Yangdi Li

Vincent Garnier

Philippe Steyer

Catherine Journet

Bérangère Toury
email: toury@univ-lyon1.fr

Millimeter-Scale Hexagonal Boron Nitride Single Crystals for Nanosheet Generation

Keywords: Boron Nitride, 2D material, Nanosheet, Polymer Derived Ceramics, Sintering

Development of next generation two-dimensional (2D) transistors or photo-electronic devices is closely linked to advances in 2D materials. Due to its outstanding properties (insulating, stable, inert, transparent, isostructural to graphene…), hexagonal boron nitride (hBN) crystal and in particular its exfoliated nanosheets form, is a choice material to fabricate sensors or plasmonic and photonic devices. However, a wide development of these heterostructures still suffers from a lack of large samples and in ample supply. In this context, we propose the fabrication of large exceptional quality hBN single crystals of more than few millimeters lateral size by using polymer route combined with a sintering process. The structural quality and compositional purity are retained after exfoliation and dry transfer of these free standing Boron Nitride NanoSheets (BNNSs) onto Si substrates. This developed method can be achieved under short and soft conditions and leads to BNNSs with lateral sizes of several hundreds of microns. This work paves the way for a wide use of BNNS for 2D material applications.

INTRODUCTION

Produced as nanomaterial, hBN, as an excellent dielectric material, can be suitable for many applications that require BNNSs ranging from one to hundreds of layers. Its atomically flat surface, with no dangling bonds nor charge traps on the surface 1 make it very interesting as a substrate [START_REF] Dean | Boron Nitride Substrates for High-Quality Graphene Electronics[END_REF][START_REF] Decker | Local Electronic Properties of Graphene on a BN Substrate via Scanning Tunneling Microscopy[END_REF][START_REF] Jain | Effect of Substrate on Graphene-Based Interconnects[END_REF] or encapsulating layer [START_REF] Gerber | Dependence of Band Structure and Exciton Properties of Encapsulated WSe2 Monolayers on the HBN-Layer Thickness[END_REF][START_REF] Shautsova | Hexagonal Boron Nitride Assisted Transfer and Encapsulation of Large Area CVD Graphene[END_REF] for two-dimensional materials, intercalant in Van der Waals heterostructures, [START_REF] Geim | Der Waals Heterostructures[END_REF] gate dielectric, [START_REF] Britnell | Electron Tunneling through Ultrathin Boron Nitride Crystalline Barriers[END_REF][START_REF] Kim | Synthesis and Characterization of Hexagonal Boron Nitride Film as a Dielectric Layer for Graphene Devices[END_REF] counter electrode in dye-sensitized solar cells, 10 and many others. [START_REF] Wang | Electrical Properties and Applications of Graphene, Hexagonal Boron Nitride (h-BN), and Graphene/h-BN Heterostructures[END_REF] hBN also possesses excellent photoelectric properties such as distinct violet or ultraviolet (UV) luminescence emissions, making it all the more attractive for optoelectronic devices, such as deep ultraviolet light emitting devices, [START_REF] Vuong | Deep Ultraviolet Emission in Hexagonal Boron Nitride Grown by High-Temperature Molecular Beam Epitaxy[END_REF][START_REF] Jiang | Hexagonal Boron Nitride for Deep Ultraviolet Photonic Devices[END_REF] UV photoconductive detectors [START_REF] Aldalbahi | Development of 2-D Boron Nitride Nanosheets UV Photoconductive Detectors[END_REF] and single photon emitters. [START_REF] Xu | Single Photon Emission from Plasma Treated 2D Hexagonal Boron Nitride[END_REF] In this rich applicative context, BNNSs are highly desirable as a building blocks (substrate, intercalant or encapsulating layer) for 2D heterostructures, and 2D-hBN has become among the most sought inorganic 2D material. [START_REF] Wang | Hexagonal Boron Nitride, and Their Heterostructures: Properties and Applications[END_REF] However, it is obvious that generating efficient 2D electronic devices requires from the beginning high quality hBN substrate displaying crystalline and chemical purity as well as wafer scale size. Up to now, two main strategies to produce BNNSs have been proposed, involving either "bottom-up" or "topdown" approaches. [START_REF] Zhang | Two Dimensional Hexagonal Boron Nitride (2D-HBN): Synthesis, Properties and Applications[END_REF] Bottom-up routes mainly include Chemical Vapor Deposition (CVD) [START_REF] Khan | Few-Atomic-Layered Hexagonal Boron Nitride: CVD Growth, Characterization, and Applications[END_REF][START_REF] Lee | Wafer-Scale Single-Crystal Hexagonal Boron Nitride Film via Self-Collimated Grain Formation[END_REF][START_REF] Lu | Synthesis of Large Single-Crystal Hexagonal Boron Nitride Grains on Cu-Ni Alloy[END_REF] and derivatives (LPCVD, [START_REF] Park | Large-Area Monolayer Hexagonal Boron Nitride on Pt Foil[END_REF] MOCVD, [START_REF] Siegel | Growth of Multi-Layer HBN on Ni(111) Substrates via MOCVD[END_REF][START_REF] Rice | Effects of Deposition Temperature and Ammonia Flow on Metal-Organic Chemical Vapor Deposition of Hexagonal Boron Nitride[END_REF] ), Ion Beam Sputtering Deposition (IBSD) [START_REF] Meng | Aligned Growth of Millimeter-Size Hexagonal Boron Nitride Single-Crystal Domains on Epitaxial Nickel Thin Film[END_REF] and Molecular Beam Epitaxy (MBE) [START_REF] Xu | Large-Area Growth of Multi-Layer Hexagonal Boron Nitride on Polished Cobalt Foils by Plasma-Assisted Molecular Beam Epitaxy[END_REF] . While these bottom-up approaches have the potential for large surface areas, the synthesis of a single-crystal hBN film still remains elusive and let alone high quality transfer at the wafer-scale. [START_REF] Wu | Large-Roll Growth of 25-Inch Hexagonal BN Monolayer Film for Self-Release Buffer Layer of Free-Standing GaN Wafer[END_REF] Furthermore, they may be affected by the morphology of the substrate and the reactants purity. [START_REF] Wang | Recent Progress in Synthesis of Two-Dimensional Hexagonal Boron Nitride[END_REF][START_REF] Kim | Growth of High-Crystalline, Single-Layer Hexagonal Boron Nitride on Recyclable Platinum Foil[END_REF][START_REF] Bayer | Introducing Overlapping Grain Boundaries in Chemical Vapor Deposited Hexagonal Boron Nitride Monolayer Films[END_REF] Top-down methods rely on mechanical [START_REF] Zhang | Two Dimensional Hexagonal Boron Nitride (2D-HBN): Synthesis, Properties and Applications[END_REF][START_REF] Gorbachev | Hunting for Monolayer Boron Nitride: Optical and Raman Signatures[END_REF][START_REF] Novoselov | Two-Dimensional Atomic Crystals[END_REF] or chemical [START_REF] Coleman | Two-Dimensional Nanosheets Produced by Liquid Exfoliation of Layered Materials[END_REF] exfoliation from bulk hBN crystals that can be either commercial ones or lab-scale samples. A first commercial source [START_REF] Clere | Method for Making High Thermal Diffusivity Boron Nitride Powders[END_REF] is obtained from an oxygen-containing boron compound reacting with a nitrogen-containing source. These materials exhibit quite small crystalline domains (from sub-micron up to 10 µm) which are not so convenient for exfoliation. Besides, HQ Graphene, [START_REF]h-BN -Hexagonal Boron Nitride[END_REF] a commercial supplier, claims the production of high quality crystals with a size reaching 1 mm, but there is no real information about the chemical process used to synthesize this material and the exfoliated sheets demonstrate a loss of their lateral size. [START_REF]h-BN -Hexagonal Boron Nitride[END_REF][START_REF] Zomer | Fast Pick up Technique for High Quality Heterostructures of Bilayer Graphene and Hexagonal Boron Nitride[END_REF] Beyond commercial ones, samples supplied by NIMS lab are used by most of the research groups over the world. [START_REF] Zastrow | Meet the Crystal Growers Who Sparked a Revolution in Graphene Electronics[END_REF][START_REF] Taniguchi | Synthesis of High-Purity Boron Nitride Single Crystals under High Pressure by Using Ba-BN Solvent[END_REF][START_REF] Watanabe | Direct-Bandgap Properties and Evidence for Ultraviolet Lasing of Hexagonal Boron Nitride Single Crystal[END_REF] Since they can offer exceptional quality samples with large lateral size which can be almost retained after exfoliation, the fabrication technique is based on severe conditions of pressure and temperature that could limit upscaling or industrial processes. [START_REF] Zastrow | Meet the Crystal Growers Who Sparked a Revolution in Graphene Electronics[END_REF] Still starting from a molten solvent system, Edgar's group is now coming close to achieving the similar quality samples by a simpler and cheaper process. [START_REF] Liu | Single Crystal Growth of Millimeter-Sized Monoisotopic Hexagonal Boron Nitride[END_REF][START_REF] Edgar | Characterization of Bulk Hexagonal Boron Nitride Single Crystals Grown by the Metal Flux Technique[END_REF] However, they currently have ten times more crystal defects, or imperfections, in their structure [START_REF] Zastrow | Meet the Crystal Growers Who Sparked a Revolution in Graphene Electronics[END_REF] and it can be mentioned that the process is a bit long (more than 80 hours). [START_REF] Liu | Single Crystal Growth of Millimeter-Sized Monoisotopic Hexagonal Boron Nitride[END_REF] In our group, we have recently developed a new hBN synthesis approach by combining a polymer route with a sintering process to achieve polycrystalline samples made of more than 200 µm 2 single crystals. [START_REF] Yuan | Pure & Crystallized 2D Boron Nitride Sheets Synthesized via a Novel Process Coupling Both PDCs and SPS Methods[END_REF][START_REF] Li | Advanced Synthesis of Highly Crystallized Hexagonal Boron Nitride by Coupling Polymer-Derived Ceramics and Spark Plasma Sintering Processes-Influence of the Crystallization Promoter and Sintering Temperature[END_REF] This process deals with softer conditions of pressure and temperature and shorter time but gives samples that do not reach yet the required quality for 2D devices. In this paper, we will show that, by improving our process in term of sintering conditions and chemistry of the system, we are now able to deliver transparent exceptionally high structural quality boron nitride single crystals of more than 1 mm in lateral size.

