Annick Loschetter
email: a.loschetter@brgm.fr

Maud Watkinson

Simona Regenspurg

Setareh Rad

Laurent André

Arnault Lassin

Guido Blöcher

Sylvain Stephant

Niels Hartog

Martin Van Der Schans

Sylvain Stéphant

Philip J Vardon

Water concerns in UTES: what can be learnt from geothermal experience & what issues need to

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

ISTO, France

The European project PUSH-IT's ambition is to overcome the seasonal mismatch between heat demand and heat generation from sustainable sources using Underground Thermal Energy Storage (UTES) at high temperatures, i.e. up to 90°C (https://www.push-it-thermalstorage.eu). PUSH-IT showcases three UTES technologies at six pilot sites: Aquifer Thermal Energy Storage (ATES) in the Netherlands and Germany, Mine Thermal Energy Storage (MTES) in Germany and the UK, and Borehole Thermal Energy Storage (BTES) in Germany and the Czech Republic.

Water quality issues represent technical challenges for viable long-term thermal energy storage, whatever the technology. These include: Biogeochemical perturbations in the storage reservoir: the temperature gradient influences the chemical composition of the fluids that may lead to (bio)clogging in near-wells and loss of injectivity/productivity, notably for ATES; Corrosion and scaling in the wells and facilities; Shallower aquifer perturbation by temperature increase and saline brines from deeper aquifers.

The lessons learnt over decades of geothermal exploitation and low temperature thermal energy storage provide a solid basis for anticipating, monitoring, managing and remediating these issues in a variety of geological contexts. However, for increasing the temperatures of thermal energy storage in geothermal reservoirs several specificities have not been thoroughly investigated, such as the thermal storage at high temperature, the need to use reversible wells, reversible fluxes in the reservoir, temperature and pressure cycling. Furthermore, the role of microbiology has often been neglected and is anticipated to be more sensitive in storage applications.

At the current stage of the project, the main concerns for each site have been mapped. The modelling and monitoring works are at different stages of progress depending on the sites. The project will go beyond the simple feedback on the experience from pilot sites by providing recommendations to anticipate and deal with water quality issues for future sites. We will provide guidelines to assist decision-makers in identifying the main issues, in implementing the necessary modelling, in sizing and adjusting the monitoring plan, in assessing possible water treatment benefit vs. environmental impact. Anticipating and managing water-related issues as far as possible is the best way of making the right choices, guaranteeing the performance and longevity of operations, limiting environmental impact and encouraging society engagement and support.

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Acknowledgements: Funded by the European Union under grant agreement 1011096566 (PUSH-IT project). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or CINEA. Neither the European Union nor CINEA can be held responsible for them.


Phuong Vuong

Suresh Sundaram

Vishnu Ottapilakkal

Gilles Patriarche

Ludovic Largeau

Ashutosh Srivastava

Adama Mballo

Tarik Moudakir

Simon Gautier

Paul L Voss

Jean-Paul Salvestrini

Abdallah Ougazzaden
email: abdallah.ougazzaden@georgiatech-metz.fr

Influence of Sapphire Substrate Orientation on the van der Waals Epitaxy of III-Nitrides on 2D Hexagonal Boron Nitride: Implication for Optoelectronic Devices

Keywords: van der Waals epitaxy, Metal-organic chemical vapor phase epitaxy (MOVPE), twodimensional materials, hexagonal Boron Nitride, III-nitrides, substrate orientations

published or not. The documents may come

Introduction:

Van der Waals (vdW) epitaxy was discovered as early as 1984 [START_REF] Koma | Fabrication and Characterization of Heterostructures with Subnanometer Thickness[END_REF] and has proven to be a beneficial approach for heteroepitaxy growth [START_REF] Chen | Van Der Waals Epitaxy of III-Nitrides and Its Applications[END_REF][START_REF] Alaskar | Towards van Der Waals Epitaxial Growth of GaAs on Si Using a Graphene Buffer Layer[END_REF][START_REF] Koma | Van Der Waals Epitaxy for Highly Lattice-Mismatched Systems[END_REF][START_REF] Liang | Quasi van Der Waals Epitaxy Nitride Materials and Devices on Two Dimension Materials[END_REF][START_REF] Li | Van Der Waals Epitaxy of GaN-Based Light-Emitting Diodes on Wet-Transferred Multilayer Graphene Film[END_REF] . Recently, vdW epitaxy of three-dimensional (3D) materials on two-dimensional (2D) layers has attracted tremendous attention. Compared to conventional 3D/3D epitaxy, the bonds between 3D epilayer and 2D buffer layer are about two orders of magnitude weaker [START_REF] Alaskar | Towards van Der Waals Epitaxial Growth of GaAs on Si Using a Graphene Buffer Layer[END_REF] . This weak vdW bond can be very advantageous for 3D/2D epitaxy, accommodating thermal and lattice mismatches with substrates, which may dramatically improve the crystalline quality of 3D materials [START_REF] Li | Van Der Waals Epitaxy of GaN-Based Light-Emitting Diodes on Wet-Transferred Multilayer Graphene Film[END_REF][START_REF] Zhou | Direct van Der Waals Epitaxy of Stress-Free GaN Films on PECVD Grown Graphene[END_REF][START_REF] Chang | Quasi-2D Growth of Aluminum Nitride Film on Graphene for Boosting Deep Ultraviolet Light-Emitting Diodes[END_REF] . Moreover, thanks to the layered structure of 2D materials, 3D heterostructures can be mechanically detached from their substrate over a large area and transferred as membranes to arbitrary carriers with simple flexible, soft or hard holders (tapes, PDMS, metals) [START_REF] Kobayashi | Layered Boron Nitride as a Release Layer for Mechanical Transfer of GaN-Based Devices[END_REF][START_REF] Ayari | Wafer-Scale Controlled Exfoliation of Metal Organic Vapor Phase Epitaxy Grown InGaN/GaN Multi Quantum Well Structures Using Low-Tack Two-Dimensional Layered h-BN[END_REF] . III-nitride semiconductors are well known as perfect candidates for light-emitting diodes (LEDs), lasers diodes (LDs), high electron mobility transistors (HEMTs) and other opto-electronic devices. VdW epitaxy has been confirmed to be a suitable method for III-nitride epitaxy, which has the potential to enhance the performance of III-nitride devices. Among vdW 2D materials, h-BN is an excellent choice as a buffer layer for the III-nitride vdW epitaxy due to the following reasons: i) chemical stability at III-N growth temperature, ii) the surface is favorable for the nucleation of 3D III-nitride materials iii) the growth conditions are compatible with different industrial deposition systems (MOVPE, MBE, CVD), and iv) the availability of the boron precursors as organometallic gas sources.

In addition, the substrate used in vdW III-Nitride epitaxy also plays an important role because it affects the crystal orientation and the strain of the vdW epilayers. The growth of 2D h-BN and 3D III-Nitride semiconductors has been performed on different types of substrates ranging from metals (Ni , Cu) [START_REF] Inoue | Epitaxial Growth of GaN on Copper Substrates[END_REF][START_REF] Ramesh | Structural and Optical Properties of GaN Film on Copper and Graphene/Copper Metal Foils Grown by Laser Molecular Beam Epitaxy[END_REF][START_REF] Cho | Growth Kinetics of White Graphene (h-BN) on a Planarised Ni Foil Surface[END_REF] to dielectric surfaces and graphene [START_REF] Yu | Demonstration of Epitaxial Growth of Strain-Relaxed GaN Films on Graphene/SiC Substrates for Long Wavelength Light-Emitting Diodes[END_REF][START_REF] Nepal | Epitaxial Growth of III-Nitride/Graphene Heterostructures for Electronic Devices[END_REF] . However, sapphire substrates are standard in industry, and exhibit high hardness, good light transmittance and thermal stability [START_REF] Bruni | Crystal Growth of Sapphire for Substrates for High-Brightness, Light Emitting Diodes[END_REF][START_REF] Ryou | 3 -GaN on Sapphire Substrates for Visible Light-Emitting Diodes[END_REF] . As an anisotropic material, the different crystal orientations have different surface and mechanical properties and thereby, can have an impact on vdW epitaxy. It has been reported that GaN grown directly on a-and m-plane sapphire substrates is non-polar and semi-polar [START_REF] Wang | A Comparative Study on the Properties of C-Plane and a-Plane GaN Epitaxial Films Grown on Sapphire Substrates by Pulsed Laser Deposition[END_REF][START_REF] Wernicke | Semipolar GaN Grown on M-plane Sapphire Using MOVPE[END_REF][START_REF] Armitage | M-Plane GaN Grown on m-Sapphire by Metalorganic Vapor Phase Epitaxy[END_REF] , which leads to better luminescence efficiency of the devices when compared with GaN grown on c-plane sapphire, which suffers from the quantum-confined stark effect due to strong piezoelectric fields [START_REF] Ambacher | Role of Spontaneous and Piezoelectric Polarization Induced Effects in Group-III Nitride Based Heterostructures and Devices[END_REF] . However, the epitaxy of III-Nitride heterostructures on non-polar sapphire substrates with a 2D interfacial layer has not been previously reported.

