Monique Tillard
email: mtillard@univ-montp2.fr

Claude Belin Agrégats

Investigation in the Ga-rich side of the Mn-Ga system: Synthesis and crystal structure of MnGa 4 and MnGa 5-x (x ~ 0.15)

Keywords: A-manganese gallides, B-phase transformation, B-electronic structure, E-abinitio calculations, F-X-ray diffraction

Crystalline compounds MnGa4 and MnGa5-x were successfully prepared by direct synthesis from the elements. The crystal structure of MnGa4 was solved and refined in the cubic Im 3m space group, a = 5.5941(2) Å, Z = 2. The compound MnGa5-x was found under two variants: MnGa4.96, tetragonal, P4/mnc with a = 6.3395(2), c = 10.0275(7) Å and MnGa4.83, triclinic, P 1 with a = 6.3047(5), b = 9.9441(9), c = 18.901(2) Å, α = 90.382(7), β = 90.766(6), γ = 90.356(7) °. The latter can be viewed as a superstructure deriving from the tetragonal form by tripling one parameter of the cell. The structures of MnGa4 and MnGa5-x are built on the basis of a three-dimensional packing of Mn@Ga8 units, cubic in MnGa4 and square antiprismatic in MnGa5-x. In the latter these units are more or less distorted and capped by an extra gallium atom.

Introduction

Among intermetallic alloys combining manganese and gallium, those formed with addition of nickel have attracted significant attention as magnetic shape memory materials, like the Heusler phase Ni2MnGa [1-5]. Ferromagnetic metal/semiconductor layered structures MnGa/GaAs or MnGa/GaN have interesting applications in spintronic devices such as light emitting diodes [6][7][8][9]. Due to the particular nature of the elements Mn and Ga, both having several allotropic forms with rather complex structures, their combinations are of special interest and a lot of their binary alloys have been cited in literature. A pioneering approach based on thermal analysis and X-ray studies, has unveiled the richness of the Mn-Ga binary system, found to contain not less than ten intermediate phases [10]. The unit cell parameters and space groups have been given for six of these phases: hexagonal ε-Mn2Ga, tetragonal ζ1-Mn2Ga, rhombohedral η-MnxGa (x = 1.1 to 1.6), tetragonal Mn2Ga5, cubic MnGa4 and orthorhombic MnGa6. A short but informative report, published several years later, described a compound having the same orthorhombic cell as MnGa6 but with a lesser gallium content, it was identified as MnGa5.2 [11]. A few additional contributions were inserted in the redrawn phase diagram published several years later in the second edition of Binary alloy phase diagrams [START_REF] Massalski | Binary alloy phase diagrams[END_REF]. Curiously, at that time, the compound MnGa4 was not mentioned in the diagram. A look at the Pearson Crystal Structure Database reveals that at least thirteen different structures are listed for Mn-Ga binary compounds [START_REF] Villars | Pearson's Crystal Data : crystal structure database for inorganic compounds release 2009/10[END_REF], but some of them are not very well characterized. Actually, most of these structures were determined before 1988 from powdered samples except four of them that were more recently determined from single crystals: rhombohedral MnGa [START_REF] Gourdon | [END_REF], tetragonal Mn3Ga5 [15], monoclinic Mn123Ga137 [16] and cubic MnGa4 [START_REF] Dolotko | Coll. Abs. 9th Int. Conf. Crystal Chem. Intermet. Compd[END_REF]. The latter was qualified of incompletely published work whereas the structure of MnGa4 was reported elsewhere in a general study of the Hume-Rothery intermetallic compounds having the PtHg4 structure [START_REF] Haussermann | [END_REF]. Some of the Mn-Ga binary compounds have been described as quasicrystal approximants. This is precisely the case for orthorhombic Mn3Ga5 and Mn5Ga7, also for Mn5Ga6 (with two closely related orthorhombic cells) and MnGa (two orthorhombic and monoclinic related forms), compounds characterized by means of transmission electron microscopy [19]. Such intermetallic compounds were found to display a pseudo ten-fold distribution of strong diffraction spots and are then considered as crystalline approximants of a quasicrystal containing 45-50 at. % Mn. The latter, discovered in the same work, is a decagonal quasicrystal that displays periodicity along the ten-fold axis. Subsequently, a structural model based on HREM studies, was proposed for the crystalline compound Mn5Ga7 found to coexist with the decagonal quasicrystal in the Mn42Ga58 alloy [20]. The similarity with the Al-Mn system, in which the first quasicrystal was discovered [21], is most probably at the origin of a renewed interest for the Mn-Ga system.

The first aim of this work was to prepare the Ga-richer phase MnGa6 but so far, attempts have not succeeded. Instead has been obtained a phase identified as MnGa5-x, x ~ 0.15, the preparation and crystal structure of which are reported below, next to the synthesis and the complete structural determination of MnGa4.

Experimental section

The elements Mn (powder, Fluka > 99%) and Ga (Rhone Poulenc, 6N) were used without further purification. Reagents taken in the appropriate proportions were mixed in weld-sealed tantalum tubes protected from oxidation inside evacuated stainless steel jackets. According to the already known phase diagram, appropriate thermal treatments were applied to samples in a classic horizontal tubular furnace. Homogenization of the melts was obtained by a slow and continuous rotation of the tantalum tube on its axis.

The compound MnGa4 was obtained from a melt containing 18 % at. Mn, heated at 700°C for 15 hours and subsequently quenched. Some small crushed pieces displayed crystallinity so that the structure could be determined from single crystal X-ray data. Their EDX analyses were found in very good agreement with the compound formula.

Because the Ga-rich part of the phase diagram is uncertain, several alloys were prepared with compositions ranging from 0-20 at. % Mn, in this domain any excess of gallium would play the role of metallic flux and then be beneficial to a better crystallization. Starting from a mixture containing 14 at. % Mn, heated and homogenized at 380°C and then slowly cooled at the rate of 10°/h, a crystallized product was obtained. Several crystalline pieces previously checked by X-ray diffraction were analyzed by EDX spectroscopy. With a Ga/Mn ratio of ~4.9, their composition significantly differs from MnGa6 and is rather close to MnGa5. Structural studies of these crystals (type A) revealed some unusual extinction conditions within the X-ray diffraction data. Hence, modified thermal treatments (higher temperature up to 500°C and different cooling rates) intended to improve the crystallization step were used, but crystals then obtained still displayed the same characteristics.

A Pb-excess was added as a metallic flux to a Mn-Ga mixture containing 14 at. % Mn which was heated to 600°C before cooling. A few crystals were grown on the surface of the Pb ingot, they were picked to be analyzed by EDX spectroscopy and were found Pbfree. Since they display rather different crystallographic features, they were designated as type B crystals. An other alloy was prepared at 10 at. % Mn and heated without flux at 570°C. From the analysis of some crystalline pieces selected from this preparation, it appears that it also contains type B crystals. The EDX analysis of several type B crystals selected from either experiment (with and without flux) and previously checked by Xray diffraction, gave a gallium-to-manganese ratio of ~4.9 indicating that type B crystals have the same composition as type A crystals.

The most regular-shaped and best diffracting crystals of each type were chosen for X-ray diffraction intensity measurements. For this purpose, crystals were glued at the tip of a polymer fiber and mounted on the Xcalibur CCD (Oxford diffraction) four-circle diffractometer that uses MoK radiation. Details on the single crystal data collection and structural refinements are given in table 1. The powder X-ray diffraction patterns were recorded on a Philips analytical X'pert diffractometer (copper tube and hybrid monochromator).

It was reported that the structure of MnGa4 belongs to the PtHg4-type [START_REF] Haussermann | [END_REF]. In the present work, it was refined both from powder pattern and from single crystal data. The powder pattern of MnGa4 was completely indexed using program Jana2006 [START_REF] Petricek | The crystallographic computing system[END_REF] with a I-centered cubic cell of 5.5942(3) Å. The single crystals, with a cell parameter of 5.5941 (2) Å, confirmed the cubic symmetry and the Im 3m space group. Unit cell parameters are in very good agreement with those previously reported [START_REF] Haussermann | [END_REF]. The 2964 reflections (including symmetry equivalent and redundant) recorded within the complete diffraction sphere ( from 5.15 to 35.61°) from the single crystal were used to solve and refine the structure with SHELX programs [START_REF] Sheldrick | SHELXS 97. A Program for Crystal Structures Solution[END_REF][START_REF] Sheldrick | SHELXL 97: A Program for Refining Crystal Structures[END_REF]. The data set was corrected for the absorption effects ( = 33.6 mm -1 ) using the procedure included in the CrysAlis software [START_REF]CrysAlis'Red' 171 software package[END_REF]. After merging equivalent reflections, the final data set used for the refinement of atomic positions and displacement parameters contains 57 unique reflections observed according to the criterion I > 2(I). The refined parameters are given in table 2. [11] are drawn in red.

Crystals of MnGa5-x type

The overall data could be suitably indexed using two components with an orthorhombic unit cell of parameters a = 6.30, b = 18.89, c = 10.03 Å and the data did not display any centering nor special extinction conditions. However, the angular cell parameters significantly deviate from the 90° angle, this was first attributed to the bad quality of the crystal but it was observed systematically for all the checked crystals. In fact, fine indexation indicates the triclinic cell of parameters a = 6.3047(5), b = 18.9013 (15), c = 9.9441(9) Å, α = 90.382 (7), b = 90.766 (6), γ = 90.356(7) ° for type A crystals (figure 1, green-filled cell). Note that the powder pattern recorded for this alloy can also be properly indexed in the triclinic cell while too many diffraction lines are discarded when indexed using the tetragonal cell.

The reflections recorded within the complete diffraction sphere ( from 2.96 to 33.00 °) were first corrected for the absorption effects ( = 35.4 mm -1 ) in the tetragonal apparent cell of parameters a = 18.9 and c = 9.9 Å. The reflections were divided in two sets: hkl reflections with indices k = 3n which are common to the two twin components, were assigned batch number 2 and hkl reflections with indices k  3n (twin component 1) batch number 1. The resulting data set of 38305 reflections (8777 unique of which 2942 observed) was then reindexed in the true triclinic cell and the structure solution was found in the centrosymmetric space group P 1 . Structural refinements carried out using SHELXL97 with the HKLF5 instruction and one BASF scale parameter led to a R-factor of 8.47 % and the twin fraction converged to 0.634. The refined parameters are given in table 3 and a selection of interatomic distances in table 4.