RESULTS AND DISCUSSION

Material synthesis.

Polymer Derived Ceramics pathway is known for many years to produce hexagonal boron nitride from borazine precursor. However, this chemical process requires quite high temperatures (more than 1800°C) to get perfectly crystallized hBN. [START_REF] Bernard | Polymer-Derived Boron Nitride: A Review on the Chemistry, Shaping and Ceramic Conversion of Borazine Derivatives[END_REF] In this context, addition of a crystallization promoter (like Li 3 N) is now commonly used to enhance cristallinity at lower temperatures. [START_REF] Lu | Synthesis of Large Single-Crystal Hexagonal Boron Nitride Grains on Cu-Ni Alloy[END_REF][START_REF] Wang | Catalytic Transparency of Hexagonal Boron Nitride on Copper for Chemical Vapor Deposition Growth of Large-Area and High-Quality Graphene[END_REF] In order to go further in the crystallization rate, our group has previously demonstrated the possibility to use an additivated preceramic polymer in a SPS system. [START_REF] Yuan | Pure & Crystallized 2D Boron Nitride Sheets Synthesized via a Novel Process Coupling Both PDCs and SPS Methods[END_REF][START_REF] Li | Advanced Synthesis of Highly Crystallized Hexagonal Boron Nitride by Coupling Polymer-Derived Ceramics and Spark Plasma Sintering Processes-Influence of the Crystallization Promoter and Sintering Temperature[END_REF] Here, we show how, by tuning the sintering process and the additive content, we can get millimeter-scale hBN single crystal that can be used to generate BNNSs. Figure 1 illustrates the whole process. Freshly distillated borazine is first polycondensed into a less volatile and thus more processable liquid polyborazilene (PBN). A mixture of PBN and 35 wt.% Li 3 N is then preceramized at 650°C under N 2 for 1h to form the preceramic powder which is placed into a BN crucible itself introduced into a pressure-controlled furnace. Based on preliminary results, optimal sintering conditions have been determined to be a temperature of 1800°C, a pressure of 180MPa and a dwelling time of 8h. As-obtained bulk material. Naked eyes and optical microscopy observations of the as-sintered sample (Figure 2a and2b) reveal that it is composed of faceted millimeter-sized regions, which is similar with the domain size of ~1 mm obtain by Edgar's group [START_REF] Liu | Single Crystal Growth of Millimeter-Sized Monoisotopic Hexagonal Boron Nitride[END_REF] and a bit lower than the few millimeters obtain by NIMS group. [START_REF] Taniguchi | Synthesis of High-Purity Boron Nitride Single Crystals under High Pressure by Using Ba-BN Solvent[END_REF] The X-Ray Diffraction (XRD) pattern (Figure 2c) shows only well-separated, thin single peaks that all can be assigned to the crystallographic planes of hBN crystal, as described in the standard JCPDS database (00-034-0421). This demonstrates the perfect structural ordering of the hBN sample, as confirmed by Raman spectrometry. The Raman spectra were recorded in two frequency shift ranges and exhibit two single peaks (Figure 2d and2e). The low frequency peak at 52.6 cm -1 (FWHM of about 1.2 cm -1 ) corresponds to interlayer Polycrystalline hBN vibrations, referred to as the interlayer shear mode. [START_REF] Kuzuba | A Low Frequency Raman-Active Vibration of Hexagonal Boron Nitride[END_REF][START_REF] Stenger | Low Frequency Raman Spectroscopy of Few-Atomic-Layer Thick HBN Crystals[END_REF] The second peak, measured at 1366.0 cm - 1 , exactly matches the value expected for the in-plane shear mode E 2g symmetry of hBN. 29,44 46,47 This high frequency peak has a FWHM of about 7.6 cm -1 , which is comparable to the best value reported for hBN single crystals obtained by NIMS lab (7.3 cm -1 ) using the High Pressure High Temperature (HPHT) method [START_REF] Taniguchi | Synthesis of High-Purity Boron Nitride Single Crystals under High Pressure by Using Ba-BN Solvent[END_REF][START_REF] Schué | Characterization Methods Dedicated to Nanometer-Thick HBN Layers[END_REF] and by Edgar's group (7.8 cm -1 ) using nickel-chromium solvent. [START_REF] Liu | Single Crystal Growth of Millimeter-Sized Monoisotopic Hexagonal Boron Nitride[END_REF] The integrated intensity of the 52.6 cm -1 signal is about a fortieth of the 1366.0 cm -1 one (I low /I high ≈ 1/43), which is consistent with published results. [START_REF] Kuzuba | A Low Frequency Raman-Active Vibration of Hexagonal Boron Nitride[END_REF][START_REF] Stenger | Low Frequency Raman Spectroscopy of Few-Atomic-Layer Thick HBN Crystals[END_REF] Both optical and Raman analyses fully attest the excellent crystallinity of the produced hBN. Obtaining hBN with such crystalline quality may be explained by using a large amount of Li 3 N (35 wt.%) which plays a key role in the liquid-solid sintering mechanism. By comparing with previous studies in which only 5 wt.% of Li 3 N was added, [START_REF] Yuan | Pure & Crystallized 2D Boron Nitride Sheets Synthesized via a Novel Process Coupling Both PDCs and SPS Methods[END_REF][START_REF] Li | Advanced Synthesis of Highly Crystallized Hexagonal Boron Nitride by Coupling Polymer-Derived Ceramics and Spark Plasma Sintering Processes-Influence of the Crystallization Promoter and Sintering Temperature[END_REF] the growth mechanism is different.