The goal of this work is to study the effect of orientation of sapphire substrate on the growth of 2D h-BN layer and subsequent 3D III-Nitride material epilayers through the h-BN buffer layer.

We have first investigated the impact of a-, c-and m-plane oriented sapphire substrates on the growth mechanism and alignment of 20 nm thick h-BN layers. Then, vdW epitaxy of GaN/AlGaN epilayers using 1.5 nm thick h-BN as interfacial layer were grown on a-, c-and m-plane oriented sapphire substrates. The dependence of the crystalline structure orientations, morphology of the 2D h-BN layer and III-N epilayers and their adhesion epilayer with different substrate orientations will be discussed. This study can give us a better understanding of the vdW epitaxy of 3D III-Nitride on 2D h-BN materials, motivating further exploration of III-nitride device structures based on vdW epitaxy for opto-electronic devices such as LEDs, high power electronics and detectors.

Experiments:

The growth was performed in an Aixtron MOVPE Close Coupled Showerhead (CCS) reactor on 3x2 inch sapphire substrates. Triethylboron (TEB), trimethylaluminium (TMAl), trimethylgallium (TMG), and ammonia (NH3) were used as B, Al, Ga, and N precursors, respectively. Two sets of samples were grown. The first set consists of 20 nm thick h-BN layers grown on 2-inch (a-, c-and m-plane) sapphire substrates at 1280°C, which allows us to investigate the effect of the substrate orientations on the growth of h-BN template. The growth rate of h-BN on different sapphire orientation was estimated by scratch and AFM technique (see supplementarysection 1). The second set consists of 500 nm thick GaN layers, using an intermediate 300 nm thick AlGaN (14% Al) layer, grown on 1.5 nm h-BN layer/sapphire substrates (a-, c-and m-plane).

Growth of all three sapphire substrates (a-, c-and m-plane) took place in the same run under identical conditions. Scanning electron microscope (SEM) and atomic force microscopy (AFM) were used to study the surface morphology of the samples before and after mechanical lift-off. The crystalline structure of the h-BN layer and the GaN/AlGaN/h-BN epilayers grown on differently oriented sapphire substrates was investigated by high-resolution X-ray diffraction (HR-XRD) scans, performed in a Panalytical X'pert Pro Materials Research Diffractometer system using Cu K𝛼 radiation in triple axis mode. This type of experiment allows us to study the diffraction of crystallographic planes parallel to the surface. It will be referred as out-of-plane diffraction in the following. To identify and confirm the orientation of h-BN ultra-thin layers, non-coplanar grazingincidence X-ray diffraction (GIXRD) measurement were performed using a Rigaku Smartlab diffractometer equipped with a Cu rotating anode and a 5-circle goniometer. The non-coplanar GIXRD geometry allows us to collect the diffraction of the crystallographic planes normal to the sample surface. This type of experiment will be called in-plane diffraction in the following. Highangle annular dark field scanning transmission electron microscopy (HAADF-STEM) characterizations were performed on an aberration-corrected ThermoFisher Titan 200 keV electron transmission microscopy to investigate the structural characterization at the nanoscale. Prior to this study, cross-sectional lamellae were prepared using focused ion beam (FIB) thinning and ion milling after coating a 100 nm thick carbon for layer protection.

Results and discussions:

We first address characterization of 20 nm h-BN grown on a-, c-, and m-plane sapphire substrates. Figure 1 presents SEM and AFM images of the three set of samples. A wrinkled surface is observed for the three h-BN samples grown on a-, c-and m-plane sapphire substrates with a variation in the size and shape of the wrinkles in each sample. The root mean square (rms) roughness of the h-BN grown on a-, c-and m-plane sapphire substrates are 3.2 nm, 3.7 nm, and 2.7 nm, respectively. As reported earlier [START_REF] Li | Large-Area Two-Dimensional Layered Hexagonal Boron Nitride Grown on Sapphire by Metalorganic Vapor Phase Epitaxy[END_REF][START_REF] Chugh | Flow Modulation Epitaxy of Hexagonal Boron Nitride[END_REF][START_REF] Sundaram | Wafer-Scale MOVPE Growth and Characterization of Highly Ordered h-BN on Patterned Sapphire Substrates[END_REF] , the formation of wrinkles in h-BN layer surface is an indicator of the high structural quality of the layered h-BN. It results from the thermal expansion coefficient (TEC) difference between h-BN and sapphire substrates, which induces a compressive strain in the layer during the cooling process. The wrinkling instability releases the energy, which creates roughness in the sample. The observation of wrinkles in the samples confirms the growth of h-BN layers on the three different sapphire orientations.

An interesting observation is the difference in wrinkle size and shape of the h-BN layer grown on a-, c-and m-plane sapphire substrates. Wrinkled surface of h-BN grown on a-and cplane sapphire exhibited an organized semi-hexagonal shape with an average size of 416 nm and 490 nm, respectively. The larger size of h-BN wrinkles grown on c-plane sapphire substrate can be explained by isotropic biaxial compressive strain which originates due to difference in values of the thermal expansion coefficients (TEC) in the oriented sapphire substrates. The compressive strain [START_REF] Saha | Comprehensive Characterization and Analysis of Hexagonal Boron Nitride on Sapphire[END_REF] can be expressed as follow:

∆𝜀 = ∫ 𝛼 ℎ-𝐵𝑁 (𝑇) -𝛼 𝑠𝑎𝑝𝑝ℎ𝑖𝑟𝑒 (𝑇)𝑑𝑇 𝑇 𝐺 𝑅𝑇 (1)
where 𝛼 ℎ-𝐵𝑁 (1.91 × 10 -9 T -2.96 × 10 -6 ) ○ C -1 ) and 𝛼 𝑠𝑎𝑝𝑝ℎ𝑖𝑟𝑒 are the linear thermal expansion coefficients of h-BN and the sapphire substrate; TG and RT are the growth temperature and room temperature, respectively. Since the values of TEC is different for a-plane (𝛼 𝑎-𝑠𝑎𝑝𝑝ℎ𝑖𝑟𝑒 (T) = (9.5 × 10 -9 T + 3.83 × 10 -6 ) ○ C -1 ) and c-plane sapphire (𝛼 𝑐-𝑠𝑎𝑝𝑝ℎ𝑖𝑟𝑒 (T) = (13.6 × 10 -9 T + 3.46 × 10 -6

) ○ C -1 ) [START_REF] Sundaram | Wafer-Scale MOVPE Growth and Characterization of Highly Ordered h-BN on Patterned Sapphire Substrates[END_REF][START_REF] Leszczynski | Thermal Expansion of Gallium Nitride[END_REF] , using these values in equation ( 1) results in two different values of compressive strain which are -1.76% and -1.47% respectively. This 0.3% difference in the strain value due to TEC of h-BN grown on a-and c-plane sapphire has an impact on wrinkle formations, resulting in different size of h-BN wrinkle domains as seen in figure 1a-b &d-e.