Crystals of MnGa5-x type B displayed the perfect tetragonal symmetry with parameters a = 6.3395(2), c = 10.0275(7) Å. Although the existence of close metric relationships with type A crystals might suggest an undetected larger cell for type B, the recorded data for several crystals did not contain any additional diffraction spots regardless of the exposure time. The 9938 recorded reflections (including symmetry equivalent and redundant) within the complete diffraction sphere ( from 3.80 to 32.04) did not reveal any centering of the cell. Systematic extinctions were observed for 0kl (k+l odd) and hhl (l odd) reflections indicating the possible space groups P4/mnc and P4nc. Data were corrected for absorption effects ( = 35.6 mm -1 ) and merged into 373 unique reflections used for the final refinement. Atomic positions and displacement parameters (table 5) were refined to R1 = 3.76 % in the centrosymmetric space group P4/mnc. The main selected interatomic distances are listed in table 6.

Differential thermal analyses (DTA) were performed with a Setaram Labsys analyzer for samples of MnGa4 and MnGa5-x. The crystalline powders prepared as described above were inserted in homemade niobium containers which where then sealed under argon atmosphere.

Calibration accuracy was verified by measuring the melting points of pure elements (Al, Ag) indicating a maximal standard deviation of 2 °C. For the MnGa4 sample, four endothermal events are observed on the heating curve. The first one, of weak intensity, at about 372 °C was attributed to the peritectic decomposition of MnGa5-x (present in small quantity as a side compound in the sample). The second peak at 397 °C corresponds to the peritectic decomposition of MnGa4. The two following events that occur at higher temperatures, 496 and 535 °C, are characteristic of the peritectic invariants associated with MnGa3 and Mn2Ga5 compounds, respectively. The end of melting (liquidus curve) was observed at about 600 °C.

On the other hand, the temperature behavior of MnGa5-x samples was also analyzed. The heating curves displayed four endothermal events at 372, 397, 498 and 535 °C, the end of melting could be detected slightly below 600 °C. The first thermal event at 372 °C was attributed to the peritectic decomposition of the compound MnGa5-x while the three following events are related to the successive peritectic decompositions of compounds MnGa4, MnGa3 and Mn2Ga5. In the light of these results, the Ga-rich part of the binary diagram was redrawn and a schematic representation is proposed in figure 2. It should be noted that, when heating the MnGa5-x sample, an additional endothermal event of rather small amplitude was observed at a temperature close to 205 °C that could be the sign of the polymorphic phase transition from triclinic to tetragonal MnGa5-x. Calculations were performed at the DFT level with the code CASTEP [START_REF] Kresse | [END_REF]27] using the gradient-corrected GGA-PW91 exchange and correlation functional [28]. CASTEP uses plane-wave basis sets to treat valence electrons and pseudo potentials to approximate the potential field of ion cores. Ultra-soft pseudo potentials (USPP) generated for each element according to the Vanderbilt [29] scheme were chosen. Kinetic cut-off energies were set at fine qualities (300 eV) and Monkhorst-Pack uniform grids of automatically generated k-points were used [30].

Results and Discussion

The crystal structure of compound MnGa4 is represented in figure 3. The Ga atoms located at 8c special positions are arranged at the vertices of a cube (Ga-Ga distance of 2.797 Å) centered by Mn atom (2a special position), the Mn-Ga distance is 2.422 Å. The resulting cubic Mn-centered Ga8 units (Mn@Ga8) are packed within a three-dimensional network by sharing all their corners. Figure 3: The MnGa4 cubic unit cell emphasizing packing of cubic Mn@Ga8 units.

The compound MnGa5-x was found to display either triclinic or tetragonal unit cells. For the triclinic type A and tetragonal type B crystals, structural refinements led to the very close refined compositions MnGa4.83 and MnGa4.96, respectively. The three-dimensional atomic arrangement mainly proceeds through the packing of distorted square antiprisms of gallium centered by Mn atoms. Though different in geometry from the cubic units in MnGa4, the square antiprismatic units encountered in the MnGa5-x structures can also be formulated Mn@Ga8. Through square face sharing, two Mn@Ga8 antiprisms form a "double drum" unit, which is capped by gallium atoms on its remaining free square faces to finally result into a Mn2@Ga14 oblong unit. The Mn atoms are separated by 3.086 Å in the tetragonal structure of MnGa5-x and the Mn-Mn interatomic distances range from 3.043 to 3.102 Å in the triclinic form. The structure of compound MnGa5-x can be described as a three-dimensional stacking along the c-axis of more or less distorted Mn2@Ga14 oblong units that share basal vertices and are interlinked through waist atoms.

Figure 4: Atomic arrangement in the tetragonal MnGa4.96 (type B) unit cell emphasizing the Mn2@Ga14 polyhedra (fused and capped Mn@Ga8 antiprisms).

Beyond symmetry considerations, the atomic arrangement is very close in the two forms of MnGa5-x. The main difference between them stems from the occurrence in the tetragonal (type B) structure of some atomic disorder in the capping region (figure 4).

In the course of the structure determination of type B tetragonal crystal, the atoms involved in the Mn@Ga8 square antiprisms were located first and the Fourier synthesis subsequent to the refinement of their atomic parameters revealed two remaining positions for the capping atoms. Actually, these positions are located near the origin of the cell, either on the 4-fold axis at 4e special position (0,0,z) or slightly apart from the axis at a 16i general position and they were assigned to gallium atoms Ga(4) and Ga(5), respectively. Since atoms placed at these sites would be too close, partial site occupation factors had to be taken into account.

According to disorder, the 16i general position cannot be filled by more than 25 %, furthermore it should be empty when an atom is present at 4e position. This restrictive condition was tuned by a constrained refinement of Ga(4) and Ga(5) site occupation factors.

Even when freely refined, these occupations did not deviate much from their constrained values. The final refined composition is then MnGa4.96(2) for the tetragonal structure. As expected, expanded ellipsoids featuring the disorder were obtained when the displacement parameters of these atoms were refined anisotropically. Atom Ga(4) displayed an ellipsoid elongation along the c-axis (U33 ≈ 5  U11 = 5  U22) while the Ga(5) ellipsoid was found elongated within the ab plane and practically along the b-axis direction (U22 ≈ 4  U11 ≈ 11  U33). In summary, the tetragonal structure of MnGa4.96 consists of Mn2@Ga14 building blocks three dimensionally packed sharing Ga(2) basal vertices and interlinked through Ga(1) waist atoms. Moreover, depending upon the local disorder, these units achieve their coordination through capping, with either Ga(4) apex sharing or Ga(5)-Ga(5) interlinking (figure 5).

Owing to the lower global symmetry, the triclinic structure of MnGa4.83 is built of somewhat distorted Mn2@Ga14 units that share basal vertices and are interlinked through waist and capping atoms (figure 6). Excepted at center of drawing, the interpolyhedral bonding was omitted for clarity According to the crystallographic results and the very close compositions for the two kinds of crystals studied in this work, we assert that compound MnGa5-x may exist under two polymorphs, depending on subtle variations in the synthesis conditions. The tetragonal structure corresponds to the high temperature form stabilized under specific conditions while the low temperature triclinic structure is obtained by relaxation of packing constraints at the expense of a symmetry loss. This assumption supported by thermal analyses of present work is in agreement with the announced polymorphism for a compound labeled Mn6Ga29 (MnGa4.83) which was cited recently in conference abstracts [START_REF] Antonyshyn | 12th European Conference on Solid State Chemistry (ECSSC XII)[END_REF][START_REF] Antonyshyn | 18th International Conference on Solid Compounds of Transition Elements (SCTE)[END_REF]. Furthermore, it has long been known that crystals having high-low temperature transformations possess related symmetries, which allow the main structural framework to be retained. Some symmetry elements are lost in the low temperature form so that the transformation frequently would give rise to twinning [START_REF] Buerger | [END_REF]. [18] while V8Ga41 contains hybrid (half cube-half icosahedra) V@Ga10 polyhedra [35] and FeGa3 is built of Fe-capped distorted Fe@Ga8 square antiprisms [36]. On the other hand, it is worth recalling that MnGa5.2 diffraction patterns contained some superstructure reflections and special pseudo extinctions [11]. Assuming that a 3  3  1 superstructure is built from the C-centered orthorhombic cell of parameters a = 8.81, b = 8.95 and c = 9.94 Å (figure 1, red lines), the pseudo-extinctions were attributed by authors to the non filling (or the only filling) of some special sites in their structure but no further structural characterization has been given. A special attention should be paid to the position of these superstructure reflections which were observed in rows parallel to the [110] and [11 0] directions. In order to analyze bonding in the Mn-Ga binary compounds obtained in present work, geometry optimizations were carried out by varying the cell parameters and the atomic positions. During the optimization, unit cell parameters did not deviate by more than 1.7% from the experimental values. The calculated CASTEP band structures indicate a metallic character for the two compounds MnGa4 and MnGa5-x. As can be seen in figure 7 where are represented the partial densities of states (PDOS) calculated for MnGa4 and for the two forms of MnGa5-x, atomic contributions in the total density of states (DOS) at Fermi level mostly involve the Ga 4p and Mn 3d states. This is in very good agreement with FLAPW calculations showing strong covalent bonding between Mn and Ga atoms [START_REF] Haussermann | [END_REF]. The highest positive values for the overlap populations are calculated for Mn-Ga atomic pairs in the two compounds MnGa4 and MnGa5-x. This result indicates that bonding therein is mainly achieved through Mn-Ga bonds.