Although the Li based solvent seems to play an important role, the crystal growth process of hBN does not appear as a simple precipitation from a solution in molten lithium and the hBN crystals rather look like the product of a reaction in the ternary Li-B-N system. In that case, we can assume that the growth occurs in the liquid phase and the proposed crystallization mechanism is based on previous studies reported by Bezrukov 49 and other groups. [START_REF] Yamane | High-and Low-Temperature Phases of Lithium Boron Nitride, Li 3 BN 2: Preparation, Phase Relation, Crystal Structure, and Ionic Conductivity[END_REF][START_REF] Li | Fracture Morphology and XRD Layered Characterization of CBN Cake[END_REF][START_REF] Xu | Thermodynamic Analysis of the V-Shaped Area of High Pressure and High Temperature in Cubic Boron Nitride Synthesis with Li3N as a Catalyst[END_REF] At around 600-700 °C, Li 3 BN 2 formed by reaction between Li 3 N and preceramic BN, melts, and infiltrates amorphous BN to dissolve it, leading to highly crystallized hBN. Moreover, it can be noticed that our experiments have been performed in BN-crucibles, which may favor the nucleation of hBN.

hBN freestanding crystals and nanosheets. At the macroscopic scale, the raw material shows evidence for intertwining of large crystals. Freestanding, colorless and transparent hBN crystals of about 2 mm, can be easily extracted from this bulk sample, by simple sliding with tweezers (Figure 3a and3b). To further reduce the crystals thickness in the c-axis direction, yet keeping them as large as possible along in-plane dimension, crystals have been exfoliated using a polydimethylsiloxane (PDMS) dry transfer (Figure 3c) and deposited onto an oxidized silicon substrate (285 nm thick SiO 2 ) (Figure 3d). Such isolated BNNSs present flat and smooth surfaces over distance varying from 100 μm to more than 1 mm, that is larger than what is obtained with commercial samples which show a loss of their lateral size after exfoliation. [START_REF]h-BN -Hexagonal Boron Nitride[END_REF][START_REF] Zomer | Fast Pick up Technique for High Quality Heterostructures of Bilayer Graphene and Hexagonal Boron Nitride[END_REF] Their thicknesses were measured by Atomic Force Microscopy (AFM) (Figure 3e and 3f) and line profiles (Figure 3g) give typical step values of 4 -6 nm, corresponding to approximately ten layers. After deposition, the crystalline signature of crystals was confirmed by XRD, and only hBN (002) and (004) peaks are observed (Figure 4a). This results from the perfect planar alignment of the (002) lattice planes onto the silicon supporting substrate. From the (002) line, we deduced an interplanar spacing of 3.328Å, consistent with the JCPDS data file (00-034-0421) for hBN.

Further investigations of hBN thin crystals and nanosheets compared the Raman spectra (Figure 4b-d) for areas of different thicknesses, as identified by optical contrast (yellow spot on Figure 4e-g). Each region displays only the expected hBN E 2g vibration mode around 1365.5 cm -1 , with FWHM ≈ 8 cm -1 . When decreasing the hBN crystal thickness, the Raman peak intensity decreases, as already described in literature [START_REF] Gorbachev | Hunting for Monolayer Boron Nitride: Optical and Raman Signatures[END_REF] . At the same time, the FWHM increases from 8.1 cm -1 to 8.7 cm -1 . Note that the FWHM of the E 2g peak is higher here than that observed previously on hBN bulk crystals (7.7 cm -1 ). This feature has already been reported in the literature and can be attributed to a local strain occurring when nanosheets are transferred onto a substrate. 29 Chemical analyses by X-ray Photoemission Spectroscopy (XPS) were performed on a hBN single crystal before and after a 2 μm Ar + etching (Figure 5a). The diameter of the X-ray beam used in these XPS measurements is about 100μm, which is smaller than the crystal dimension (≈200x200μm 2 ). The XPS-B1s (189 eV), N1s (397 eV), O1s (532 eV) and C1s (283 eV) peaks are observed on the sample surface, corresponding to an elemental composition of 45.9, 46.2, 0.9 and 7.0 at.%, respectively, which gives a perfect stoichiometric B/N ratio of 0.99. The C1s and O1s peaks are no longer present in the spectrum after etching of the top crystal surface (Figure 5d and 5e, respectively), indicating that both are due to surface impurities and that the synthesized sample presents an excellent chemical purity. However, because of the preferential sputtering of nitrogen atoms during the Ar + sputtering process, the B/N ratio cannot be used for quantitative composition analysis inside the crystal. Both the B1s and N1s core level spectra (Figure 5b and 5c, respectively) show binding energy loss features at ~9 and ~25 eV, respectively, higher than the core peak. These peaks are attributed to π plasmons (πP) and bulk plasmons (BP), respectively. [START_REF] Trehan | Auger and X-ray Electron Spectroscopy Studies of h BN, c BN, and N + 2 Ion Irradiation of Boron and Boron Nitride[END_REF] These XPS features are used in the literature as the fingerprints of hBN confirming the high quality and purity of hBN single crystals. [START_REF] Trehan | Auger and X-ray Electron Spectroscopy Studies of h BN, c BN, and N + 2 Ion Irradiation of Boron and Boron Nitride[END_REF][START_REF] Weissmantel | 4 -Preparation, Structure, and Properties of Hard Coatings on the Basis of i-c and i-Bn[END_REF][START_REF] Barton | Transition Metal Dichalcogenide and Hexagonal Boron Nitride Heterostructures Grown by Molecular Beam Epitaxy[END_REF] When deposited on the Transmission Electron Microscopy (TEM) grid, the nanosheet folds onto itself, due to its extremely low thickness (Figure 6a). On a folded well-oriented area, the observed aligned layers allow to determine the interplanar distance of 3.3 , as expected for hBN (Figure 6b). The Selected Area Electron Diffraction (SAED) pattern recorded on a flat part presents the expected set of six bright diffraction spots with hexagonal symmetry (Figure 6a inset). This demonstrates that the crystal has a single hexagonal structure orientation with a AA' atomic stacking along the c-axis. [START_REF] Yuan | How to Increase the H-BN Crystallinity of Microfilms and Self-Standing Nanosheets: A Review of the Different Strategies Using the PDCs Route[END_REF] This is also confirmed, at higher resolution, by the six hexagonally distributed dots observed on the Fast Fourier Transform (FFT) image obtained from the in-plane atomic arrangement of the nanosheets (Figure 6c, inset). A filtered image, reconstructed from this FFT (Figure 6c), confirms the well-crystallized structure. A 2.