In the case of h-BN grown on m-plane sapphire, wrinkles are in a different formation and shape compared to the ones grown on a-and c-plane sapphire. They are aligned along sapphire aaxis, together with some line feature parallel to sapphire m-axis, which is less pronounced (figure 1c&f). Apart from TEC, another factor that can also affect the formation of wrinkles is the crystallographic difference between oriented sapphire substrates. Although, the a-plane and mplane are both parallel to the c-axis, they might exhibit different material properties such as surface energy, mechanical property due to their different atomic arrangements. This phenomenon may lead to variation in incorporation probability and diffusion length of surface atoms along different crystallographic directions, subsequently causing wrinkles to be more pronounced along sapphire a-axis in case of h-BN grown on m-plane sapphire substrate. This result provides the first evidence of the effect of sapphire orientation on h-BN. HR-XRD measurements can also provide better understanding on the structural properties and orientation of these set of h-BN layers. Figure 2 shows the out-of-plane 2θ-ω scans of 20 nm h-BN. The prominent diffraction peaks for a-, c-and m-plane sapphire are observed at 37.6°, 41.5°, and 68.7° respectively. The three sets of h-BN layers grown on different plane sapphire substrates exhibit a diffraction peak at around 26.0° and 53.7° which is attributed to h-BN (002) and (004) crystal planes, respectively. It is to be noticed that the (004) plane diffraction peak is very weak for the h-BN layer grown on a-and m-plane sapphire substrates. The observation of (002) h-BN diffraction peak in these out-of-plane 2θ-ω scans for the three set of samples indicates that the preferred orientation of h-BN is along the c-axis (figure 2b). h-BN has strong in-plane sp2 covalence bonds compared to vdW force between atomic layers. During the growth process, boron and nitrogen atoms may tend to bond to each other inside the layer, resulting in preferable c-axis growth direction. This is consistent with the report that under specific thermodynamic conditions, hexagonal materials have tendency to self-align along its natural axis. Miyagawa et al. [START_REF] Miyagawa | Growth of High Quality C-Plane AlN on a-Plane Sapphire[END_REF] reported that at high growth temperature (1430-1500°C), c-plane AlN was obtained when it was grown on a-plane sapphire. Shigeya's group also reported that variation of growth temperature of GaN on rplane sapphire led to different oriented GaN (c-plane GaN was obtained when grown at low temperature -less than 675°C whereas, a-plane GaN was obtained at middle growth temperature 675-690°C) [START_REF] Shigeya | GaN Remote-epitaxy on Graphene/r-plane Sapphire Substrates[END_REF] . The same behavior is obtained for 2D h-BN material where its orientation is found to be in a preferred c-axis under our growth temperature at 1280°C.

In addition, the low intensity and the higher broadness of the full width at half maximum (FWHM) of (002) h-BN diffraction peak indicates the misorientation of h-BN (or disordered BN) grown on m-plane sapphire, where the h-BN layered sheets are confined in short domains and irregularly oriented, losing long range order (figure 2c). The misorientation of h-BN/m-plane sapphire and the structural property difference of h-BN grown on a-, c-and m-plane sapphire may be related to the surface energy of different sapphire substrates. Several studies have demonstrated that the surface energy of substrates have a pronounced impact on the crystallographic orientation [START_REF] Chen | Van Der Waals Epitaxy of III-Nitrides and Its Applications[END_REF][START_REF] Körber | Surface Energy Controlled Preferential Orientation of Thin Films[END_REF][START_REF] Pu | 5 -Cryogenic Machining and Burnishing of Magnesium Alloys to Improve in Vivo Corrosion Resistance[END_REF] . It has been shown that SnO film orientation is related to surface energy of growth substrates [START_REF] Körber | Surface Energy Controlled Preferential Orientation of Thin Films[END_REF] . Qi Chen et al. [START_REF] Chen | Van Der Waals Epitaxy of III-Nitrides and Its Applications[END_REF] also reported that high surface energy or low migration barrier of substrates may induce misorientation or the 3D island growth mode for epitaxial layers. Surface free energy of sapphire with various orientations have been studied theoretically and experimentally [START_REF] Nosov | Faceting of Sapphire Crystals Grown from a Melt by the Stepanov Method[END_REF][START_REF] Bakholdin | Simulation of Surface Energies of Sapphire Crystals[END_REF] . It was reported that the surface energy of c-plane sapphire (3.357 J/m 2 ) < a-plane sapphire (3.858 J/m 2 ) < m-plane sapphire (7.126 J/m 2 ) [START_REF] Bakholdin | Simulation of Surface Energies of Sapphire Crystals[END_REF] . The high surface energy of m-plane sapphire compared to a-and c-plane sapphire may explain the misorientation of h-BN grown on m-plane sapphire.

To identify and confirm the orientation of h-BN ultra-thin layers, we have performed inplane non-coplanar GIXRD diffraction on the three set of h-BN samples grown on a-, c-and mplane sapphire as seen in figure 2d-f. The schematic of the experiments is shown in the inset of figure 2d. For a-and c-plane sapphire samples, the figure 2d&e shows 2/ scans collected along the in-plane <100> Al2O3 azimuthal direction. Since no monochromator has been used for these measurements, substrate Cu-K and W-L diffraction peaks are observed as displayed in figure 2d-f. We have identified two peaks at 41.62° and 75.98°, which may be attributed to (100) BN and (110) BN. The observation of both (100) BN and (110) BN peaks in the same 2/ scan indicates that within the whole volume probed by the X-Rays, there are some crystalline parts with in-plane <100> direction parallel to the <100> Al2O3 direction and others with <110> direction parallel to the <100> Al2O3 direction. It suggests that the h-BN layer is made of grains c-textured but with different in-plane orientations. To confirm this point, a 360°  scan has been performed for h-BN grown on c-plane sapphire (see supplementary-section 2). For h-BN grown on m-plane sapphire, the figure 2f shows 2/ scans collected along the in-plane <001> Al2O3 azimuthal direction. A diffraction peak at 76.6° was observed and attributed to (110) BN. It reveals that (110) BN is aligned with the (001) Al2O3. These observations of (100) BN and (110) BN parallel to (100) Al2O3 for a-and c-plane sapphire, and (110) BN parallel to (001) Al2O3 for m-plane sapphire confirm that the h-BN growth direction is c-axis in these three cases. In addition, we also observe a peak at 33.45° in figure 2d, which may correspond to (100) AlN. It can be related to the presence of AlN underneath h-BN layer due to nitridation, which will be discussed later.

Fig. 2. (a) HR-XRD 2θ-ω scan; b-c) schematic of preferred orientation of h-BN grown on different sapphire orientation; (d-f) GIXRD of 20 nm h-BN on a-, c-and m-plane sapphire. Inset of figure 2d: The schematic of the GIXRD experiments.

To investigate the impact of orientation of sapphire substrates on the control of the mechanical adhesion of h-BN, mechanical lift-off of 20 nm h-BN grown on a-, c-, and m-plane sapphire was studied. Corresponding optical and AFM images are presented in figures 3a-d. For h-BN grown on c-plane sapphire the mechanical lift-off occurred using simple scotch tape (figure 3b), which is in agreement with our previous study [START_REF] Vuong | Control of the Mechanical Adhesion of III-V Materials Grown on Layered H-BN[END_REF] . Figure 3e shows the corresponding profile as extracted from the AFM image (figure 3d). A thickness difference between the lifted-off region and non-lifted-off region was measured to be around 18±2 nm. However, for a-and m-planes sapphire, the lift-off of h-BN was not possible despite several attempts (figure 3a&c). It is an interesting result, which has never been reported and shows that the vdWs h-BN layer cannot be mechanically detached in all type of substrate orientations by using soft holder like scotch tape in our case. A possible interpretation of this could be linked to the structural quality (i.e.: the ordered layered lattice) of h-BN layer as reported by Sundaram et al. [START_REF] Sundaram | MOVPE of GaN-Based Mixed Dimensional Heterostructures on Wafer-Scale Layered 2D Hexagonal Boron Nitride-A Key Enabler of III-Nitride Flexible Optoelectronics[END_REF] . The misorientation of h-BN grown on m-plane sapphire may hinder complete lift-off of the grown layer. Another possible explanation for this might be related to a surface energy of sapphire substrates. The a-and m-plane sapphires have higher surface energy (as mentioned above) that can enhance the mechanical adhesion between substrate and h-BN, thereby impacting the possibility of lift-off of this layer. We believe that the mechanical lift-off of h-BN grown on a-, c-and m-plane substrates depends on several factors such as structural quality of h-BN and/or surface energy of sapphire substrates. For more quantitative interpretation, further investigations are needed.

Fig. 3: (a-c) Optical microscope of 20 nm h-BN grown on a-, c-, m-plane sapphire and AFM image (d-e) of 20 nm h-BN grown on c-plane sapphire after lift-off.

