Pascal Jouquet
email: pascal.jouquet@ird.fr

Floriane Jamoteau

Sabyasachi Majumdar

Pascal Podwojewski

Prakash Nagabovanalli

Laurent Caner

Doris Barboni

Jean-Dominique Meunier

Adresses

The distribution of Silicon in soil is influenced by termite bioturbation in South Indian forest soils

Keywords: Si, clay, mineralogy, phytoliths, bioturbation, soil profile

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Introduction

Silicon (Si) is the second most abundant element in the earth's crust after oxygen, with approximately 28 and 47% of its mass, respectively [START_REF] Singer | Acidity and salinity. Soils: An Introduction[END_REF]. It is not included in the list of elements essential for plants but there is an abundant literature showing its beneficial effects on the resistance of plants to parasites and drought [START_REF] Liang | Silicon in agriculture[END_REF][START_REF] Datnoff | The use of silicon for integrated disease management: reducing fungicide applications and enhancing host plant resistance[END_REF].

In soil Si is a major constituent of parent rock minerals (such as quartz, feldspars) and of secondary minerals originated from pedogenesis, such as clay minerals and amorphous silica.

Biogenic amorphous silica particles can also be found in soil as plant and microorganism remains, i.e., phytoliths [START_REF] Cornelis | Soil processes drive the biological silicon feedback loop[END_REF] and diatom frustules or thecamoebian tests [START_REF] Sommer | Silicon pools and fluxes in soils and landscapes-a review[END_REF]. These amorphous silica particles can play an important role in the cycling of Si because they constitute a pool of highly reactive silica [START_REF] Fraysse | Surface chemistry and reactivity of plant phytoliths in aqueous solutions[END_REF]. Large fauna like grazers can also affect the cycling of Si through the accelerating transfer of plant Si to aquatic environments [START_REF] Schoelynck | Hippos (Hippopotamus amphibius): The animal silicon pump[END_REF] or through the increase production of biogenic silica [START_REF] Melzer | Fire and grazing impacts on silica production and storage in grass dominated ecosystems[END_REF]. The amount and quality of the different Si pools vary also with soil depth. Soil horizons are usually identified by different clay contents and minerals while phytoliths are usually concentrated in the topsoil and their content rapidly decreases with depth [START_REF] Alexandre | Plant impact on the biogeochemical cycle of silicon and related weathering processes[END_REF]. The pool of Si extracted by 0.01 M CaCl 2 (Si CC ) is used to estimate the Si immediately available for plants [START_REF] Haysom | Some aspects of the calcium silicate trials at Mackay[END_REF]. The distribution of Si CC along soil profile may increase with depth and be associated with the clay fraction [START_REF] Vandevenne | Silicon pools in human impacted soils of temperate zones[END_REF]. Another pool considered bioavailable for plant is the pool of Si adsorbed on the surface of minerals estimated by 0.05 M acetic acid extraction (Si AA ) [START_REF] Sauer | Review of methodologies for extracting plant-available and amorphous Si from soils and aquatic sediments[END_REF]. Si AA seems to be controlled by oxides and clay minerals and may also increase with depth (Cornelis et al., 2011 PLSO;[START_REF] Vandevenne | Silicon pools in human impacted soils of temperate zones[END_REF]. Surprisingly and despite their importance in the cycling of nutrients, the impact of soil macrofauna on Si dynamic has been poorly documented, with the exception of a recent article focusing on earthworms [START_REF] Georgiadis | Do earthworms affect the fractionation of silicon in soil?[END_REF], and there is a dearth of information on how soil macrofauna impacts clay mineralogy and the availability of Si for plants.

Amongst the soil macrofauna, organisms from the soil engineering group (sensu [START_REF] Lavelle | Soil function in a changing world: the role of invertebrate ecosystem engineers[END_REF] impact soil functioning at different spatial and temporal scales [START_REF] Bottinelli | Why is the influence of soil macrofauna on soil structure only considered by soil ecologists?[END_REF]. This role is played by termites in tropical dryland ecosystems, and especially by termites from the fungus-growing functional group (Macrotermitinae subfamily) in Africa and Asia (Jouquet et al., 2016). Termites are key decomposers of the litter in tropical environments [START_REF] Amadou Issoufou | Effects of termites growth on litter decomposition: a modeling approach[END_REF] and their building activity is associated to the redistribution of soil organic matter and elements in their biomass and organo-mineral constructions. Studies carried out in Africa and Asia showed that fungus-growing termites impact the distribution, the type of clay minerals (kaolinite vs. smectite) and the mineralogical properties of phyllosilicates [START_REF] Jouquet | Effect of termites on clay minerals in tropical soils: fungus-growing termites as weathering agents[END_REF][START_REF] Jouquet | Role of the fungusgrowing termite Pseudacanthotermes spiniger (Isoptera, Macrotermitinae) in the dynamic of clay and soil organic matter content. An experimental analysis[END_REF]. Termites are also known to impact the dynamic of Si at the profile scale through the selective use of material coming from the deep soil layers within their nests, then resulting in the redistribution of clay minerals and elements [START_REF] Holt | Termites and soil properties. Termites: evolution, sociality, symbioses[END_REF][START_REF] Abe | Soil particle accumulation in termite (Macrotermes bellicosus) mounds and the implications for soil particle dynamics[END_REF][START_REF] Mujinya | Termite bioturbation effects on electro-chemical properties of Ferralsols in the Upper Katanga (DR Congo)[END_REF][START_REF] Mujinya | The origin of carbonates in termite mounds of the Lubumbashi area, D.R. Congo[END_REF][START_REF] Mujinya | Clay composition and properties in termite mounds of the Lubumbashi area, D.R. Congo[END_REF][START_REF] Erens | The origin and implications of variations in soil-related properties within Macrotermes falciger mounds[END_REF]. However, the depth at which termites fetch the clay particles remains mostly unknown and termite bioturbation and the upward translocation of soil from the deeper layers to the surface are likely to be associated with a redistribution of Si CC and Si AA pools in termite mounds and thereafter in the surrounding soil environment with the erosion of termite mounds.

In Southern India, the termite species Odontotermes obesus is known to play an important role in the decomposition of litter [START_REF] Shanbhag | Imported wood decomposition by termites in different agro-eco zones of India[END_REF] and its mounds are conspicuous features of the landscapes [START_REF] Shanbhag | Rainfall and soil properties influence termite mound abundance and height: A case study with Odontotermes obesus (Macrotermitinae) mounds in the Indian Western Ghats forests[END_REF]. These mounds are especially abundant in protected areas such as in the deciduous forests of the Bandipur Tiger Reserve. In this environment termite mounds have specific soil physical and chemical properties (Jouquet et al., 2017a) and a recent study showed that they are mainly made of soil collected between 70 to 120 cm depth (Jouquet et al., 2017b). The aim of this study was therefore to determine the impact of O. obesus bioturbation on the distribution of Si in soil. Our hypothesis was that termite feeding and building activities (i.e., the construction of mounds from material selected in the deep soil layers) participate in a selective redistribution of clay minerals, phytoliths and available Si (Si CC ), which are thereafter redistributed to the soil surface.

Material and Methods

Study site

Soils were sampled in the Mule Hole experimental watershed (4.1 km 2 ). This dry deciduous forest is located in the Bandipur Tiger reserve in Southern India at 11°44′N and 76°26′E (Chamarajanagar district, Karnataka state). The Mule Hole watershed is located in the subhumid zone of the sharp climatic gradient induced by the Western Ghats. As a result of the short-term variability of the South-West Monsoon, the experimental watershed is characterized by rainfall ranging from 1000 to 1500 mm yr -1 , usually concentrated during the monsoon from June to August and from October to November. The mean annual temperature is 27°C [START_REF] Braun | Contemporary versus long-term weathering rates in Tropics: Mule Hole, South India[END_REF]. The elevation of the watershed ranges from 820 to 910 m a.s.l. The relief is mostly undulating with gentle slopes. The soil cover of the watershed has been mapped by [START_REF] Barbiero | Using a structural approach to identify relationships between soil and erosion in a semi-humid forested area, South India[END_REF] based on the FAO terminology (IUSS-Working-Group-WRB, 2015). Parent rocks consist of peninsular gneiss intermingled with much less abundant mafic to ultramafic rocks, mostly amphibolite. Soil depth is variable but ranging from 1 to 3 m in average [START_REF] Barbiero | Using a structural approach to identify relationships between soil and erosion in a semi-humid forested area, South India[END_REF][START_REF] Braun | Contemporary versus long-term weathering rates in Tropics: Mule Hole, South India[END_REF]. The main soil types are Ferralsols and Chromic Luvisols, with clay mineralogy dominated by kaolinite (1:1 clay) and characterized by an accumulation of iron and aluminum oxides. The soils have less than 20 g kg -1 of C in the first soil layer and < 10 g kg -1 below 20 cm depth. The clay content ranges from 30 to 40% and clays minerals are also dominated by 1:1 clays (kaolinite) (Jouquet et al., 2016b). The vegetation is a dry deciduous forest. In this environment, cathedral-shaped termite mounds are built by O. obesus [START_REF] Chhotani | Nesting behaviour and nests of Indian termites[END_REF]Jouquet et al., 2016aJouquet et al., ,b, 2017a) ) (Figure 1). The soil of termite mounds has similar clay contents but it is impoverished in C (0.54-fold) in comparison with the surrounding topsoil (Jouquet et al., 2016(Jouquet et al., , 2017a,b),b).