distance between two adjacent atomic columns is deduced (white dots, Figure 6d), which corresponds to the distance between the centers of two neighboring hexagonal rings and therefore to the lattice spacing of hBN (Figure 6e). A B-N bond distance of 1.44 can then be calculated. This value is consistent with previous results, again attesting to the perfect structural quality of the synthesized hBN. up to 180MPa with N 2 . The dwelling time is 8 hours before cooling down to room temperature together with pressure release. The material is characterized by optical microscopy, X-ray diffraction (XRD) and Raman spectroscopy using a green laser (λ = 32 nm). The material can be quite easily separated from the bulk with tweezers, thereby yielding self-standing crystals.

Finally, these crystals are exfoliated using the PDMS dry transfer method and deposited onto Si/SiO 2 (285 nm) substrates or holey carbon coated copper Transmission Electron Microscopy (TEM) grids. These freestanding thin crystals and nanosheets are characterized as being hBN by optical microscopy, Atomic Force Microscopy (AFM), Scanning Electron Microscopy (SEM), TEM, X-Ray Photoemission Spectroscopy (XPS), XRD and Raman spectroscopy

Figure 1 .

 1 Figure 1. Scheme illustrating the hBN synthesis starting from borazine.

Figure 2 .

 2 Figure 2. Characterization of the bulk sample, a)-optical image; b)-optical microscopy image;

Figure 3 .

 3 Figure 3. Microstructural characterization of hBN freestanding crystals and nanosheets, a, b)-

Figure 4 .

 4 Figure 4. Structural characterizations of hBN freestanding crystals and BNNSs, a)-XRD pattern

Figure 5 .

 5 Figure 5. Chemical characterization of hBN single crystal surface, a)-XPS general survey

Figure 6 .

 6 Figure 6. TEM-scale microstructural characterization of BNNSs, a)-BNNS deposited on a holey

ACKNOWLEDGMENT This work was financially supported by ANR through the project 14-CE08-0018 «GoBN», European Union Horizon 2020 Program under the Graphene Flagship (grant number 785219), the iMUST LABEX program MUSCAT-2D and Chinese Scholarship Council (CSC). Authors also thank the CTμ (Centre Technologique des Microstructures) of the Université Lyon 1 and the CLYM (Centre Lyonnais de Microscopie) for access to SEM and TEM, CECOMO for access to Raman spectroscopy and Science et Surface (Ecully, France) for XPS analyses.

CONCLUSION

In conclusion, a dual process involving a preceramic polymer combined with a sintering step has been used to produce millimeter-sized high purity hBN single crystals. Their perfect chemical and structural quality was shown from the nm to the mm scale in the as produced bulk, freestanding crystals and exfoliated nanometer thick sheets. It is worth mentioning that this process is conducted under softer conditions and/or much shorter time than the ones currently used to produce other free standing single crystals. This new synthesis method provides access to an ample supply of large hBN single crystals that can be easily exfoliated into BNNSs for integration in advanced 2D devices.

METHODS

hBN layers preparation and characterization. Pure borazine is obtained from a reaction between ammonium sulfate [(NH 4 ) 2 SO 4 , 99% purity, Aldrich] and sodium borohydride (NaBH 4 , 98% purity, Aldrich) in tetraglyme heated to 120 °C according to a procedure described elsewhere [START_REF] Wideman | Convenient Procedures for the Laboratory Preparation of Borazine[END_REF] and purified twice by distillation. The liquid-state polymeric precursor is then obtained by polycondensation of borazine at 50 °C inside a pressure-sealed system under argon for 5 days, generating colorless polyborazylene (PBN) with a chemical formula (B 3.0 N 3.8 H 4.0 ) n as given by elemental analysis. A mixture of liquid PBN and 35wt% lithium nitride (Li 3 N) is preceramized at 650°C during 1h under inert atmosphere of N 2 . The preceramic powder is then introduced under nitrogen into a BN crucible and thereafter transferred into a pressure-controlled furnace. The chamber is purged with 3 cycles (N2 filling followed by pumping) to remove oxygen and moisture. The temperature and the pressure are both increased in 30 minutes up to 1800°C and

AUTHOR INFORMATION

Corresponding Author * E-mail: toury@univ-lyon1.fr

For Table of Contents Only :


A Benaglia
email: andrea.benaglia@cern.ch

M Lucchini

K Pauwels

C Tully

T Medvedeva

A Heering

C Dujardin

V Kononets

K Lebbou

N Aubry

S Faraj

G Ferro

P Lecoq

Auffray

Test beam results of a high granularity LuAG fibre calorimeter prototype

Keywords: light guides; Scintillators, scintillation and light emission processes (solid, gas and liquid scintillators)

A

: The progresses in the micropulling-down technique allow heavy scintillating crystals to be grown directly into a fibre geometry of variable shape, length and diameter. Examples of materials that can be grown with this technique are Lutetium Aluminum Garnets (LuAG, Lu 3 Al 5 O 12 ) and Yttrium Aluminum Garnets (YAG, Y 3 Al 5 O 12 ). Thanks to the flexibility of this approach, combined with the high density and good radiation hardness of the materials, such a technology represents a powerful tool for the development of future calorimeters. As an important proof of concept of the application of crystal fibres in future experiments, a small calorimeter prototype was built and tested on beam. A grooved brass absorber (dimensions 26 cm × 7 cm × 16 cm) was instrumented with 64 LuAG fibres, 56 of which were doped with Cerium, while the remaining 8 were undoped. Each fibre was readout individually using 8 eightfold Silicon Photomultiplier arrays, thus providing a highly granular description of the shower development inside the module as well as good tracking capabilities. The module was tested at the Fermilab Test Beam Facility using electrons and pions in the 2-16 GeV energy range. The module performance as well as fibre characterization results from this beam test are presented.

K

: Calorimeter methods; Calorimeters; Scintillators and scintillating fibres and

Introduction

Detectors at future high energy colliders will have to withstand unprecedented operating conditions in terms of particle energy, flux and collision rates. High radiation tolerance as well as fast response will be key properties of the potential scintillator materials to be employed in such a harsh environment. Moreover, a large number of physics channels foresee multiple jets in the final state, and would therefore benefit from a hadronic jet resolution significantly better than the one of current detectors (∼ 10%). For example, with 4% energy resolution for jets of 100 GeV or higher, separation of W and Z bosons via their invariant mass reconstruction in di-jet final states becomes possible.