We first conclude that there is an impact of the sapphire substrate orientation on the morphology, structural properties and the mechanical lift-off of h-BN layers. Under our growth temperature (~1280°C), h-BN exhibits a preferred orientation which is c-axis with slight misorientation on m-plane sapphire. In addition, mechanical lift-off and spontaneous delamination of this material can be prevented when grown on a-and m-plane sapphire, resulting in mechanically inseparable robust h-BN layers. This investigation of the impact of different orientation sapphire substrates on h-BN layers provides deeper insight and support for a better understanding of the growth mechanism for vdW epitaxy of GaN/AlGaN on h-BN/a-, c-, and mplane sapphire, which is presented in the following.

The indirect influence of different orientation of sapphire substrates through hBN on vdW epitaxy of GaN was studied by growing 500 nm GaN/300 nm AlGaN (14%Al) on 1.5 nm h-BN on a-, c-, and m-plane sapphire. The surface morphology of these samples is shown in figure 4.

The surface morphology of GaN/AlGaN/h-BN layers grown on a-and c-plane sapphire were smooth with the presence of V-pits, more markedly for the sample grown on a-plane sapphire, indicating varying degrees of the GaN layer coalescence (figures 4a-b). On contrary, 3D GaN morphology is present on m-plane sapphire as shown in figure 4c. The surface exhibits the terraced structure, indicating that the GaN is not highly oriented along c-axis. This can be related to the above results of the misoriented hBN grown on m-plane sapphire, which can induce excess of misorientation spread. These results indicate that the different sapphire orientation affects the quality of the h-BN layer (discussed above), and this impacts the morphology of the GaN layer grown on ultra-thin h-BN layer. Further characterizations which were performed to validate this and will be discussed below. Additionally, HR-XRD measurements were made on the GaN films grown on h-BN layers on different oriented sapphire substrates. The 2θ-ω scan, in the 20°-80° measurement range were performed for the three samples as shown in figure 5a. For GaN/AlGaN/h-BN grown on a-and cplane sapphire substrates, two diffraction peaks were clearly identified at 34.55° and 34.79°, which correspond to the (002) reflection of 𝜔-GaN and buffer layer 𝜔-AlGaN (14% Al), respectively.

No other diffraction peak related to GaN was observed by HR-XRD scans, suggesting a good caxis alignment of the GaN/AlGaN/h-BN grown on a-and c-plane sapphire substrates. On the other hand, the 2θ-ω scan of GaN/AlGaN/h-BN grown on m-plane sapphire exhibits several low intensity diffraction peaks at 34.7°, 46.3° and 63.2°. The closest crystallographic planes corresponding to these values are (002) GaN, (102) GaN and (103) GaN, respectively [START_REF] Pang | Structure, Optical Properties, and Photocatalytic Activity towards H2 Generation and CO2 Reduction of GaN Nanowires via Vapor-Liquid-Solid Process[END_REF][START_REF] Keyan | Synthesis of GaN Nanorods by a Solid-State Reaction[END_REF] . The intensity of the (002) GaN peak increases from m-, a-to c-plane sapphire substrates, which is in accordance with the (002) h-BN peak intensities reported in the previous section (figure 2a). Figure 5b shows the rocking curves of the GaN (002) peak for the three samples. We determine the FWHM values to be 0.39°, 0.29°, and 1.18° for a-, c-, and m-plane sapphire respectively. The (002) diffraction peak is affected by screw dislocations, and the dislocation density is estimated to be 4E+09/cm 2 , 2.2E+09/cm 2 , and 5.1E+10/cm 2 for GaN/AlGaN/BN on a-, c-, and m-plane sapphire respectively. The lower dislocation density of GaN/AlGaN/BN on c-plane supports for the observation in SEM images (figure 4). Furthermore, the φ scan for a (102) plane of the three samples were also performed (see figure S3 -Supplementary). 6a-c. The thickness of the AlGaN and GaN layer was estimated to be approximately 300 and 500 nm, respectively. We also observe a thin continuous layer of h-BN represented by a thin, higher contrast area at the bottom of these figures. The threading dislocation density (TDD) is estimated to be around 5E+09/cm 2 for GaN/AlGaN/h-BN on a-and c-plane sapphire. The slight difference in TDD of GaN compared to calculation based on FWHM (002) rocking curve can be attributed to the limitation of grid size in TEM measurements. These dislocations may originate from the AlGaN layer and can be explained by the growth mechanism of 3D layers on 2D crystals.

Indeed, since the III-Nitride structure is grown on h-BN surface with no dangling bonds, these threading dislocations mostly originate from the formation of grain boundaries during the nucleation of AlGaN layer on h-BN [START_REF] Karrakchou | Effectiveness of Selective Area Growth Using van Der Waals H-BN Layer for Crack-Free Transfer of Large-Size III-N Devices onto Arbitrary Substrates[END_REF] . For GaN/AlGaN/h-BN grown on m-plane, the cross-section STEM image is completely different when compared to a-and c-plane, where a terraced structure has been observed, in agreement with the SEM image.

Further, figures 6d-f show zoomed-in images of both the Al2O3/h-BN and h-BN/AlGaN interfaces. The TEM images exhibit a crystalline structure of 2-3 layers h-BN with the lattice oriented along the c-axis for a-and c-plane sapphire. The interlayer distance of the h-BN layers is calculated to be 0.359 ± 0.003 nm for a-and c-plane sapphire. In case of m-plane sapphire, the h-BN sheets are not sufficiently well oriented, with respect to the substrate, leading to the lack of visibility of BN structure. In addition, we observed an un-intentionally grown AlN layer at the sapphire/h-BN interface in all the three samples, which may be due to nitridation. It is confirmed from the obtained AlN peak in GIXRD measurement of h-BN on a-plane sapphire (mentioned above). The orientation of the AlN layers underneath BN layer is systematically c-axis for a-and c-plane sapphire, while for m-plane sapphire AlN seems amorphous (or polycrystalline). A similar observation has been previously reported [START_REF] Vuong | Control of the Mechanical Adhesion of III-V Materials Grown on Layered H-BN[END_REF] with the assumption that different growth temperature can affect the structural quality of AlN layer at sapphire/h-BN interface. However, we believe that apart from growth temperature, the structural quality of this AlN layer can also depend on the orientation of sapphire substrates, which will need further study to confirm.

To evaluate an orientation relationship existing between the GaN/AlGaN layers and h-BN as well as different oriented sapphire substrates, we have examined selected area electron diffraction (SAED) pattern for oriented sapphire substrates (see supplementary-section 4) and for the AlGaN layer of the three samples as shown in figure 6 g-i. A well-ordered SAED pattern with single orientation spots can be seen for the samples grown on a-and c-plane sapphire substrates (figure 6g&h), indicating good crystalline quality of the AlGaN layer. The growth axis for the both AlGaN layers is [001], independent of the sapphire substrate orientation, but in the same growth orientation with h-BN layers. For the sample grown on m-plane sapphire, the SAED pattern consists of split spots, indicating a misorientation of the AlGaN crystal (figure 6i). From these results, we can conclude that the AlGaN (or GaN) layer is c-plane oriented and is strongly impacted by the orientation of h-BN buffer layer.

Conclusions

In summary, we have studied the effect of differently oriented sapphire substrate on 2D h-BN layer and on vdW epitaxy of 3D GaN/AlGaN on 2D h-BN materials. We found that there is an impact of sapphire substrates with different orientation on the morphology and structural properties of h-BN layer. Under certain growth temperature, h-BN can align itself to its preferred axis c-axis with a slight misorientation on m-plane sapphire. In addition, mechanical lift-off and spontaneous delamination of this material can be prevented when grow on a-and m-plane sapphire, resulting in mechanically inseparable robust h-BN layers. Further, vdW epitaxy of GaN/AlGaN exhibits strong dependence on h-BN layers from morphology to crystalline orientation. These results bring deeper understanding of vdW epitaxy combined with the orientation of sapphire substrates, giving more potential approach of using h-BN or III-Nitride materials in opto-electronic devices such as LEDs, high power electronics and detectors.

Supporting information

The Supporting Information is available free of charge.

Fig. 1 .

 1 Fig. 1. SEM and AFM images of h-BN grown on a-plane (a&d), c-plane (b&e) and m-plane (c&f) sapphire.

Fig. 4 .

 4 Fig. 4. SEM images of GaN/AlGaN (14%Al)/1.5nm h-BN on: (a) a-plane sapphire, (b) c-plane sapphire and (c) mplane sapphire.

Fig. 5 .

 5 Fig. 5. (a) 2θ-ω scan and (b) (002) rocking curve of GaN/AlGaN/1.5 nm h-BN on a-, c-and m-plane sapphire; (c-d) schematic of preferred orientation of GaN/AlGaN/BN grown on different sapphire orientation (e) SEM image of GaN/ AlGaN/1.5 nm h-BN on c-plane sapphire after lift-off.