Soil sampling

Termite mounds built by O. obesus vary considerably in size [START_REF] Shanbhag | Rainfall and soil properties influence termite mound abundance and height: A case study with Odontotermes obesus (Macrotermitinae) mounds in the Indian Western Ghats forests[END_REF] and only large mounds from 1.5 to 1.8 m high and > 0.5 m 3 were considered in this study. Samples were collected from the outer-wall of three termite mounds (TM) and from their periphery in a distance of about 15 cm (impacted by mound erosion, EROD). Soils were also sampled in the surrounding soil environment (control) in a distance > 5-10 m ahead of the mounds in taking into account the gentle slope of the watershed (not impacted by mound erosion) at several soil depths down to 4.0 m in three different locations (n = 39). Data were grouped according to their depths (Ctrl 0-5 : 0-5 cm, Ctrl 70-120 : 70-120 cm) with the assumption that termites collect the soil mainly from the 70-120 cm soil layer for building their mounds (Jouquet et al., 2017b).

Analysis of soil properties

The soil physical properties measured included the particle-size distribution, after destruction of organic matter and dispersion with sodium hexametaphosphate (AFNOR, NFX 31 107): clay (< 2 µm) and silt (2-50 µm) were obtained by pipette method and sand (50-2000 µm) by sieving. To assess Soil Organic Matter (SOM) content, the C and N concentrations were measured using an elemental analyzer Flash 2000 HT. The cationic exchange capacity and the content of exchangeable cations (Ca, Mg, Na, K, Fe, Mn and Al) were determined at soil pH by exchange with cobaltihexamine (AFNOR, NF ISO 23470). The amount of SiO 2 , Fe 2 O 3 and Al 2 O 3 were measured by ICP-OES after fusion with lithium metaborate LiBO 2 and subsequent dissolution in a mixture of HNO 3 (1 mol L-1), H 2 O 2 (0.5 % v/v) and glycerol (10 % v / v) at the CNRS Service d'Analyse des Roches et des Minéraux (SARM) [START_REF] Carignan | Routine analyses of trace elements in geological samples using flow injection and low pressure on-line liquid chromatography coupled to ICP-MS: a study of geochemical reference materials BR, DR-N, UB-N, AN-G and GH[END_REF]. All these analyses were carried out on soil aggregates >2 mm that were ground before analyses to homogenize the material.

Si pools and phytoliths

Plant available Si was measured in comparing the pools of readily soluble Si extracted by 0.01 M CaCl 2 (Si CC , [START_REF] Haysom | Some aspects of the calcium silicate trials at Mackay[END_REF] and the pool of adsorbed Si extracted by 0.5 M acetate-acetic acid (Si AA , [START_REF] Korndörfer | Effect of silicon on plant growth and crop yield[END_REF]Narayanaswamy andPrakash, 2009, 2010). Phytoliths were extracted using HCl (33%) to remove carbonates, 2/3 nitric plus 1/3 perchloric acid to remove organic matter. Soil clays were removed by repeated decantations, and separation of biogenic silica particles from heavy minerals was achieved by densimetric separation using ZnBr 2 set at d = 2.3 g cm -3 . The extracts were weighted and phytoliths were mounted on slides for observation under optical microscope. More than 250 phytoliths were counted per sample. Morphotypes with clear taxonomical identification were silica short cell phytoliths (rondel, bilobate, polylobate and cross) from Poaceae (grasses), spheroid psilate and decorated from woody dicotyledons (considered forest indicator phytoliths), and spheroid echinate from Arecaceae (palms). Other phytoliths included bulliform flabellate, acute bulbosus (silicified hair cells), and various elongate and blocky morphotypes which were mostly nondiagnostic (International Code for Phytolith Nomenclature, 2019). The ratio of spheroid decorated versus the sum of grass silica short cells (or D/P° index) increases with the increasing abundance of trees and shrubs versus grasses and is commonly used to trace the tropical forest/savanna boundary [START_REF] Bremond | Definition of grassland biomes from phytoliths in West Africa[END_REF]). On the same slides, but in a separate counting session we measured the proportion of corroded vs. plain phytoliths to identify the origin of phytoliths with the assumption that phytoliths at depth likely underwent prolonged dissolution than the more recent phytoliths located at the soil surface following [START_REF] Sommer | Silicon pools and fluxes in soils and landscapes-a review[END_REF].

Phytoliths relative abundance were calculated based on the total phytolith sums.

Clay mineralogy

Clay mineralogy from termite mound soil samples (TM and EROD) was compared to the mineralogy of the soil at 0-5 and 70-120 cm depths (Ctrl 0-5 and Ctrl 70-120 ) (n = 3 per treatments).

Clay mineralogy was determined after extraction of the clay size fraction (particles < 2 µm) from the bulk soil samples. The fractions < 50 µm were obtained by wet sieving and then dispersed into 1 mol L -1 NaCl (five saturations) and ultrasonication. The < 2 µm fractions were obtained by sedimentation and were subsequently flocculated and saturated with 0.5 mol L -1

CaCl 2 [START_REF] Caner | Basalt and rhyo-dacite weathering and soil clay formation under subtropical climate in southern Brazil[END_REF]. XRD patterns of oriented preparations were recorded in the air-dried state (Ca-AD) and after saturation with ethylene glycol (Ca-EG) to identify the clay minerals [START_REF] Caner | Basalt and rhyo-dacite weathering and soil clay formation under subtropical climate in southern Brazil[END_REF]. Since no additional information was obtained from the saturation with ethylene-glycol, only results from the Ca-AD preparation was shown. The X-Ray diffraction patterns were decomposed into elementary peaks [START_REF] Lanson | Decomposition of experimental X-ray diffraction patterns (profile fitting): a convenient way to study clay minerals[END_REF] using Fityk software over the 3-14°2θ range. The procedure included removal of baseline and decomposition of the signal into Gaussian elementary curves. The diffractograms were fitted with the minimum curves to obtain a reliable fit of the experimental pattern. The parameters of the elementary curves (position, full-width at half maximum -FWHM and maximum intensity, surface area) were used to identify the soil clay mineral (kaolinite, illite, smectite, mixed layers illite/smectite) species according to [START_REF] Righi | Characterization of clay-organicmatter complexes resistant to oxidation by peroxide[END_REF] and [START_REF] Velde | Clay minerals in the agricultural surface soils in the Central United States[END_REF]. A semi-quantitative phase analysis was performed using the relative surface peak area of each peak of clay minerals over the sum of the peak surface areas. The relative surface peak area of each peak does not correspond to the proportion of the respective mineral, however, the variations of relative surface areas correspond to variations in mineral quantities if the samples comes from the same sequence [START_REF] Lanson | Decomposition of experimental X-ray diffraction patterns (profile fitting): a convenient way to study clay minerals[END_REF]). Peaks at ∼7.20 and 7.30-7.40 Å were attributed to kaolinite (K). The peak of illite at ∼10 Å was decomposed into well crystallized illite (WCI) at 10.0 Å and poorly crystallized illite (PCI) at 10.2-10.4 Å. The peaks at ∼15 Å in AD state that displace to ∼17 Å were attributed to smectite (S) and the peaks between 10 and 15 Å in AD state that displaced between 10 and 17 Å in EG were attributed to mixed layers illite/smectite with variable proportion of the two components.

Statistical analyses

Residues were tested for normality of variance using the Shapiro-Wilk test and log10transformed if required. Soil chemical and physical properties were analyzed by analysis of variance (ANOVA) with treatments as independent variables. LSD tests were then performed to assess differences between means. Post-hoc planned pairwise comparisons were performed by Wilcoxon-Mann-Whitney U tests when parametric ANOVA were impossible to use, even after data transformation. Impact of the treatments on soil variables and soil mineralogy were analyzed using a principal component analysis (PCA). Correlations between variables and the amount in Si CC , Si AA and phytoliths were carried out using the spearman test. 95% confidence intervals associated to the percentages in phytoliths and 99% confidence intervals associated with the D/P° ratios were calculated following [START_REF] Suchéras-Marx | Statistical confidence intervals for relative abundances and abundance-based ratios: Simple practical solutions for an old overlooked question[END_REF]. All statistical parameters were calculated using R studio and R version 3.2.1 with ade4, factoextra, factoMineR and corrplot packages. Differences among treatments were declared significant at the 0.05 probability level.

Results

Difference in soil chemical and physical properties

The chemical properties of the 4 soil materials are shown in Table 1 and a PCA-projection of the samples from significant variables is shown in Figure 1. Soil materials were mainly differentiated along the first axis while the variability within the samples was evidenced on the second axis, which explained 63.0 and 18.5% of the total variability, respectively. Samples varied from the soil surface (Ctrl 0-5 ) to TM, EROD and finally Ctrl 70-120 . No significant difference in soil particle size fractions, in pH and in exchangeable Mg 2+ and K + contents could be measured between the four soil materials (P > 0.05 in all cases) (Table 1). Ctrl 0-5 was enriched in C and N and characterized by a greater CEC and exchangeable Ca 2+ content but lower exchangeable Al 3+ content in comparison with the other treatments. Conversely, Ctrl 70- 120 were impoverished in C and N but enriched in exchangeable Na + , Al 2 O 3 and Fe 2 O 3 in comparison with the other soil materials. In general, TM and EROD had intermediate properties in comparison with the Ctrl 0-5 and Ctrl 70-120 (Figure 1) and no significant difference occurred between them, with the exception of the concentration in exchangeable Mn 2+ that was similar in TM and Ctrl 70-120 but higher than in EROD and Ctrl 0-5 (P > 0.05 between them, Table 1).