It is quite usual that gallium and aluminum combine similarly with other elements but

It is now interesting to check present results against those already reported in

The reciprocal lattice of

Conclusion

The structural determinations of MnGa4 and MnGa5-x bring new insights in the knowledge of the gallium rich part of the Mn-Ga binary system. MnGa4 and MnGa5-x display cubic and tetragonal/triclinic structures, respectively. These Ga-rich structures are characterized by the presence of "isolated" manganese atoms enclosed in gallium polyhedra. While the manganese atoms are placed in a cubic environment of gallium in MnGa4, the atomic arrangement is somewhat more complex in the Ga-richer MnGa4.96 and MnGa4.83. The latter crystals displaying very close stoichiometries were considered as two structural forms, correlated by a superstructure-type relationship, of the MnGa5-x compound. In the structure of MnGa5-x, the manganese atoms are surrounded by gallium neighbors arranged at vertices of a capped square-antiprism. Remarkable is the absence of structural analogy with the aluminum-rich compounds in which Mn atoms are located inside coordination polyhedra whose geometries mainly derive from the isosahedron. In the gallium-rich compounds studied in this work, bonding mainly proceeds through Mn-Ga interactions, a result which validates the description of their structures in terms of Mn-centered polyhedral units. The observation of rather high electron density at interpolyhedral linking is an additional argument for such a description of MnGa5-x compound where some covalence locally occurs in a material predicted with a metallic behavior by DFT calculations. [11] are drawn in red. Excepted at center of drawing, the interpolyhedral bonding was omitted for clarity

FIGURE CAPTIONS

  A might be indexed in a tetragonal cell with parameters a = 6.3, c = 9.9 Å but such indexation would leave unassigned a large number of intermediate reflections occurring at reciprocal lattice axes. Instead, all these extra diffractions are well indexed in the 3  3  1 tetragonal super-cell of parameters a = 18.9 Å and c = 9.9 Å (figure 1, blue-filled cells). Yet, examination of the reciprocal lattice revealed strange extinctions of the hkl reflections having h  3n and k  3n, suggesting the occurrence of twinning. The first structural model found in this tetragonal super-cell considered as untwinned, refined poorly to a R factor of 30 %. At this stage, a thorough interpretation of the reciprocal lattice was necessary. Actually, this puzzling diffraction figure results from the twinning of an orthorhombic crystal having two unit cell parameters in the b/a special ratio of 3. By a 4-fold rotation around c-axis, the reciprocal lattices of twin components superimpose and the resulting composite reciprocal lattice then simulates a higher tetragonal symmetry.

Figure 1 :

 1 Figure 1: The reciprocal lattice projected along the 9.9Å parameter and the different unit cells mentioned in this paper. The tetragonal cell (a = 6.34, c = 10.03 Å, type B crystals) and its 3  3  1 super-cell are drawn as large and small blue-filled squares, respectively. The greenfilled rectangle refers to the triclinic cell (a = 6.30, b = 18.90, c = 9.94 Å, α = 90.38, β = 90.77, γ = 90.36 °, twin 1 component, type A crystals). The C-centered orthorhombic cell (a = 8.81, b = 8.95, c = 9.94 Å) and its 3  3  1 super-cell given for MnGa6 in reference[11]

Figure 2 :

 2 Figure 2: Schematic representation of the Ga-rich side of the Ga-Mn binary diagram.

Figure 5 :

 5 Figure 5: The tetragonal (type B) structure of MnGa5-x: apex-sharing or interlinked Mn2@Ga14 units depending upon the local disorder.

Figure 6 :

 6 Figure 6: Packing of Mn2@Ga14 polyhedra in the triclinic unit cell of MnGa4.83 (type A).

  , with manganese, they form rather different binary compounds. In addition to the orthorhombic structure of MnAl6, are known those of cubic MnAl12 and MnAl4.87 as well as those of hexagonal MnAl4.33 and MnAl4.11 (reported as  and -MnAl4) but no MnGa4 aluminum analogue has been reported. Besides, the existence of a MnAl4 compound having the PtHg4 type was excluded by theoretical investigations [18]. With an Al/Mn ratio of 4.87, very close to the Ga/Mn ratio in MnGa5-x, the compound Mn8Al39 yet crystallizes in a very different cubic structure where Mn atoms lie at centers of Al icosahedra (full Al12, atom deficient Al11 or Al10) [34]. For the gallium combinations involving transition metals close to manganese such as vanadium, chromium and iron, a look at the reported structures indicates that the gallium richest compounds are V8Ga41, CrGa4 and FeGa3, respectively. CrGa4 is isostructural to MnGa4

  literature for the Ga-richest binary compounds of manganese. The Ga-rich compound identified as MnGa6 by Meissner et al. was reported to display orthorhombic symmetry with Cccm space group and unit cell parameters a = 8.81, b = 8.95, c = 9.94 Å [10]. Later, Girgis and Schulz obtained a Ga-rich compound whose composition, MnGa5.2, was established by chemical analysis [11]. This compound was reported to crystallize as either prismatic or needle-shaped single crystals with the same crystal parameters as MnGa6. Then authors assumed this compound to be a gallium analogue of the compound MnAl6 characterized with Cmcm space group (a = 6.498, b = 7.540, c = 8.858 Å), but the relationship between their cell parameters is not obvious.

  MnGa5-x crystals is represented in figure 1, it would be indexed within a C-centered orthorhombic cell of parameters a = 8.81, b = 8.95, c = 9.94 Å (red lines) which is very similar to that previously given for MnGa5.2. It is then straightforward to establish a relation between this orthorhombic cell and the unit cells determined in present work for the two MnGa5-x polymorphs: tetragonal (a = 6.34, c = 10.03 Å, blue lines) and triclinic (a = 6.30, b = 18.90, c = 9.94 Å, α = 90.4, β = 90.8, γ = 90.4 °, green lines). Actually, twinning of MnGa5-x triclinic crystals provides additional diffraction spots that occur along the reciprocal axes of the triclinic cell. These axes coincide with the diagonals of the C-centered orthorhombic cell defined just above. It might be possible that the MnGa5.2 crystals obtained by Girgis and Schulz [11] are twinned which would explain the additional spots observed along the diagonals of the orthorhombic cell and the curious extinctions incorrectly attributed to a superstructure. Consequently, it is reasonable to believe that we have obtained the same phase as those previously identified as "MnGa5.2" by Girgis or MnGa6 by Meissner. This phase would undergo a polymorphic transformation between two closely related (high and low temperature) crystalline forms and would have a narrow composition domain. Furthermore, polymorphism is also reported for the compound Mn6Ga29 (MnGa4.83) [32] which is triclinic below 145 °C, then monoclinic and finally transforms into tetragonal at 210°C [37]. The triclinic and tetragonal cells given for Mn6Ga29 are very close to that of triclinic and tetragonal cells of MnGa5-x. Although displaying a lower symmetry (P4/m), the tetragonal form of Mn6Ga29 looks like the tetragonal P4/mnc MnGa5-x [38]. No sign of phase transformation was detected for MnGa5-x around 145 °C, nevertheless the existence of a monoclinic form, similar to monoclinic Mn6Ga29 (a = 6.29, b = 9.97, c = 31.43 Å, β = 90.8 °) claimed to exist in the range 145 -210 °C [32], cannot be excluded. Note that we have learnt from a reviewer that Bostrom's dissertation reports work about the Mn-Ga binary system [39]. A Ga-rich compound identified as -MnGa6 was obtained either as multi-crystalline fibers or as crystals twinned at the micoscopic level. Its crystal structure, mainly based on capped antiprisms, was described in monoclinic P2 space group (a = 6.295, b = 9.964, c = 18.931 Å, β = 90.88 °). Mn and Ga atoms were not differentiated, several atoms were refined on split positions and temperature factors were not entirely satisfactory so that author believes its structure could be an approximation of a real incommensurate structure. Is is likely that an incorrect symmetry attribution, monoclinic instead of triclinic, would also explain the rather poor quality of this structural determination and very probably, -MnGa6 is the same compound as Mn6Ga29 and MnGa5-x.

Figure 7 :

 7 Figure 7: Castep partial densities of states (PDOS) calculated for MnGa4, tetragonal MnGa5-x and triclinic MnGa5-x. The total DOS at Fermi level mainly results from gallium 4p and manganese 3d contributions.

Figure 8 :

 8 Figure 8: The electron density difference calculated with CASTEP for MnGa4 (left) and triclinic MnGa5-x (right). High densities, indicative of bond formation, are found at Mn-Ga atomic pairs and between the Ga atoms involved in interpolyhedral bonding in MnGa5-x

Figure 1 :

 1 Figure 1: The reciprocal lattice projected along the 9.9Å parameter and the different unit cells mentioned in this paper. The tetragonal cell (a = 6.34, c = 10.03 Å, type B crystals) and its 3  3  1 super-cell are drawn as large and small blue-filled squares, respectively. The greenfilled rectangle refers to the triclinic cell (a = 6.30, b = 18.90, c = 9.94 Å, α = 90.38, β = 90.77, γ = 90.36 °, twin 1 component, type A crystals). The C-centered orthorhombic cell (a = 8.81, b = 8.95, c = 9.94 Å) and its 3  3  1 super-cell given for MnGa6 in reference[11]

Figure 2 :

 2 Figure 2: Schematic representation of the Ga-rich side of the Ga-Mn binary diagram.

Figure 3 :

 3 Figure3: The MnGa4 cubic unit cell emphasizing packing of cubic Mn@Ga8 units.

Figure 4 :

 4 Figure 4: Atomic arrangement in the tetragonal MnGa4.96 (type B) unit cell emphasizing theMn2@Ga14 polyhedra (fused and capped Mn@Ga8 antiprisms).

Figure 5 :

 5 Figure 5: The tetragonal (type B) structure of MnGa5-x: apex-sharing or interlinked Mn2@Ga14 units depending upon the local disorder.

Figure 6 :

 6 Figure 6: Packing of Mn2@Ga14 polyhedra in the triclinic unit cell of MnGa4.83 (type A).

Figure 7 :

 7 Figure 7: Castep partial densities of states (PDOS) calculated for MnGa4, tetragonal MnGa5-x and triclinic MnGa5-x. The total DOS at Fermi level mainly results from gallium 4p and manganese 3d contributions.

Figure 8 :

 8 Figure 8: The electron density difference calculated with CASTEP for MnGa4 (left) and triclinic MnGa5-x (right). High densities, indicative of bond formation, are found at Mn-Ga atomic pairs and between the Ga atoms involved in interpolyhedral bonding in MnGa5-x

Acknowledgements

The authors are grateful to D. Granier for data collection measurement on the CCD diffractometer.