Fig. 6 .

 6 Fig. 6. (a-f) HAADF-STEM images of GaN/AlGaN/1.5 nm h-BN on a-, c-and m-plane sapphire; (g-i) Selected area electron diffraction (SAED) patterns was obtained from AlGaN layers of the three samples.

( i )

 i Estimation of the growth rate of h-BN; (ii) Phi scan of h-BN/c-plane sapphire; (iii) Phi scan of GaN/AlGaN/BN on a-, c-, and m-plane sapphire; (iv) TEM image of GaN/AlGaN/BN and SAED pattern of the a-, c-, and m-plane sapphire Acknowledgement This study was partially funded by the French National Research Agency (ANR) under the GANEX Laboratory of Excellence (Labex) project and the Grand EST Region in France. It has been also partly supported by the French Renatech network and the ANR "Investissement d'Avenir" program (TEMPOS project no. ANR-10-EQPX-50).

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Notes:

The authors declare no conflict of interest.


Gilles Boucherit
email: gilles.boucherit@univ-rennes2.fr

Fomoire

Cath Magh Tuired

Orin

Danu An

Tuatha Dé

Danann Zo

Ken Pell

Between Siberia and Anatolia ?

INTRODUCTION

Some people may be amazed by the subject of this study when many searchers seem to think that the problem of Ana / Dana is solved: Ana is Dana. But fortunately everybody does not agree with this: "[...], Anu, who was especially connected with Munster, was considered to be mater deorum hibernensium, while the deities of Ireland were known as Tuatha Dé Danann [...]. There has been a great deal of confusion between Anu and Danu and it is in question whether they are actually distinct persons in origin or not." 1 At first sight however, anybody can notice that Ana is close to Neolithic, milk and the country, whereas *Danu is mother of three gods related to warrior tribes invading an island. In this study we have chosen to follow the steps of the two characters, each one separately. The first one *Danu will bring us to the great rivers of Siberia, the second one Ana to the Hittites and Neolithic farmers from Anatolia ultimately. But obviously both are said to be Mother Goddesses. One more remark: we think to have succeeded in getting rid of the legend of Anna's early Christian cult in Brittany.

*DANU

The first thing to notice when examining Dana's name is that it can be found nowhere in the Old Irish texts. The nominative *Danu has been built up again from the genitive Danann, as in the well-known Tri Dé Danann for example or Tuatha Dé Danann. 2 The Dana entry is not even found in the Dictionary of the Irish Language neither in the Lexique Etymologique de l'Irlandais Ancien, only *Danu wherefrom the reader is sent to the genitive Danann. The form *Danu is very close to the hypothetic Indo-European *Donu ha *Donuva both deduced from Indo-European attested languages. Concerning the invisible character under this name we only know that she is a goddess, moreover a prehistoric watercourse which would have been named *Donu and personalized in several Indo-European civilizations." 3 The Trí Dé Danann are well known : Brían, Iuchar and Iucharbha, as *Danu's sons, herself Delbaeth's daughter and in the same time Tuireann Picreo's wife, her father "because Tuireann Picreo is only an other name of Dealbáeth." 4 Etymology *Danu is a Mother Goddess whose name is derived from watercourses known by searchers as the Don, Dnieper, Donets, Dniester, all names built on Danuvian roots. [START_REF]Tome cinquième[END_REF] The list can be lengthened with the Proto-Indo-European *Deh3nu or Dehanu. Although there is a large consensus about *Danu's philological analysis, this does not prevent scientists to stay uneasy about her character: "In summary, one may deduce that there was a prehistoric, probably Neolithic tribe, which inhabited an area near a watery place, perhaps river or stream. This water became personified as a feminine deity, and the goddess gave her name to the tribe. The tribe was probably not Indo-European but one with which the Proto-Indo-Europeans came in contact early on." 6 In fact, even this large consensus on *Donu's etymology is questioned because of new phonological considerations:

The Slavic river-names Don, Dnieper, and Dniestr are borrowings from Scythian *Dānu, *Dānu apara 'upper river', *Dānu nazdya 'lower river'. [...], Welsh Donwy leaves no doubt that Celtic and Iranian had the same inherited river-name. Despite the views of earlier scholars [...], who took Danube to be Iranian in origin, a Celtic source cannot be ruled out on linguistics grounds, and the name Dānuvius is first attested in the Celtic-speaking western region of the Danube basin. [START_REF] Hemon | Geriadur istorel ar brezhoneg. Levrenn III, 1995-1998[END_REF] So far, so good, but where is the problem? The Danube's name <*Dānouiohas been associated with *Danu, the Irish Goddess name. Here is the point, following the author: "the Irish has a short a or short o, the Welsh a Celtic short o, and Danube < *Dānouio-a long ā."8 However, when one remember that *Danu is not a Celtic word, but, as we have seen, a word adaptated in Celtic from the Indo-European *Donu, and "because the Danuva tribe were borrowings into Celtic (rather than formulated in Celtic), as well as the other IE languages, one does not have to account so closely for the vowels as one would if *Danu had been of Celtic origin."9

Origin of the word *Donu

To go forward regarding the origin of the word, one can turn on Neolithic Siberia. When one try to study early Evenk concepts, there is a word often met with, that is buga, meaning the world around, the world as a whole. Everything around the Tungus, earth, living place, taiga, country, region was Buga or Dunne:

The stem dun || don is apparently of very ancient origin, and existed before the crystallization of the linguistic stocks [which form the basis of] modern language families. In Sanskrit the word dhuni meant "river. 10 With this form dhuni one recognize the Proto-Indo-European form *deh3nu mentioned previously. 11 Vasilevich explains: "A. Afanasyev points out that [the] word dhuni was introduced into the Slavic languages from the east ("Don," "Danube," and, in general, "river" in the songs of the Poles and Galicians). [...]. As, it developed further, its original meaning, "surrounding nature" (mountains, rivers, forests) was restricted differently in the different linguistic stocks: in some to "land" (mountains, forest), in others to "river." 12 River banks used to be inhabited because of the fish and the animals in the neighbouring woods. Elk would come to quench their thirst in them. Therefore we think to have found a tribe which would meet Miriam Dexter's requirements, the Evenk of the Podkammenaya Tunguska 13 for instance. The Evenk have produced the concept Bugady Enintyn : mother of the universe, the plants, the animals, and the people, which explains her animal and human shapes.

"The Evenks of the Podkamennaya Tunguska called by the name "mother" the taiga, mountains, and rivers, and even their place of settlement, saying of the latter that it is their clan mother-land." 14 The same could be said also of Evenk Yenisei of the north, for whom the earth is a mother and they call her dunne enin "mother earth". As we can see it is possible to give a Tungusic origin even a far one to the Indo-European *Donu, which will probably split diachronically in two Celtic roots, Gaelic *Donu / *Danu and Brythonic Don.

ANA

This does not bring us back the name Ana, which could derive by analogy from Nana or from Anāhita as well:

"If Tanaïs and Dānav are, as it seems, borrowings to the pre-Iranian languages, one may find may be in Tanaï-/ Nanaï an old name of water or of river changed later as Nana as if it were a Lallname." 15 And although we know that "Tanaïs, the name of the Great Goddess in Asia Minor, means in the Scythians country the river which later will be called Don" 16 , there is no linguistic evidence as far as we know, which would enable to pass from Nana to Ana or from Anāhita who is also an Indo-European river goddess to Ana.

