Dong Han

Rahma Moalla

Ignasi Fina

Valentina M Giordano

Marc D'esperonnat

Claude Botella

Geneviève Grenet

Régis Debord

Stéphane Pailhès

Guillaume Saint-Girons

Romain Bachelet

Giant tuning of electronic and thermoelectric properties by epitaxial strain in p-type Sr-doped LaCrO 3 transparent thin films

Keywords: P-type transparent conductors, (La1-xSrx)CrO3 solid solution, Electronic transport, Thermoelectric properties, Epitaxial films, Strain effect

. The lattice mismatch between the LSCO films and the substrates induces in-plane strain ranging from -2.06% (compressive) to +1.75% (tensile). The electric conductivity can be controlled over two orders of magnitude, σ ranging from ~0.5 S cm -1 (tensile strain) to 35 S cm -1 (compressive strain). Consistently, the Seebeck coefficient S can be finely tuned by a factor of almost two from ~127 µV K -1 (compressive strain) to 208 µV K -1 (tensile strain). Interestingly, we show that the thermoelectric power factor (PF = S 2 σ) can consequently be tuned by almost two orders of magnitude. The compressive strain yields a remarkable enhancement by a factor of three for 2% compressive strain with respect to almost relaxed films. These results demonstrate that epitaxial strain is a powerful lever to control the electric properties of LSCO and enhance its thermoelectric properties, which is of high interest for various devices and key applications such as thermal energy harvesters, coolers, transparent conductors, photo-catalyzers and spintronic memories.

I. INTRODUCTION

Crystalline transition-metal oxides, so-called functional oxides, represent an important class of materials since they exhibit a wide range of remarkable properties useful for advanced applications such as non-volatile memories, smart sensors, actuators and energy harvesters. Among others, both thermoelectric oxides (TEO) and transparent conducting oxides (TCO) have attracted rising attention in the last decades because of their potential use as coolers or thermal energy harvesters which can power autonomous wireless sensor networks [START_REF] Disalvo | Thermoelectric Cooling and Power Generation[END_REF][START_REF] He | Advances in Thermoelectric Materials Research: Looking Back and Moving Forward[END_REF][START_REF] He | Oxide Thermoelectrics: The Challenges, Progress, and Outlook[END_REF] , and/or as transparent conductors in numerous optoelectronic devices [START_REF] Zhang | Correlated Metals as Transparent Conductors[END_REF][START_REF] Minami | Transparent Conducting Oxide Semiconductors for Transparent Electrodes[END_REF][START_REF] Ginley | Transparent Conducting Oxides[END_REF][START_REF] Zhang | P-Type Transparent Conducting Oxides[END_REF] . In the broad perovskite-oxide family of general chemical formula ABO3, in which the chemical and the resulting physical properties can be widely tuned, TCO and TEO properties can be adjusted and even both optimized in a single material, as in wellstudied titanates such as n-type La-doped SrTiO3 that can exhibit both transparency in the visibleinfrared range (more than 60%) together with high electrical conductivity and large thermoelectric power factor at room temperature (around 40 μW cm -1 K -2 ) [START_REF] Okuda | Large Thermoelectric Response of Metallic Perovskites: Sr1-xLaxTiO3 (0 ≤ x ≤ 0.1)[END_REF][START_REF] Jalan | Large Seebeck Coefficients and Thermoelectric Power Factor of La-Doped SrTiO3 Thin Films[END_REF][START_REF] Ravichandran | An Epitaxial Transparent Conducting Perovskite Oxide: Double-Doped SrTiO3[END_REF][START_REF] Apreutesei | Thermoelectric La-Doped SrTiO3 Epitaxial Layers with Single-Crystal Quality: From Nano to Micrometers[END_REF][START_REF] Bouzerar | Unified Modelling of the Thermoelectric Properties in SrTiO3[END_REF][START_REF] Bouras | Perovskite-Oxide Based Hyperbolic Metamaterials[END_REF] . These last few years, advanced n-type TCO have been intensively investigated, e.g. high-mobility stannates such as Ladoped BaSnO3, the electrical conductivity and thermoelectric properties of which can be tuned by aliovalent cationic substitution [START_REF] Luo | High Carrier Mobility in Transparent Ba1-xLaxSnO3 Crystals with a Wide Band Gap[END_REF][START_REF] Kim | Physical Properties of Transparent Perovskite Oxides (Ba, La)SnO3 with High Electrical Mobility at Room Temperature[END_REF][START_REF] Raghavan | High-Mobility BaSnO3 Grown by Oxide Molecular Beam Epitaxy[END_REF][START_REF] Prakash | Wide Bandgap BaSnO3 Films with Room Temperature Conductivity Exceeding 10 4 S cm -1[END_REF][START_REF] Paik | Adsorption-Controlled Growth of La-Doped BaSnO3 by Molecular-Beam Epitaxy[END_REF] , vanadates such as SrVO3 [START_REF] Zhang | Correlated Metals as Transparent Conductors[END_REF][START_REF] Mirjolet | Independent Tuning of Optical Transparency Window and Electrical Properties of Epitaxial SrVO3 Thin Films by Substrate Mismatch[END_REF][START_REF] Boileau | Tuning of the Optical Properties of the Transparent Conducting Oxide SrVO3 by Electronic Correlations[END_REF] , and more recently molybdates such as SrMoO3 [START_REF] Stoner | Chemical Control of Correlated Metals as Transparent Conductors[END_REF][START_REF] Ha | Oxygen-Vacancy-Endurable Conductors with Enhanced Transparency Using Correlated 4d 2 SrMoO3 Thin Films[END_REF] . In contrast, effective p-type TCO or transparent TEO are still to be found, which is a crucial issue for the continued development of oxide-based thermoelectric and optoelectronic devices. Sr-doped LaCrO3 (La1-xSrxCrO3 solid solutions) has shown for more than forty years both p-type conduction and thermoelectricity [START_REF] Karim | Localized Level Hopping Transport in La(Sr)CrO3[END_REF] , and more recently rather good optical transparency in the visible and near-infrared range [START_REF] Zhang | Perovskite Sr-Doped LaCrO3 as a New p-Type Transparent Conducting Oxide[END_REF] . It has received increasing attention as a ptype transparent thermoelectric perovskite oxide these last few years [START_REF] Zhang | Hole-Induced Insulator-to-Metal Transition in La1-xSrxCrO3 Epitaxial Films[END_REF][START_REF] Woods-Robinson | Assessing High-Throughput Descriptors for Prediction of Transparent Conductors[END_REF][START_REF] Han | Poisson Ratio and Bulk Lattice Constant of (Sr0.25La0.75)CrO3 from Strained Epitaxial Thin Films[END_REF] . La2/3Sr1/3VO3 has recently been found to be a p-type TCO with properties similar to that of La0.75Sr0.25CrO3. Its thermoelectric properties have not been reported yet [START_REF] Hu | La2/3Sr1/3VO3 Thin Films: A New p-Type Transparent Conducting Oxide with Very High Figure of Merit[END_REF] . Although of critical importance in the thin-film form, requested for advanced devices such as on-chip thermal energy harvesters or coolers, transparent diodes/electrodes, photocatalyzers or spintronic memories [START_REF] Zhang | Perovskite Sr-Doped LaCrO3 as a New p-Type Transparent Conducting Oxide[END_REF][START_REF] Du | An All-Perovskite p-n Junction Based on Transparent Conducting p-La1-xSrxCrO3 Epitaxial Layers[END_REF][START_REF] Stoerzinger | Impact of Sr-Incorporation on Cr Oxidation and Water Dissociation in La(1-x)SrxCrO3[END_REF][START_REF] Marti | Room-Temperature Antiferromagnetic Memory Resistor[END_REF] , the impact of strain on the physical properties of La1-xSrxCrO3 has not been studied yet.