Dr Thibault Kervarrec
email: thibaultkervarrec@yahoo.fr

Mohanad Aljundi

Silke Appenzeller

Mahtab Samimi

Eve Maubec

Bernard Cribier

Lydia Deschamps

Bhavishya Sarma

Eva-Maria Sarosi

Patricia Berthon

Maria Sarosi

Annie Levy

Guilhem Bousquet

Anne Tallet

Antoine Touzé

Serge Guyétant

David Schrama

Roland Houben

Polyomavirus-positive Merkel cell carcinoma derived from a trichoblastoma suggests an epithelial origin of this Merkel cell carcinoma

Keywords:

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

Introduction

Merkel cell carcinoma (MCC) is a rare, aggressive neoplasm of the skin with a 5-year overall survival rate of 40% [START_REF] Becker | Merkel cell carcinoma[END_REF]). In about 80% of MCC cases the Merkel cell polyomavirus (MCPyV), an ubiquitous virus causing asymptomatic infections in the general population, is integrated into the genome of the tumor cells [START_REF] Feng | Clonal integration of a polyomavirus in human Merkel cell carcinoma[END_REF]. In addition to the random integration of MCPyV, alterations of the viral sequence resulting in a truncated Large T antigen (LT) devoid of replicative abilities seem to be essential for MCC oncogenesis. Together with the truncated LT a viral small T antigen (sT) with multiple oncogenic properties is expressed in MCC cells, and both oncoproteins are considered as the main drivers for development and growth of MCPyV-positive MCC [START_REF] Becker | Merkel cell carcinoma[END_REF].

Although it is well established that MCPyV is a crucial oncogenic trigger in MCC pathogenesis, the nature of the cell in which virus integration occurs is unknown. Despite close phenotypic similarities with MCC such as expression of keratin (KRT) 20 and neuroendocrine markers, the eponym Merkel cell (MC) is considered as an unlikely candidate because this mechanoreceptor cell is post-mitotic [START_REF] Van Keymeulen | Epidermal progenitors give rise to Merkel cells during embryonic development and adult homeostasis[END_REF], insensitive to oncogenic stimuli in mice [START_REF] Shuda | Merkel Cell Polyomavirus Small T Antigen Induces Cancer and Embryonic Merkel Cell Proliferation in a Transgenic Mouse Model[END_REF], and -while MCCs are predominantly dermal or hypodermal [START_REF] Pulitzer | Merkel Cell Carcinoma[END_REF]) -resides in the basal layer of the epidermis [START_REF] Halata | Friedrich Sigmund Merkel and his "Merkel cell", morphology, development, and physiology: review and new results[END_REF].

Alternatively, MCPyV integration could occur in a non-MC, and an MC-like phenotype might be acquired during tumorigenesis [START_REF] Sunshine | Are there multiple cells of origin of Merkel cell carcinoma?[END_REF]. In this respect, epithelial, fibroblastic, lymphoid as well as a neural crest origin of MCC have been discussed as potential candidates for MCC origin [START_REF] Liu | Identifying the Target Cells and Mechanisms of Merkel Cell Polyomavirus Infection[END_REF][START_REF] Sunshine | Are there multiple cells of origin of Merkel cell carcinoma?[END_REF][START_REF] Tilling | Which are the cells of origin in merkel cell carcinoma?[END_REF][START_REF] Zur Hausen | Early B-cell differentiation in Merkel cell carcinomas: clues to cellular ancestry[END_REF]. Here, analysis of a rare combined tumor consisting of trichoblastoma and MCC parts, suggests that an MCPyV-positive MCC can arise from an epithelial cell.

Results

An MCPyV-positive MCC within a benign epithelial follicular tumor

In this study, a case of combined trichoblastoma/MCC tumor was subjected to extensive analyses. Details of the case are available in Supplementary Table S1 andSupplementary Figures S1-2. Briefly, morphological examination revealed a well-delimitated tumor located in the subcutis, without connection to the epidermis and harboring two different components (Figure 1a andb). On the borders, the combined tumor displayed typical trichoblastoma features with epithelial follicular germinative cells arranged in nodules or anastomotic strands entrapped in a prototypic stroma mimicking the dermal papillae (Figure 1a-b and Supplementary Figure S1). By contrast, the MCC part, located in the center of the combined tumor, was composed of sheets of round, medium-sized tumor cells with scant cytoplasm, round nucleus and dusty clear chromatin (Figure 1a-b). Immunohistochemical investigations (Figure 1c-e/Supplementary Figure S2) confirmed the diagnosis, notably revealing coexpression of KRT20 and neuroendocrine markers in all MCC cells and scattered KRT20positive MCs in the trichoblastoma, a hallmark of this entity [START_REF] Kurzen | Cytokeratins as markers of follicular differentiation: an immunohistochemical study of trichoblastoma and basal cell carcinoma[END_REF].

It has been suggested that MCPyV is not involved in the development of combined MCCs [START_REF] Martin | Merkel cell carcinoma with divergent differentiation: histopathological and immunohistochemical study of 15 cases with PCR analysis for Merkel cell polyomavirus[END_REF]) which account for 5-10% of all MCCs (Kervarrec et al. 2018a). However, quantitative PCR demonstrated a substantial MCPyV viral load (20 copies/cell) in the MCC component, and staining for MCPyV-LT (Figure 1c) revealed moderate expression in the MCC cells suggesting an MCPyV-driven oncogenesis. In contrast, most of the trichoblastoma stained negative, and only in one restricted area a fraction of cells expressed LT (Figure 1c).

It could, however, not be concluded whether these cells represented MCPyV-infected trichoblastoma cells or disseminated cells from the adjacent MCC tumor (Figure 1b).

Interestingly, an increased number of cells expressing the MC differentiation markers SOX2, KRT8 and KRT20 was present in this area, with KRT8 and KRT20 frequently displaying a distinct paranuclear dot-like pattern dissimilar from the diffuse cytoplasmic KRT20distribution in normal MCs in the rest of the trichoblastoma component (Figure 1de/Supplementary Figure S3a-c). Furthermore, co-expression of KRT20 and LT in about 50% and KRT20 and the proliferation marker MKi67 in about 10% of the KRT20-expressing cells was observed (Supplementary Figure S3a, c-d).

In summary, the morphological and immunohistochemical analyses of the combined tumor revealed presence of MCPyV in specific trichoblastoma areas and widespread presence of MCPyV in the MCC part suggesting a virus-induced MCC oncogenesis.

MCPyV integration and LT truncation in the MCC

Two molecular features characterize MCPyV-associated MCC. First, the virus genome is clonally integrated into the genome of the tumor cells [START_REF] Feng | Clonal integration of a polyomavirus in human Merkel cell carcinoma[END_REF]) and second, the LT antigen coding sequence is always affected in a way leading to expression of a truncated protein [START_REF] Shuda | T antigen mutations are a human tumor-specific signature for Merkel cell polyomavirus[END_REF]. Applying combination of whole genome and Sanger sequencing onto DNA isolated from the MCC part, we could detect and confirm integration of MCPyV in chromosome 3 of the tumor genome (Figure 2a-b). Moreover, the presence of MCPyV sequences beyond the unique break points suggest integration of a concatemer consisting of one or more viral copies in addition to the sequence between the break points. Sequencing further indicates that even two differently truncated LT proteins may be expressed in the MCC part. One truncation caused by the integration break point at 1956, the other by a deletion spanning base pairs 2248 -2542 (both according to GenBank EU375803) (Fig. 2b).

In conclusion, the genetic analysis of MCPyV in the MCC part of the combined tumor revealed that this carcinoma harbors the hallmarks of an MCPyV-positive MCC.

Importantly, amplification of the insertion sites and a fragment specific for the LT-truncating deletion was only achieved with DNA from the MCC while from the trichoblastoma DNA only wild type LT sequence could be amplified (Figure 2c). These results clearly indicate that the trichoblastoma tumor cells do not harbor the integrated form of the virus found in the MCC.

Shared mutations in trichoblastoma and MCC component

In order to prove a genetic relationship between the MCPyV-positive MCC and the trichoblastoma part of the combined tumor, DNA isolated from the different tumor components and healthy tissue was analyzed by whole exome sequencing and somatic mutations were identified (Supplementary Tables S2-4). Several acquired variants were present in only one of the tumor samples indicating that each tumor component partly experienced its own genetic history. Strikingly, however, the six acquired non-synonymous variants detected with the highest allelic frequencies in the trichoblastoma were also present in the MCC part (Supplementary Table S2). This was confirmed by Sanger sequencing (Figure 3) thus suggesting a common origin of the two tumor parts. Since integrated MCPyV could only be detected in the MCC part (Fig. 2c), these results imply that upon MCPyV integration occurring in an epithelial cell of the trichoblastoma component the MCC developed. In line with this, allelic frequencies of approximately 50% for the shared somatic mutations in the MCC part (lacking significant stroma (Figure 1)) are in accordance with heterozygous mutations being present in all MCC tumor cells. Measured allelic frequencies of 21-32% in the trichoblastoma part (Figure 3 and Supplementary Table S2), which harbors more extensive stroma (Figure 1), may reflect heterozygotic presence of the shared mutations in most if not all trichoblastoma cells. Interestingly, all further mutations detected in the trichoblastoma part were less frequent (Supplementary Table S2) suggesting that they are not present in all trichoblastoma cells. This is in line with a scenario where MCPyV integration has occurred in a trichoblastoma cell lacking these mutations. Among the somatic variants present in only the MCC part there are some which were detected with frequencies close to those of the shared mutations (e.g. GRIK4 and FAM219A) (Supplementary Table S2). They either may represent (i) mutations, present below the detection limit in the trichoblastoma but, nevertheless existent in the specific "MCC cell of origin", or (ii) may have been acquired early during MCPyV-mediated oncogenesis. Finally, the low number of mutations lacking any UV-signature (Supplementary Table S4) confirms that the MCC part of the combined tumor matches also these attributes of MCPyV-positive MCC [START_REF] Becker | Merkel cell carcinoma[END_REF].

In conclusion, the data provided so far, clearly indicate that an MCPyV-positive MCC can arise from an epithelial cell.