In Hittite though, which is the oldest written Indo-European language, we have Hanna-for 'grandmother', "the name of the goddess HannaHanna which is built up by the doubling of Hittite substantive hanna-[...] means probably 'great-grand-mother' or 'ancestress'." 17 Hanna-became 'anna' for "mother", 18 Contrary to the goddess Dana, the form Ana is testified in the Dictionary of the Irish Language : "Ana name of a goddess [...] : A. .i. mater deorum Hibernensium."20 She is a goddess and a mother like *Danu. She is Sovereignty and personifies Ireland : Anann .i. Eireann. 21 A very well known detail helps us to distinguish between the two goddesses: Dā Chīc[h] nAnund or Da Chigh Anann. 22 On top of being national Ana is also regional. How can we conciliate these two aspects of her social role and nature? In Cath Magh Tuired we learn that the TDD have no knowledge of agriculture. This enables Dumézil to write: "[...] before the battle, the Tuatha Dé Danann did not have all the competences necessary in a sedentary community: they had command of druidic magic, warrior prowess, all the arts and crafts, and the techniques of medicine and smithcraft, but they lacked competence in agriculture." [START_REF] Cathasaigh | Cath Maige Tuired as exemplary myth in Folia Gadelica[END_REF] This remark is followed by another one on the Indo-European teomachy or gods war: "which [Dumézil] interprets as a war between representatives of the first two functions and those of the third, leading to the incorporation of the later into the community of the former." 24 This is probably what happened to the defeated: they have been incorporated in the Tuatha Dé Danann's community, including their Neolithic agricultural deities identified sometimes as two hills symbolizing the milk of the earth as if it were a mother. This tribal "native" deity has been given the Celtic name Ana and be raised to the level of the island, symbolising now Irish sovereignty as becomes a warrior people. Ana will take place *Danu's social function. The process at least fits in the concepts of the History of Religions. One must keep in mind that most goddesses assimilated into Indo-European pantheons have their origin in neolitik Europa and the Near East, not in the Indo-Europeans. 25 Their origin does not mean their name. They may have been assimilated in the "Celtic social organisation" forming therefore a new syncretism always based on the triad already present apparently in the three *Danu' sons for instance, Brian, Iucharba and Iuchair, in which the (Proto-)Indo-European traces of the twin brothers or Dioskouri may be noticed. This organisation probably persist in the future canonical pantheon "formed by its basic triad Lug, Dagda-Ogme." "Dagda-Ogme are two brothers who form the diptych of the great double divinity corresponding to Mitra-Varuna in Vedic terms." [START_REF] Guyonvarc'h | Dagda et Ogme, qui sont deux « frères », forment le dyptique de la grande divinité double correspondant à Mitra-Varuna en définition védique[END_REF] Mingling Ana / *Donu I made a rapid survey in part 7 of the Lebor Gabála Erenn, and listed the phrases mentioning Ana: out of 6 occurrences, [START_REF] Macalister | Lebor Gabála Érenn, Part IV, Levrenn XLI[END_REF] I found only one mingling Danann with Ana: "In Mor-rigu, ingen Delbaith mathair na mac aile Dealbaith .i. Brian 7 Iucharba 7 Iuchair: 7 is dia forainm Danand o builead Da Chich Anann for Luachair, 7 o builed Tuatha De Danann." [START_REF] Macalister | The Morrigu, daughter of Delbaeth, was mother of the other sons of Delbaeth, Brian, Iucharba, and Iuchair: and it is from her additional name "Danann" the Paps of Ana in Luachair are called, as well as the Tuatha De Danann[END_REF] We can but notice that the confusion occurred with the variant Danann so that we think that euphony may have been an incentive to confusion: "It should be noted that the confusion between the two names occur with "the variant Tuatha Dé Danann [...] of the later Middle Ages, [succeeding to] Tuath(a) Dé Donann, [after] the sporadic shift o > a characteristic of the modern Gaelic languages occurred". [START_REF] Carey | Tuath Dé in Celtic culture[END_REF] I extended the survey to 8 other writings all chosen in entries Ana and *Danu of the Dictionary of the Irish Language: Keating, Cath Maige Tuired, Coir Anmann, Cormac's glossary, O'Clery's Irish glossary, Eriu XIII, O'Donovan, and O'Davoren's glossary. In Keating I have found "dá chich Dhanann" [START_REF] Keating | The history of Ireland[END_REF] in O'Donovan "Dá chich Danainne, i.e. the two paps of Danann" [START_REF]Supplement to O'REILLY, Edward. An Irish-English dictionary[END_REF] , and in Sanas Chormaic, again on the part of O'Donovan "Ana, or as she is most usually called Danann, [...]". That is only three confusions, on the part of two recent authors (without forgetting Macalister himself who mingles the names twice). [START_REF] Macalister | See also D.A. Binchy in Celtica[END_REF] On the other hand, out of 9 occurrences I have found 8 times *Danu as the Tri Dé Danann's mother in the LGE part 7. 33 Here is the phrase which best characterises her in my view: nomadic society now settled on farmer lands in an island named Eireann, [START_REF] Koch | [END_REF] after the final victory of CMT 1 and 2. One should not forget that the Ancient Celts (before writing) would not distinguish between mythical cosmology and history.

Chronology

We cannot really give dates to the Tuatha Dé Danann because those mythological texts are no ordinary ones to read. All the same the Dagda's cauldron in CMT2 is in brass [START_REF] Gray Elizabeth | A gold, silver, and bronze smith (cerd). Crédne's epithet, cerd, "craftsman, artisan[END_REF] (or bronze) which cannot be dated earlier than the tenth or even twelfth century BC [START_REF] Koch | An atlas for Celtic studies[END_REF] . But we find "iron" [START_REF] Mallory | The Indo-Europeanization of Atlantic Europe[END_REF] in the first battle of Moytura (between the TDD and the Fir Bolg), the language of which is more recent. 40 There is another archaeological piece of information in CMT1 about where the first sheep landed in the island: "The wind freshened, and the storm drove Gann and Sengann till they put in at Inber Douglas, where Corcamruad 41 and Corcabaisginn meet. There they landed, and this is the first place to which sheep were brought in Ireland, and Sheep's height is its name." 42 This event brings us back to about the fourth millennium BC at the beginning of Neolithic in Ireland, that is of agriculture, and there is no other solution than to admit the people kept the memory of the event in their minds. In Corcomroe Co. Clare (Munster) they still take care of sheep today: "Large quantities of corn, butter, sheep, and pigs are shipped here [Burren] [...]". [START_REF] Lewis | A topographical dictionary of Ireland[END_REF] Contemplating some awful(ly interesting) vistas [START_REF] Tresset | French Connections II: of cows and men in Neolithic Settlement in Ireland and Western Britain / School of archaeology and palaeoecology (Belfast)[END_REF] Killarney, Co. Kerry is still in Munster where lies "Dá Chích Anann", the two fabulous hills: "There is a stream running between the hills. One half flows north into a small lake called Lough Nageeha and the other half flows south into the Clydagh River." 48 The presence of water, usually not emphasized is nevertheless as much important as the famous two paps from a farmer's point of view landing in a new land. All the animals, sheep, cattle and goat that the Neolithic people brought with them produce milk. So that water can be associated with the land and the milk they get from their beasts which live upon the land as if it were a mother. They came to Ireland from the Atlantic shores as we know. In Armorica, the bond between water, milk and the land as a mother is clearly evidenced in the Briec (sur Odet) area for instance, in the Menez Du or Black Mountains, where three fountains can be found: "The first one, huge and spacious, is dedicated to Our Lady, a typical statue of whom can be found in her niche. It is her that nurses would hasten to, not long ago, since the Sources Virgin was also the "Milk Mother"." [START_REF] Braz | Les saints Bretons d'après la tradition populaire en Cornouaille (1893-1894[END_REF] Around Carhaix in the Menez Are or Aré Mountains: "There was neither a mother nor a nurse throughout the country who didn't think they had to go [to the Frout chapel] once a year to invoke or to thank the "Milk Virgin" known as the "Sources Mother". Sources spring from everywhere in the small stony and sunken way which goes down to the oratory. Their water would come in mains to fill a round basin dug in the holy enclosure. [...]. It was the nurses' duty to clear and clean the water basin and then to throw needles in it from their blouse as a gift, and recite this short prayer:

Lady of the Frout, mother and Virgin Good health to the child, and to us milk!" 50