Epitaxial strain is a powerful lever to tune the structural and physical properties of a wide range of materials [START_REF] Shi | Strain Engineering in Functional Materials[END_REF][START_REF] Ramesh | Creating Emergent Phenomena in Oxide Superlattices[END_REF][START_REF] Hwang | Tuning Perovskite Oxides by Strain: Electronic Structure, Properties, and Functions in (Electro) Catalysis and Ferroelectricity[END_REF] . Strain engineering has been successfully applied to various transition metal perovskite oxides of different properties such as ferroic, conducting, phase changes or metalinsulator transitions (MIT) [START_REF] Ramesh | Creating Emergent Phenomena in Oxide Superlattices[END_REF][START_REF] Hwang | Tuning Perovskite Oxides by Strain: Electronic Structure, Properties, and Functions in (Electro) Catalysis and Ferroelectricity[END_REF][START_REF] Schlom | Elastic Strain Engineering of Ferroic Oxides[END_REF][START_REF] Tokura | Orbital Physics in Transition-Metal Oxides[END_REF][START_REF] Rondinelli | Structure and Properties of Functional Oxide Thin Films: Insights from Electronic-Structure Calculations[END_REF][START_REF] Koster | Structure, Physical Properties, and Applications of SrRuO3 Thin Films[END_REF][START_REF] Pesquera | Surface Symmetry-Breaking and Strain Effects on Orbital Occupancy in Transition Metal Perovskite Epitaxial Films[END_REF][START_REF] Catalano | Rare-Earth Nickelates RNiO3: Thin Films and Heterostructures[END_REF][START_REF] Guo | Switchable Orbital Polarization and Magnetization in Strained LaCoO3 Films[END_REF] . Even subtle, strain in transition metal perovskite oxides modifies the fundamental B-O bond length and/or <B-O-B> bond angle through BO6 octahedral distortions, tilts and rotations, and this affects the electronic band structure such as dorbital bandwidth, degeneracy, occupancy, hybridization and ordering, with strong impact on the macroscopic physical properties. More particularly in conducting perovskite oxides, intersite hopping is established from overlap (hybridization) between transition metal B d-orbitals and ligand O p-orbitals, which depends on strain [START_REF] Tokura | Orbital Physics in Transition-Metal Oxides[END_REF][START_REF] Rondinelli | Structure and Properties of Functional Oxide Thin Films: Insights from Electronic-Structure Calculations[END_REF][START_REF] Catalano | Rare-Earth Nickelates RNiO3: Thin Films and Heterostructures[END_REF][START_REF] Imada | Metal-Insulator Transitions[END_REF] . For instance, it has been shown that epitaxial strain can be an efficient parameter to tune electrical resistivity and/or metal-insulator transitions in manganites such as La1-xSrxMnO3 [START_REF] Tokura | Orbital Physics in Transition-Metal Oxides[END_REF][START_REF] Adamo | Effect of Biaxial Strain on the Electrical and Magnetic Properties of (001) La0.7Sr0.3MnO3 Thin Films[END_REF] , ruthenates such as SrRuO3 [START_REF] Koster | Structure, Physical Properties, and Applications of SrRuO3 Thin Films[END_REF][START_REF] Vailionis | Room Temperature Epitaxial Stabilization of a Tetragonal Phase in ARuO3 (A = Ca and Sr) Thin Films[END_REF][START_REF] Grutter | Enhanced Magnetization in Epitaxial SrRuO3 Thin Films via Substrate-Induced Strain[END_REF][START_REF] Kan | Strain Effect on Thermoelectric Properties of SrRuO3 Epitaxial Thin Films[END_REF] , nickelates such as LaNiO3 [START_REF] Catalano | Rare-Earth Nickelates RNiO3: Thin Films and Heterostructures[END_REF] , or vanadates such as SrVO3 [START_REF] Mirjolet | Independent Tuning of Optical Transparency Window and Electrical Properties of Epitaxial SrVO3 Thin Films by Substrate Mismatch[END_REF] . Roughly speaking (i.e. disregarding possible consequences of orbital ordering, Jahn-Teller distortion, symmetry lowering and bond disproportionation effects) [START_REF] Varignon | Origin of Band Gaps in 3d Perovskite Oxides[END_REF] , in-plane tensile strain (or enlargement of unit-cell volume) tends to increase electrical resistivity and/or MIT temperature (mainly because of a decrease orbitals overlap, bandwidth and delocalized states), as in nickelates [START_REF] Catalano | Rare-Earth Nickelates RNiO3: Thin Films and Heterostructures[END_REF][START_REF] Liu | Heterointerface Engineered Electronic and Magnetic Phases of NdNiO3 Thin Films[END_REF] , manganites [START_REF] Tokura | Orbital Physics in Transition-Metal Oxides[END_REF][START_REF] Adamo | Effect of Biaxial Strain on the Electrical and Magnetic Properties of (001) La0.7Sr0.3MnO3 Thin Films[END_REF] , ruthenates [START_REF] Koster | Structure, Physical Properties, and Applications of SrRuO3 Thin Films[END_REF][START_REF] Vailionis | Room Temperature Epitaxial Stabilization of a Tetragonal Phase in ARuO3 (A = Ca and Sr) Thin Films[END_REF][START_REF] Grutter | Enhanced Magnetization in Epitaxial SrRuO3 Thin Films via Substrate-Induced Strain[END_REF][START_REF] Kan | Strain Effect on Thermoelectric Properties of SrRuO3 Epitaxial Thin Films[END_REF] , and vanadates [START_REF] Mirjolet | Independent Tuning of Optical Transparency Window and Electrical Properties of Epitaxial SrVO3 Thin Films by Substrate Mismatch[END_REF] , and compressive strain (or reduction of unit-cell volume) induces a decrease of electrical resistivity and/or MIT temperature (mainly because of increase of orbitals overlap, bandwidth and delocalized states) as observed in nickelates [START_REF] Catalano | Rare-Earth Nickelates RNiO3: Thin Films and Heterostructures[END_REF] . Consistently, high hydrostatic pressure studies confirm this tendency in nickelates [START_REF] Catalano | Rare-Earth Nickelates RNiO3: Thin Films and Heterostructures[END_REF] and even beyond oxides in more conventional thermoelectric materials for which compressive strain in the few GPa range (equivalent of epitaxial strain) tends to enhance the mobile-charge carrier concentration by reducing the bond length and the bandgap [START_REF] Morozova | Strategies and Challenges of High-Pressure Methods Applied to Thermoelectric Materials[END_REF] . It is worth reminding that thermopower (thermoelectric Seebeck coefficient) and electrical resistivity have similar tendencies [START_REF] Jalan | Large Seebeck Coefficients and Thermoelectric Power Factor of La-Doped SrTiO3 Thin Films[END_REF][START_REF] Apreutesei | Thermoelectric La-Doped SrTiO3 Epitaxial Layers with Single-Crystal Quality: From Nano to Micrometers[END_REF][START_REF] Bouzerar | Unified Modelling of the Thermoelectric Properties in SrTiO3[END_REF][START_REF] Zhang | Perovskite Sr-Doped LaCrO3 as a New p-Type Transparent Conducting Oxide[END_REF][START_REF] Morozova | Strategies and Challenges of High-Pressure Methods Applied to Thermoelectric Materials[END_REF][START_REF] Snyder | Complex Thermoelectric Materials[END_REF] .

LaCrO3 is a G-type antiferromagnetic insulator (TN  290 K) with charge transfer gap of 3.3 eV and orthorhombic structure [START_REF] Weinberg | Electron Paramagnetic Resonance and Antiferromagnetism in LaCrO3[END_REF][START_REF] Arima | Variation of Optical Gaps in Perovskite-Type 3d Transition-Metal Oxides[END_REF][START_REF] Yang | Structural Analysis of Perovskite LaCr1-xNixO3 by Rietveld Refinement of X-Ray Powder Diffraction Data[END_REF] . While the electrical conductivity (σ) and Seebeck coefficient (S) of La1-xSrxCrO3 can be tuned by the partial aliovalent cationic substitution ratio x on the A-site of the perovskite structure, which forms shallow impurity energy level and associated mobile hole carriers [START_REF] Karim | Localized Level Hopping Transport in La(Sr)CrO3[END_REF][START_REF] Marsh | Theory of the Seebeck Coefficient in LaCrO3 and Related Perovskite Systems[END_REF] , the corresponding thermoelectric power factor (PF = S 2 σ) being maximum for x around 0.25 keeping rather good optical transparency [START_REF] Karim | Localized Level Hopping Transport in La(Sr)CrO3[END_REF][START_REF] Zhang | Perovskite Sr-Doped LaCrO3 as a New p-Type Transparent Conducting Oxide[END_REF] . At room temperature, La0.75Sr0.25CrO3 (LSCO) is a transparent thermoelectric semiconductor with a orthorhombic bulk structure (a = 5.503 Å, b = 5.467 Å, c = 7.76 Å, and <Cr-O-Cr> bond angles around 162°, both rather temperature-independent), pseudo-cubic bulk lattice constant of 3.876 Å, and within 25% Cr 4+ 3d t2g 2 electronic configuration [START_REF] Zhang | Perovskite Sr-Doped LaCrO3 as a New p-Type Transparent Conducting Oxide[END_REF][START_REF] Han | Poisson Ratio and Bulk Lattice Constant of (Sr0.25La0.75)CrO3 from Strained Epitaxial Thin Films[END_REF][START_REF] Chakraborty | Magnetic Ordering in La0.75Sr0.25CrO3: A Neutron Diffraction Study[END_REF] . No study has been reported yet concerning the strain impact on p-type Sr-doped LaCrO3 properties, despite its technological importance as p-type TEO and TCO and the strain-engineering potential. However, preliminary observations have mentioned that the epitaxial strain on La1-xSrxCrO3 films can critically impact its electronic transport properties: purely metallic behavior has been observed at x  0.65 only for compressively strained epitaxial thin films [START_REF] Zhang | Hole-Induced Insulator-to-Metal Transition in La1-xSrxCrO3 Epitaxial Films[END_REF] . In addition to partial aliovalent cationic substitution (doping level), the epitaxial strain is expected to be a powerful lever to tailor its physical properties. Indeed, in this paper, we show that epitaxial strain is an efficient parameter to control to a large extent the electronic and thermoelectric properties of p-type LSCO transparent thin films, which is of critical importance for integrated LSCO-based devices.

II. METHODS

About 30 nm thick La0.75Sr0.25CrO3 (LSCO) epitaxially-strained thin films were grown on three single-side polished (001)-oriented (pseudo)cubic perovskite-oxide substrates with different lattice parameters: LaAlO3 (LAO), (LaAlO3)0.3(Sr2AlTaO6)0.7 (LSAT), and DyScO3 (DSO) from SurfaceNet GmbH. They provide in-plane strain (εxx) ranging from -2.06% to +1.75% due to lattice mismatch (see Notes and Figure 1). The samples shown here were also used for another study published elsewhere [START_REF] Han | Poisson Ratio and Bulk Lattice Constant of (Sr0.25La0.75)CrO3 from Strained Epitaxial Thin Films[END_REF] , and were grown successively in the same period and the same growth conditions after proper calibration [START_REF] Han | Poisson Ratio and Bulk Lattice Constant of (Sr0.25La0.75)CrO3 from Strained Epitaxial Thin Films[END_REF][START_REF] Han | Structural Properties of Strained Epitaxial La1+δCrO3 Thin Films[END_REF] .