Analogy between trichoblastoma and MC progenitor

Next, we asked whether the analyses of the combined tumor would allow further conclusions regarding the cellular origin of this MCPyV-positive MCC. As expected, an epithelial lineage descendance was confirmed by widespread expression of cytokeratins in trichoblastoma cells.

Moreover, trichoblastoma cells characteristically bear intrinsic MC-differentiation capability and phenotypically resemble hair follicle stem cells [START_REF] Kurzen | Cytokeratins as markers of follicular differentiation: an immunohistochemical study of trichoblastoma and basal cell carcinoma[END_REF]) (Figure 4a-c) which have been demonstrated to be essential for MC development [START_REF] Nguyen | FGF signalling controls the specification of hair placode-derived SOX9 positive progenitors to Merkel cells[END_REF][START_REF] Perdigoto | Polycomb-Mediated Repression and Sonic Hedgehog Signaling Interact to Regulate Merkel Cell Specification during Skin Development[END_REF]. In particular, GLI1 activation in the hair follicle and the surrounding touch domes is critical for the maintenance of the MC lineage [START_REF] Perdigoto | Polycomb-Mediated Repression and Sonic Hedgehog Signaling Interact to Regulate Merkel Cell Specification during Skin Development[END_REF][START_REF] Xiao | Neural Hedgehog signaling maintains stem cell renewal in the sensory touch dome epithelium[END_REF].

Interestingly, we could demonstrate in the trichoblastoma part of the combined tumor, like in normal hair follicles, widespread expression of KRT17 and SOX9, two markers shared by hair follicle and MC-progenitors as well as GLI1 nuclear localization (Figure 4c-e) [START_REF] Brownell | Nerve-derived sonic hedgehog defines a niche for hair follicle stem cells capable of becoming epidermal stem cells[END_REF][START_REF] Larouche | Vibrissa hair bulge houses two populations of skin epithelial stem cells distinct by their keratin profile[END_REF][START_REF] Moll | Special program of differentiation expressed in keratinocytes of human haarscheiben: an analysis of individual cytokeratin polypeptides[END_REF][START_REF] Nguyen | FGF signalling controls the specification of hair placode-derived SOX9 positive progenitors to Merkel cells[END_REF][START_REF] Nguyen | FGF signalling controls the specification of hair placode-derived SOX9 positive progenitors to Merkel cells[END_REF][START_REF] Xiao | Neural Hedgehog signaling maintains stem cell renewal in the sensory touch dome epithelium[END_REF] in association with the interspersed presence of KRT8-and KRT20-positive MCs (Figures 1c and4f, Supplementary Figure S3b-d). Therefore, the trichoblastoma cell in which MCPyV integration occurred as demonstrated by genomic analyses could be either a cell resembling an epithelial progenitor cell of the hair follicle or an already differentiated MC.

A second case of MCPyV-positive MCC arising within a trichoblastoma

Our study has limitations and most prominent, our conclusions are based on only one case.

Due to the exceedingly low incidence of combined trichoblastoma/MCC, we could identify only one additional case published previously [START_REF] Battistella | Primary cutaneous neuroendocrine carcinoma within a cystic trichoblastoma: a nonfortuitous association?[END_REF]. Analyses of this second combined MCC by immunohistochemistry confirmed a further case of MCPyV-positive MCC arising within a trichoblastoma composed of KRT17-and SOX9-positive MC-precursor-like cells and interspersed KRT20-and KRT-8 expressing MCs (Supplementary Figure S4/Supplementary Table S5). Unfortunately, additional molecular analyses could not be performed due to very poor DNA quality related to Bouin fixation.

Discussion

Identification of the cellular origin of MCPyV-positive and virus-negative MCC are considered as high-priority research questions not only to improve our understanding of the initiation of this disease, but also for developing appropriate models and possibly new therapeutic approaches [START_REF] Harms | The biology and treatment of Merkel cell carcinoma: current understanding and research priorities[END_REF][START_REF] Sauer | Reviewing the current evidence supporting early B-cells as the cellular origin of Merkel cell carcinoma[END_REF][START_REF] Sunshine | Are there multiple cells of origin of Merkel cell carcinoma?[END_REF]. Due to close phenotypic similarities with MCC, MC -a highly specialized mechanoreceptor, and a descendant from KRT14-positive epidermal progenitors [START_REF] Halata | Friedrich Sigmund Merkel and his "Merkel cell", morphology, development, and physiology: review and new results[END_REF][START_REF] Van Keymeulen | Epidermal progenitors give rise to Merkel cells during embryonic development and adult homeostasis[END_REF]) -was historically regarded as the cell of origin of MCC. Proposed alternatives as potential MCC origin include pre/pro-B cells, dermal fibroblasts, dermal mesenchymal stem cells and epithelial progenitor cells [START_REF] Becker | Cells of origin in skin cancer[END_REF][START_REF] Kervarrec | Histogenesis of Merkel cell carcinoma: a comprehensive review[END_REF][START_REF] Lemasson | Presence of putative stem cells in Merkel cell carcinomas[END_REF][START_REF] Liu | Identifying the Target Cells and Mechanisms of Merkel Cell Polyomavirus Infection[END_REF][START_REF] Tilling | Which are the cells of origin in merkel cell carcinoma?[END_REF][START_REF] Verhaegen | Merkel Cell Polyomavirus Small T Antigen Initiates Merkel Cell Carcinoma-like Tumor Development in Mice[END_REF][START_REF] Woo | Identification of epidermal progenitors for the Merkel cell lineage[END_REF][START_REF] Zur Hausen | Early B-cell differentiation in Merkel cell carcinomas: clues to cellular ancestry[END_REF].

Although investigating only a single case belonging to an exceptionally rare tumor entity, the results presented here provide a clear proof that MCPyV-positive MCC can arise from the epithelial lineage, i.e., either from already differentiated MCs or their progenitors. Moreover, while an alternative histogenesis either in mesenchymal or lymphoid cells could not formerly be excluded for other MCPyV-positive MCC cases such scenario appears unlikely because a tumor cell phenotype is determined by both, the tumorigenic alterations and by the primary nature of the cell of origin , [START_REF] Bailleul | Skin hyperkeratosis and papilloma formation in transgenic mice expressing a ras oncogene from a suprabasal keratin promoter[END_REF][START_REF] Brown | The malignant capacity of skin tumours induced by expression of a mutant H-ras transgene depends on the cell type targeted[END_REF][START_REF] Visvader | Cells of origin in cancer[END_REF]. This concept referred to as "oncogene lineage-addiction" [START_REF] Garraway | Lineage dependency and lineage-survival oncogenes in human cancer[END_REF] was proven for MCPyV oncoproteins using transgenic mice. Indeed, in such model, ectopic expression of the T antigens (sT alone or in combination with LT) failed to generate tumors with an MCClike phenotype in all tested compartments [START_REF] Shuda | Merkel Cell Polyomavirus Small T Antigen Induces Cancer and Embryonic Merkel Cell Proliferation in a Transgenic Mouse Model[END_REF][START_REF] Spurgeon | Tumorigenic activity of merkel cell polyomavirus T antigens expressed in the stratified epithelium of mice[END_REF][START_REF] Verhaegen | Merkel cell polyomavirus small T antigen is oncogenic in transgenic mice[END_REF] except for the Merkel cell lineage [START_REF] Verhaegen | Merkel Cell Polyomavirus Small T Antigen Initiates Merkel Cell Carcinoma-like Tumor Development in Mice[END_REF]. In light of these findings, while trichoblastoma tumors could not be considered as a frequent site of MCPyV integration, it is conceivable that MCPyV induced carcinogenesis occurs in a similar cellular context i.e. an epithelial cell of the MC lineage being either an hair follicle progenitor or an already differentiated MC.

Indeed, we confirmed trichoblastoma as a benign epithelial tumor phenotypically resembling progenitor cells of the hair follicle [START_REF] Kurzen | Cytokeratins as markers of follicular differentiation: an immunohistochemical study of trichoblastoma and basal cell carcinoma[END_REF]) and bearing MC differentiation ability [START_REF] Katona | Does the panel of cytokeratin 20 and androgen receptor antibodies differentiate desmoplastic trichoepithelioma from morpheaform/infiltrative basal cell carcinoma?[END_REF][START_REF] Kurzen | Cytokeratins as markers of follicular differentiation: an immunohistochemical study of trichoblastoma and basal cell carcinoma[END_REF][START_REF] Leblebici | CD10, TDAG51, CK20, AR, INSM1, and Nestin Expression in the Differential Diagnosis of Trichoblastoma and Basal Cell Carcinoma[END_REF]. Under physiological conditions, the hair follicle is a privileged niche for MC differentiation and accordingly, abrogation of hair follicle development in transgenic mice resulted in complete MC loss [START_REF] Perdigoto | Polycomb-Mediated Repression and Sonic Hedgehog Signaling Interact to Regulate Merkel Cell Specification during Skin Development[END_REF]. Furthermore, Sox9-and Fgfr2-expressing cells in the embryonic hair follicle were identified as MC progenitors, and active Sonic hedgehog signaling was shown to be critical for establishment of this population , and for subsequent MC differentiation [START_REF] Nguyen | FGF signalling controls the specification of hair placode-derived SOX9 positive progenitors to Merkel cells[END_REF][START_REF] Perdigoto | Polycomb-Mediated Repression and Sonic Hedgehog Signaling Interact to Regulate Merkel Cell Specification during Skin Development[END_REF]. Interestingly, all these features can also be found in the trichoblastoma germinative cells of the presented combined tumor and accordingly sparse MCs were detected. Therefore our results suggest that hair follicles with potential for MC differentiation might represent a major cellular origin of MCPyV-positive MCC. This notion has been suggested earlier [START_REF] Tilling | Which are the cells of origin in merkel cell carcinoma?[END_REF], and is also corroborated by rare cases of MCC found within follicular cysts [START_REF] Requena | Merkel cell carcinoma within follicular cysts: report of two cases[END_REF][START_REF] Su | Merkel cell carcinoma in situ arising in a trichilemmal cyst: a case report and literature review[END_REF].

Furthermore, frequent connections between MCC tumors and hair follicles have been described [START_REF] Walsh | Primary neuroendocrine (Merkel cell) carcinoma of the skin: morphologic diversity and implications thereof[END_REF] although one might also argue that collision with a hair follicle is an inevitable consequence when a dermal tumor reaches a certain size.