Two breasts close to the chamber 51 Commana in the Aré Mountains is a good instance of this possible complex because of Ana included in the place-name, but also because of the Neolithic grave "Ti lia ven [START_REF] Goffic | Commana et les monts d'Arrée[END_REF] " in Mougev Vihan dated to the 3 rd millennium BC [START_REF][END_REF] . It has been built close to the source of a watercourse the Mougau, which flows into the Elorn and to the sea. On the northern pillar of the passage grave 54 can be found the (double) breasts of a Mother-Goddess or "stele idol" as it is called by archaeologists. The name Commana is usually analysed this way: Komm means "valley", which suits well "the high place of the village between two nascent hills [START_REF] Tanguy | Dictionnaire de noms de communes, trèves et paroisses du Finistère[END_REF] ", and An(n)a, or even Mana after Joseph Loth. [START_REF]Les noms des saints Bretons[END_REF] But from Mana 57 you are directed to An(n)a. Mana therefore is only a matter of tonic stress. One of the oldest form of the place-name, second half of the XIth century, is de cvmmanna attested in the Cartulaire de l'abbaye de Landevenec [START_REF] Borderie | Cartulaire de l'abbaye de Landévenec[END_REF] as part of a list of place-names like for instance de Pleiben or de Bratberth, and is contemporary with « Cummana ». 59 Two ecclesiastics, Peyron and Abgrall, referring to the La Borderie edition explain: « Le Cartulaire de Landévennec tells us that the monastery possesses two lands in Commanna (de Cummanna), Caer Niuguinen and Caerthnou". [START_REF] Peyron | nous apprend que le monastère possédait en Commanna (de Cummanna), deux terres[END_REF] Actually, in order to object to the popular tradition reported by father Auguste Laurent (1875), of an older eponymous Venus whom the inhabitants would call Sainte Anne, Peyron and Abgrall don't want 'Cvmmanna' to be an eponymous place-name and say instead that it is the word: " Coummand, coummanha, which means to give a land as a fief, to enfeoff, where the words Kemened, Commendatio et Convenant (Le Gonidec) come from". 61 La Borderie mentions in the Variantes of his cartulaire edition: "In the middle-Ages, in Breton, kemenet = fief". No doubt he would have mentioned Commanna had it been a Kemenet. But he did not because "in the beginning of the XIth century [...] the name Kemenet-Ili [...] is translated Commendatio Ili." 62 Le Men-Ernault in a note of their 1886 edition of the cartulary write that Cummanna belongs to the Berrien (Berriun) parish [START_REF] Le Men René | Cartulaire de Landevennec[END_REF] which Peyron and Abgrall will quote.

All this explanations to make clear that whichever edition is concerned and whoever may be right or wrong on the true location of Commanna in the cartulary, none of the editors consider Cvmmanna to be a Kemenet. On top of that Albert Deshayes writes: « Komanant (commanant, 1464), « Coumanāt » in the Katolikon (Tréguier, 1499), is a borrowing from ancient French covenant, agreement, stipulation, promise, word (1155), with a false restitution of the internal syllable". [START_REF] Deshayes | … est un emprunt à l'ancien français covenant, accord, stipulation, promesse, parole (1155)[END_REF] Now, we've just read that Cvmmanna and Cumana are dated to the (middle of the) XIth century, therefore we can reasonably say that Comman(n)a is neither Kemenet, nor Commendatio nor Convenant, but what is left, that is probably the eponymous Komm + An(n)a.

As a chronology, we propose that there has been a gallo-roman Venuz christianized as Sainte-Anne in Comman(n)a. But Sainte-Anne's worship is not older than the XIIIth century in the West, whereas An(n)a is attested in the middle of the 11 th century in the eponymous placename Cumman(n)a as just seen. We know that in the fourth-fifth centuries, "the migrants land in a country stayed mainly rural and remained devoted to their religious observances inherited from the old autochthonous background partly romanised." [START_REF]Landevennec : aux origines de la Bretagne. XVe centenaire de la fondation de l'abbaye de Landevennec[END_REF] Why not imagine that the galloroman Venuz is herself a romanization of an older stele-idol called An(n)a by the Celts and christianized later on as Sainte-Anne by the people because no other name would fit them?

With this place-name we come to the problem of Christian Anne whose cult would have been supposedly earlier in Brittany than anywhere else. This is the way after Lallemand: 70 "in 610 saint Colomban landed in Nantes for Ireland on a ship coming from the island to bring goods to the harbour, and may be also some pilgrim to the Vannes country, who had been to Jerusalem with sant Arculphe 71 on saint Anne's and Joachim's grave." 72 Following saint Anne's words who appeared to Nicolazic for the first time in August 1622, a small chapel had been built in her honour at the time in the field called 'Bocénno', 73 close to a source, 74 before the very existence of Kêr Anna. Saint Anne would speak Breton because Nikolazic knew only the vernacular, but we're only left with a French translation: "It's been 924 years and 6 months since it has been ruined" [START_REF]Il y a neuf cens vingt et quatre ans et six mois qu'elle a été ruinée[END_REF] said also Anna to Nicolazic, that is the 25 of January 700. This chronology strangely fits in with Largillières words: "The Les-, Ker-are much more recent archaeologically and they sometimes have the eponym of the parish, because these are real ancient names". [START_REF] Largilliere | Les saints et l'organisation chrétienne primitive dans l'Armorique bretonne[END_REF] First of all, Lallemand makes a Breton out of Arculfe, and of Adamnan an abbot from sant Colomba instead of Iona. Secondly he deduces that the idea to build a sanctuary to Anna must date back to 610, that is during Columban's time ( † 615). But actually: "Arculfe was a Franc bishop from the second half of the 7 th century, [...]. Around the year 670 he went on pilgrimage to the Holy Land and stayed 9 months in Jerusalem." On his way home to Gaul, he would have been caught in a tempest and his boat drawn on the west shores of Britain: "One can hardly imagine that wrecked Arculfe would have reached Adamnan's monastery, or that he would have been drawn there by the tempest". [START_REF] Delierneux | Arculfe, sanctus episcopus gente Gallus : une existence historique discutable[END_REF] Arculfe's pilgrimage has been narrated by Adamnan.

J.-P. Migne mentions the year 690 [START_REF] Migne | Arculfus, urbis cujusdam in Gallia episcopus, claruit 690. Suscepto, religionis causa, in Orientem itinere, ac lustratis locis sanstic, Damascum quoque, Constantinopolim, Alexandriam aliaque loca adiit, ac demum in Galliam rediens, vi tempestatis in occidentalia Britanniae littoral delatus, et ab[END_REF] when Arculfe became famous. [START_REF] Delierneux | Arculfe « whose Gaulish see has still to be identified[END_REF] Anyway if the small chapel would have been built just after Arculfe's pilgrimage, that is between 670 (or 690) and 700, how is it that "the nature of the remains described by the eyewitness Hughes de saint-François "stones of a church window and else, hewed and squared" But all this does not tell us who pre-Celtic Ana is. Archaeology shows us what is called a "stele idol" in Armorica. One of the oldest found in Mane Vihan (Morbihan) dates back to the beginning of the 5 th millennium BC. [START_REF] Lecornec | Documents Archéologiques de l'Ouest[END_REF] In Locmariaquer (Morbihan) there will be found another one inside the passage grave called the Merchants Table, but which had been outside before. [START_REF] Le Roux | Carnac, Locmariaquer et Gavrinis[END_REF] The evolution must have taken place at the eve of the 4 th millennium BC. There is a theory which says that the 'stele idol' had been placed under ground because death had been added to the Mother-Goddess' functions as can be seen in Commana for instance dated to the 3 rd millennium BC. Since "the long abandoned attempt to derive the megaliths of Europe from the east Mediterranean [...]",87 the ultimate origin of the 'stele idol' cannot be Anatolia, but could Anatolia be the original place of the Mother worship: Anna in Hittite, Ana in Turkish, whose name would have been spread in Europe by the Celts? I'm not sure the name Ana could join with the case of Old Irish carn (cairn), a Gaulish cognate of which is demonstrated by Carnac in Brittany. John T. Koch "can think of no Celtic word more likely to be a legacy from the age of megaliths. Linguistically, this legacy looks to be neither Celtic nor even Indo-European." 88 CONCLUSION Following our study, it is safer to treat separately the two mother-goddesses, *Danu and Ana. They may represent both the same mythological function but not in the same time, nor for the same type of society. *Danu still represents a society of warriors with their divinities, invading an island as shown in Cath Maige Tuired. Whereas there is already with Ana some farmer-breeder traits as water and milk for instance which indicate that the evolution has gone a step farther after the battle when the island has turned Irish. One should not be surprised at the far Siberian root involved in *Donu's name, after Jozef Weisweiler's pioneering work on the bull and deer cults in Europe. [START_REF] Weisweiler | Die Kultur der Irischen Heldensage, in Peideuma. Frankfurt, 1950, p. 149-170, and Vorindogermanische Schichten der Irischen Heldensage[END_REF] The Early Hittites had a deer cult [START_REF] Thierry | Le culte du cerf en Anatolie et la vision de saint-Eustathe[END_REF] and traces of one can be found in Buile Suibhne § 40 [START_REF] O'keeffe | A mathair na groidhi-si[END_REF] the origin of which could be Siberia. Today I would approve of the theory never evidenced before of the identity of the Breton An(n)a with the Irish one, despite the numerous attempts to Christianise her. Finally, one should reflect that if we were sent back at about the 7 th millennium BC in the south Urals area, we could make out hunter-gatherers learning to domesticate animals thanks to people coming from the Levant 92 . This area is not very far from Anatolia which the agriculturists left at about the same time to south-east Mesolithic Europe [START_REF] Mazurie De | Genèse et diffusion de l'agriculture en Europe[END_REF] . In their turn, Kurgan people living in a steppe region adjacent to the Urals made their way to the West in the fourth/third millennia BC and confronted the agricultural population of Old Europe. It is the cultural history of these two waves of population which we have tried to document in this study.