The films were grown by solid-source oxide molecular beam epitaxy (MBE) in an ultra-high vacuum (UHV) chamber with a base pressure of less than 1×10 -9 Torr. Sr, La, and Cr were evaporated from effusion cells in co-deposition. The fluxes were calibrated using a Bayard-Alpert Gauge and checked with a quartz microbalance in UHV (Fig. S1) [START_REF] Han | Poisson Ratio and Bulk Lattice Constant of (Sr0.25La0.75)CrO3 from Strained Epitaxial Thin Films[END_REF][START_REF] Han | Structural Properties of Strained Epitaxial La1+δCrO3 Thin Films[END_REF] . The substrates were annealed under the growth conditions for 15 minutes to remove surface impurities before starting the growth at 750 °C and P(O2) = 1×10 -7 Torr, and at a growth rate of 0.15 nm per minute. After deposition, the substrate temperature was lowered to 200 °C at a rate of 50 °C per minute while the background O2 was pumped out. All LSCO films were subjected to post-growth ex-situ annealing in air at 300 °C for 2 hours to ensure complete oxidation of the perovskite phase and re-oxidation of the oxide substrates. Backside resistivity measurements were carried out to confirm that the substrates were insulating, which is crucial to avoid artifacts during transport and thermoelectric measurements [START_REF] Scullin | Anomalously Large Measured Thermoelectric Power Factor in Sr1-xLaxTiO3 Thin Films due to SrTiO3 Substrate Reduction[END_REF] .

Reflection high-energy electron diffraction (RHEED) was used to monitor the epitaxial growth (Fig. 1). The structural properties of the films were investigated by X-ray diffraction (XRD) and X-ray reflectometry (XRR) using a Rigaku Smartlab diffractometer equipped with a high-brilliance rotating anode and a double-crystal Ge(220) monochromator (Figs. 2, S2-S3, S5, Table S1).

Atomic force microscopy was used in tapping mode to characterize the film surface (Figs. S4-S5, Table S1). X-ray photoemission spectroscopy (XPS) was used to characterize the main chemical properties of the films (Fig. S6) [START_REF] Han | Poisson Ratio and Bulk Lattice Constant of (Sr0.25La0.75)CrO3 from Strained Epitaxial Thin Films[END_REF] . Electrical resistivity was determined using the van der Pauw method in the 100-400 K temperature range. For that purpose, Cr/Au electrodes were placed at the vortexes of the films. These electrical transport measurements were performed in a physical property measurement system (PPMS) from Quantum Design (Fig. S7). Seebeck coefficients (S)

were measured using the differential method S = ΔV/ΔT (Figs. S8-S9), where ΔV is the thermoelectromotive force induced by the thermal gradient ΔT, in a high-temperature set-up, similar to that described elsewhere [START_REF] Rouleau | Measurement System of the Seebeck Coefficient or of the Electrical Resistivity at High Temperature[END_REF] . S(T) has then been measured just above room temperature, a temperature range of high interest for most of the applications. According to our former work [START_REF] Han | Poisson Ratio and Bulk Lattice Constant of (Sr0.25La0.75)CrO3 from Strained Epitaxial Thin Films[END_REF] , the lattice constant of bulk LSCO with 25% Sr concentration is 3.876 Å at room temperature, which lies close to the lattice constant of LSAT (Figure 1). LSCO is thus grown almost relaxed on LSAT (exactly under slight compressive strain of -0.21 %), under compressive strain (-2.06 %) on LAO, and under tensile strain (+1.75 %) on DSO (see Notes). The RHEED patterns of the LSCO layers grown on the three substrates (LAO, LSAT, and DSO) are

III. RESULTS AND DISCUSSION

shown in Figure 1(d-f). All the patterns present well-contrasted integer-order reflections attesting for single-phase epitaxial films. For the films on LSAT and DSO, the RHEED reflections are streaky attesting for flat films, whereas for the film with the large compressive strain on LAO (-2.06%), RHEED reflections are slightly spotty, suggesting a certain surface roughness, as frequently observed in strongly compressively-strained epitaxial layers. However, XRR and AFM analysis reveal rather low root-mean-square (rms) surface roughnesses, lower than 0.7 nm, in the same order of magnitude than the two other samples (see Supporting Information, Figs. S3, S4, S5, and Table S1). For instance, the differences of rms surface roughness between LSCO/LAO and LSCO/LSAT are small (0.14 nm measured macroscopically by XRR, and 0.26 nm measured microscopically by AFM). The LSCO films are confirmed to be rather well transparent (Figure 1g and 1h) with slightly brown color in good agreement with the observations made by Zhang et al.

(transmittance between 40 % and 65 % in the visible and near-infrared range for this LSCO composition and with 80 nm thick films [START_REF] Zhang | Perovskite Sr-Doped LaCrO3 as a New p-Type Transparent Conducting Oxide[END_REF] ). The LSCO transmittance appears very similar to other emergent perovskite TCO, such as n-type SrVO3 for instance (<65% with 45 nm thick films) [START_REF] Zhang | Correlated Metals as Transparent Conductors[END_REF] , and somehow lower than standard TCO such as n-type Indium-Tin Oxide (ITO) but which is limited by indium scarcity and not of perovskite structure [START_REF] Minami | Transparent Conducting Oxide Semiconductors for Transparent Electrodes[END_REF][START_REF] Zhang | P-Type Transparent Conducting Oxides[END_REF] . -c) [START_REF] Han | Poisson Ratio and Bulk Lattice Constant of (Sr0.25La0.75)CrO3 from Strained Epitaxial Thin Films[END_REF] . Figure 2a shows the 2/ scans recorded around the (002) reflections of the LSCO films and the substrates. The (002) peaks attributable to the LSCO films are indicated by stars. The presence of Pendellösung fringes around the diffraction peaks of the films, especially on LSAT and DSO substrates, attest to their high crystalline quality and abruptness of their interfaces. These fringes seem to appear more clearly with in-plane tensile strain for which the rms surface roughness is lower (see Supporting Information, Figs. S3, S4, S5, Table S1). All films have low mosaicity, below 0.1° for LSCO on LSAT and DSO, and 0.2 ° for LSCO on LAO (see Supporting Information, Fig. S2d, Table S1).

A gradual shift in the Qz position of the (002) reflection of the films is observed with in-plane strain in Figure 2a. The corresponding measured out-of-plane lattice parameters (cLSCO) of the films for each film ranges from 3.941 Å (in-plane compressive) to 3.804 Å (in-plane tensile), as shown in Figure 2c. The XRD reciprocal space maps (RSM) around the asymmetrical (103) reflection indicates that all LSCO films are coherently strained to their substrates with undetectable strain relaxation (Figure 2b). The in-plane epitaxial strain (εxx) of the LSCO films varies from -2.06%

(compressive) to +1.75% (tensile), depending upon the substrate (see Notes). The out-of-plane strain (εzz) of the LSCO films ranges from +1.68% (in-plane compressive) to -1.86% (in-plane tensile). Elastic strain is rather large in LSCO because of its relatively large Poisson ratio (ν = 0.32) [START_REF] Han | Poisson Ratio and Bulk Lattice Constant of (Sr0.25La0.75)CrO3 from Strained Epitaxial Thin Films[END_REF] . Figure 2c shows that the unit-cell volume of LSCO films (VLSCO, blue triangles in Figure 2c) increases from 56.8 Å 3 (compressive) to 59.2 Å 3 (tensile) [START_REF] Han | Poisson Ratio and Bulk Lattice Constant of (Sr0.25La0.75)CrO3 from Strained Epitaxial Thin Films[END_REF] . The VLSCO of the film grown almost relaxed on LSAT is about 58.4 Å 3 , close to the bulk LSCO volume value (58.2 Å 3 ). The density of all LSCO films was then extracted from unit-cell volume and is plotted as a function of strain in Figure 2c (red circles). It decreases quasi-linearly from 6.61 g cm -3 (compressive) to 6.35 g cm -3

(tensile) (DLSCO-bulk = 6.45 g cm -3 ) with increasing strain. with this LSCO composition [START_REF] Karim | Localized Level Hopping Transport in La(Sr)CrO3[END_REF][START_REF] Zhang | Hole-Induced Insulator-to-Metal Transition in La1-xSrxCrO3 Epitaxial Films[END_REF] . However, the resistivity values are very different depending on the film (strain), and they vary over almost two orders of magnitude, the in-plane compressively (tensely) strained film being more conducting (insulating). For instance, the resistivity at 300 K is about 10 -2  cm on LAO (compressive strain), 10 -1  cm on LSAT (almost relaxed), and 1  cm on DSO (tensile strain). The compressive LSCO film on LAO has resistivity values that are more comparable to 50% than 25% Sr-doped LCO films, whereas the tensile LSCO film on DSO has resistivity values comparable to 0.04% Sr-doped LCO films [START_REF] Zhang | Perovskite Sr-Doped LaCrO3 as a New p-Type Transparent Conducting Oxide[END_REF][START_REF] Zhang | Hole-Induced Insulator-to-Metal Transition in La1-xSrxCrO3 Epitaxial Films[END_REF] . It is worth noting that the almost relaxed LSCO film on LSAT has resistivity values in good agreement with other 25% Srdoped LaCrO3 films of comparable strain [START_REF] Zhang | Hole-Induced Insulator-to-Metal Transition in La1-xSrxCrO3 Epitaxial Films[END_REF] .