We proposed earlier an innovative approach to meet these requirements, constituted by a total-absorption, fully active calorimeter, made of many heavy inorganic crystalline fibres grouped together in meta-crystals to form the detector blocks [START_REF] Lecoq | Metamaterials for novel X-or γ-ray detector designs[END_REF][START_REF] Lecoq | New crystal technologies for novel calorimeter concepts[END_REF]. As a matter of fact, the micropullingdown (µPD) technique allows heavy scintillating crystals to be grown directly into a fibre geometry of variable shape, length and diameter, with no need of a cutting and polishing stage as for traditional growth methods (i.e. Czochralski or Bridgman techniques). This represents a clear advantage towards a large-scale production. Lutetium Aluminum Garnet (Lu 3 Al 5 O 12 , LuAG) was -1 -originally considered for the assembly of the meta-crystals, thanks to its high density (6.73 g/cm 3 ), relatively high intrinsic light yield when doped with rare earths (e.g. approximately 25000 photons per deposited MeV with Cerium doping) and high refractive index (ranging from 2.14 at 190 nm to 1.85 at 520 nm) [START_REF] Kuwano | Crystal growth and properties of (Lu, Y ) 3 Al 5 O 12[END_REF][START_REF] Dujardin | LuAG:Ce fibers for high energy calorimetry[END_REF]. Recent measurements confirm the good radiation tolerance of this material, showing very little radiation-induced absorption coefficients at the emission peak (µ ind ∼ 0.5 m -1 at 520-540 nm) after γ irradiation up to an integrated dose of 100 kGy and proton irradiation up to 10 14 cm -2 integrated fluence [START_REF] Lucchini | Radiation Tolerance of LuAG:Ce and YAG:Ce Crystals under High Levels of Gamma-and Proton-Irradiation[END_REF]. These properties make LuAG a good candidate for a scintillating calorimeter, allowing for dual-readout capabilities too, when used undoped as a Cherenkov radiator.

We reported earlier [START_REF] Lucchini | Test beam results with LuAG fibers for next-generation calorimeters[END_REF] about a beam test conducted at CERN in 2012, where 9 LuAG fibres of good optical quality were inserted in a small brass absorber and exposed to high energy electrons at the H2 beam line of the CERN SPS North Area. This test allowed to extract good signals from all the fibres, although a complete characterization of the physics performance of the module was limited by the small size of the prototype itself.

In this paper, a larger scale beam test, comprising 64 LuAG crystal fibres, is presented. Fibres were inserted in a grooved brass absorber and readout individually using Silicon Photomultipliers. The module was exposed to a pion and electron beam at Fermilab in March and August 2014. After a description of the experimental setup in section 2, the fibre position reconstruction is reported in section 3, and a characterization of the LuAG fibre properties is presented in section 4. Finally, the physics performance of the calorimetric module with high energy particles is presented in section 5.

Experimental setup

The beam line at the Fermilab Test Beam Facility

The beam we used for this test was provided by the Fermilab Test Beam Facility (FTBF). Along the MTEST beam line, the primary 120 GeV proton beam is converted into a secondary beam by a 30 cm Aluminum target, and eventually delivered to the MT6.2 experimental area by a set of quadrupole magnets and collimators. Our magnet configuration allowed secondary particles to be produced in the 1-32 GeV energy range, with a momentum resolution of ∼ 2.5% or better. In this energy range, mostly electrons and pions are produced, the contamination from muons and double particle events being almost negligible. A more quantitative evaluation of the secondary beam composition can be seen in figure 1 [8].

A sketch of the experimental area hosting our setup can be seen in figure 2: a scintillation counter was located at the entrance of the hall, providing the trigger information in coincidence with the spill signals; a couple of multi-wire proportional chambers (labelled WC1 and WC2 hereafter) were situated few tens of centimeters upstream of our setup and allowed the beam position in the xy plane to be reconstructed with ∼ 1 mm spatial resolution; finally, our calorimetric module was centered on the beam by means of a remotely-controlled moving table (in the x and y directions).1

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The calorimetric module and the crystal fibres

Our calorimeter prototype (see figure 3) consisted of a grooved brass block of dimensions 255 mm × 65 mm × 160 mm. Sixty-four, 255 mm long round holes with ∼ 2.6 mm diameter were drilled along the full width of the module, and arranged in 8 staggered layers of 8 holes each. The distance between the center of two adjacent holes was 4 mm, whereas 16 mm of brass separated two consecutive layers. The holes hosted 64 LuAG fibres, which were wrapped with a thin layer of Teflon at the two ends -3 -in order to maintain an air gap of about 0.3 mm between the fibre lateral surface and the brass absorber. The module was exposed to the beam in two different configurations, hereafter referred to as transverse and pointing configurations. In the former case, the beam was impinging at cross angle with respect to the fibres, the electromagnetic/hadronic shower developing progressively in the 8 fibre layers. In the latter, the beam was aligned with the fibres and the showers developed all along the fibre length, while laterally extending to only a few fibre layers. When used in transverse configuration, the module size along the z axis (160 mm) corresponds to about 11 radiation lengths (X 0 ∼ 14.7 mm) and to 0.8 pion interaction lengths (λ I ∼ 200 mm).

Round LuAG fibres were grown with the µPD technique at the Institute of Light and Matter (ILM, Lyon) [START_REF] Xu | Ce-doped LuAG single-crystal fibers grown from the melt for high-energy physics[END_REF] and by the company Fibercryst. All fibres had a diameter of 2 mm and were cut to have a length of approximately 220 mm. Of the 64 fibres we used, 55 were doped with various concentration of Cerium (LuAG:Ce) to produce scintillation light, while the remaining 9 were undoped, and therefore more suitable to detect Cherenkov light. As shown in figure 3, undoped fibres were inserted in the fourth layer of the module (layer 3), which corresponds approximately to the location of the shower maximum for 16 GeV electrons impinging onto the module in transverse configuration, and in position 63.

The photodetectors and the acquisition system

One end of each crystal fibre was coupled to a K Silicon PhotoMultiplier (SiPM) using optical grease. Each SiPM had a 2.2 mm × 2.2 mm active area and was composed of 12100 cells of 20 × 20 µm 2 each. The breakdown voltage and the recovery time were measured in laboratory to be 25.4 V and 30 ns respectively. The choice of this particular SiPM model was mainly dictated by the photon detection efficiency (PDE), which is about 20% at the LuAG:Ce emission peak (520 nm) and is particularly high in the UV region (∼ 18% at 350 nm), which enhances the detection of Cherenkov photons produced in undoped LuAG fibres. A picture of the SiPM packages installed onto the SiPM Interface Board (SIB) and the PDE as a function of the photon wavelength can be seen in figure 4.