"

  The six sons of Delbaeth, s. Ogma s. Elada s. delbaeth s. Net were Fiachna Ollom Indui, Brian, Iucharba, Iuchar, Donann daughter of the same Delbaeth was mother of the last three. Of her are named the three gods of Dana, and the Tuatha De Danann, and the Hill of the Three Gods. And that Delbaeth had the name of Tuirell Biccreo." 34 Let us now compare the two characters: *DANU ANA Delbaeth / Tuirell Biccreo's Daughter and Housewife Mother-Goddess Mother-Goddess Mother of three sons -(the future TDD) Mother of the Gods of Ireland (the TDD) Hill of the Three Gods of Dana Two Hills of Ana Water and Milk It seems reasonable to think therefore that *Danu is earlier than Ana or else how could the Tuatha De Danann exist if there had not been before them the three gods named after their mother: Trí Dé Danann ? "They [Brian and Iuchar and Iucharba] were the three gods of Dana, from whom were named the Tuatha De Danann, [...]." 35 In our view, Ana as Mater deorum hibernensium plays the same role of Mother Goddess as *Danu but in what was previously a

  "The Burren name comes from the Irish word Boireann which means a place of stone." [...]. "One quarter of all the known megalithic wedge tombs in Ireland are situated in this region." 44 "The abbey of Corcumroe, county Clare [...] was under the patronage of Our Lady; and was called "the abbaye of the Fertile Rock"-probably because of its vicinity to a celebrated well dedicated to St. Patrick on the very summit of the Rosraly mountain. 45 [...]." "On the summit [there] is a well springing from the solid rock; it [...] produces water of the purest quality, which is conveyed by pipes to the road side at the foot of the mountain. » 46

  Danubius, Dānuvius, ancient nom du Danube, un des grands fleuves de la Celtique appelé Istros par Hérodote. Correspond à la rivière galloise Donwy dont le protot. est *Dānovios. Dérivation en -io-

	STERCKX, op. cit., p. 8.
	DEXTER, M.R. in Encyclopeda of Indo-European culture / ed. Mallory, Adams. London, Chicago, 1997, p.
	487.
	DELAMARRE, Xavier. Noms de lieux celtiques de l'Europe ancienne (-500 / +500). Arles, 2012. « Aut. Class.
	Δανούβιος, Δανούιος,

d'un th. i.e. *dānuqui désigne le fleuve en avestique, dānu-, et en ossète don, et qui en Europe a servi à former des noms de fleuves : Eridanos (celt. *ēri-dānos 'le fleuve de l'Ouest'), Dar-danus et les fleuves « russes » Don, Dniepr (scythique *Dānu-apara), et Dniestr (scythique *Dānu-nazdya). » p. 133. MACLEOD, Sharon paice. Mater deorum Hibenensium, in Proceedings of the Harvard Celtic Colloquium, Vol. XIX, 1999, pp. 349-363.

  a hypocoristic. The Hittite therefore gives us the best way to explain Anna (or Ana 19 )'s Celtic origin till now. 12 VASILEVICH G.M. Op. cit. p. 77, n.6 13 A Tunguska tributary 14 ANISIMOV, A.F. Cosmological concepts of the peoples of the North, in Studies in Siberian shamanism, op. cit., p. 175 15 PRZYLUSKI, op. cit. p. 37 16 Ibid.

17

KELLERMAN, Galina. La déesse Hannahanna, in Hethitica, VII, 1987, p. 110. 18 BENVENISTE, Émile. Le vocabulaire des institutions indo-européennes, 1973: « De plus, seul le groupe hittite a fait de anna-(luwi anni-) le terme pour « mère », p. 6. 19 MURPHY, Gerard. Duanaire Finn, part III. Dublin, 1953, p. 210.

  . La Borderie considers that "Commanna does not and could never belonged to Berrien (Berriun) parish: since Berrien has always been in the Cornouaille diocese, and Commanna in the Leon's one. [...]." 64 Therefore instead of: "[34] DE BRATBERTH. 65 Rudheder, Carrent Luphant, Caer Niuguinen,

	Caer Thnou
	[35] DE CUMMANNA IN PLEBE BERRIUN. Caer Budian, Trefgellan, VI
	villas" 66
	he proposes his own reading of the Quimper manuscript:
	"[XXXV] De CVMMANNA. Caer Niuguinen, Caer Thnou," 67

  [START_REF] Hughes | pierres d'un vitrage d'église, et autres taillées et écarrées[END_REF] "seemed to indicate a gallo-roman construction" 81 toLallemand? In what way does the expression "seemed gallo-roman" strengthens the necessary 'destruction' without which Lallemand could not bear his incredible thesis of a cult of Sainte Anne in Brittany brought in 610 by a travelling companion to Arculfe in the Holy Land? All this sounds contradictory. I think therefore in a possible slip of the pen may-be revealing in compensation the true antiquity of the site 'ruined' in the course of time, a situation which after all would not be unique in Brittany, but which would be in contradistinction with his arbitrary choice of the destruction by brigands led by Ogerius supposedly at the end of the VIIth century.82 On top of that, in the place-name Treanna Largillière thinks that "Anna is not saint Anne, the Virgin Mary's mother, whose worship spread at the end of the Middle Ages but undoubtedly a Celtic name."83 Therefore what more do we need, in order to consider the early Sainte Anne's Christian cult in Brittany a legend?[START_REF] Chassé | Le culte Breton de sainte-Anne et la vénération des vierges noires[END_REF]

ROSS, Ann. Pagan Celtic Britain. London ; New York, 1967, p.

Sjoedtedt, 1949: 24 f. PEB, Cw. In KOCH, John T. Celtic culture. Santa Barbara, Cal. ; Denver, Col., 2006. ANU [...]. « Danu, Danann or Donann sometimes alternates with Anu as a variant form, but was probably originally a different mythological figure whose name has a distinctly separate origin", p. 78.

LAMBERT, P.-Y. LEIA (Lexique Etymologique de l'Irlandais Ancien). Paris ; Dublin, 1996 ; D-24 : « *Danu est parfois comparé au nom de déesse Anu; mais il semble préférable de l'identifier au gall. Don, nom de la mère de nombreux dieux dans la mythologie du Mabinogi : c'est la déesse-mère, SJOESTEDT, M.-L. Dieux et Héros des Celtes,

35, 52. » 3 DEXTER, Miriam Robbins. Whence the goddesses. New York, Oxford, Beijing, 1990, p. 45 4 STERCKX, Claude. Contribution à l'étude des concepts théogoniques dans la mythologie des Celtes préchrétiens. Bruxelles, Université Libre, 1973 ; p. 12-13. 5 PRZYLUSKI, Jean. La grande déesse. Paris : 1950, p. 37

DEXTER. Reflections on the goddess *Donu. The Mankind Quarterly, XXXI, 1&2, 1990, p. 58

CW. Op. cit. "The Danube (Dānuvius)", p. 569.

Ibid. The o of Don sounds long to my informers (see n. 2).

DEXTER, Miriam. Private e-mail.

VASILEVICH G.M. Early concepts about the universe among the Evenks (materials) in Studies in Siberian Shamanism / Ed. Henry H. Michael. N°4, 1963; p. 49

CW, Op. cit., finds better *deh2nu-, p. 569

STOKES, Whitley, Ed. Sanas Chormaic = Cormac's glossary. Calcutta, 1868, p. 4.

QUIN. Dictionary of the Irish Language. Dublin, 1998 "O'Cl.", p. 40. See also n. 36.

Ibid., « Itrôn ar Frout, mamm ha gwerc'hès, / Yéched d'ar buguel ha d'emp les! », p. 934

MALLORY. op. cit. n. 34, p. 33.