Figure 3b presents the corresponding temperature dependence of the conductivity, consistent with thermally activated hopping transport in agreement with previous studies [START_REF] Karim | Localized Level Hopping Transport in La(Sr)CrO3[END_REF][START_REF] Zhang | Perovskite Sr-Doped LaCrO3 as a New p-Type Transparent Conducting Oxide[END_REF] . The different slopes indicate different activation energies (Ea) for hopping transport that depends upon the strain.

In agreement with the resistivity/conductivity trend, Ea increases with in-plane tensile strain and decreases with compressive strain, which is certainly linked with strain-dependent unit-cell volume and Cr 3d -O 2p orbital hybridizations, as in many other complex oxides (see Introduction). Ea for the most conductive film (compressive on LAO) is around 67.8 meV, more comparable to 50% Srdoped than 25% Sr-doped LCO films, whereas that of the most resistive film (tensile on DSO) is around 122 meV, more comparable to 4% Sr-doped LCO films [START_REF] Zhang | Perovskite Sr-Doped LaCrO3 as a New p-Type Transparent Conducting Oxide[END_REF] . Figure 3c summarizes the Ea values of LSCO plotted as a function of in-plane strain.

Figure 3d presents both the Seebeck coefficients S (measured in-plane, raw data in Supporting Information, Fig. S8) and the fraction of hopping sites occupied with holes (hSPH, estimated from S using a small polaron hopping model, see below) as a function of in-plane strain and corresponding stress. The positive S for all samples confirms that holes are the dominant mobile charge carriers in these films, as expected [START_REF] Karim | Localized Level Hopping Transport in La(Sr)CrO3[END_REF][START_REF] Zhang | Perovskite Sr-Doped LaCrO3 as a New p-Type Transparent Conducting Oxide[END_REF][START_REF] Zhang | Hole-Induced Insulator-to-Metal Transition in La1-xSrxCrO3 Epitaxial Films[END_REF] . The Seebeck coefficient monotonously increases with strain (from compressive to tensile) in agreement with the decrease of the electrical conductivity [START_REF] Zhang | Perovskite Sr-Doped LaCrO3 as a New p-Type Transparent Conducting Oxide[END_REF][START_REF] Snyder | Complex Thermoelectric Materials[END_REF] , by almost a factor two from 127 V K -1 (compressive) to 208 V K -1 (tensile), consistently with other observations made on various thermoelectric materials under highpressures (S decreasing with pressure) [START_REF] Morozova | Strategies and Challenges of High-Pressure Methods Applied to Thermoelectric Materials[END_REF] . It is worth noting that the Seebeck coefficients of the almost relaxed LSCO film on LSAT (160 V K -1 ) and another moderately tensile on STO substrate (180 V K -1 , see Supporting Information, Fig. S9) are in perfect agreement with Zhang et al. [START_REF] Zhang | Perovskite Sr-Doped LaCrO3 as a New p-Type Transparent Conducting Oxide[END_REF] .

As in Ref. 24, Hall measurements being unsuccessful on these samples most probably because of both low carrier mobility and relatively high resistivity [START_REF] Werner | Hall Measurements on Low-Mobility Thin Films[END_REF] , the fraction of hopping sites occupied with holes (hSPH) has been estimated from S values using a small polaron hopping model, such as:

  21 ln SPH B SPH h k S eh     
where kB is Boltzmann's constant, e is the electronic charge [START_REF] Zhang | Perovskite Sr-Doped LaCrO3 as a New p-Type Transparent Conducting Oxide[END_REF] . hSPH should be 0.25 for this LSCO composition in bulk (relaxed state). However, it rather strongly deviates here depending on strain: monotonously decreasing from 0.315 (compressive) to 0.238 (almost relaxed) and 0.152 (tensile), consistently with resistivity/conductivity data (Fig. 3a-c). It is worth noting that hSPH is about 0.2 for LSCO grown on SrTiO3 substrate (in slight tensile strain), in very good agreement with this trend (see Supporting Information, Fig. S10) [START_REF] Zhang | Perovskite Sr-Doped LaCrO3 as a New p-Type Transparent Conducting Oxide[END_REF] . The mobile hole density (pSPH) as well as hole mobility [µSPH = σxx / (e pSPH)] have then been estimated from hSPH values (Fig. 4a). Figure 4 presents the electronic transport and thermoelectric properties of the LSCO films at room temperature as a function of in-plane strain and corresponding stress (see Notes) [START_REF] Gaillac | An Open-Source Online Application for Analysis and Visualization of Elastic Tensors[END_REF][START_REF] De Jong | Charting the Complete Elastic Properties of Inorganic Crystalline Compounds[END_REF] . Figure 4a presents the values of in-plane electrical conductivity, mobile charge carrier density, and mobility assuming only one-type (hole) carrier. As presented above with resistivity (ρxx), the electrical conductivity (σxx = ρxx -1 ) at 300 K monotonously decreases by two orders of magnitude

Stress (GPa)

from 35 S cm -1 (compressive) to 0.5 S cm -1 (tensile), with intermediate 7 S cm -1 (almost relaxed) in good agreement with literature [START_REF] Zhang | Hole-Induced Insulator-to-Metal Transition in La1-xSrxCrO3 Epitaxial Films[END_REF] . The extracted mobile hole density (pSPH) monotonously decreases from 5.5 10 21 cm -3 (compressive) to 2.6 10 21 cm -3 (tensile), with intermediate value about 4.1 10 21 cm -3 (almost relaxed) in good agreement with it is expected from bulk value at this LSCO composition (25% holes per unit cell leading to p 4.3 10 21 cm -3 ). The extracted hole mobility (µSPH) largely decreases by more than one order of magnitude from 0.04 cm 2 V -1 s -1 (compressive) to 0.001 cm 2 V -1 s -1 (tensile), with intermediate value about 0.01 cm 2 V -1 s -1 (almost relaxed), in rather good agreement with ref. [START_REF] Zhang | Perovskite Sr-Doped LaCrO3 as a New p-Type Transparent Conducting Oxide[END_REF] . For general comparisons, hole mobility in LSCO appears to be about one-two orders of magnitude lower than n-type La-doped STO epitaxial films [START_REF] Apreutesei | Thermoelectric La-Doped SrTiO3 Epitaxial Layers with Single-Crystal Quality: From Nano to Micrometers[END_REF][START_REF] Son | Epitaxial SrTiO3 Films with Electron Mobilities Exceeding 30,000 cm 2 V -1 s -1[END_REF] , and threefour orders of magnitude lower than high-mobility n-type La-doped BaSnO3 epitaxial films [START_REF] Raghavan | High-Mobility BaSnO3 Grown by Oxide Molecular Beam Epitaxy[END_REF][START_REF] Paik | Adsorption-Controlled Growth of La-Doped BaSnO3 by Molecular-Beam Epitaxy[END_REF][START_REF] Kim | High Mobility in a Stable Transparent Perovskite Oxide[END_REF] or p-type doped GaAs-based III-V semiconductors (see Notes). It is worth noting that hole mobility is often lower, up to two orders of magnitude, than electron mobility for the same core semiconductor materials, as in ZnO [START_REF] Tsukazaki | High-Mobility Electronic Transport in ZnO Thin Films[END_REF][START_REF] Xiu | Photoluminescence Study of Sb-Doped p-Type ZnO Films by Molecular-Beam Epitaxy[END_REF] or GaAs (see Notes), for instance.

Figure 4b presents the thermoelectric power factor (PF = S 2 σ) at room temperature as function of in-plane strain. Interestingly, despite the Seebeck coefficient trend, the thermoelectric power factor is dominated by the electrical conductivity, decreasing largely by more than one order of magnitude from 0.56 μW cm -1 K -2 (compressive) to 0.02 μW cm -1 K -2 (tensile). All these coherent results show that the electronic and thermoelectric properties of LSCO can be finely tuned by lattice strain, and that compressive strain enhances both the electrical conductivity and thermoelectric power factor, which is of high interest for various applications.

T (K) PF (μW cm -1 K -2 ) (b) (c)