Figure 2 shows the evolution of clay content in TM and EROD and at different soil depths. The amount of clay was highly variable (e.g. from < 10 to > 50% at 150 cm depth), especially in comparison with the clay content in TM and EROD. Despite this high variability, an increase in clay content was measured at about 50-150 cm depth. but positively correlated with the total amount in Al 2 O 3 (P = 0.013). Moreover, the amount in phytoliths was positively correlated with the CEC and the amounts in C, N, Ca 2+ , Mg 2+ and Si CC (P = 0.001, 0.008, 0.008, 0.001, 0.001 and 0.028, respectively) but negatively correlated to the amount in Fe 3+ and Al 3+ (P = 0.018 and 0.011, respectively).

Si pools and phytoliths

Identification of the phytoliths shows that most of them came from grasses and woody dicotyledons (trees and shrubs), with little differences in the phytolith-inferred vegetation signal between Ctrl 0-5 and Crtl 70-120 , but strong difference with TM. In TM, phytolith pool was essentially coming from grasses (phytolith ratio Dicotyledons:Poaceae, D:P° < 0.7), while it was coming from woody plants in the Crtl samples (D:P° > 2) (Figure 4 and see appendix A for the detailed phytolith counts). A gradient of corrosion was observed from the top-soil to the deeper soil layers with a dominance of non-corroded phytoliths in Ctrl 0-5 , a dominance of corroded phytoliths in the 90-100 cm soil layer and intermediate values in the 20-40 cm soil layer (Figure 5). In TM, phytoliths had intermediate proportion of corroded phytoliths than between the 0-5 and 20-40 cm soil layers (Figures 5 and6).

Variation in clay abundance and mineralogy with soil depth

Differences in clay mineralogy between soil samples are shown in Figure 7. Soil materials were mainly differentiated by the second axis, which explained 30% of the total variability. Samples from the topsoil were enriched in smectite (S) and poorly crystallized illite (PCI) in comparison with soil sampled below 70 cm depth that were rich in kaolinite (K). TM and EROD had the same signatures and intermediate properties between those of the soils sampled in Ctrl 0-5 and Ctrl 70-120 .

Discussion

Bioturbation and translocation of clay

Bioturbation and the edification of termite mounds by fungus-growing termites is associated with a translocation of soil material from the deeper soil layers to the surface. Usually evidenced by an enrichment in clay particles or the presence of minerals that are less abundant than in the topsoil, this process of translocation as well as the depth at which termites collect the soil remain poorly quantified. In a recent study, we showed that the soil from the outer-wall of O. obesus mounds mainly comes from the ~ 70 to 120 cm soil layer (Jouquet et al., 2017b). Here, measure of the percentage of clay fraction in soil did not evidence a significant difference between soil materials, mainly because of the high variability in clay content along the soil profile. This variability in clay content was reduced in termite mound soils, showing a possible regulation of the amount of clay fraction in soil by termites for strengthening cohesion between aggregate and ensuring the resistance of TM, as evidenced in laboratory conditions [START_REF] Jouquet | Effect of termites on clay minerals in tropical soils: fungus-growing termites as weathering agents[END_REF][START_REF] Oberst | Termites utilise clay to build structural supports and so increase foraging resources[END_REF] and for a better control of their habitat and resistance to predators (Jouquet et al., 2006).

Si available pools

The 0-5 cm soil layer was enriched in SiO 2 in comparison with the 70-120 cm soil layer, which was enriched in Al 2 O 3 content (see the supplementary file 1 showing the higher concentration in Al 2 O 3 at this soil depth). Phytoliths in the 70-120 cm soil layer were also less abundant and more corroded than in the topsoil in a good agreement with previous observations [START_REF] Alexandre | Plant impact on the biogeochemical cycle of silicon and related weathering processes[END_REF][START_REF] Sommer | Silicon pools and fluxes in soils and landscapes-a review[END_REF]. Indeed, the dynamic of phytoliths in soil results from burial, abundant, older and more corroded than in the surface [START_REF] Sommer | Silicon pools and fluxes in soils and landscapes-a review[END_REF]White et al., 2012).

A similar amount of phytoliths was measured in TM and in the topsoil while EROD had intermediate phytolith contents between TM and Ctrl 70-120 . Difference in D:P° ratio between TM and Ctrl soils also shows that TM contained more phytoliths from grasses than control soil samples. Although this study does not allow to reject the assumption that phytoliths from deeper soil layers were selectively incorporated into TM, we consider this hypothesis unlikely since this would have resulted in higher representation of forest indicator phytoliths, as forest is the dominant vegetation at Mule Hole [START_REF] Riotte | Processes controlling silicon isotopic fractionation in a forested tropical watershed: Mule Hole Critical Zone Observatory (Southern India)[END_REF]. Moreover, phytolith morphotypes vary in size but grass silica short cell phytoliths and the forest indicator spheroids are in the same size range (8-30 microns). It is therefore unlikely that grass phytoliths were incorporated in TM because they were smaller and because they were differently associated to clay particles.

Despite the fact that O. obesus can feed on a variety of litter components (e.g. elephant dung, wood and leaves) [START_REF] Cheik | Fungus-growing termite foraging activity increases water infiltration but only slightly and temporally impacts soil physical properties in southern Indian woodlands[END_REF][START_REF] Cheik | Linking termite feeding preferences and soil physical functioning in Southern-Indian woodlands[END_REF][START_REF] Shanbhag | Litter Quality Affects Termite Sheeting Production and Water Infiltration in the Soil[END_REF], grasses are mostly consumed by herbivores in Mule Hole catchment. The presence of grass phytoliths in TM therefore suggests that termites act as primary decomposers of herbivore dungs in the studied area. This hypothesis is in line with recent studies carried out in southern India which showed that elephant dung material is very attractive to termites which prefer this material over carton, wood or leaves [START_REF] Cheik | Fungus-growing termite foraging activity increases water infiltration but only slightly and temporally impacts soil physical properties in southern Indian woodlands[END_REF][START_REF] Cheik | Linking termite feeding preferences and soil physical functioning in Southern-Indian woodlands[END_REF][START_REF] Shanbhag | Litter Quality Affects Termite Sheeting Production and Water Infiltration in the Soil[END_REF]. Indeed, despite inhabiting forested environments in Karnataka and the Nilgiri Region, elephants preferentially feed on Panicoideae grasses which constitute more than 84% of their annual bulk diet [START_REF] Baskaran | Feeding ecology of the Asian elephant Elephas maximus Linnaeus in the Nilgiri Biosphere Reserve, southern India[END_REF]. A large amount of these grasses is only partially decomposed, making this material very attractive to termites. Therefore, if the consumption of grasses is associated with a partial digestion of organic matter by termites for building their biomass and ensuring their activity, the Si contained in the phytoliths is not used by termites. From these findings we suggest that termites incorporate phytoliths in their constructions most likely when they moisten the soil aggregate pellets with saliva and potentially faeces. This hypothesis is consistent with the presence of monosaccharides from plant origin in the epigeous nest of fungus-growing termites [START_REF] Sall | Variation in the distribution of monosaccharides in soil fractions in the mounds of termites with different feeding habits (Senegal)[END_REF] and the higher C content measured in TM in comparison with Ctrl 70-120 and the positive correlation between phytoliths and the C content. Moreover, since phytoliths were mainly non-corroded phytoliths in TM, we even suggest that phytoliths resist to termite and microbial (including Termitomyces sp.) metabolisms.

Si CC and Si AA were respectively higher and lower in the topsoil layer in comparison with Ctrl 70-120 . Interestingly, despite the fact that TM was mainly built from the soil at 70-120 cm depth, TM had a closer signature with the topsoil than with the deeper soil with similar amounts of SiO 2 , Si CC and Si AA . Although this study does not allow to disentangle the mechanisms associated to this change in Si pools, the positive correlation between Si AA and the amount of Al 2 O 3 , but not the amount in clay, and the positive correlation between Si CC and phytoliths suggest either (i) a total reorganization of the structure of soil pellets and a decrease in the interactions between Si and oxides and a shift from Si AA to Si CC , (ii) a production of Si CC from phytolith dissolution, and/or (iii) a selection of particles from Ctrl 70-120 that were impoverished in oxides (see supplementary file 2) but enriched in clay and Si CC . Another explanation could be that the dissolution of 2:1 clay minerals, mainly found on the topsoil and TM, increases the Si CC pool, even if this process is likely to be limited with a soil pH > 6. This explanation is in line with [START_REF] Violette | Modelling the chemical weathering fluxes at the watershed scale in the Tropics (Mule Hole, South India): Relative contribution of the smectite/kaolinite assemblage versus primary minerals[END_REF] who found that the dissolution of smectite provides large amount of dissolved silica (i.e., 75% of the export of dissolved silica) in the study watershed.