Two 32-channel Amplifier-Digitizer boards (PAD-E) [START_REF] Rubinov | Measurements of Photoelectron Yields for Prototype Mu2e Cosmic Ray Veto Scintillation Counters[END_REF], interfaced with the SIB, provided bias and signal readout from the attached SiPMs. The boards were triggered by the signal from the scintillator counter and connected to a standard PC running the acquisition software and where the data were stored. A built-in sensor allowed the temperature of the boards and the SiPMs to be continuously monitored. A temperature stabilization of (20 ± 1) • C was achieved.

The PAD-E boards, originally conceived for medical physics applications, have a 20 MHz analog bandwidth and a double differentiation stage that generates a bipolar pulse. Due to the slow shaping time of the board and the ADC sampling frequency of 75 MHz (1 sample every 13.3 ns), the system was not optimized to perform timing measurements. It was nevertheless possible to clearly distinguish the fast Cherenkov signals from the slower scintillation pulses just by looking at the different pulse shape, as shown in figure 5.

In order to estimate the amount of light produced in the crystal fibres, an absolute calibration of the photodetector response was required. We used a LED driver to produce pulsed light at two different wavelengths (blue and green) that was distributed and injected into each fibre from the side opposite to the SiPM by means of clear optical fibres (see figure 6 left). During SiPM calibration runs, the trigger to the acquisition system was provided by the LED pulser itself. For most of -4 - the channels, the reconstructed distribution clearly showed the signal corresponding to 0, 1, and 2 photoelectrons (ph.e.), as shown in figure 6 right, which allowed the ADC-to-ph.e. calibration factor to be extracted. Calibration constants obtained with the blue and the green LED were found to correlate, and the average of the two was taken as final value. On average, a signal of maximum amplitude of 100 ADC counts was found to correspond to about 11 ph.e. A channel-to-channel spread of about 6% in the SiPM calibration factors was observed.

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Monte Carlo simulation

A detailed Monte Carlo (MC) simulation was realized by means of the G 4 toolkit [START_REF] Agostinelli | GEANT4: A Simulation toolkit[END_REF][START_REF] Allison | Geant4 developments and applications[END_REF]. Not only the module design specifications were precisely reproduced in the MC, but also fibre properties such as the physical length and the measured light attenuation length (as will be described in section 4) were introduced in the simulation. To truthfully reproduce the beam characteristics, the -5 -

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beam in the Monte Carlo was constituted by an energy-dependent admixture of pions and electrons, following figure 1, with an angular spread of about 1 mrad in both x and y directions.

Module alignment and fibre position reconstruction

With the module oriented in pointing configuration, a full scan of the module surface was performed and the profile of each fibre response as a function of the beam impact point was reconstructed, thanks to the information of the wire chambers. An example of such a profile is shown in figure 7a for fibre 48. The expected profile, obtained by means of the G 4 simulation of the whole setup, is superimposed and in good agreement with the data.

The x and y coordinates of each fibre were reconstructed by fitting the simulated profile to the observed distribution, allowing the MC shape to translate. The results are shown in figure 7b. By fitting the expected geometrical parameters of the module to the reconstructed fibre positions, a distance of (16.1 ± 0.1) mm between fibre layers along x and (3.7 ± 0.1) mm between adjacent fibres along y is found, in good agreement with the module specifications. This measurement allowed the module to be correctly centered on the beam.

Fibre characterization

This section is devoted to the characterization of the fibre performance. The response of individual fibres to high energy electrons and pions was studied with the calorimetric module in both transverse and pointing configuration, thus allowing for a measurement of the fibre attenuation length and light output. expands over a large portion of the fibre (e.g. if the fibre axis is at small angle with the beam line). This is why a measurement of the amount of extracted light as a function of the excitation distance from the SiPM is fundamental. For most of the fibres, a characterization of the attenuation length was initially performed in laboratory at CERN. In a dedicated bench, both a radioactive 22 Na source and a LED pulser were used to excite the fibres at variable distance from the photodetector [START_REF] Pauwels | Single crystalline LuAG fibers for homogeneous dual-readout calorimeters[END_REF].

Fibre attenuation lengths

The measurement was repeated at the FTBF with high energy particles. The calorimetric module was exposed to a 16 GeV electron+pion beam in transverse configuration, positioning the table at various (x, y) coordinates to obtain a nearly uniform scan of the entire length of the fibres. To enhance the signal, only events in which the beam was impinging within ±2 mm from the fibre center along the y axis were selected for the computation of the energy deposit of each fibre. The as pulling speed, crucible temperature, and Cerium concentration. In particular, figure 8 right shows that attenuation lengths in excess of ∼ 200 mm are only measured in fibres with relatively low light output, whereas the brightest fibres in our sample (LO larger than ∼10 ph.e./ MeV) had poor attenuation lengths (50 mm or less). This can be explained with larger Ce concentration being responsible for both higher light output and higher probability of light self absorption [START_REF] Auzel | Radiation trapping and self-quenching analysis in Yb 3+ , Er 3+ , and Ho 3+ doped Y 2 O 3[END_REF][START_REF] Weele | The Effect of Self-Absorption on the Scintillation Properties of Ce 3+ Activated LaBr 3 and CeBr 3[END_REF] as well as Ce-related defects arising during the growth process.

The attenuation profiles measured at the beam test were found to well agree with laboratory measurements, as shown in figure 9. This was an important step to cross-check and validate the fibre characterization procedure in laboratory.

Light output measurement

The fibres used in this beam test were grown with different Cerium concentrations, ranging from ∼ 0 for undoped fibres to up to ∼ 600 ppm for highly doped ones. Moreover, fibres differed in the quality of the optical surface and in the presence of internal defects, both affecting the light transmission. Therefore, large fibre-to-fibre differences in the amount of both produced and extracted light were expected.

The average signal measured at the SiPM with the module in both the transverse and the pointing configuration can be used to measure the light output of the fibres, that is the light extracted from a fibre end per deposited MeV. Light propagation effects need to be properly accounted for in the measurement, in order that the LO be disentangled from them.

In transverse configuration, the extrapolation at 0 distance from the SiPM of the signal attenuation profiles represents an estimate of the light extracted in case of a perfectly transparent fibre (i.e. no light loss due to absorption or diffusion effects). To turn this number into LO, the knowledge of the average energy (in MeV) deposited by electron and pions in the fibres is required. This was estimated using the G 4 simulation, as shown in figure 10 electromagnetic shower development in the module in transverse configuration, the average energy deposit is not flat with respect to the fibre depth in the brass, but exhibits a maximum around the 4 th or 5 th fibre layer. The measured LO is shown in figure 11 left. On average, Ce-doped fibres yielded about 6 ph.e. per deposited MeV, while the LO from Cherenkov light in undoped fibres was about 1.5 ph.e. per deposited MeV. A few fibres yielded a very small amount of light, which can be attributed to a bad coupling to the SiPM, while few others yielded up to about 15 ph.e. per MeV due to a higher Cerium concentration.