Compression Tension Tension Compression

Figure 5 presents the temperature-dependence of the Seebeck coefficient (S), the electrical conductivity (σxx) and the thermoelectric power factor (PF) for all LSCO films measured just above room temperature (300-400 K), in a range of high interest for the main applications. The Seebeck coefficients decrease with increasing temperature for the two most conductive samples, driven by the temperature dependence of electrical conductivity. This decrease is all the faster that the film is conductive. In contrast, for the most resistive (tensile) film, S increases with increasing temperature, in contradiction with the temperature dependence of electrical conductivity. However, the S measurement uncertainties are larger for this resistive sample. The S can be considered almost constant with temperature in this range within these uncertainties, which can be observed elsewhere in bulk LSCO [START_REF] Karim | Localized Level Hopping Transport in La(Sr)CrO3[END_REF] . We note that the thermal expansion coefficients of the substrates are very similar (see Notes) so that the slight differences in thermal expansion mismatch between the substrates and the films are too small (and not consistent with the trend) to explain the differences in the observed temperature-dependent variations. The electrical conductivity differences between films are maintained whatever the temperature. Interestingly, considering the measurement uncertainties of S, the PF of this resistive film increases slightly with temperature, contrary to the most conductive film (Figure 5c). The PF of the intermediate almost relaxed film appears monotonous with temperature. Nevertheless, no important change is observed with temperature in this range, in agreement with previous studies on structural, electronic and thermoelectric properties of bulk LSCO [START_REF] Karim | Localized Level Hopping Transport in La(Sr)CrO3[END_REF][START_REF] Chakraborty | Magnetic Ordering in La0.75Sr0.25CrO3: A Neutron Diffraction Study[END_REF] . At 350 K for instance, depending on the strain, the Seebeck coefficients still differ by a factor of two (Figure 5a), the electrical conductivity by two orders of magnitude (Figure 5b) and the PF by one order of magnitude (Figure 5c), similarly to 300 K. As mentioned in the introduction, the lattice strain of perovskite oxides can largely modify their physical properties, which has led to strain engineering of various thin films by heteroepitaxy [START_REF] Ramesh | Creating Emergent Phenomena in Oxide Superlattices[END_REF][START_REF] Hwang | Tuning Perovskite Oxides by Strain: Electronic Structure, Properties, and Functions in (Electro) Catalysis and Ferroelectricity[END_REF][START_REF] Schlom | Elastic Strain Engineering of Ferroic Oxides[END_REF][START_REF] Rondinelli | Structure and Properties of Functional Oxide Thin Films: Insights from Electronic-Structure Calculations[END_REF] . In conducting perovskite oxides (ABO3) with d-electron transition metal (B), the lattice strain/distortion (change in the B-O bond length and/or <B-O-B> bond angle) affects the band structure due to strong electron-orbital-lattice couplings, such as bandwidth, orbital hybridizations, orbital level splitting (splitting of t2g and eg levels depending on the crystalline symmetry), and subband filling responsible for possible doping and metal-insulator transitions [START_REF] Rondinelli | Structure and Properties of Functional Oxide Thin Films: Insights from Electronic-Structure Calculations[END_REF][START_REF] Imada | Metal-Insulator Transitions[END_REF] . In tetragonal LSCO epitaxial films, the Cr 3d -O 2p orbital hybridization and level at the top of the valence band, together with the empty split Cr 3d t2g orbital level at the bottom of the conduction band, which allow hole hopping transport [START_REF] Zhang | Perovskite Sr-Doped LaCrO3 as a New p-Type Transparent Conducting Oxide[END_REF] , are certainly altered because of such lattice strain/distortion even at constant band filling [START_REF] Rondinelli | Structure and Properties of Functional Oxide Thin Films: Insights from Electronic-Structure Calculations[END_REF][START_REF] Imada | Metal-Insulator Transitions[END_REF] . As observed with other perovskite oxides such as nickelates [START_REF] Catalano | Rare-Earth Nickelates RNiO3: Thin Films and Heterostructures[END_REF] , the biaxial in-plane tensile strain in LSCO (larger Cr-O bond length, <Cr-O-Cr> bond angle up to 180° and unit cell volume) would decrease the Cr 3d -O 2p orbital hybridization (bandwidth) at the valence band. This would then decrease the hopping transport probability and consequently decrease the mobile hole density responsible for p-type electrical (semi)conductivity by small polaron hopping. Additionally, a Jahn-Teller like distortion may occur as observed in CrO2 [START_REF] Zimmermann | 1s2p Resonant Inelastic X-Ray Scattering Magnetic Circular Dichroism as a Probe for the Local and Non-Local Orbitals in CrO2[END_REF] or other perovskite oxides such as La2/3Sr1/3MnO3 [START_REF] Pesquera | Surface Symmetry-Breaking and Strain Effects on Orbital Occupancy in Transition Metal Perovskite Epitaxial Films[END_REF][START_REF] Koohfar | Effect of Strain on Magnetic and Orbital Ordering of LaSrCrO3/LaSrMnO3 Heterostructures[END_REF] , LaCoO3 [START_REF] Guo | Switchable Orbital Polarization and Magnetization in Strained LaCoO3 Films[END_REF] and SrVO3 [START_REF] Mirjolet | Independent Tuning of Optical Transparency Window and Electrical Properties of Epitaxial SrVO3 Thin Films by Substrate Mismatch[END_REF] where in-plane tensile strain would lower and favor the occupied in-plane Cr 3d t2g (xy) orbital ground state (Figure 6).

On the contrary, the biaxial in-plane compressive strain (smaller Cr-O bond length, <Cr-O-Cr> bond angle than 162°, and unit-cell volume) would increase the Cr 3d -O 2p orbital hybridization (bandwidth) and/or lower the occupied out-of-plane Cr 3d t2g (xz and yz) orbitals that would tend to be more delocalized and increase the hopping transport probability (Figure 6). The orbital configurations proposed here in Figure 6 have obviously to be confirmed by further studies.

Various ground state configurations are possible from more complex spin-orbital-lattice couplings with different orbital occupancy/ordering and consequent magnetic ordering [START_REF] Karim | Localized Level Hopping Transport in La(Sr)CrO3[END_REF][START_REF] Chakraborty | Magnetic Ordering in La0.75Sr0.25CrO3: A Neutron Diffraction Study[END_REF] since the orbital energy levels and orbital occupancy in CrO2 can be easily switched [START_REF] Zimmermann | 1s2p Resonant Inelastic X-Ray Scattering Magnetic Circular Dichroism as a Probe for the Local and Non-Local Orbitals in CrO2[END_REF] . Additional more complex features may also occur, such as orbital ordering/patterning or bond disproportionation as observed with other 3d perovskite oxides [START_REF] Varignon | Origin of Band Gaps in 3d Perovskite Oxides[END_REF][START_REF] Varignon | Mott Gapping in 3d ABO3 Perovskites without Mott-Hubbard Interelectronic Repulsion Energy U[END_REF] .

Alternatively, slight cationic stoichiometry deviations or introduction of point/planar defects in the lattice depending on strain, driven by partial strain relaxation, could also significantly impact the transport properties [START_REF] Hwang | Tuning Perovskite Oxides by Strain: Electronic Structure, Properties, and Functions in (Electro) Catalysis and Ferroelectricity[END_REF][START_REF] Rondinelli | Structure and Properties of Functional Oxide Thin Films: Insights from Electronic-Structure Calculations[END_REF][START_REF] Ohnishi | Defects and Transport in Complex Oxide Thin Films[END_REF] . However, i) the films here are epitaxially strained (Fig. 2b), ii) the film composition has been checked by XPS to be at the targeted stoichiometry, although the instrumental uncertainty is larger than 5 at.% (Supporting Information, Fig. S6) [START_REF] Apreutesei | Thermoelectric La-Doped SrTiO3 Epitaxial Layers with Single-Crystal Quality: From Nano to Micrometers[END_REF][START_REF] Han | Poisson Ratio and Bulk Lattice Constant of (Sr0.25La0.75)CrO3 from Strained Epitaxial Thin Films[END_REF] , iii) proper flux measurements and composition calibrations have been performed with our best accuracy (less than 3 at.%, Supporting Information, Fig. S1) [START_REF] Han | Poisson Ratio and Bulk Lattice Constant of (Sr0.25La0.75)CrO3 from Strained Epitaxial Thin Films[END_REF] , iv) the transport properties of LSCO film on SrTiO3(001) substrate are in perfect agreement with literature and the strain-dependent trend (Supporting Information, Figs. S9-S10) [START_REF] Zhang | Perovskite Sr-Doped LaCrO3 as a New p-Type Transparent Conducting Oxide[END_REF] , v) the c/a ratio has a linear trend with in-plane strain, as expected from Poisson ratio at this composition [START_REF] Han | Poisson Ratio and Bulk Lattice Constant of (Sr0.25La0.75)CrO3 from Strained Epitaxial Thin Films[END_REF] , and vi) the mosaicity of the films is below 0.1° on LSAT and DSO and around 0.2° on LAO, partially caused by substrate quality (Supporting Information, Fig. S2), meaning a low defect density in the films [START_REF] Han | Poisson Ratio and Bulk Lattice Constant of (Sr0.25La0.75)CrO3 from Strained Epitaxial Thin Films[END_REF] .

Although accurate microscopic physical mechanisms responsible for these strain-dependent transport properties of LSCO would require further investigations, our experimental results present a robust basis and already show the critical impact of strain on the LSCO transport properties, which is of high interest for LSCO-based applications and devices.

IV. CONCLUSION

In summary, high-quality p-type thermoelectric transparent La0.75Sr0.25CrO3 (LSCO) epitaxial thin films have been grown by molecular beam epitaxy on different (pseudo)cubic (001)-oriented perovskite-oxide substrates: LaAlO3, (LaAlO3)0.3(Sr2AlTaO6)0.7, and DyScO3, which results in epitaxial strain ranging from -2.06 % to +1.75 %. We have shown that the structural properties (lattice parameters, unit-cell volume, density), as well as electronic transport (conductivity, hole concentration, and mobility) and thermoelectric properties (Seebeck coefficient and power factor), can be efficiently tuned by epitaxial strain. At room temperature, electrical conductivity that is consistent with thermally activated hopping transport increases by two orders of magnitude, from 0.5 S cm -1 (tensile) to 35 S cm -1 (compressive), whereas the Seebeck coefficient increases by almost a factor of two, from 127 V K -1 (compressive) to 208 V K -1 (tensile), coherently. These results show that the thermoelectric power factor increases by one order of magnitude, from 2 W m -1 K -2 (tensile) to 56 W m -1 K -2 (compressive), and that it can be interestingly enhanced by compressive strain by more than a factor of three with respect to the bulk value. Hole density has been estimated to decrease with electrical conductivity from compressive to tensile strain, indicating a certain concomitant decrease of the Cr 3d t2g -O 2p orbital hybridizations on the valence band. These results are of high interest for engineering various LSCO-based devices such as thermal energy harvesters, coolers, transparent diodes/electrodes, photocatalyzers or spintronic memories.

ASSOCIATED CONTENT

Supporting

Notes

The pseudo-cubic bulk lattice constant (abulk) of La0.75Sr0.25CrO3 is 3.876 Å (see Ref.