Modification in clay mineralogy

The 70-120 cm soil layer was characterized by a higher percentage of clay fraction and higher contents in kaolinite and Al 2 O 3 that are characteristics of kandic horizons [START_REF] Brady | The nature and properties of soils[END_REF]Soil Survey Staff, 2014). The presence of the kandic horizon was confirmed with the X-ray diffraction data that revealed the presence of smectites and poorly crystallized illite (i.e. 2:1 phyllosilicates) in the topsoil and on the contrary a mineralogy dominated kaolinite (1:1 phyllosilicate) in the kandic horizon. The presence of smectite on the topsoil was unexpected and suggests a high level bioturbation activity with the upward movement of soil and neoformation processes. The concentration of Mn 2+ in soil solutions is largely controlled by oxidation and reduction reactions and the higher concentration of this cation in the kandic horizon also confirms a process of accumulation at this soil depth. Therefore, similar concentration in Mn 2+ between the 70-120 cm soil layer and TM confirms the utilization of soil from the kandic horizon for building termite mounds. However, the lower concentration in Mn 2+ in EROD is likely to be explained by the high solubility of this cation in solution [START_REF] Gilkes | Geochemistry and Mineralogy of Manganese in Soils[END_REF] and its rapid leaching from the soil eroded from the mound, despite the fact that this soil is poorly permeable in comparison with the surrounding topsoil [START_REF] Traoré | Termite mounds impact soil hydrostructural properties in southern Indian tropical forests[END_REF]. Although TM were mainly made of soil coming from the kandic horizon, clay minerals in termite mounds had intermediate properties between those observed in the topsoil and those sampled in the deeper soil layers. Differences in clay minerals or in Si:Al ratio between TM and the surrounding topsoil have been evidenced in different environment (e.g., [START_REF] Wielemaker | Soil formation by termites: a study in the Kisii area, Kenya[END_REF][START_REF] Abe | Soil particle accumulation in termite (Macrotermes bellicosus) mounds and the implications for soil particle dynamics[END_REF]. They are usually explained by the use of specific clay minerals and/or the ability of termites to modify the properties of clay minerals [START_REF] Schaefer | Brazilian latosols and their B horizon microstructure as long-term biotic constructs[END_REF][START_REF] Jouquet | Influence of termites on ecosystem functioning. Ecosystem services provided by termites[END_REF]. Since the modification of clay minerals by termites is limited to the swelling ability of 2:1 clay minerals [START_REF] Jouquet | Effect of termites on clay minerals in tropical soils: fungus-growing termites as weathering agents[END_REF]2007), our results suggest that 2:1 clay minerals may be selected by O. obesus for building their nests than kaolinite, most likely because of their better physical properties in terms of plasticity and water retention [START_REF] Andrade | Measuring the plasticity of clays: A review[END_REF][START_REF] Spagnoli | Statistical variability of the correlation plasticity index versus liquid limit for smectite and kaolinite[END_REF]. Another explanation could be 2:1 clay minerals found in TM could be produced from the dissolution of phytoliths and the interaction between Si CC and kaolinite [START_REF] Sommer | Silicon pools and fluxes in soils and landscapes-a review[END_REF]. In a highly weathered Oxisols in the Amazon forest, [START_REF] Lucas | The relation between biological activity of the rain forest and mineral composition of soils[END_REF] showed that the occurrence of kaolinite, instead of gibbsite, in the topsoil (or surface horizon) was attributed to the resilication of gibbsite by the soluble silica provided by phytolith dissolution. A similar process of resilication of kaolinite could be suggested for the formation of smectite in TM by the biological uplift of cations and highly reactive silica from the dissolution of phytoliths. Over longer period of time, the accumulation of 2:1 clay minerals in TM is likely to be important at the ecosystem scale. Indeed, O. obesus mound turnover rate has been estimated to reach a soil turnover of 3.1-31 mm ky -1 in the same study site (Jouquet et al., 2017). Since clay minerals accumulated in termite mounds return to the surrounding soil environment after termite mound degradation, further research is needed to determine if the accumulation of this material contributes and/or explains the presence of 2:1 clay minerals in the topsoil.

Conclusion

Findings from this study show that O. obesus has a significant impact on the distribution of Si in soil. First, we explained the lower variability in clay content in comparison with the high variability measured along the soil profile by the need of termites to control the properties of their nests, i.e., the amount of clay fraction in TM, then highlighting the importance of this material for termites. The higher phytolith content in TM was unexpected but could be explained by termite foraging activity (i.e., the consumption of grasses) and the excretion of phytolith in termite saliva. Higher amount in Si CC was also surprising and raised the question of a possible impact of termites on the interaction between Si and minerals in soil. In perspective, we consider that more research is now needed to better understand the fate of the phytoliths in TM. Further studies are also needed to determine if the increase in Si CC content in TM contribute to explain the presence of 2:1 minerals in termite constructions [START_REF] Jouquet | Effect of termites on clay minerals in tropical soils: fungus-growing termites as weathering agents[END_REF] and the specific vegetation growing in the vicinity or on termite mounds in Africa (e.g., [START_REF] Mehra | Iron oxide removal from soils and clays by dithionite-citrate systems buffered with sodium bicarbonate[END_REF][START_REF] Schwertmann | Differenzierung der Eisenoxide des Bodens durch Ekstraktion mit saurer Ammoniumoxalat-Lösung[END_REF] along the soil profile, in the outer part of termite mound (TM, arbitrary displayed at + 50 cm depth) and in the soil eroded from TM (EROD, arbitrary displayed at + 5 cm depth).

Figures and table captions

Supplementary file 2

Table 1 Major physical (contents in clay, silt and sand, in %) and chemical properties (contents in C and N in %, CEC, Ca 2+ , Mg 2+ , Na + , K + , Fe 3+ , Mn 2+ and Al 3+ in cmol (+) kg -1 ) in the control soils at 0-5 and 70-120 cm depth (Ctrl 0-5 and Ctrl 70-120 , respectively) and in termite

Figure 3

 3 Figure3shows that the proportion of SiO 2 and the amount of Si CC were the lowest in Ctrl 70-120 ,

Figure 1 .

 1 Figure 1. Biplot showing the principal components analysis (PCA) from variables describing

Figure 2 .

 2 Figure 2. Clay content along the soil profile, in the outer part of termite mound (TM, arbitrary

Figure 3 .

 3 Figure 3. Histograms showing the percentages in SiO 2 and phytoliths (%), and the amounts in

Figure 4 .

 4 Figure 4. Abundance and diversity of phytoliths.

Figure 5 .

 5 Figure 5. Proportion of corroded, non-corroded and undetermined phytoliths for termite

Figure 6 .

 6 Figure 6. Examples of blocky and elongated non-corroded (a, b) and corroded phytoliths (c, d)

Figure 7 .

 7 Figure 7. Biplot showing the principal components analysis (PCA) from variables describing

  Figure 1

  mound (TM) or the soil eroded from TM (EROD). Values in parentheses are standard errors, values with the same letter are similar at P = 0.05. Results from the ANOVA (F and P-values) and Wilcoxon-Mann-Whitney U (Chi 2 and P-values) tests are also given.

Acknowledgements

This project was supported by the French Institute for research for development (IRD) through "Allocations de recherche pour une thèse au Sud" (ARTS) grant and data from this study were partially obtained from the ALYSES facility (IRD-UPMC) which was supported by grants from Région Ile de France. The Mule Hole basin is part of the ORE-BVET project (Observatoire de Recherche en Environnement -Bassin Versant Expérimentaux Tropicaux, http://bvet.omp.obsmip.fr/) supported by the French Institute of Research for Development (IRD), CNRS and Toulouse University. The project also benefited from funding from the Indo-French Cell for Water Science (LMI CEFIRSE, http://www.cefirse.ird.fr) and the French National Program EC2CO-Biohefect "MACROFLUX". Finally, we thank the Karnataka Forest Department and the staff of the Bandipur National Park for all the facilities and support they provided.

Appendix A. Supplementary data to this article can be found online at Bardoni, D.; Meunier, J-D.; Jouquet, P., 2019, Phytoliths in termite mounds and in the soil environment, India, 2017. https://doi.org/10.23708/G3HWON, Jouquet, P.; Jamoteau, F.; Majumdar, S.; Nagabovanalli, P.; Caner, L.; Meunier, J-D., 2019, Soil physical, chemical and mineralogical properties. Comparison between termite mounds and the soil environment in Mule Hole, Karnataka, India, https://doi.org/10.23708/MHUF7F


Ivana Petković
email: ivana.petkovic@yale.edu

F.I ‡ B Williams

D Christian Glattli

Edge magnetoplasmons in graphene

We have observed propagation of Edge Magneto-Plasmon (EMP) modes in graphene in the Quantum Hall regime by performing picosecond time of flight measurements between narrow contacts on the perimeter of micrometric exfoliated graphene. We find the propagation to be chiral with low attenuation and to have a velocity which is quantized on Hall plateaus. The velocity has two contributions, one arising from the Hall conductivity and the other from carrier drift along the edge, which we were able to separate by their different filling factor dependence. The drift component is found to be slightly less than the Fermi velocity as expected for graphene dynamics in an abrupt edge potential. The Hall conduction contribution is slower than expected and indicates a characteristic length in the Coulomb potential from the Hall charge of about 500 nm. The experiment illustrates how EMP can be coupled to the electromagnetic field, opening the perspective of GHz to THz chiral plasmonics applications to devices such as voltage controlled phase shifters, circulators, switches and compact, tunable ring resonators.