With the module oriented in pointing configuration, the estimate of the fibre LO was more complicated. First of all, since the showers developed all along the fibre length, it was more difficult to disentangle the effect of light attenuation from the measured light output. The simulation was used to estimate the amount of light actually reaching the SiPM by attenuating, channel by channel, the light generated along the fibre according to the measured attenuation profiles (in figure 10 right, the energy deposition profile as a function of the beam transverse distance from the fibre axis is shown for a perfectly transparent fibre, i.e. in which the LO is not affected by attenuation effects). An additional source of complexity came from the saturation of the ADC channels, occurring especially in bright fibres and when the beam was impinging at small distance from the fibre axis. The estimate of the LO was obtained from a fit of the tails of the measured energy profiles, . Average energy deposited in a single fibre as a function of the fibre layer in the absorber module, as predicted by the simulation. Fibres are at cross angle with respect to the beam. Only events in which the beam distance from the fibre center was such that |∆x| < 80 mm and |∆y| =< 2 mm were selected. A pure electron beam as well as an admixture of electrons and pions are simulated, as expected from the beam specifications of the FTBF MT6 line, as in figure 1 (left). Profile of energy deposition in a perfectly transparent fibre (i.e. no effects of attenuation length) as a function of the distance of the incoming particle from the fibre axis, when fibres are parallel to the beam direction (right). where the fraction of saturated events was negligible, using the simulated profiles as fit templates. Despite a lesser accuracy, a correlation of the LO obtained in pointing configuration with the one estimated in transverse configuration was observed, as shown in figure 11 right. For undoped fibres, a systematically larger LO is observed, with the ratio LO pointing /LO transverse being ∼ 1.7. This can be attributed to the non isotropic emission of Cherenkov light, which favors its extraction in pointing configuration.

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fraction of events 3 - Simulation plot representing the number of active fibres (i.e. the number of fibres with a deposited energy above a given threshold) vs. the sum of the energy deposits in all the fibres, for pions (left) and electrons (right). The different signature of the two particle species in the calorimetric module is visible. An incident beam energy of 8 GeV is assumed, and only particles impinging in a region of ∆x = ±10 mm and ∆y = ±7.5 mm around the center of the module are considered.

Performance of the calorimetric module

In this section, the measured performance of the crystal fibre module with high energy particles is reported. In particular, the potential for particle identification and the energy resolution are discussed.

Particle identification

The high granularity of our calorimetric module was exploited to identify the nature of the impinging particle (electrons vs. pions), based on the multiplicity of active fibres. Due to the small size of our module compared to the characteristic interaction length of pions in brass (160 mm vs. λ I ∼ 200 mm), pions behaved like minimum ionizing particles, depositing a small amount of energy in only few (≤ 8) fibres, whereas in the case of electrons, the electromagnetic shower was almost fully contained in the module, with a larger fraction of energy deposited in a higher number of fibres (≥ 20). The different behavior of electrons and pions is illustrated in figure 12, where a scatter plot of the number of active fibres versus the total energy deposited in the fibres is shown for the two particle species, as derived by the simulation.

When analyzing the beam test data, a fibre was considered to be active if the signal was larger than 10 times the standard pedestal fluctuation, which corresponded to 15 ADC counts. By requiring that the number of active fibres per event was larger than 13 + 4 • log 2 E beam , an effective rejection of pion events was achieved, and the expected electron purity of figure 1 was reproduced, as shown in figure 13.

Energy resolution and linearity

Beam energies ranging from 2 to 16 GeV were used to study the response of the calorimetric module to high energy electromagnetic showers. In this energy range, the showers were reasonably contained in the module, the maximum being located around the 3 rd or 4 th fibre layer, and a satisfactory electron purity (between 30 and 80%) was provided by the beam line. Higher beam energies were not taken into account due to a too low electron purity (≤ 10%) and to an increasingly larger shower leakage outside the module. The pion background was rejected applying the cut on the number of active fibres described in the previous paragraph. To allow for the electromagnetic showers to be well sampled by the fibres, only events where the beam was impinging in a region of transverse dimensions 20 mm × 15 mm around the centre of the module were considered in the analysis.

Figure 14a shows the distributions of the response of the whole module for different beam energies, obtained by summing the signal of all the fibres. In order to account for the large variations in the fibre-to-fibre response, as described in section 4.2, an intercalibration factor was computed and applied to each individual signal. Fibres belonging to the same fibre layer were equalized by extrapolating, for each of them, the measured LO profile (eq. (4.1)) to the point corresponding to the centre of the module ( x = 110 mm). The inverse of this value, normalized by the average LO in that fibre layer, was taken as the fibre intercalibration coefficient, under the assumption that fibres at the same depth in the brass absorber should provide the same average response upon an uniform transverse beam profile. The different fibre layers were then intercalibrated by adjusting the average layer response in data according to the longitudinal shower profile predicted by the simulation using 8 GeV electron events. Summarizing, the whole module amplitude can be written as

S tot = 63 i=0 c i • S i , (5.1)
where S i is the signal amplitude measured in fibre i in ADC and For each beam energy point, the mean response is obtained from a Gaussian fit to the signal amplitude distributions shown in (a). A linear function is fitted to data and MC points for beam energies between 2 and 8 GeV. The resulting function is superimposed (black and red line, respectively). Deviation from linearity at 16 GeV is due to increased shower leakage. Data and simulation points in the figure correspond to the left and right y-axis, respectively. (c) Energy resolution of the calorimetric module as measured in the data (black dots) compared to expectations from an ideal simulation, i.e. fibres have an infinite attenuation length. of the calorimetric module was measured to be linear to within 0.7% up to 8 GeV, with a ∼ 5% deviation from linearity at 16 GeV due to an increased longitudinal shower leakage. This effect is confirmed by the simulation, as shown in figure 14b.

c i = η layer • LO i ( x)/ LO i ( x) i ∈layer
From a Gaussian fit to the signal amplitude peaks, the energy resolution of the calorimetric module was estimated. The performance was limited by the small module size and the consequent longitudinal shower leakage. The result, shown in figure 14c, is compared with the expectation from an ideal MC simulation where light propagation effects can be neglected, representing the 2016 JINST 11 P05004 ultimate performance limit of our experimental setup. The energy resolution observed in the data has roughly and additional 12% contribution added in quadrature to the MC limit, which is most likely due to the finite λ att of the fibres and the limited precision of the intercalibration procedure.

Longitudinal energy profile

The high granularity of our calorimetric prototype provided useful information to study the shower shape on an event-by-event basis. Selecting electron events with the same criteria used to study the energy resolution discussed in the previous paragraph, the longitudinal shower profile was reconstructed by adding the signal from the fibres belonging to the same vertical layer and displaying the average amplitude as a function of the fibre layer. Figure 15 shows the shower profile as measured in data and compared to the expectation from the MC simulation. A good level of agreement is found. Unfortunately, due to a malfunction of the voltage supplier, the SiPMs of the last two layers were not operational during these runs, which limited the measurement to the first six fibre layers.

Conclusions

This beam test confirmed the potential of crystal fibres for calorimetry applications. The crystal fibre prototype tested at the Fermilab Test Beam Facility confirmed the importance of high granularity for an effective separation of electron from pion events. The module response linearity and the electron shower longitudinal profiles were studied with high energy particles and found to well agree with simulation predictions.

The most important factors still limiting the performance of the module for calorimetric measurements were found to be non-uniformities in the light yield and light collection efficiency of the fibres. The large number of channels in this prototype implied the selection of fibres belonging to different production batches, in which different growth parameters and conditions were used. The characterization of the fibre response obtained with this beam test will help identify a set of -15 -beam energy (GeV) optimized parameters for the growth of fibres with good properties for calorimetry applications. A good reproducibility of the fibre optical quality is a crucial point towards a large-scale fibre production for a high granularity detector.