Figure 1 .

 1 Figure 1. Lattice mismatch/strain, RHEED patterns, and photographs of the samples. (a-c)

Figure 2 .

 2 Figure 2. XRD characterizations. (a) XRD 2/ scans (reciprocal space units) around the (002)

Figure 2

 2 Figure 2 presents the structural properties of all LSCO films investigated by XRD. Wide 2/

Figure 3 .

 3 Figure 3. In-plane electronic and thermoelectric transport characterizations. (a) Temperature

Figure 3

 3 Figure 3 presents the in-plane electronic and thermoelectric transport measurements performed

Figure 4 .

 4 Figure 4. In-plane electronic transport and thermoelectric properties at 300 K, plotted as a

Figure 5 .

 5 Figure 5. Temperature-dependent thermoelectric properties. (a) Seebeck coefficient (S), (b) electrical conductivity (σxx) and (c) thermoelectric power factor (PF = S 2 σxx) for each film as a

Figure 6 .

 6 Figure 6. Summarizing sketch of the strain-dependent electrical resistivity trend with possible preferential occupancy of the Cr 4+ 3d t2g 2 orbitals within the crystal field.

  information: MBE flux measurements (BEP-T), Structural characterizations by X-ray diffraction and reflectometry (XRD & XRR), Surface characterizations by atomic force microscopy (AFM), Chemical characterizations by X-ray photoemission spectroscopy (XPS), Summary of the structural properties, Electrical characterizations, Thermoelectric characterizations, Summary of the physical properties at room temperature, References of the supporting information. thermoelectric characterizations at INL. G.G. contributed to XPS characterizations and discussions on band structure and orbital physics. D.H. and R.B. wrote the manuscript with contributions of all authors.

  28), whereas those of LAO, LSAT, STO and DSO substrates (asub) are 3.796 Å, 3.868 Å, 3.905 Å and 3.944 Å, respectively. The out-of-plane and in-plane epitaxial strain (εzz and εxx, respectively) due to the lattice mismatch f = (asubafilm)/afilm are defined here as: εzz = (cfilm -abulk)/abulk and εxx = (afilm -abulk)/abulk, where cfilm and/or afilm is the measured out-of-plane/in-plane lattice parameter of the film, abulk the bulk lattice constant.The thermal expansion coefficients at room temperature of LCO, LAO, LSAT, STO, and DSO are 8.5×10 -

K -1 , 10×10 -6 K -1 , 8.2×10 -6 K -1 , 9×10 -6 K -1 , and 8.4×10 -6 K -1 , respectively.For the stress estimation, the Young modulus has been taken as the one of cubic LaCrO3 along the[001] axis (E = 316.5 GPa). Retrieved from: https://materialsproject.org/materials/mp-18841/.Parameters of GaAs-based III-V semiconductors and heterostructures, retrieved from: http://www.ioffe.ru/SVA/NSM/Semicond/index.html.

ACKNOWLEDGMENTS

Financial support from the European Commission through the project TIPS (H2020-ICT-02-2014-1-644453), the French national research agency (ANR) through the projects MITO (ANR-17-CE05-0018), LILIT (ANR-16-CE24-0022), DIAMWAFEL (ANR-15-CE08-0034-02), the CNRS through the MITI interdisciplinary programs (project NOTE), IDEX Lyon-St-Etienne through the project IPPON, the Spanish Ministerio de Ciencia e Innovación, through the "Severo Ochoa"

AUTHOR INFORMATION

The authors are also grateful to Jean-Baptiste Goure, Philippe Regreny, Aziz Benamrouche and Bernat Bozzo for their technical support, and the reviewers for their valuable and constructive comments that have improved the quality of the manuscript.


Alain Clément

Bertrand Vigouroux

Unsupervised classification of pixels in color images by hierarchical analysis of bi-dimensional histograms

Unsupervised classification of pixels in color images by hierarchical analysis of bi-dimensional histograms

Alain Clement, Bertrand Vigouroux Laboratoire d'Ingenierie des Systemes Automatises Institut Universitaire de Technologie BP 42018 -ANGERS CEDEX-France bertrand. vigouroux@univ -angers.fr

Abstract -This paper presents an ew unsupervised algorithm for classifying pixels in color images, by means of a hierarchical analysis of color bi dimensional histograms. The algorithm proceeds in two steps : a learning step and a decision step. It provides a number of classes which is fu nction of an adjustable parameter (threshold S) depending on the precision required in terms of differenciation between colors.

Index termscolor image, unsupervised classification, hierarchical classification, bi-dimensional histogram.

I -INTRODUCTION

A pixel in a color image can be considered as a three dimensional (JD) vector whose components depend on the color space used (RGB, HSV, ... ). Due to this vectorial nature, the pixel classification algorithms based on histogram analysis can be divided in three categories : (i) marginal algorithms in which the mono dimensional (ID) histogram of each color plane is handled separately [l -5] ; (ii) full vectorial algorithms working on the color JD-histogram ; and (iii) intermediate algorithms using bi-dimensional (2D) histograms by projection onto two of the three color planes. The first type (i) inherits all the existing work on monochrom images, but it does not take into account the correlation between color planes [START_REF] Uchiyama | Color image segmentation using competitive learning[END_REF], unlike the second type (ii). However, handling a color JD-histogram is not an easy task, due to the huge required memory space [START_REF] Ciement | Un histogramme compact pour /'analyse d'images multi-composantes[END_REF]. The difficulty can be overcome by requantifying each color component on a lower level number [START_REF] Xuan | Maximum likelihood clustering method based on color features[END_REF]. The third way (iii) has not been explored very much to date [START_REF] Schmid | Segmentation of Digitized Dermatoscopic Images by Two-Dimensional Color Clustering[END_REF]IO]. We propose here a new unsupervised algorithm for classifying pixels in color images, based on the hierarchical analysis of 2D-histograms (section 2).The results are illustrated by applying the algorithm to the so-called image peppers (section J).

II -CLASSIFICATION

The objective is to merge into distinct classes the pixels that present similar colorimetric characteristics in a color image, in an unsupervised way Whatever the 2D-space used (RG, RB ot GB), Ne increases when S decreases. Obtaining a given number of classes is insensitive to S on a range �S which tends •to decrease as S decreases. For example, one obtains two classes for S ranging from 13% to 23% (classification by RG-histogram, see figure 3), or for S ranging from 9% to 23% (classification by RB histogram, see figure 4). . • --Q:-: .... .ii "\ , . ') -":"'. /"

Figure I :

 I Figure I : An example of hierarchical decomposition. The circled leaves (part b) correspond to signifi cant peaks as obtained at the end of the iterative decomposition (part a), whereas leaves marked <S (part b) correspond to unsi gnificant peaks (dotted lines in part a). The number of classes Neis taken equal to the number of kernels (the class corresponding to kernel Kt is noted C;). Therefore Ne depends on the threshold S, i.e. on the precision the image colors are analyzed with. B -Decision step The mass center µ(K;) of each kernel K; can be calculated in the color 2D-space. Let us design by B the color corresponding to the point of coordinates (xi.x2) in the color 2D-space. Two cases happen : if (xi,x2) belongs to K;, color B is attributed to class C; ; if not, let us design by Pk the peak (xi.x2) belongs to; color B is attributed to class C; corresponding to kernel K;, son of Pk, such that d[µ(K;), (xi.x2)] is minimum, where d[a,b] is the distance between a and b. Many choices of distances are possible (e.g. Euclidean distance, Mahalanobis distance, ... ).

Figure 2 :

 2 Figure 2 : Image peppers. The thresholds S to be explored range from Smin to Sm ax , where Smax is the minimum threshold leading to one class only (no classification) and Smin is the maximum threshold corresponding to the detection of the less populated class. Since ac lass contains one pixel at least, we have in our case : [ 100 ] smi n <!: = 0.00038% 512x512 Table l gives the values of Smax, Smin and Ne max (the maximum number of classes, obtained for S = Smin), when the image peppers is classifi ed from its RG-, RB and GB-histograms respectively.

Table 1 :17528

 1 Threshold ranges and maximum number of classes for image peppers classified from its RG-, RB-and GB hi sto.erams.If all the allowed colors in the RG (or RB, or GB) space were present, the maximum number of classes would be 256 2 = 65536. It is never the case in practice[START_REF] Ciement | Un histogramme compact pour /'analyse d'images multi-composantes[END_REF], leading to much lower values of Ne max (last column oftable 1). The variation of the number of classes Nca s a function of the threshold S is presented on figures 3 to 5 (for thresholds such that Ne is lower than 100).

Figure 3 :Figure 4 :

 34 Figure 3 : Number of classes as a function ofS (RG histogram).

Figure 5 :

 5 Figure 5 : Number of classes as a fuction of S (GB histogram).

Figure 6 :

 6 Figure 6: RO-histogram (image peppers).

Figure 7 :

 7 Figure 7 : RB-histogram (image peppers).

Figure 8 :

 8 Figure 8: GB-histogram (image peppers).

(a) 2 Figure 9 :

 29 Figure 9 : Classification from the RG-histogram (image peppers, B-component forced to zero). The starting image (figure 2) provides the 2D histograms shown on figures 6 to 8. The results of the classification obtained from the RG-histogram are shown on figures 9a to 9d, for thresholds leading respectively to 2, 3, 4 and 10 classes (since the classification is operated from the RG-histogram, the component B has been forced to zero on figures 9a to 9d). Operating with the RB-histogram provides similar results in terms of class numbers, as can be seen by comparing the curves Nc(S) on figures 3 and 4. This follows from the fact that the RG-histogram (figure 6) and the RB-histogram (figure 7) are similar for the image peppers. Moreover, in the case where two classes are detected, the classification is practically the same, whatever the 2D-space used (RG or RB). This can be seen by comparing figure 9a (two classes in

Figure 10 :

 10 Figure 10: Two classes o b tained in the RB-space (S = 16%, G component forced to zero). �� . ... -.. /-� ...._,. ....... . , '�/Jr / _.,

Figure 11 :

 11 Figure 11 : Image of pixels ( b lack points) attri b uted to different classes on figures 9a (RG-space) and 10 (RBspace).