Introduction

Edge magnetoplasmons (EMP) are a set of elementary excitations of edge charge distribution which propagate along the periphery of 2-dimensional systems of charge in magnetic field. They arise by the action of the Lorentz force in accumulating charge against the constraining wall of the sample edge and can be thought of as a dynamic manifestation of the Hall effect, the symmetry properties of which are reflected in the chirality of propagation of the EMP. Their propagation velocity is a function of the Hall conductivity and of properties specific to the type of edge and particle dynamics. They have been observed in both classical [1,2,3] and quantum [4,[START_REF] Govorkov | Pis'ma[END_REF][START_REF] Volkov | Pis'ma[END_REF]7,8,9] systems with inertial dynamics and soft electrostatic edges and are usefully reviewed in reference [10]. It is of fundamental interest to observe them in graphene which has non-inertial, ultrarelativistic type dynamics and a hard edge, both from the point of view of the excitations themselves and of the light they can shed on graphene. They show promise too of forming the basis of chiral plasmonics.

Graphene is a monatomic layer of sp 2 bonded carbon atoms which form a two dimensional planar honeycomb array. Its electron dynamics is determined by the linear crossings of the band energies at two degenerate but inequivalent points K and K ′ on the Brillouin zone edge which set the Fermi level for global charge neutrality [11]. The linear dispersion around these points indicates constant speed (magnitude of velocity) ultra relativistic-like massless dispersion. Neutrality can be broken by capacitive charge transfer to explore a reciprocal space Fermi circle on either side of the crossing points. Although the remarkable through-transport properties of this system have been much studied, particularly in the Quantum Hall Effect (QHE) regime that led to the positive identification of single layer graphene [12,13], few experiments have as yet explored the low energy collective excitation spectrum. Monochromatic laser source experiments [14,15] have probed the wavelength of room temperature zero-field plasmons by observing the interference pattern between a point excitation source and reflection from a line boundary. Broadband far infrared experiments [16] on periodic strips of graphene have given independent information on density and wavevector dependence of room temperature zero field plasmon absorptions. Other infrared experiments show the spectral behaviour in magnetic field of an array of dots [17] and the field dependence of the absorption lines for a continuous sheet of graphene in the presence of substrate disorder [18]. The latter two works revealed modes decreasing in frequency with magnetic field in accordance with an evolution towards a low frequency, possibly edge localised mode as observed in conventional 2D electronic systems (2DES) with Newtonian dynamics.

The present work investigates directly how an electrical perturbation applied on the edge of an exfoliated sample of graphene in the QHE regime is transmitted to a local probe placed further along the edge. The electrical perturbation, set up by a fast voltage pulse, creates an EMP wavepacket of edge charge whose time of flight to another edge electrode is recorded. The technique [9] enables an immediate demonstration of chirality and edge propagation, a measurement of the propagation velocity and an estimate of attenuation. The experiment reveals a branch of low frequency gapless modes which propagate unidirectionally around the edge with exceptionally low loss at a velocity which is the sum of single particle drift and Hall conductance whose sign (product of charge and applied magnetic field direction) determines the chirality. It is a good tool for investigating the nature of the edge and shows promise of opening up a new branch of chiral plasmonics with several foreseeable applications for the manipulation of radio to infrared electromagnetic waves.

First results of this work have been reported in reference [19] and similar work has been reported very recently on edge mode propagation in larger samples at slower time scales in graphene formed on silicon carbide [20].

Experiment

Principle

The core idea of the experiment is to investigate the propagation of an electrical perturbation between two points on the edge of an exfoliated graphene sample. We measured the time of flight of a 7 ps rise time voltage pulse applied to a ∼ 2 × 2 µm 2 electrode on the sample edge to a similar electrode placed about 1/3 the way around the ∼ 40 µm perimeter as indicated in Figure 1. Although considerably faster and on a smaller sample, the technique is similar to the pulsed EMP experiment on conventional 2DES [9]. The spatial and temporal definition of the pulse sets up a wavepacket superposition of charge density which propagates out from the source and can be detected by the remote detector as the density waves arrive. The arrival time, spread and amplitude of the signal give information on propagation path, dispersion and scattering of the excitations. We interpret the results of the experiment in terms of edge propagating density waves in the Coulomb interacting plasma of excess charge.

Fabrication

We fabricated the sample by mechanically exfoliating graphene from natural graphite onto a thermally grown 290 nm silicon-oxide surface of a high resistivity Si wafer (8 kΩcm at 300 K). The high resistivity avoids microwave loss and the oxide film facilitates visual identification of single layer graphene [21]. Identification and sample quality were confirmed by micro-Raman spectroscopy which indicated low disorder by the relative areas of the 2700 cm -1 and 1600 cm -1 Raman peaks [22]. Spuriously deposited graphite, a possible source of unwanted signal and electrical short circuiting, was removed by oxygen plasma etching using a bilayer of PMMA (PolyMethylMethAcrylate) and e-beam polymerised HSQ (Hydrogen SilsesQuioxane) as an etching mask (see Fig. 2). After liftoff only graphene remained on the wafer onto which were then patterned broadband (50 GHz) tapered Ti/Au coplanar waveguides (CPW) by standard e-beam lithography. The extremities of the CPW centre conductors contact the sample edge over a 2 ×2 µm 2 area, one resistively and the other capacitively. A sample photo and further fabrication details are given elsewhere [19]. The resulting 3 × 3 mm 2 sample "flip-chip" is mounted face down on a sample holder (see Figure 3) on which the CPWs are continued to mini-SMP strip-to-coaxial microwave connectors to join the vertical coaxial transmission lines which exit the cryostat insert. Elasticity of the flip-chip to sample holder contacts was carefully engineered to ensure flatness and good electrical connection across the entire CPW (left, right and centre) when pressed into place. Soldering was avoided entirely because the subsequent annealing of the graphene at 150 • C for several hours would have risked melting the solder and contaminating the sample.

The sample holder, shown in Figure 3, was designed using CST Microwave Studio (3D Maxwell equation solver) and fabricated on a high dielectric constant ceramic wafer Rogers TMM10 with copper ground and top planes joined by a set of densely spaced vertical interconnection via holes and thin enough not to support transverse standing modes over the 50 GHz frequency band. The assembly was mounted in vacuum in a cryogenic insert which fits into the liquid helium filled bore of a 19 T magnet at 2.2 K.

Experimental Procedure

We conducted time domain measurements using a Tektronix DSA8200 digital serial analyzer and sampling oscilloscope with time-domain reflectometry (TDR) 80E10 (50GHz bandwidth) and 80E08 (30GHz bandwidth) modules in transmission mode. A 7ps (80E10)/11ps (80E08) rise time voltage step was injected into one side of the circuit and the response voltage measured at the other as a function of time. A low frequency (1Hz) square wave voltage is added at the ohmic input via a bias tee in order to modulate the density on the edge with the aim of separating out the density sensistive graphene signal from crosstalk. For each excursion of the modulation the signal is averaged over a maximum of pulse injections (∼ 10 3 ) and the resulting picosecond files subtracted to demodulate and thereby retain only that part which is sensitive to variation in edge density of the sample. The procedure for extracting arrival times from the demodulated signal is described below.

Results

The absolute signal arrival time includes the travel time through the transmission lines and therefore it is necessary to determine the zero time, i.e. the moment the excitation signal reaches the sample, in order to extract the time of flight. We set the zero by the arrival time for zero field, supposing it to originate in the surface propagation of the fast surface plasmon mode, as there is nothing to impose chirality and the surface mode propagation time is of the order of 1ps, which is comparable with our time resolution. .

We employ the fitting procedure described below to extract the signal propagation times for the longer and shorter paths as a function of field and we find that they scale as the path lengths (see Figures 4,5). Taken together with the absence of a simultaneous counter-propagating signal, the scaling shows clearly the unique chirality of the modes.

The propagation time is a non linear function of field and exhibits a plateau-like structure (see Figure 5) which we attribute to the onset of the quantum Hall effect. We are able to identify the ν = 2 and ν = 6 plateaus and although we were unable to make DC transport measurements on this sample to confirm the plateau sequence, we have done so on similarly fabricated samples which all show the characteristic onset of a very wide ν = 2 plateau characteristic of graphene. Since the ν = 6 plateau is narrow and centered on 6T we infer the centre of the ν = 2 plateau to be at 18 T and tentatively pick out the ν = 10 to be at 3.6 T although clear identification of this latter plateau is lacking. A seemingly anomalous feature is the dip at 8 T in the propagation times for the shorter path only. We were unable to ascertain the origin of this dip.

