interlayer distance in MgO covered and uncovered regions, respectively. with the experimental error bars. Other interface geometries can be completely ruled out by the data analysis. This is the case for the configuration with both oxygen and magnesium atoms on bridge sites. This geometry was considered by DFT calculations, resulting in an intermediate energy in-between the former two [31]. In our SXRD analysis it gives a χ 2 of 24. We note here that the specular CTR instead is only sensitive to the interface distance and not to the chemisorption site.

The best fit bilayer model considered above results in an interface distance of about 280 pm, quite large compared to the calculated DFT values published in literature. However, up to now we fitted a unique top Ag layer position for MgO covered and uncovered regions. Indeed, we need to take into account the presence of two kind of domains, whose diffracted intensity sums up to give the measured CTRs. The first kind consists of MgO islands covered regions, the second one of uncovered Ag surface. We optimized then the first Ag interlayer spacing independently for these two regions, obtaining a better agreement with a χ 2 of 2.6. In MgO-free surface regions the spacing d'Ag1-Ag2 is contracted by more than 1% with respect to the bulk value. This result qualitatively agrees with previous experiments on clean Ag(001) surface [33] (see table 1). Instead, in MgO covered regions this distance is bulk-like. This has an impact on the best fit interface distance dMgO-Ag1, which is now equal to 272(4) pm. Such a value is in excellent agreement with the Ag-O distance of 270(15) pm obtained recently by EXAFS measurements [34], and with that one calculated by the same authors for a two-layer-thick MgO/Ag(001) film (271 pm).

But it is somewhat larger than the values of 239( 6) pm [35] and 251 pm [6] calculated previously by other groups. Indeed, it has been recently shown that calculated values spreads as function of the used functional, ranging from 249 pm to 270 pm [22]. DFT calculations indicate also a rumpling of a few pm of the interface with Mg ions closer to the surface Ag layer than O ones. Our SXRD data are not sensitive to this rumpling, which does not improve the agreement. The MgO covered surface fraction, SMgO-1,2, is of 0.38 (3), in good agreement with the calibrated deposited amount of 0.8 Mg ML. Fitting independently the coverages of the first and second MgO layer, SMgO-1 and SMgO-2, the same occupancy was found within an error bar of 3%. This shows that the film grown at 620 K has an almost ideal bilayer structure. The best fit substrate roughness β=0.05(1) corresponds to a R.M.S. value of about 50 pm [24]. This moderate roughness of the Ag substrate arises during the first stages of MgO epitaxial growth. The removal of Ag atoms from the substrate with the formation of monatomic islands, the formation of embedded MgO islands and carpet-like growth of the films were observed by STM [17,18,20]. Strain simulations performed on this system [34] revealed the existence of a small-size regime. Calculation showed that unsupported ultrathin Mg films are naturally compressed inplane, which reduces the misfit with the Ag substrate. The out-of-plane Mg-Mg nearest neighbour distance is also slightly compressed in calculations. EXAFS measurements from the same authors confirmed this trend. For a film thickness equivalent to that one of our samples, they found an in-plane Mg-Mg interatomic distance identical to the Ag-Ag one. They also found an out-of-plane Mg-Mg nearest neighbour distance of about 294 pm. This corresponds to a spacing between Mg layers of about 211 or 212 pm, slightly expanded compared to bulk. These results qualitatively agree with ours. We find a 2% expansion of the interlayer film spacing dMgO with respect to the bulk, which compensates only in part the in-plane compressive strain.

Finally, we have to emphasize that the same model fits at the same time the reflectivity and the non-specular CTRs. The former is only sensitive to the electronic density perpendicular to the surface, while the latter are sensitive to films with the same in-plane lattice constant as the substrate. We can therefore exclude the presence of any significative amount of relaxed islands.

The discrepancy between the interface distance obtained here and most of the DFT calculations is in favor of the presence of extra oxygen at the interface. Accumulation of oxygen at the interface was recently demostrated, under well defined growing conditions, by a carefull comparison of STM data and DFT calculations [36]. Oxygen atoms would be located in the hollow site of the Ag top layer. The site occupancy was estimated at 10-20% for experimental conditions close to ours [37]. Calculations performed for 1 ML MgO/Ag(001), with and without the presence of 0.25 ML interface interstitial oxygen, resulted in an interface distance of about 270 pm and 250 pm, respectively [38]. This drove us to fit our SXRD data with a trial model including oxygen in this interface site. We obtain an occupancy of 0.20 (6), and a position shifted outward of the Ag atomic plane by about 40 pm (to compare with about 50 pm calculated in ref. [38]), while the other parameters do not change within the error bar. However, the contribution of this interstitial oxygen to the structure factor is very weak. The χ 2 decreases only by 0.1 (to 2.5), and therefore we can neither confirm nor exclude its presence.