S Ouattara

A Clement

B Vigouroux

Ouattara Sie

Full 3D Compact Histogram Segmentation of Color Images 1 •

Keywords: Color image, unsupervised segmentation, 3D compact histogram, fuzzy neighborhoods, re-quantization, evaluation of segmentations

In this study we present a fast unsupervised segmentation method of color images based on the 3D compact histograms. In order to resolve the problems of handling 3D histograms and to palliate the defects of the marginal and bi-marginal approaches, the use of the 3D compact histogram to accomplish classification in the color space RGB proved to be necessary. The interest of this study is based on the use of compact histogram which is a structure with reduced volume of colors without loss of data of the classical histogram and favouring a fast segmentation of color images. Knowing that there is no universal method of segmentation, our aim is to realize an acceptable segmentation that is the most relevant in the sense of a criterion of evaluation of segmentation. The relevance of the choice of peaks is not evident generally and is complexified when the dimension of the space increases; because of the integration of fuzzy neighborhood associated with an algorithm of connected components labeling in our algorithm of classification establishes the first approach of segmentation. The second approach consists in re-quantifying the colors of the histogram before making the classification, this limit the time consuming of segmentation and the effects of over-segmentation; this also the purpose of the first approach. A stage of performance appraisal of segmentation allows bringing to light the relevance of both methods and a comparison of both approaches is so discussed.

INTRODUCTION

Image segmentation is an essential step in image analysis because it determines the quality of future interpretation of the component image and substantially influences the decision. It is a major problem, difficult and for which there is no universal solution. Several methods of segmentation of color images give very good results and can be classified into two families according to whether or not using the spatio-colorimetric.

Pixel classification, apart from the clustering methods [START_REF] Saidur | Investigation of energy performance and usage behavior of domestic refrigerator freezer using clustering and segmentation[END_REF], other methods when working on the concept of color face the problem of data dimension. Therefore a comprehensive analysis of articles [START_REF] Clement | Unsupervised segmentation of scenes containing vegetation (Forsythia) and soil by hierarchical analysis ofbidimensional histograms[END_REF][START_REF] Tremeau | Image Numerique Couleur: De L'acquisistion au Traitement[END_REF][START_REF] Lezoray | Color image segmentation using morphological clustering and fusion with automatic scale selection[END_REF][START_REF] Haidar | Video macrosegmentation using automatic analysis of similarity matrices[END_REF][START_REF] Yuan | Road detection and corner extraction using high definition lidar[END_REF] allow us to distinguish five color segmentation approaches: the scalar approach, the marginal approach, bi-marginal approach, the approach bi-scalar and vector approach. The scalar approach is to first merge the components into a single color and then segmenting it or choose the plan most appropriate to perform the segmentation. The approach makes a marginal segment on each color component and then merges the segmentation maps into one [START_REF] Busin | Color space selection for unsupervised color image segmentation by histogram multithresholding[END_REF]. The bi-marginal approach segments colorimetric matching components, or RG, RB and GB in the RGB space and then merges the segmentation maps [START_REF] Lezoray | Color image segmentation using morphological clustering and fusion with automatic scale selection[END_REF][START_REF] Xue | Multi-band segmentation using morphological clustering and fusion application to color image segmentation[END_REF][START_REF] Kurugollu | Color image segmentation using histogram multithresholding and fusion[END_REF]. The bi-scalar approach is to choose a couple of plans to conduct a colorimetric or principal component analysis and then choose the two largest components of energy to perform the segmentation. The segmentation approach vector segmented image directly using a vector information [START_REF] Geraud | Color image segmentation based on automatic morphological clustering[END_REF][START_REF] Park | Color image segmentation based on 3-D clustering: Morphological approach[END_REF]. The main disadvantage of marginal and scalar approaches is not taking into account the inter-color correlation component. Their advantage is that it is generally simpler and faster than the vector methods. Faced with the increasing development of microprocessor perlormance and optimization techniques, vectorial approaches of segmentation can be developed.

In this study, we present a 3D method for unsupervised hierarchical clustering based on the analysis of 3D compact histogram incorporating a fuzzy neighborhood concept for the extraction of peaks. One advantage of the method is conditioned by the speed advantages of compactness of the histogram as representing optimal and flexible use of classical histogram which is a reminder that the next section. A second advantage of the method is the appearance vector which takes into account the correlation between the components of the image. The difficulty of the analysis of 3D histogram for the extraction of the peaks is generally related to the volume of data, the dimension of space, 3D in our study which must be added a fourth axis which is the population of colors. An adequate extraction of the peaks means taking into account the dispersion of colors in the 3D space [START_REF] Fisher | Maximum likelihood clustering method based on color features[END_REF] and their staff to resolve problems of over-segmentation and relevance of the choice peaks and thus the integration of a process of labeling connected components by fuzzy neighborhoods in the process of looking for peaks of histogram improves the quality of segmentation. In a second phase to solve the problem of dispersion of colors that can bias the choice of the best peaks we do a re-quantization of color prior to extraction of peaks and classification, a comparison of two approaches and is discussed through a step evaluation of segmentation results. Our two methods are compared with K-means which is a famous method, powerful and widely used in image processing and statistics. Part of this project was realized during my PhD thesis at the University of Angers in France and aure part within the framework of my research activity to the INPHB since 2006 until now.

Compact multidimensional histograms:

The histogram of a color image has a data volume of 128 MB, this amount of data poses difficulties of manipulation, making it prohibitive implementation of many methods of segmentation based on color histogram analysis and 3D.

To solve the problem of multidimensional histograms, [START_REF] Clement | A compact histogram for the analysis of multicomponent images[END_REF] was proposed an algorithm for computing a compact multidimensional histogram to reduce considerably without loss of information storage space occupied by the classical histogram, it contains only the colors actually present in the color image, an example of compact (3D) color histogram is shown in Fig. 1. For example for a color image of size MxN, the compact 3D histogram reduces the volume of the compact histogram by a factor a:

R G B 0 0 5 0 0 23 255 10 0 255 251 254 2 J Q a. = C(l + 3.Q/log 2 (M x N)) Population 70 4 31 7 (1)
where Q is the number of bits which is encoded on each color plane and C = MxN. An illustration of the advantages of compact 3D histogram is shown in Table 1.

Connected component labeling and fuzzy neighborhoods:

The Connected Component Labeling (CCL) play an important role because it allows the master data spread in the topological space considered, in image analysis this step is important because it guides and facilitates the segmentation of images. The choice of a neighborhood as defined by Rosenfeld for labeling data in the images affects the result of segmentation by [START_REF] Ouattara | Labelhng of compact multidimensional histograms for analysis of multicomponent images[END_REF], we chose the full-connectivity for the labeling of tuples in a multidimensional space, but this n eighborhood is also limite d in a way usually, it is for this reason that we propose in this study using fuzzy neighborhoods in an attempt to improve the quality of the segmentations produced by our algorithm segmentation proposed in the next section. Many studies [START_REF] Udupa | Relative fuzzy connectedness and object definition, theory algorithms and applications in image segmentation[END_REF][START_REF] Herman | Multiseeded segmentation using fuzzy connectedness[END_REF][START_REF] Miyamoto | A fuzzy neighborhood model for clustering, classification and approximations[END_REF]) carried out on fuzzy connectedness or connectivity have shown their effectiveness in the segmentation by a rational choice of the m e mbership function of proximity, similarity and affinity. The m e mbership function of fuzzy n eighborhood considered here is classic b ecause of its use in current approaches to fuzzy segmentation [START_REF] Miyamoto | A fuzzy neighborhood model for clustering, classification and approximations[END_REF][START_REF] Bloch | Fuzzy spatial relationship for image processing and interpretation: A review[END_REF]. Let P , a 3D color of histogram and Q that any color of histogram, fuzzy neighborhood with respect to Pis the following:

l l If d (P,Q) ~ K 11(P,Q)= l+d 00 (P,Q) 00 0 Otherwise (2)
where d 00 the distance of Chebyshev and KEN*. The neighborhood set corresponds to a set of fuzzy neighborhoods because K varies, which can appreciate the color dispersion in the topological space in the 3D connected component labeling. Table . 2 shows an example of fuzzy neighborhood for K = 2 needed to achieve labeling.

The algorithm for labeling Connected Components (CC) realized by [START_REF] Ouattara | Labelhng of compact multidimensional histograms for analysis of multicomponent images[END_REF] remains vahd for the neighborhoods defined by Eq. 2. In [START_REF] Ouattara | Labelhng of compact multidimensional histograms for analysis of multicomponent images[END_REF] was treated the case K = 1, there is widespread labeling component for K>l. The difficulty of this generalization lies in the search for neighboring fuzzy due to the fact of non-linearity of the histogram compact. The complexity of the labeling algorithm is at worst in El (N 2 ), with N the number of colors in the 3D histogram compact. Table 3 shows some statistics of connected components of color images for different values of K.