Arrival times are extracted from the demodulated signal by a functional fitting procedure. A typical measured modulated voltage as function of time is given in Figure 6 in black. The excitation step voltage is not an ideal Heaviside function but has exponentially rounded corners which are well represented by a Fermi function f (t) = (exp α(t -t 0 ) + 1) -1 , where α is a parameter set by the rise time and t 0 the position of the step. We suppose this to set up an EMP wavepacket of the same shape which propagates as sketched in red in Figure 1, later times appearing closer to the injection point. When this wavepacket arrives at the receiver electrode it is transformed into a time domain signal which is differentiated by the RC of the capacitive contact. The slow uniform modulation of edge density has a twofold effect: it can modulate the amplitude of the wavepacket, which does not change its arrival time, and it can modulate its propagation velocity which changes its arrival time, but not its amplitude. Taking account of the additional RC differentiation, the attenuation action gives rise to a symmetric first derivative and the velocity action to an antisymmetric second derivative in the demodulated signal (supposing the action of each to be linear in modulation voltage). The relative contributions of the two effects can differ in different conditions, but the arrival time is common to both. We therefore fit each demodulated signal individually to a weighted sum of first and second derivatives of a Fermi function with a common arrival time as shown in Figure 6 where an experimental signal is shown in black and the two derivative components in dashed blue and pink, their sum being the fit in red. The arrival time is represented by the blue dot. Modulation acts differently on and off a plateau since the relative contributions of attenuation and propagation velocity vary, resulting in a change of shape with field.

The relative amplitude of the signal along the longer and shorter paths informs us on attenuation over the difference in path lengths and we are able to estimate roughly an attenuation length of 70 ± 30 µm corresponding to a relaxation time of 50 ± 20 ps, three orders of magnitude longer than the Drude relaxation time relevant for the damping of surface plasmons as deduced from the DC mobility µ = eτ /m * → ev F hk F τ [23] measured on similar samples (see below for origin of effective inertial mass m * ).

Summary

The experiment has shown that: (i) The perturbation is transmitted from one contact to the other with a time delay that is proportional to the perimeter path length, the shorter or longer path being chosen by the sign of the applied perpendicular magnetic field. There is no evidence for simultaneous propagation along both. This establishes chirality and edge propagation. (ii) The time of flight is a function of magnetic field and shows quantisation on QHE plateaus. This identifies the excitation to be associated with the QHE. (iii) The shorter path length gives a larger signal amplitude. This enables us to estimate the attenuation length of the wave by comparing the relative signal amplitudes for left and right paths.

The ensemble of data features is well described in terms of edge magnetoplasmons.

Plasmons

Surface plasmons

It is helpful to situate the edge magnetoplasmons in the more general context of plasmons. Plasmons are propagating charge density waves whose restoring force arises from Coulomb interaction. The Fourier transform

E (D) k ∼ k (2-d) n (D) k in dimension D = d of the Coulomb field from charge density variation n (D)
k cos k.r is the root of the dimension sensitive frequency-wavevector dispersion: finite dispersionless frequency in 3-, square root in 2-and linear in 1-dimension. Graphene has two-dimensional ultrarelativistic type dynamics according to which a force cannot change the magnitude v F but only the orientation θ of the velocity which is always aligned with the particle momentum. The momentum p is tilted by δθ ∼ F dt/p by the action of a force F for a time dt leading to a change in velocity dv ∼ v F δθ ∼ (v F /p)F dt which, somewhat paradoxically, behaves like an effective inertial mass m * ∼ p F /v F . Although this does not change the wavevector dependence, ω ∼ k 1/2 , the appearance of the density dependent Fermi momentum k F = √ πn s does alter the density dependence

from ω ∼ √ n s k for inertial 2DES dynamics to ω ∼ n 1/2
s k and in practice scales the dispersion to much higher frequency. A fuller, quantum description can be found in reference [24].

We attribute the arrival time at zero field in Figure 5 to surface plasmon propagation whose group velocity diverges as k -1/2 .

Edge plasmons

In perpendicular magnetic field the dynamics is dominated by mass independent Lorentz force drift, as in conventional 2D electron systems (2DES), because fundamentally it only depends on the Lorentz transformation to the electron velocity frame. We can therefore transfer to graphene much of the insight gained from the study of inertial 2DES. As observed in those systems, upon applying a magnetic field perpendicular to the graphene the longitudinal plasmon modes split into frequency increasing and frequency decreasing branches. While for the former the wave amplitude remains spread over the whole interior of the sample, for the latter it progressively confines itself to the sample boundary. This is the creation of the edge magneto-plasmon (EMP) mode with which we identify the observed propagation of edge charge.

This low frequency gapless (ω → 0 as q → 0) mode is a quasi one dimensional charge density wave propagating around the edge of the electron pool. In a classical description [1,2,10,25] an EMP wave propagates by depositing charge on the edge by virtue of internal drift currents set up by the field of its own periodic edge charge distribution. The particle motion associated with the wave is Lorentz drift in the superposition of the single particle constraining edge potential and the electrostatic interaction potential of the edge charge density variation. The velocity v D of the drift of electrons along the edge potential determines a reference frame for the Hall conduction propagation, adding to its propagation velocity when seen from the laboratory. The Hall conductance contribution always dominates the propagation velocity in the usual semiconductor heterojunction 2DES except in the fractional QHE regime [8] but not, as we shall see, in graphene. The currents are confined to a depth given by the shorter of the screening length or the wavelength. They propagate unidirectionally along the edge with chirality determined by the Lorentz drift, imposing propagation in a direction set by the sign of the Hall conductance σ xy = nsec B ≡ ν e 2 h if the filling factor is regarded as carrying the sign of the product of the signs of excess charge and magnetic field. They propagate at group velocity

v g = dω dq = 2 σ xy ǫ eff ln 2 | q| w + C -1 + v D , (1)
where ǫ eff is the effective dielectric substrate screening constant, q the wave vector, w a lower cut off length associated with effective penetration of the distribution of charge accumulated at the edge or by the screening length set by the mobility of the compressible parts of the 2D gas. C is a density profile sensitive constant of order 1 [25].

We associate the higher field (B > 2.5 T) part of Figure 5 with these excitations.

Electronic structure of the edge

A more detailed analysis of the EMP propagation velocity calls for a model of the edge. It will situate the relative importance of the single particle and interaction (Hall effect) contributions and make more explicit the quantum description of EMPs.

Inspired by Halperin's early work [26] we think of the graphene edge, i.e. the border of the carbon network, as a wall beyond which the electron wavefunction must vanish. By virtue of being squeezed between the sample edge and the position set by the wavevector parallel to the edge (in the Landau gauge), it acquires extra quantum confinement energy. The electronic edge is then not the sample edge but rather the position at which the energy of the lowest Landau level crosses the Fermi level. The characteristic energy for the crossing, hv F /ℓ B , is reached over a magnetic length ℓ B = hc/eB (the width of a wavefunction) from which it is straightforward to estimate v D = cE c /B ∼ v F , the electric confinement field E c representing the slope of the Landau level energy on approaching the edge. The interaction (QHE) contribution to the velocity at the lowest integral filling factor ν = 2 is proportional to 2e 2 /hǫ eff and ≈ 7×10 7 cm s -1 , comparable to the Fermi velocity v F ≈ 10 8 cm s -1 . It is interesting to note that, for conventional 2DES too, v D ∼ v F /ν 1/2 , but there v F is set by the average electron spacing rather than the band crossing slope which is related to the carbon-carbon spacing of the graphene lattice.

Thus far we have implicitly assumed that the value for the electronic density at the edge is that associated with the stationary QHE on the grounds that the edge is also where the transport current flows and the Hall charge accumulates. To link it to the value in the interior we have to take into account the charge distribution across the sample which is set principally by electrostatics modified somewhat by the Landau level structure [27]. In our configuration there is no screening back gate, only a surrounding ground plate a few micrometres distant by which we electrostatically modulate the charge density. If we were to think of the sample as a conducting disc of radius R without nearby screening electrodes, the electrostatic solution for excess charge density as a function of the radial coordinate r would be n(r) = n 0 (1-(r/R) 2 ) 1/2 which diverges at the edge as (R -r) -1/2 as it must on approach to the edge of any unscreened 2D conductor, at least over a distance comparable to that to the nearest screening electrode. The implicit assumption in this electrostatic result is that the charges are held in by the edge of the electrode. This is to be contrasted with a depletion edge commonly met in conventional 2DES where an outside electrode imposes a potential which would call for a charge deficit at the edge in order for the sample to remain everywhere a conductor. Unlike a simple metal, mobile excess charge of a semiconductor with a gapped electronic band structure, or mobile charge on an insulating substrate, can be pushed away from the edge leaving a charge depleted insulating strip until the potential reaches the point where charges from the band on the other side of the gap can furnish charge of opposite sign (inversion). The general form of the charge density on approach to a depletion edge, n(r) ∝ (R -r) 1/2 is very different. Graphene, however, has no gap, only a crossing (Dirac) point at which it remains conducting. Evolution from excess to deficit (hole) charge is continuous as in a metal and there is always a density divergence on the edge (except for the special point where the edge coincides with charge neutrality). In magnetic field, the electrostatic solution minimising the Coulomb energy still globally dominates, but the Landau level structure does modify the electrostatic density distribution locally on either side of areas of complete Landau level filling where the addition of a particle requires a Landau level spacing energy. This gap incompressibility leaves constant density, filled Landau level, narrow strips within which no screening occurs and the potential varies by the Landau energy gap. They separate wider, unfilled Landau level, constant potential varying density bands across the sample, but the smoothed average of the density follows closely the electrostatic distribution [27,28]. Quantum Hall plateaus result when the Fermi level lies between Landau levels in the sample interior and the filled levels emerge from the Fermi sea at the edge. The EMP modes are carried along these emergence lines as QHE excitations.