In addition to that, the still limited module dimension prevented a full sampling of the particle shower, especially at high energy. In order to evaluate the intrinsic potential of a crystal fibre calorimeter, a full-size detector was simulated with G 4 using the same materials and fibre arrangement as in our prototype, and assuming good attenuation lengths for all the fibres (> 20 cm). As shown in figure 16, such a configuration would ensure a good reconstruction performance of both electrons and pions, with a small constant term ( 2%) contributing to the energy resolution at high energy.

Figure 1 .Figure 2 .

 12 Figure 1. Secondary beam composition in the low energy pion magnet configuration (1-32 GeV) as measured by the CALICE collaboration [8].

Figure 3 .

 3 Figure 3. Picture of the grooved brass absorber loaded with crystal fibres. The fourth layer from the right contains undoped LuAG fibres, while all other layers are filled with LuAG:Ce fibres, as clearly visible from the greenish color (top). Schematic view of the module and labelling of the fibres and fibre layers. The two different beam configurations (transverse and pointing) are represented on the right, together with their respective frame of reference (bottom).

  A non-uniformity along the fibre length in the efficiency of the light extraction at the fibre ends can seriously affect the performance with high energy showers, especially if the excitation volume !"#$"!%% & !'()*+!),-!./#!01.2324567!! 8&! !"#$"!%% & !'()* KETEK 8 channel Arrays Version = 2011 Wafer 8 v4 Active area = 2.2 x2.2 mm Cell size = 20 micron # cells = 12100 Recovery time = 30 ns Vbreak down ~ 25.4 +-0.2V (T=23 C) dVb/dT = 25 mV ?? 31V 22C Thursday, February 27, 2014

Figure 4 .

 4 Figure 4. The 8 eightfold K SiPM packages used to read out each crystal fibre individually, mounted on the SiPM Interface Board (left). The SiPM PDE as measured in laboratory (right).

Figure 5 .

 5 Figure 5. Normalized pulse shape for various Cerium-doped fibres (green) and undoped LuAG fibres (blue).In undoped fibres, the promptly emitted Cherenkov photons give rise to a faster pulse than scintillation photons, which instead dominate the signal in doped fibres.

Figure 6 .

 6 Figure 6. LED pulser and clear fibre distribution system to inject LED light into the fibres (left). SiPM signal of fibre 62 when LED blue light was injected at the opposite end. The peaks corresponding to 0 and 1 ph.e. detected are clearly visible, whereas the 2 ph.e. peak is not fully resolved (right).

Figure 7 .Figure 8 .

 78 Figure 7. (a) Average response profile fibre 48 as a function of the beam impact x (left) and y (right) coordinate, as reconstructed by WC2 (solid black points). The simulated profile is superimposed (red line). (b) Reconstructed x (left) and y (right) coordinates of all fibre centers from a fit to the energy profiles as in top figures.

9 -Figure 9 .

 99 Figure 9. (a) Attenuation profiles for three different fibres (fibre 8, 14, and 52) as obtained in laboratory (red points) and at the beam test (black squares). (b) Scatter plot showing the attenuation length as measured at the beam test vs. the same parameter extracted from laboratory measurements.

Figure 10

 10 Figure10. Average energy deposited in a single fibre as a function of the fibre layer in the absorber module, as predicted by the simulation. Fibres are at cross angle with respect to the beam. Only events in which the beam distance from the fibre center was such that |∆x| < 80 mm and |∆y| =< 2 mm were selected. A pure electron beam as well as an admixture of electrons and pions are simulated, as expected from the beam specifications of the FTBF MT6 line, as in figure1(left). Profile of energy deposition in a perfectly transparent fibre (i.e. no effects of attenuation length) as a function of the distance of the incoming particle from the fibre axis, when fibres are parallel to the beam direction (right).

Figure 11 .

 11 Figure 11. Estimated light output, expressed in ph.e. per deposited MeV, for all the 64 fibres with the module in transverse configuration (left). Correlation between the measured LO in transverse and pointing configuration (right). Green dots and blue squares represent LuAG:Ce and undoped LuAG fibres respectively.

  Figure12. Simulation plot representing the number of active fibres (i.e. the number of fibres with a deposited energy above a given threshold) vs. the sum of the energy deposits in all the fibres, for pions (left) and electrons (right). The different signature of the two particle species in the calorimetric module is visible. An incident beam energy of 8 GeV is assumed, and only particles impinging in a region of ∆x = ±10 mm and ∆y = ±7.5 mm around the center of the module are considered.

Figure 13 .

 13 Figure 13. (a) Scatter plot of the number of active fibres vs. the sum of the signal amplitudes in all the fibres, as seen in beam test data for 8 GeV impinging beam. (b) Fraction of events surviving after the cut on the number of active fibres, compared to the expected electron fraction as measured by the CALICE collaboration, cf. figure 1.

- 1 isFigure 14 .

 114 Figure 14. (a) Distribution of signal amplitudes obtained by the sum of the intercalibrated signals from all the fibres, for different beam energies. Beam test data are shown on the left, whereas the expected MC distribution are shown on the right. (b) Linearity of the response for TB data (black dots) and MC simulation (red squares).For each beam energy point, the mean response is obtained from a Gaussian fit to the signal amplitude distributions shown in (a). A linear function is fitted to data and MC points for beam energies between 2 and 8 GeV. The resulting function is superimposed (black and red line, respectively). Deviation from linearity at 16 GeV is due to increased shower leakage. Data and simulation points in the figure correspond to the left and right y-axis, respectively. (c) Energy resolution of the calorimetric module as measured in the data (black dots) compared to expectations from an ideal simulation, i.e. fibres have an infinite attenuation length.

Figure 15 .

 15 Figure 15. Profile of the longitudinal development of electron shower in the module for different beam energies. Colored dots represent the average signal in each fibre layer as measured in the data, whereas lines show the expected profile as predicted by the simulation. Data points are not shown for 8 GeV beam energy since they were used to derive layer-to-layer intercalibration factors.

Figure 16 .

 16 Figure16. Intrinsic energy resolution of a brass+ LuAG fibre calorimeter. Fibre arrangement is the same as the one of the small prototype tested on beam.

1The frame of reference used throughout this paper has the x-axis horizontal on the experimental table, the y-axis pointing vertically downwards, and the z-axis aligned with the beam line and pointing in the opposite direction, as can be seen in figure2.

Acknowledgments

Research is conducted in the frame of the Crystal Clear Collaboration. We acknowledge support from the French National Agency for Research under grand agreement ANR-10-BLAN-0947 (INFINHI). This research project is supported by a Marie Curie Early Initial Training Network Fellowship of the European Union's Seventh Framework Programme (FP/2007-2013) under Grant Agreement Agreement 289355-PicoSEC-MCNet. The funding support for the Princeton University group comes from DOE Award n • ER-41850. We would like to thank all Fermilab experts and technicians of the FTBF division for making the test beam facility available, and in particular Paul Rubinov for providing the PAD-E boards for readout and constant support.