Unsupervised hierarchical 3D color classification and state of the art of evaluating results of Segmentation: The absolute similarity between two colors is something very complex and difficult to model using a mathematical model, however, we may refer to the work of [START_REF] Macadam | Color Measurement, Theme and Variation[END_REF]. Many works are based on the definition of a fuzzy model [START_REF] Miyamoto | A fuzzy neighborhood model for clustering, classification and approximations[END_REF], hence the interest of the definition of a fuzzy model of neighborhoods in this study.

The dimension of color space creates an over-segmentation generated by the classification methods [START_REF] Lezoray | Color image segmentation using morphological clustering and fusion with automatic scale selection[END_REF]. To solve the problem of the color dispersion, we have also implemented a second approach consisting in re-quantify colors and performing the classification for K = 1 (classical CC). This second approach can be considered as dual to the concept of fuzzy neighborhood. A comparison of two approaches is discussed. From a geometrical point of view, the Hcec does not modify the choices of the peaks and the results of segmentation. Further, it speeds up the classification process (optimization of algorithmic complexity).

The hierarchical principle of classification based on the Hcec illustrated in Fig. 2 requires as input a population threshold (S), which sets the minimum population of a peak and a value of K for the considered fuzzy neighborhood. In the re-quantization approach, K is set to 1.

The nodes really built are indexed by numbers; The leaves surrounded by a circle correspond to the peaks recognized. In black, set the branches explored and the nodes or leaves unsuccessful due to a lower population than threshold S.

State of the art of evaluating results of segmentation: Many segmentation algorithms have

been proposed in recent decades [START_REF] Lezoray | Color image segmentation using morphological clustering and fusion with automatic scale selection[END_REF][START_REF] Freixenet | Yet another survey on image segmentation: Region and boundary information integration[END_REF][START_REF] Gouiffes | Contributions of the color and the models of reflections for the extraction and the follow-up of the primitives[END_REF]. They are based on different approaches: contour, region and texture.

With a multitude of methods proposed, the problem of assessing the quality of segmentation becomes paramount. Usually, the efficacy of a new algorithm is illustrated by presenting some results of segmentation, which allows only subjective conclusions. There is currently no method of absolute and generic to complete this assessment task, however, many studies dealing with this subject.

By Philipp-Foliguet and Guigues (2006) and [START_REF] Zhang | Image segmentation evaluation: A survey of unsupervised methods[END_REF] methods of assessment are grouped into two broad classes that are evaluating unsupervised and supervised evaluation: (1) The first group consists of assessment methods do not require any knowledge of the results segmentation to evaluate. Their principle is to estimate analytical criteria, or to estimate the quality of a segmentation result from statistics calculated on each region, detected contours and textures [START_REF] Chabrier | Unsupervised performance evaluation of image segmentation, special issue on performance evaluation in image processing[END_REF][START_REF] Barsotti | Quantitative evaluation of color image segmentation results[END_REF][START_REF] Zeboudj | Filtering, Automatic thresholding, contrast and contours: The Pre-treatment with the image analysis[END_REF]. ( 2) The second contains the methods that assess the quality of a segmentation result by exploiting a priori knowledge [START_REF] Vinet | Segmentation and mapping of areas of stereoscopic pairs of images[END_REF]. This knowledge usually consist of a segmented image reference called ground-truth. It is directly accessible in the case of images, per account in the case of real images must be built by hand by an expert in the field of application: tracings made by physicians, geographers using computer tools drawings.

If you want to objectively compare methods, it is easier to use images, for which truth is well known, namely the segmentation was used to synthesize an image. The disadvantage of this approach is that these images do not represent all possible situations of real utilization.

Although, the assessment of real images is certainly more realistic, it raises other difficulties, the main one being that there is usually no single solution to the division of an image into regions relevant. Relevance of a region is indeed a concept highly dependent on the application. To evaluate the segmentation, we choose three methods as follows:

Vinet measure: This technique is a supervised evaluation method and therefore requires knowledge of reference segmentation, we consider here only the segmented images and segmentation of reference have the same number of classes. Let R, a segmentation consisting of regions Ri, i = 1, ... , M where Mis the number of regions and V the reference segmentation consists ofregions Vj such as j = 1, ... , M. The method of Vinet is to find pairs ofregions Ck= Rik n Vjk with maximum coverage and it is defined by:

(3)

Where A is the number of pixel in the image.

Levine and nazif criterion: For this criterion when the deviation (ok) of each region is zero, the value of this criterion is 1, it means that segmentation is ideal.

(4) Zeboudj criterion: Various studies have shown that this criterion is best suited to evaluate unsupervised segmentation [START_REF] Chabrier | Unsupervised performance evaluation of image segmentation, special issue on performance evaluation in image processing[END_REF]. This index takes into account the inside contrast and the outside contrast regions measured on a neighborhood W (s) of the pixels.

Consider the contrast between two pixels s and t, with f representing the intensity and L the maximum intensity defined by:

C(s,t) ~ l f C _ s ) _ -_ f ( t l l L-1
The inside contrast of a region Riis:

I I, -L ; r n a x { C ( s , t ) , t E W ( s ) n R , } A, SER,
The outside contrast of a region Riis:

I E, ~ -L;max {C(s,t), t E W(s), t ~ R,} A, SEF,
where Fi is the boundary of Ri and Ii the length of Fi. The contrast of Riis:

C(R,) ~
The global contrast is finally:

_ _1_ Si 0<1, <E, E, E, Si I, = 0 0 Othen.vise _I_" A C(R) A -7 , , (5) (6)
(7) (8) (9)
The tests were performed on images of 24-bit color; it means 8 bits per color component. Regarding the re-quantization, each color component is recorded on q bits (q<S) with. The principle of the re-quantization is to keep the q bits of the 8 bits. However, the limit of q to 5 is justified by the fact that the visual quality of color images is generally preserved.

The segmentations were performed for K varying from 1 to 5 and q from 5 to 7 and the evaluation of segmentation in the following section recognizes that these values of Kand q.

Figure 3 shows some results of image segmentation in Fig. 1 for the parameters K = {1, 3} and q = {5, 6}. Overall, the results are visually acceptable; an evaluation stage of segmentation results can highlight the interest of our segmentation approaches.

The evaluation of segmentation was performed on multiple images for different values of the parameters for the two segmentation approaches. Some images have been chosen to illustrate our results as shown in Fig. 4a-e. From these results several remarks and discussions can be made:

• From a general point of view, the introduction of fuzzy neighborhoods in the process of segmentation improved the quality of segmentation as indicated by one or more of three valuation methods

•

The second approach (re-quantization method) is also shown effectiveness in improving the quality of segmentation and also has the advantage of being fast •

The difference between the two approaches feel better in real images because the merger generally involved the removal of certain peaks and changes in most cases the morphology of histograms, which influences the choice of the peaks of the hierarchical principle of method • An important note is that assessment methods do not converge to the same relevant segmentations • Fuzzy method is generally better than K-means and can thus be used in certain problems of segmentation •

The poor performance of K-means are often due to arbitrary selection of centers of gravity of the classes and the non-convergence to the global minimum of the intra-class total energy, The performance can depend of evaluation criterion •

The evaluation methods of evaluation do not converge to the same segmentation pertience, the choice of a method will depend on the set aim. In any rigor the criterion of Levine is advised

CONCLUSIONS

Taking into account inaccuracies in the images by using fuzzy neighborhoods and the dual approach to what the acoustic re-quantization improved the quality of segmentation compared to the classic account of a neighborhood (K = 1). However, the re-quantization approach has weaknesses on the segmentation of noisy images but has the advantage of being fast and produce coarse segmentation for q = 5.

One of the difficulties which the image processors are facing is the selection of the appropriateness of evaluation methods which do not converge to the same levels of classification for segmentation with the same number of classes due to higher segmentations with a number of different classes.

We have in view the integration of a fuzzy clustering approach in our classification.

Unlike the usual methods of segmentation, they can be used to segment textured images little less noisy. In addition they offer a range of possible segmentations whose best indicated by the endpoint considered.

Fig. 1 :

 1 Fig. 1: Advantage of compact 3D histogram, M = N = 256 and Q = 8 bits per compone nt

Fig. 2 :

 2 Fig. 2: An example of hierarchical classification illustrated with a lD Hcec

  Fig. 3: Segmentation results of 24-bit color images (a) (b) Images

Fig. 4 :

 4 Fig. 4: Evaluation of some segmentation results compared to K-means results (in bold the best se gme ntation by criterion)

Table 1 :

 1 An example of compact 3D histogram of a color image in RGB space (8 bits per plane)

Table 2 :

 2 Neighborhood in 2D space. with K = 2

	0.33	0.33	0.33
	0.33	0.5	0.5
	0.33	0.5	p

Table 3 :

 3 Statistics of connected components based on fuzzy neighborhoods of color images

				0.33		0.33
				0.5		0.33
		K	Synt_gdr	House	Peppers	Mandrill
	Number of colors in compact histogram		6	33925	53488	61662
	Number of CC	1	6	6812	12443	21859
		2	6	2000	3277	5939
		3	6	684	1130	2016
		4	6	252	514	736
		5	6	108	261	279
	Population of the largest CC(%)	1	68.80	31.43	33.51	26.99
		2	68.80	59.03	90.90	63.09
		3	68.80	97.44	97.07	94.80
		4	68.80	98.85	98.59	97.89
		5	68.80	99.33	99.21	99.37
	Population of the second largest CC (%)	1	13.81	28.33	23.13	09.29
		2	13.81	35.37	0.21	12.27
		3	13.81	0.39	0.14	0.038
		4	13.81	0.39	0.057	0.30
		5	13.81	0.39	0.063	0.026