Quantum description of EMP and drift velocity

The quantum description of the EMP wave can now be understood as a propagating variation in local chemical potential which, according to the QHE, is accompanied by a periodic Hall current. The spatial variation of the current redistributes the charge along the edge by shrinking or expanding the electron pool [8]. The local chemical potential is determined by the combination of the electrostatic interaction and position of the electronic edge in the the single particle quantum confinement energy of the Landau level. The result for the velocity in the simple case of a single conduction channel i is the same as in the semi-classical picture outlined above, v

(i) D = c eB ∂W (i) LL ∂r | µ (in terms of the quantum capacitance per unit length C Qi = ∂N i e/L
∂µ/e = e 2 B Φ 0

dr i dµ i , v (i)
D = σ 0 C Qi for each channel i, σ 0 = e 2 /h being the conductance quantum). W (i) LL = W (i)
LL (r) is the energy of the corresponding Landau level and the derivative is evaluated at the equilibrium Fermi level µ = µ F . Charge spread is expected to be of order of the magnetic length ℓ B . When ν ≥ 1, multiple Landau levels emerge through the Fermi level and the question arises of how to take into account differing drift velocities of multiple channels. If the differences of drift velocities between channels are small compared with the EMP velocity, the drift velocity for the EMP mode associated with the ν interacting channels is a simple average

v D = ν -1 ν i=1 v (i)
D of the drift velocities at the points where each Landau level emerges through the equilibrium Fermi level (in the language of quantum capacitance

v D = σ 0 ν -1 ν i=1 1 C Qi ).
The group velocity would then become

v g = dω dq = 2 σ xy ǫ eff ln 2 | q| w -γ -1 + v D (2)
if all the levels are supposed to emerge at the same position. The electrostatic potential has here been assimilated to that from a circular wire of diameter 2w and γ ≈ 0.577... is the Euler constant. The degrees of liberty introduced by multiple Landau levels allow for higher order modes, analogously to the classical system [29,30]. In the quantum picture they are described by different weights of chemical potential variation over the multiple Landau level channels. The EMP mode corresponds to in phase charge oscillations over all the channels together and constitutes the fastest mode. The higher, multipolar modes propagate more slowly, approximately at drift velocity little influenced by the EMP mode. are however not expected to be excited by our electrodes which are considerably larger than the magnetic length. The characteristic length in the log of Equation 2 results from the electrostatic potential of a strip of width w with periodic charge distribution along its length. w ∼ ℓ B in the quantum picture. Equation 2supposes all the Landau levels to emerge from the Fermi sea at the same location and to have the same width, but in reality they emerge in groups corresponding to the Landau level indices. The effect of taking into account the separation between different groups is to reduce the electrostatic contribution due to the separation. For our situation, the reduction is estimated to be of order 10% for ν=6 and 20% for ν=10 [31].

Calculation of drift velocities in graphene for a hard wall

Berry and Mondragon solved the Dirac equation with perpendicular magnetic field considering hard wall confinement of the sample edge which enters into the equation as an infinite mass term, rather than an infinite electrostatic barrier [32]. They also formulated the appropriate boundary conditions which for graphene are different for a zigzag or an armchair edge [33]. We consider a zigzag edge which we believe to be more appropriate to a random edge obtained by oxygen plasma etching. Following this approach and along the lines adopted in other papers [34,35,36] we calculate numerically the Landau level energies W LL for graphene for a hard wall and a zigzag edge as a function of distance to the edge as shown on the left hand panel of Figure 7.

The splitting of levels at the edge corresponds to lifting of valley degeneracy. The right hand panel shows the spatial derivative of the energies from which the drift velocities

v (i) D = 1 h dW (i) LL dk = c eB ∂W (i) LL
∂r are deduced by transposing the positions at which the energy levels cross the Fermi level in Figure 7(a) to the derivative curves in Figure 7(b). The Fermi level µ for a given filling factor ν is taken to be midway between the Landau levels of indices N = (ν -2)/4 and N + 1 far from the edge as appropriate to a QHE. The drift velocities for the valley split branches are evaluated individually for each quantum Hall plateau. The results for the positions and individual drift velocities for ν = 2, 6, 10 as well as their averages are recorded in Table 1 together with the measured group velocities and the Hall effect coefficient v 0 = νσ 0 ε eff multiplying the (ln(2/qw) -γ -1) term of Equation 2. The Landau levels in play for each filling factor ν are labeled by their indices N and the broken valley degeneracy is shown explicitly whereas spin degeneracy is not; ∆ 10 is the energy splitting between the N = 0 and N = 1 Landau levels and v F ≈ 10 8 cm s -1 . 1.

Table 2 illustrates the different steps in our analysis of the data. The initial step is to derive the log term of Equation 2 by fitting v g = βv 0 + v D to the measured velocities v g at each filling factor upon taking v D from the above calculation. Equation 2 identifies β with (ln(2/qw) -γ -1) enabling us to evaluate qw. q is deduced from the pulse rise time which we assimilate to one side of a Gaussian in time which we convert to a spatial Gaussian of half width ℓ = v g τ , the Fourier transform of which gives a Gaussian distribution of half width q = ℓ -1 . Given q we go on to evaluate the effective width w.

In the last column of the table we compare w with the magnetic length ℓ B = hc/eB at the field of the experiment(ℓ B ∼ 25.6 nm for 1 tesla). Because the exponential is strongly non linear over the range of the experimental error limits, we have given the asymmetric limits for w on either side of the median value corresponding to the extremes of the experimental error estimations. The argument of the log term, which is the ratio of the EMP wavelength/2π to the unspecified effective width w, is expected to be ≫ 1. As is clearly seen in the table, the slow log dependence in that region has the consequence that the relative precision in qw is much reduced over the precision in the measured group velocity (limited primarily by the temporal resolution of our finite bandwidth setup). From Table 2 we see a window of 200 < w < 700 nm, some 30-50 times the magnetic length ℓ B . Even though it scales roughly like ℓ B we feel that because the factor is so large it is probably unconnected. An alternative method to analyze the data was to keep the product of the edge width and wave vector qw and the Fermi velocity v F as two fitting parameters. By dividing Eq. ( 2) by v 0 we obtain v g /v 0 = κ + (1/v 0 ) v D /v F v F , where κ = ln(2/qw) -γ -1. We measure v g , calculate v D /v F and keep κ(qw) and v F as fitting parameters. In this case the fit turns out to be rather good in terms of linearity (see Figure 8), but overestimates the Fermi velocity to 1.7 * 10 8 cm s -1 and we find qw = 0.1. We have estimated q = 14µm (ν = 2), 18µm (ν = 6), 25µm (ν = 10) from the spatial width of the measurement pulse rise time as mentioned previously, and that yields w of the order of 1 µm. Large w represents slow propagation, slower than expected by a factor of ∼ ln(w/ℓ B ) ∼ 3.5. Although this may be good news for edge plasmonics (see next section), it is unsatisfactory for our understanding. The reduced Coulomb interaction between channels mentioned earlier would only reduce v 0 by about 10% for ν=6 and 20% for ν=10. A less fundamental, though technically important possibility is that the edge formed by the oxygen plasma etch meanders across w ∼ 500 nm on length scales ∼ q -1 over which the electrostatic potential averages. That possibility could be checked using an imaging technique like atomic force microscopy or alternatively by doing EMP experiments on well defined regular edges. As concerns the importance of the drift term, we remark that if it were absent altogether the argument of the log term would have to change by three orders of magnitude in order to account for the measured change of the group velocity between filling factors 2 and 10, posing an even greater challenge to our understanding.

Chirality and scattering

The Lorentz force dynamics imposes chirality. The low frequency, edge magnetoplasmon branch is confined to the edge and travels to the left or right according to the sign of the Hall conductance set by the product of the signs of perpendicular field (up or down) and excess charge (electrons or holes). The other, high frequency, branch is delocalised over the sample, has opposite chirality and is gapped by the cyclotron frequency. This raises questions on when chirality sets in and its effect on the attenuation of the wave. Guidance can be sought from the classical analysis of a circular sample [2] where opposite chiralities are labelled by positive and negative azimuthal quantum numbers ±m whose frequencies are degenerate at zero field where they combine to form a longitudinally propagating non-chiral surface plasmon mode. One of these states evolves with magnetic field to localise on the edge while the other remains delocalised over the surface and participates in the gapped magnetoplasmon branch. Such a pair of states can be mixed by an electrical potential which breaks the continuous rotational symmetry with a 2mpolar moment produced by a random set of impurity scattering potentials. We are therefore led to expect that chirality and confinement to the edge set in properly only once the magnetic splitting becomes large in comparison with the random potential created by the impurities. Once it has established its unidirectionality and has become confined to the edge it has no counter-propagating wave into which it can elastically scatter since the counter-propagating interior modes all have higher frequencies as long as ω plasmon < ω cyclotron . The EMP modes can then no longer be attenuated by energy conserving back scattering. In contrast, if there were a gapless branch propagating in the backwards direction strong elastic backscattering off random impurities or roughness could result. As it is, elastic backscattering can only occur into the opposite edge, but even that is considerably reduced by virtue of confinement of the EMP to the edge and the separation between edges.