Of note, while the lineage from which tumor cells derived have been identified for several solid cancers, the precise differentiation degree of the cell in which transformation occurs remains elusive in most cases [START_REF] Visvader | Cells of origin in cancer[END_REF]). In the analyzed tumor, oncogenic virus integration may have occurred in one of the differentiated MCs present in the trichoblastoma.

On the other hand, arguments against the possibility that MCCs arise from already differentiated MCs include i) lack of mitotic activity of MCs [START_REF] Moll | Proliferative Merkel cells were not detected in human skin[END_REF], although a recent publication demonstrated some proliferative activity [START_REF] Narisawa | Evidence of proliferative activity in human Merkel cells: implications in the histogenesis of Merkel cell carcinoma[END_REF], ii) poor MCPyV infectibility [START_REF] Liu | Identifying the Target Cells and Mechanisms of Merkel Cell Polyomavirus Infection[END_REF]) and iii) insusceptibility of these cells to oncogenic stimuli (including T antigens) in mice [START_REF] Shuda | Merkel Cell Polyomavirus Small T Antigen Induces Cancer and Embryonic Merkel Cell Proliferation in a Transgenic Mouse Model[END_REF][START_REF] Van Keymeulen | Epidermal progenitors give rise to Merkel cells during embryonic development and adult homeostasis[END_REF] , .

Alternatively, MCC could derive from MC progenitors [START_REF] Tilling | Which are the cells of origin in merkel cell carcinoma?[END_REF]) which can arise from GLI1-expressing hair follicle stem cells. Interestingly, this population has been demonstrated to be highly susceptible to tumorigenic stimuli, and can serve as an important cellular origin in the development of other skin cancers [START_REF] Peterson | Basal cell carcinoma preferentially arises from stem cells within hair follicle and mechanosensory niches[END_REF]. In such a scenario phenotypic changes may arise during oncogenesis [START_REF] Fletcher | The evolving classification of soft tissue tumours: an update based on the new WHO classification[END_REF]. In this regard, it has been suggested that TA expression can induce an MC-like differentiation process [START_REF] Sunshine | Are there multiple cells of origin of Merkel cell carcinoma?[END_REF]. Indeed, expression of LT of the polyomavirus simian virus 40 in gastric or prostate murine epithelial cells can induce an epithelial to neuroendocrine differentiation [START_REF] Kaplan-Lefko | Pathobiology of autochthonous prostate cancer in a pre-clinical transgenic mouse model[END_REF][START_REF] Syder | A transgenic mouse model of metastatic carcinoma involving transdifferentiation of a gastric epithelial lineage progenitor to a neuroendocrine phenotype[END_REF]). Moreover, in human prostate cancer as well as mouse models, inactivation of RB1 and TP53 -both expected outcomes of MCPyV-TA expression [START_REF] Houben | An intact retinoblastoma protein-binding site in Merkel cell polyomavirus large T antigen is required for promoting growth of Merkel cell carcinoma cells[END_REF][START_REF] Park | Dual inhibition of MDM2 and MDM4 in virus-positive Merkel cell carcinoma enhances the p53 response[END_REF]) -have been demonstrated to induce the epigenetic reprogramming factors SOX2 and EZH2 [START_REF] Ku | Rb1 and Trp53 cooperate to suppress prostate cancer lineage plasticity, metastasis, and antiandrogen resistance[END_REF], i.e. two critical actors involved in Merkel cell differentiation. In line with these published results, we observed an increase in cells positive for the MC markers KRT8, SOX2 and KRT20 in a trichoblastoma region containing MCPyV-LT expression. Although a metastatic spreading of the MCC tumor cells with "small cell morphology" into the trichoblastoma might explain these findings, it could alternatively be the result of LT-induced MC proliferation, or indicate a differentiation process promoted by MCPyV oncoproteins. This notion is supported by more frequent cells expressing SOX2 and KRT8 which appear earlier during MC differentiation than the less frequently expressed KRT20 (Supplementary Figure 3) [START_REF] Perdigoto | Embryonic maturation of epidermal Merkel cells is controlled by a redundant transcription factor network[END_REF].

Taken together, it is conceivable that MCPyV-TAs contribute to the development of a MClike phenotype upon expression in an epithelial precursor cell.

Irrespective of these more speculative considerations, the mutational overlap between a benign epithelial tumor and a MCPyV-positive MCC provides a clear proof that an MCPyVpositive MCC can evolve from an epithelial cell. Moreover, close similarities between trichoblastoma and MC progenitors suggest that cells of the MC lineage might represent a prominent cellular target of MCPyV in MCC carcinogenesis.

Methods

Ethics

This study was approved by the local ethics committee (Tours, France, N° ID RCB2009-A01056-51), and written, informed consent of the patient was obtained.

Immunochemistry

Immunohistochemical staining for CD274, CHGA, pan-KRT (AE1/AE3), KRT14, KRT20, MKI67, MCPyV-LT, TP53, SOX9, TDT and TTF1 as well as double staining for KRT20/MCPyV-LT and KRT/MKI67 was performed using a BenchMark XT Platform as instructed (Kervarrec et al. 2018b;Kervarrec et al. 2018a). Immunohistochemical staining for GLI1, KRT8, KRT15, KRT17 and SOX2 was performed manually. Antibodies and dilutions are provided in Supplementary Materials. TP53 as well as MCPyV-LT were analyzed using an Allred score [START_REF] Moshiri | Polyomavirus-Negative Merkel Cell Carcinoma: A More Aggressive Subtype Based on Analysis of 282 Cases Using Multimodal Tumor Virus Detection[END_REF]. Quantification of LT,SOX2 and MKI67 positive cells in MCPyV(+) and (-) trichoblastoma areas was performed by counting cells in 8 independent fields (0.027 mm 2 ) and compared using a Mann-Whitney test.

DNA isolation and MCPyV quantitative PCR

After microdissection of the two tumor components and of the healthy tissue under a binocular magnifier, genomic DNA was isolated by use of the Maxwell 16 Instrument (Promega) with the Maxwell 16 formalin-fixed and paraffin-embedded Plus LEV DNA purification kit (Promega). MCPyV-LT real-time PCR was performed as described (Kervarrec et al. 2018b). Of note, dissection of the trichoblastoma was performed in areas devoid of LT expression. Briefly, 50 ng DNA was mixed with primers (0.2 µM), probe (0.1 µM) and Mix Life technologies GoTaq Probe real-time PCR Master Mix 2X (Promega) in a final volume of 20 µl. PCR reactions were performed with the LightCycler 480 II (Roche) with an initial denaturation at 95°C × 2 min, followed by 45 cycles at 95°C × 15 sec and 58°C × 60 sec. Albumin was used as reference gene for normalization. The 2 -∆Ct method was used for quantification, and results expressed as number of MCPyV copies per cell (Kervarrec et al. 2018b). Sequences of the primers used for quantitative PCR are available in Supplementary Materials.

PCR amplification and Sanger sequencing.

Nested PCRs with primers listed in Supplementary Materials were performed to amplify the respective regions. PCR reactions were carried out in a total volume of 20 µl containing 1x HF buffer, 1 µM of each primer, 200 µM dNTPs, 1 unit Q5 Phusion (NEB) and 1 µl of template. After an initial denaturation at 98°C for 1 min, the thermal profile consisted of denaturation at 98°C for 10 sec, annealing at the optimal temperature for 30 sec and elongation at 72°C for 1 min (30 cycles for pre-amplification and 40 cycles for amplification).

After PCR purification the amplicons were sent to Seqlab (Microsynth) for sequencing.

Next Generation Sequencing

For the library preparation of the exomes the SureSelectXT Library Prep Kit (Agilent) was used. Enrichment was performed using Agilent's SureSelectXT Human All Exon V6 Kit. The genomic library was prepared using TruSeq Nano DNA (Illumina). Paired end sequencing with a read length of 100 bps (exomes) and 150 bps (genome) was performed on a NovaSeq 6000 (Illumina).

Data analysis

Demultiplexing of the sequencing reads was performed with Illumina bcl2fastq (v2.19).

Adapters were trimmed with Skewer, v0.2.25 [START_REF] Jiang | Skewer: a fast and accurate adapter trimmer for nextgeneration sequencing paired-end reads[END_REF]). An initial quality assessment was performed using FastQC, v0.11.5 (Andrews S., 2010. Available online at: http://www.bioinformatics.babraham.ac.uk/projects/fastqc).Low-quality reads were trimmed with TrimGalore, v0.4.0 (Krueger, F., 2012: Available online at: http://www.bioinformatics.babraham.ac.uk/projects/trim_galore/) powered by Cutadapt, v1.86 [START_REF] Martin | Cutadapt removes adapter sequences from high-throughput sequencing reads[END_REF]. The trimmed reads were mapped to the human reference genome (hg19) using BWA mem, v0.7.127 [START_REF] Li | Fast and accurate short read alignment with Burrows-Wheeler transform[END_REF] and sorted and indexed using Picard, v1.125

(available online at: http://broadinstitute.github.io/picard/) and SAMtools, v1.38 (Li et al. 2009) respectively. Duplicates were marked with Picard. For the exomes local realignment around indels was executed with GATK, v3.59 (McKenna et al. 2010). GATK was also used for coverage calculations.

Somatic variant calling

MuTect1, v 1.1.410 [START_REF] Cibulskis | Sensitive detection of somatic point mutations in impure and heterogeneous cancer samples[END_REF]VarScan2, v2.4.111(Koboldt et al. 2012) were used to identify somatic single nucleotide variants (SNVs). Samtools (mpileup) with

VarScan2 and Scalpel, v0.5.312 [START_REF] Fang | Indel variant analysis of short-read sequencing data with Scalpel[END_REF] were applied to identify small somatic insertions or deletions. All variants were annotated with ANNOVAR, v2017-06-0113 [START_REF] Wang | ANNOVAR: functional annotation of genetic variants from high-throughput sequencing data[END_REF]. Six somatic variants shared by the trichoblastoma and the MCC were visually examined using the Integrative Genomics Viewer, v2.3.6814 [START_REF] Thorvaldsdóttir | Integrative Genomics Viewer (IGV): high-performance genomics data visualization and exploration[END_REF]) and confirmed with Sanger sequencing if they have an impact on the protein sequence or affect a splice site, are rare in the population (below a frequency of 2 % in 1000g2015aug_all, ExAC_nontcga_ALL, gnomAD_exome_ALL and gnomAD_genome_ALL) and the position is covered by at least 20 reads and the alternative allele is covered by at least 8 reads and comprised at least 5 %. Mutational signatures were identified using MuSiCa (Díaz-Gay et al.