CTRs measured on the film grown at 670 K suggest a different morphology (figure 1). However, the quantitative analysis shows quite a bad agreement of data with a monolayer thick MgO film model (χ 2 larger than 10) meaning that the morphology is more complex. The agreement improves using the same bilayer model as for the film grown at 620 K (χ 2 ~ 5). This agreement is still unsatisfactory and the simulation shows a bump along the CTRs in the middle between Bragg peaks, which is not observed in the data (see figure 4). To fit them, a model consisting of three MgO layers needs to be considered. In this case an excellent agreement is obtained (χ 2 =1.7, see figure 4). To reduce the fitting parameters, the Ag interlayer spacings of both MgO covered and uncovered regions were kept fixed to the value found for the sample grown at 620 K. Only the interface and a unique MgO-MgO interlayer spacing were optimized, giving identical results than for the 620 K grown sample, within the error bar. The only difference at 670 K is that, on top of a MgO bilayer, a third incomplete MgO layer is present, which covers almost 20% of the sample surface. (SMgO-3=0.17 (2)). This shows how sensitive the film structure is to the precise growing conditions.

Summary and conclusions

We have performed a SXRD investigation of the morphology and interface structure of MgO(001)/Ag(001) films about 1 ML thick. The morphology has already been investigated by several groups mainly using STM. Results are function of the specific growing conditions. Islands are formed whose size depends on the substrate temperature during elaboration [21]. Their thickness is often difficult to establish, due also to the presence of embedded MgO. Combining AFM and STM, it was shown that deposition of ~2 ML MgO/Ag(001) at Ts = 480 K results in films with coexisting 1 ML, 2 ML and 3 ML thick regions [18]. STM measurements as function of temperature support a bilayer growth mode at 1 ML coverage [21]. Another group found a transition between a multilayer structure for films grown at Ts = 500 K and monolayer islands for samples elaborated at 450 K [36]. The same authors observed nearly perfect MgO monolayers by slow cooling films grown at Ts=773 K. Cooling speed is then an essential parameter in the film growth [19]. This also supports the interpretation that multilayer growth is the thermodynamically stable phase above 500 K, which is preserved at room temperature by cooling the sample quickly enough. Here we demonstrate that reactive deposition of 0.8 Mg ML at Ts=620 K, followed by a relatively fast cooling, results in an almost perfect bilayer growth mode, with islands of ~50 nm average size.

The ability of tailoring the film thickness is essential in several applications, tuning the tunnelling current between adlayers and the substrate.

SXRD is also an ideal tool to investigate the interface structure. In this way, we could provide a direct confirmation that oxygen atoms of the film are on top of silver, as overseen by DFT calculations and indirectly confirmed by photoemission experiments. We find an interface Ag-MgO interlayer distance of 272(4) pm, which is relatively large compared to DFT calculations. This distance supports the presence of additional oxygen at the interface, which we could not however confirm directly, and has an important impact on its electronic properties, and in particular on the work function.

Figure 1 .

 1 Figure 1. Experimental MgO/Ag(001) CTRs with error bar, measured after depostion of about 0.8 ML of Mg on Ag(001) in 10 -6 mbar O2 at Ts=620 K (filled black circles) and at 670 K (crosses, red online). The continuous lines are plotted for eyes guide.

Figure 2 .

 2 Figure 2. Sketches of the monolayer (left) and bilayer (right) models for MgO/Ag(001). On the right, the fitting distance and coverage parameters are indicated. dAg1-Ag2 and d'Ag1-Ag2 represent the first Ag-Ag interlayer distance in MgO covered and uncovered regions, respectively.

Figure 3 .

 3 Figure 3. Upper panels: experimental MgO/Ag(001) CTRs, with error bars, for the sample grown at Ts=620 K (filled circles) and best fits for the MgO monolayer model (dashed curves, red online), the bilayer model with magnesium on top of surface Ag sites (dotted curves, blue online) and the best model with oxygen on top (black continuous lines). The error bar was increased very close to Bragg peaks to consider a systematic error, which is intrinsic in SXRD measurements collected in such a position of the rod. Lower panels: structure factor differences ∆|F| between measured and calculated structure factors for the corresponding models. They are compared with experimental error bars.

Figure 4 .

 4 Figure 4. Experimental MgO/Ag(001) CTRs for the sample grown at Ts=670 K (filled circles), fit with the same 2 ML model of the sample grown at 620 K (dotted red lines) and best fit with a model including a 3 rd incomplete MgO layer (black continuous lines).

Acknowledgements

Financial support through ANR EQUIPEX ANR-11-EQPX-0010 and beam time at the French CRG BM32 beamline of the ESRF are acknowledged. KS, VL and XT acknowledge the EU Fund for Regional Development (FEDER) through the Interreg-POCTEFA program of the Project EFA194/16/TNSI.