2018) investigating somatic variants comprised at least 10%.

Detection of the virus integration site

Seeksv, v1.2.315 [START_REF] Liang | Seeksv: an accurate tool for somatic structural variation and virus integration detection[END_REF] was used with the human reference genome sequence (hg19) and the MCPyV MCC350 genome sequence (GenBank EU375803) to detect the virus integration site. depicted. To note, human sequences adjacent to the integration break points were found to be swapped. Moreover, sequencing revealed a deletion in the viral genome (∆2248-2542).

Legends

Frequently, MCPyV integrates as head to tail concatemer. In this case, nucleotides 1557-1956 are followed by one or more full length copies

Figure 1 .

 1 Figure 1. Microscopic and immunohistochemical features of the trichoblastoma/MCC

Figure 2 .

 2 Figure 2. The MCC part of the combined tumor fulfills the hallmarks of MCPyV-

  which is predicted to lead to (b) one or two different truncated Large T antigen proteins expressed in the MCC part. One premature stop codon is caused by the integration break point at nucleotide 1956 in the final MCPyV genome of the concatemer and will lead to expression of the 443 N-terminal amino acids of LT followed by 3 additional amino acids. A second larger truncated LT is encoded in case that the concatemer encompasses more than two full copies of the MCPyV genome. The ∆2248-2542 deletion leads to an LT sequence coding for the 540 N-terminal amino acids followed by three frame shifted amino acid codons prior to a stop codon. (c) PCR was performed with primers for general MCPyV detection (MCPyV; product size = 84 bp), flanking ∆2248-2542 (∆ region), or for the 5' (5' integ.; product size = 171 bp) and 3' (3' integ.; product size = 172 bp) integration sites, respectively. For MCPyV wt the ∆ region PCR will produce a PCR product of 398 bp, while it will be only 103 bp when the MCPyV contains the deletion. Notice a faint band for the 5' integration site with DNA from the trichoblastoma part at around 200 bp. Sanger sequencing, however, confirmed it to be an unspecific product.

Figure 3 .

 3 Figure 3. Trichoblastoma and MCC cells of the combined tumor share six protein-

Figure 4 .

 4 Figure 4. Shared morphologic and immunohistochemical features of MC progenitors in

Acknowledgements

The authors thank Dr A. Balaton, Dr L. Durand, Dr J Mabille and Dr S. Manela for their help and contribution.

Institutional review board:

The local Ethics Committee of Tours (France) approved the study (no. RCB2009-A01056-51)

Data availability statement

The datasets generated during and/or analysed during the current study are available in European Genome-phenome Archive (ID: EGAS00001003784).

Competing interests

The authors declare no competing interests. well as in the hair follicle cells, the progenitor markers (c) KRT17 and (d) SOX9 are frequently present. The same applies to nuclear localization of GLI1 (e) indicating activation of the sonic hedgehog pathway which is known to be critical for the maintenance of MC progenitors and their subsequent MC differentiation. In accordance with the presence of many markers indicating MC differentiation capability in the hair follicle and TB KRT20-positive MCs (f) can be found in both tissues.


D Boudier

Bogdan Cretu
email: bogdan.cretu@ensicaen.fr

E Simoen

G Hellings

T Schram

H Mertens

D Linten

Low frequency noise analysis on Si/SiGe superlattice I/O n-channel FinFETs

Low frequency noise analysis on Si

I. Introduction

Fully depleted and multiple gate MOSFETs are the best candidates for the ultimate CMOS technologies below 5 nm node. In the framework of a study initiated to compare in particular the noise performances between superlattice FinFETs and gate all around nanowires (GAA NWs) designed using the same process flow, with some additional steps for nanowires, in this work preliminary low frequency noise (LFN) results obtained on Si/SiGe superlattice Input/Output (I/O) n-channel devices are shown.

The investigated devices, fabricated at imec on 300 mm silicon wafers present a fin width of 10 nm, a fin height of 10 nm and four fins in parallel, leading to an equivalent channel width of 120 nm. As the gate oxide stack includes 2 nm high-k dielectric (HfSiO) on top of a 5 nm interfacial SiO2, an equivalent oxide thickness (EOT) of 5.6 nm is considered. A complete description of the devices fabrication flow is provided in [START_REF] Hellings | Si/SiGe superlattice I/O finFETs in a verticallystacked Gate-All-Around horizontal Nanowire Technology[END_REF]. Details on the experimental set-up are given in [START_REF] Boudier | Low frequency noise assessment in n-and p-channel sub-10 nm triple-gate FinFETs: Part I: Theory and methodology[END_REF].

In the second section, the methodology to extract the LFN parameters, in particular the 1/f noise level and the plateau and the characteristic frequency of the GR component is fully described through a noise spectrum example which contains several GR components .

In the third section, the low frequency noise as a function of the applied gate voltage is firstly characterized at room temperature in order to investigate the quality of the oxidation process using the 1/f noise analysis. LFN measurements as a function of the temperature at fixed drain current polarisation are effectuated in order to have information on the quality of the depleted Si film. This preliminary LFN spectroscopy investigation allows to identify several processing induced traps.

II. Methodology for LFN parameters estimation

The input-referred gate voltage noise (Svg) may be modelled assuming that the noise power spectral density contains contributions of three uncorrelated noise sources: white noise, flicker noise and GR noise. The white noise is independent on the frequency (in particular in the low frequency range), the flicker noise decreases with the increase of the frequency and the GR noise is characterised by a plateau and a characteristic frequency. The input-referred Svg power spectral density can be written as follow (e.g. equation 6 of [START_REF] Achour | Identification of Si film traps in pchannel SOI FinFETs using low temperature noise spectroscopy[END_REF]):

2 1 0 ( ) ² 1 g N f id i v n i m i K S A S f W g f f f = = = + +   +     ∑ (1)
This model -equation can be successfully used to estimate the 1/f noise levels (noted Kf and corresponding to the 1/f noise level at a frequency of 1 Hz), the white noise level (Wn) and the characteristic frequency (foi) and the plateau (Aoi) of the GR noise contributions for all measured noise spectra, in particular when the input-referred noise is multiplied by the frequency. Indeed, in Svg•f representation, the flicker noise will present a plateau giving the Kf level, and each GR contribution will be represented by bumps centred at their characteristic frequencies.

The slope of the linear increase of the SVG•f with the frequency in the highest frequency range from lin-lin scale representation gives the white noise level.

An example of a noise spectrum containing several GR contributions is presented in Figure 1a.

In a first step input values for the plateau and the characteristic frequency corresponding to the most pronounced GR contribution, in our case in the highest investigated frequencies, are obtained. For the maximum of the bump, the estimation of the characteristic frequency may be made (f01 ≈ 6700 Hz). In first approximation, it is considered that:

-the other GR contributions have limited impact on the behaviour of the first considered GR contribution;

-the flicker noise is firstly considered as the mean value of SVG•f at f = 1 Hz (i.e. 3•10 -7 V 2 ), and so it can be neglected;

-the white noise may be in first approximation also neglected as no clear increase of the SVG•f may be observed in the highest frequency range (around 100 kHz),.

In these conditions, at f = f01 Equation 1 becomes: For the maximum of the bump (mean value of SVG•f01 ≈ 9.7•10 -6 V 2 ) an input value of about 2.9•10 -9 V²/Hz of the plateau of the first GR contribution considered may be obtained. Using these values for f01 and A01, it may be observed that the noise spectrum is not well fitted for frequencies close to 100 kHz (Figure 1b). Consequently, the white noise contribution should be considered. Using a value of 1.5•10 -11 V 2 /Hz a good agreement between the experimental data and model can be observed for frequencies higher than f01 (Figure 1c). As can be observed from Figure 1d, the admitted error on f01 estimation should be less than 15 % (f01 adjusted with respect of (2)).

1 01 01 01 ( ) 2 g v A f S f f ⋅ ⋅ ≈ (2)
One can suggest that f01 may be taken as (f01max -f01min)/2, where f01min and f01max are the minimum and the maximum values for which the noise spectra could be considered well fitted.

The same strategy is used for the second GR contribution. However, because the GR contributions are relatively close to each other, A01 and A02 may be adjusted in order to have a better fitting. A reduction with less than 10% from A01 should be made (Figure 2a). Variation of the f02 with ±15% leads to a clear disagreement between the experimental curves and the model (Figure 2b). Finally, input values for the third GR contribution are given and an adjustment for the flicker noise is made (Figure 3a). In the very low frequency range for which it may be assumed that the impact of the first, second

Lorentzian and of the white noise contributions may be neglected and for which (f /f03) 2 << 1 Considering these hypotheses, Equation 1 may be simplified as:

3 3 2 03 ( ) 1 g v f f A f S f f K K A f f f ⋅ ⋅ ≈ + ≈ + ⋅   +     (3)
Using the ( )

g v S f f
⋅ values for different frequencies for which the considered hypotheses are fulfilled, the given input values for f03 and A03 can be also verified. The results by using three different very low frequencies are summarized in Table 1. A good agreement between the experimental noise spectrum and model is observed, except for the 3 -10 Hz frequency range (Figure 3a). Further, a fourth GR contribution at f04 of about 4 Hz and a last adjustment of the Kf level may be performed in order to have a best fitting of the experimental noise (Figure 3b). However, as this last GR contribution has a very limited impact on the estimation of A01, f01, A02, f02, A03, f03 and Wn noise parameters, it affects principally the flicker noise level. The quasi-independence of the Kf level with the applied VGT close to the threshold (Figure 5a) suggests that the carrier number fluctuations mechanism prevails the flicker noise. The increase of the Kf level with the applied gate voltage after the threshold may be related to the carrier number fluctuations correlated to mobility fluctuations mechanism (δn +δµ) and may be modelled as [START_REF] Ghibaudo | Improved analysis of low frequency noise in field-effect MOS transistors[END_REF]:

( ) ( ) 2 2 2 0 0 0 2 1 1 B it f C ox GT f C ox GT ox q k T N K µ C V K µ C V WLC = + = + λ α α (4)
where kB is the Boltzmann constant, T is the temperature, Nit is the density of traps in the gate dielectrics at the quasi-Fermi level (cm -3 eV -1 ), λ is the tunnel distance, µ0 is the low field mobility, Cox the is the gate oxide The Arrhenius diagrams presented in Figure 8 are constructed using the method proposed in [START_REF] Lukyanchikova | Noise and Fluctuations Control in Electronic Device[END_REF][START_REF] Grassi | Low frequency noise versus temperature spectroscopy of recently designed Ge JFETs[END_REF], which consists to plot the variations of ( )

ln ² i T τ as a function of 1 B
k T , where τI is the characteristic relaxation time (τi = 1/(2πf0i)) and kB is the Boltzmann constant. The energy difference between the conduction band energy (EC)

and the trap energy ET and the capture cross-section σn could be extracted from the slope and the y-intercept, respectively (least-squares linear fit to the data). The physical nature of the identified traps is based on a comparison with previous results from Deep-Level Transient Spectroscopy (DLTS) studies [START_REF] Claeys | Radiation effects in Advanced Semiconductor Material and Devices[END_REF][START_REF] Hallen | Lifetime in proton irradiated silicon[END_REF][START_REF] Van Vechten | Vacancies, disclocations, and carbons interstials in Si[END_REF][START_REF] Bains | AC hopping conductivity and DLTS studies on electron-irradiated boron-doped silicon[END_REF]. The EC -ET and σn issued from the Arrhenius diagram presented in Figure 8 are summarized in Table 2. The relationship between the GR plateau and the GR characteristic time constant may be used as a second verification step for trap validation. Indeed, a linear dependence should exist between A0i and τ0i related to the same trap. This linearity is verified for all identified traps, as can be observed in Figure 9. Moreover, from the slope of A0i versus τ0i the effective surface density of the traps may be evaluated without any additional assumption. Indeed, for the estimation of the volume trap density in conventional planar devices a correction parameter (B) value of 1/3 should be considered [START_REF] Lukyanchikova | Noise and Fluctuations Control in Electronic Device[END_REF]. However, it was already demonstrated that this B parameter value is no longer a constant for multiple-gate devices [START_REF] Achour | Identification of Si film traps in pchannel SOI FinFETs using low temperature noise spectroscopy[END_REF][START_REF] Cretu | Low frequency noise spectroscopy in rotated UTBOX nMOSFETs[END_REF]. The obtained values of the surface trap density of the identified traps, summarized in Table 2 are moderately larger compared to those previously reported for other advanced technologies [START_REF] Cretu | Low frequency noise spectroscopy in rotated UTBOX nMOSFETs[END_REF][START_REF] Talmat | Low frequency noise characterization in n-channel FinFETs[END_REF].

IV. Conclusions

The noise parameters estimation protocol was fully described for a PSD noise which contains several GR noise contributions.

The evolution of the 1/f noise levels with applied bias confirms that the carrier number fluctuation mechanism explains the flicker noise origin in the studied Si/SiGe superlattice FinFETs. The correlation between the mobility and the 1/f noise levels related to the remote Coulomb scattering effect explains the important 1/f noise level variability.

Taking into account the estimation error of the GR noise parameters, the analysis of the temperature evolution of the characteristic frequency and plateau of each GR contribution permits to identify the presence of traps located in the depleted Si film related to divacancies, hydrogen and a possible carbon contamination. The linear dependencies between the GR plateau A0i versus the characteristic relaxation time τ0i additionally confirms the trap identification.

Figure 1 .

 1 Figure 1. a) example of a noise spectrum containing several GR contributions; b) model using f01 from the maximum of the bump and A01 from equation 2; c) adjusting the model by considering the white noise contribution (no impact on the A01 estimation may be observed); d) Estimation error of about ±15% on f01 does not allow a good fit to the spectrum for frequencies higher than f01.

Figure 2 :

 2 Figure 2: a) model of (1) using flicker noise, white noise and two GR contributions, b) disagreement if about ±15% variation is considered for the input f02 value. Better view may be obtained if a linear scale is chosen for the Oy-axis.

Figure 3 :

 3 Figure 3: a) model of (1) using flicker noise, white noise and three GR contributions; b) best fit if in the model of (1) flicker noise, white noise and four GR contributions are considered However, for other examples the LFN parameter estimation is made more easy, as observed from Figure 4 for device 1, where only a white noise and flicker noise contribution should be considered to obtain good agreement between the experimental and modelled spectrum. The Kf level is estimated in the frequency range where a plateau may be observed (i.e. 1 Hz -1 kHz), while the white noise level is given using the frequency range in which a direct proportional evolution between ( ) g v S f f ⋅ and the frequency may be observed (i.e. 10 kHz -100

Figure 4 .

 4 Figure 4. Experimental noise spectra for devices having the same geometry.

Figure 5 .

 5 Figure 5. Estimated 1/f noise level evolution with the applied gate voltage. The increase of the Kf level after threshold may be perfectly model in the framework of the carrier number fluctuations correlated to mobility fluctuations model

  capacitance, αC is the Coulomb scattering coefficient and Kf0 represent the flat-band noise level (Svfb ) at 1 Hz. A good correlation between the δn +δµ model and the 1/f noise behaviour presented in Figure 5a may be observed. Using the low field mobility extracted in first approximation from the maximum of the transconductance, a value of αC of 5•10 4 Vs/C is obtained. From Figure 5b, considering only the values after threshold such good agreement may be observed between the Kf versus VGT and the δn +δµ model, leading to a value of αC of about 1.2•10 4 Vs/C. Considering the low field to keep a quasi-constant Fermi level, the LFN measurements as the function of the temperature should be made at fixed drain current polarisation.

Figure 7 .

 7 Figure 7. Input -referred PSD noise multiplied by frequency evolution with the temperature

Figure 9 .

 9 Figure 9. A linear dependencies between the GR plateau Α0i versus the characteristic relaxation time τ0i exists, confirming that Α0i and τ0i are related to the same trap

Table 1 . A03 and Kf estimation using first order approximations in Equation 1, considering three different frequencies in Equation 3 f (Hz) Svg•f(V²) A03 (V²/Hz) Kf (V²) 1 3•10 -7 4•10 -8 2.3•10 -7

 1

	2	3.7•10 -7	5•10 -8	2.3•10 -7
	4	4.5•10 -7	4•10 -8	2.9•10 -7

mobility and αC values obtained for devices 3 and 4 it may be suggested that the low field mobility reduction may be linked to the increase of the Coulomb interactions. The surface trap density Dit can be extracted as in [START_REF] Ghibaudo | Improved analysis of low frequency noise in field-effect MOS transistors[END_REF][START_REF] Guo | Low-frequency noise assessment of silicon passivated Ge pMOSFETs with TiN/TaN/ HfO2 gate stack[END_REF] using the expression 4

, where z is the tunnelling distance in the depth of oxide taken at a frequency of 1 Hz.

In Figure 6 are plotted the estimated flat-band 1/f noise levels versus the corresponding low field mobility for all investigated devices. A substantial variability of Svfb of more than one decade can be observed. It may be noted that the Svfb is always higher for devices presenting lower low field mobility. The correlation between the 1/f noise levels and the mobility has been already reported in the literature for other technologies and was related to remote Coulomb scattering [START_REF] Ghibaudo | Improved analysis of low frequency noise in field-effect MOS transistors[END_REF][START_REF] Guo | Low-frequency noise assessment of silicon passivated Ge pMOSFETs with TiN/TaN/ HfO2 gate stack[END_REF]. This hypothesis corroborates with the results of Figure 5.

B. LFN as a function of the temperature

Following the arguments proposed by [START_REF] Lukyanchikova | Noise and Fluctuations Control in Electronic Device[END_REF], if the evolution of the characteristic frequency of the GR noise contribution is independent on the applied gate voltage at fixed temperature operation and varies with temperature at fixed polarisation operation condition, than it can be related to traps located in the Si fins. In order The first trap observed (noted T1) presents a ∆E and capture cross-section close to those reported in the literature for the divacancy-hydrogen V2H trap (∆E of 0.45 eV and a σn in the 10 -17 cm 2 range [START_REF] Claeys | Radiation effects in Advanced Semiconductor Material and Devices[END_REF][START_REF] Hallen | Lifetime in proton irradiated silicon[END_REF]). The V2H trap may be due to the presence of residual hydrogen after annealing.

The extracted activation energy for the T2, T3 traps suggests the impact of the single negatively charged acceptor state (0/-) of the divacancy (V2) trap (i.e. ∆E of 0.42 eV) and the phosphorus-vacancy complex (V-P) (i.e. 0.44 eV), respectively [START_REF] Claeys | Radiation effects in Advanced Semiconductor Material and Devices[END_REF][START_REF] Van Vechten | Vacancies, disclocations, and carbons interstials in Si[END_REF]. However, the capture cross-section is smaller than expected (e.g. σn in the range of 10 -15 cm 2 for both the V2(0/-) and V-P traps). The presence of these two divacancies may be explained by the recombination or the evolution to a stable state of the unstable defects like Frenkel pairs, which could be generated during ion implantation.

Concerning T4, the same activation energy of 0.17 eV is reported for traps related to the oxygen -vacancy complex V-O and for the interstitial -carbon -substitutional carbon complex CiCs [START_REF] Claeys | Radiation effects in Advanced Semiconductor Material and Devices[END_REF][START_REF] Bains | AC hopping conductivity and DLTS studies on electron-irradiated boron-doped silicon[END_REF]. The reported σn for V-O is reported in the range of 10 -14 cm 2 [START_REF] Bains | AC hopping conductivity and DLTS studies on electron-irradiated boron-doped silicon[END_REF], while no value for the capture cross-section of the CiCs complex is reported to our knowledge. Even if the CiCs complex is reported to be improbable, considering the extracted values of σn in the range of 10 -19 cm² it is more likely that T4 is related to the CiCs complex.