Chiral plasmonics

The chirality, the ease of electrical control and the low attenuation of EMP in graphene point to interesting applications in the rising field of plasmonics. Three port miniaturised microwave circulators become possible in the GHz to THz range and particularly flexible by virtue of the electrical tuning possibility: the propagation velocity can be varied linearly with gate voltage and even have its chirality reversed in a few picoseconds by the flip of a switch. This feature also confers the possibility of using the circulator as a microwave switch between a left or right port and a two port device could be made into a voltage variable phase shifter. These applications would require a static magnetic field of a few tesla, but only over the extent of the sample which can be restricted to a few tens of microns. Inasmuch as the propagation impedance of the wave is the Hall resistance R H = ν -1 h/e 2 ≈ 12.5/ν kΩ, however, the problem of impedance matching the device to external electromagnetic transmission lines would have to be overcome. Nonetheless EMP based devices would seem to have certain advantages over zero-field plasmon based devices in the much reduced attenuation and in the linear rather than fourth root gate voltage dependence of propagation velocity, although impedance matching would be somewhat easier for surface plasmons in that it can be tuned by varying the width of the sample rather than the number of Landau channels on the edge.

Conclusion

The experiments have demonstrated that edge magneto-plasmons exist on the perimeter of graphene samples and that they are described by Hall effect dynamics superimposed on the single particle Lorentz drift perpendicular to the force field created by the quantum confinement energy of the Landau level upon approach to the sample edge. The velocity of the drift is found to be close to the Fermi velocity and of the same order as the Hall conductance contribution to the propagation velocity at the lowest filling factor ν = 2. They have been shown to be chiral with a relaxation time three orders of magnitude longer than that of non-chiral, zero magnetic field plasmons. In the quantum Hall effect regime, the propagation velocity is quantized in the same manner as the Hall conductance. Both the single particle drift and the Hall contributions are sensitive to the structure of the edge, a feature of considerable interest for distinguishing zig-zag from armchair edges when these become available in pure, well defined form. On a more applied front, these excitations extend the already promising applications of graphene for plasmonics to chiral plasmonics for use in wide bandwidth, voltage tunable and reversible devices such as circulators and phase shifters.

Figure 1 .

 1 Figure 1. Schematic diagram of the experimental principle. A fast step excitation voltage pulse is applied through the left hand ohmic contact to create a wavepacket of the excitation, the spatial form of which is illustrated in the middle (red) sketch. Upon arrival at the capacitive receiver contact a time s 0 /v later, where s 0 is the path length and v the propagation velocity, it is differentiated to give the temporal form sketched on the right. The propagation path is represented by the red arrow along the sample boundary. The gold coloured strips overlapping the edge of the sample by about 2 µm represent the extremities of tapered coplanar 50 GHz bandwidth transmission lines. Only that part of the signal which is modulated by the sample density variation imposed by V MOD of the figure is retained in order to eliminate effects of cross talk between transmission lines.

Figure 2 .

 2 Figure 2. Removal of graphite from the sample. Panels from left to right: a bilayer of PMMA and HSQ is deposited, e-beam lithography on the positive resist HSQ defines the etching mask, oxygen plasma etching of graphite, liftoff.

Figure 3 .

 3 Figure 3. Sample holder showing coplanar waveguide with the 50GHz bandpass designed for the experiment. The flip chip with graphene is placed over the hole in the bottom right hand corner.

Figure 4 .

 4 Figure 4. Transmitted voltage as function of time and magnetic field. Left: colour plot of signal amplitude. Right: traces for several field values, corresponding to the integer filling factors ν = 2, 6, 10, ∞ [19]

Figure 5 .

 5 Figure 5. Left: Propagation time as function of field. Right: Propagation velocity as function of field[19].

Figure 6 .

 6 Figure 6. Example of functional fit for extracting arrival time. The experimental signal in black is fitted to a weighted sum of first (dashed blue) and second (dashed pink) derivatives of a Fermi function representing modulation of attenuation and velocity respectively. The blue filled dot indicates the arrival time. See text.

Figure 7 .

 7 Figure 7. (a) Left panel: Landau level energies for graphene in the presence of a hard wall potential as a function of distance to the edge. (b) Right panel: slope of energies in panel (a) from which the drift velocity for each channel is evaluated by transposing the crossing points between the Landau level energies in (a) with the appropriate Fermi level µ ν . The example of ν = 2, N = 0 is illustrated by the two black dots. The velocities are recorded in Table1.

Figure 8 .

 8 Figure 8. Measured EMP group velocity as function of the calculated drift velocity for the three filling factors ν = 2, 6, 10. Both quantities are scaled by the filling factor dependent velocity v 0 (ν). The slope of this curve is the Fermi velocity v F and the y-axis intercept is related to the width of the electrostatic edge w, see text.

Table 1 .

 1 Measured group velocity v g and calculated Hall velocity coefficients v 0 , Landau level positions s and drift velocities v D at Fermi level µ = µ ν . 01 v g (10 8 cm s -1 ) v 0 (108 cm s -1 ) s/ℓ B v D /v F v D /v F

	ν µ/∆ 2 N 0 0.500	1.4 ± 0.2	0.21	-0.97	0.65	0.65
	6	0 1	1.207	1.8 ± 0.2	0.64	+0.34 -0.83	0.83 0.40	0.55
						-1.29	0.42
	10	0 1	1.573	2.5 ± 0.3	1.07	+0.97 +0.35	0.87 0.64
						-0.33	0.64	0.56
		2				-1.27	0.33
						-1.77	0.34

Table 2 .

 2 Parameters extracted from experimental results

	ν	β	1/qw	w(nm)	w/ℓ B
	2 6 10	3.6 ± 0.95 1.97 ± 0.35 1.87 ± 0.35	222 > 85 > 33 25 > 17 > 12 22 > 16 > 11	63 < 160 < 400 300 < 1000 < 1500 1000 < 1500 < 2000	10 < 25 < 70 30 < 100 < 150 70 < 100 < 150

Acknowledgements

We are grateful for input from Keyan Bennaceur, Fabien Portier and Patrice Roche. We gratefully acknowledge discussions with Leonid Glazman, Barry Bradlyn, Jack Harris, Sergey Mikhailov and Allan MacDonald. We are indebted for excellent technical help to Patrice Jacques, Claudine Chaleil and Pierre-François Orfila. This work was supported mainly by the ERC Advanced Grant MeQuaNo No. 228273 and also by the RTRA Gamet Grant No. 2010-083T, the ANR PNANO grant "METROGRAPH" and the ANR white grant "SUPERGRAPH".


domain: spi phys

text:
Sophie Duzellier
email: sophie.duzellier@onera.fr

Romain Cariou
email: romain.cariou@cea.fr

Thierry Nuns
email: thierry.nuns@onera.fr

Philippe Voarino
email: philippe.voarino@cea.fr

Fabien Chabuel
email: fabien.chabuel@cea.fr

Corinne Aicardi
email: corinne.aicardi@cnes.fr

BENCHMARK AND IRRADIATION TES TS OF TERRES TRIAL S OLAR CELLS FOR LOW COS T S PACE S OLAR ARRAY

Keywords: Solar Cells, Irradiations, Electrons, Space Applications

The need for low cost photovoltaic solutions is becoming more and more important with the ongoing NewSpace revolution. In this study, we review, as comprehensively as possible, the radiation hardness of various photovoltaic solar cells technologies. Emphasis is placed on cells offering attractive cost reduction compared to standard III-V based triple junctions. In addition, the following benchmarking criteria were identified: performance, including begin and end of life evolution (BOL/EOL) when submitted to doses/fluences, mass, Technological Readiness Level (TRL) and reliability.

INTRODUCTION

A wind of change is blowing in the space sector. New orbit configurations are foreseen with, for instance, more and more spacecraft using electric propulsion to reach Geostationary Earth Orbit (GEO) [START_REF] Landis | IEEE 42nd Photovolt. Spec. Conf. PVSC[END_REF]. While this propulsion mode allows to save mass and allow thus more payloads, its main drawback is the much larger amount of time in the Geostationary Transfer Orbit (GTO) with prolonged exposure of solar arrays to electrons and protons of radiation belts [START_REF] Goldsten | [END_REF]. Solar electrical propulsion consequently requires to address key photovoltaic (PV) metrics (end of life (EOL) power, W/m 2 , W/m 3 , mass, flexible arrays, etc.) for high power systems.

Other important NewSpace [START_REF] Pelton | Space 2.0: Revolutionary Advances in the Space Industry[END_REF] trends are the mega-constellations and low-cost missions, shaking up the traditional approach by using Components Off the Shelves (COTS) and high volume production manufacturing lines. Those trends are driving low cost solar arrays innovations.

Historically, silicon solar cells were developed together with space applications since their first use on Vanguard 1 in 1958. However, in 1990s, the GaAs/Ge followed by GaInP/GaAs/Ge multi-junction solar cells gradually replaced silicon for their high efficiency and high resistance to space radiation (electrons & protons) [START_REF] Iles | [END_REF]. Thus, the current state of practice in space PV is to use optimized monolithic triple junction (3J) solar cells that combine several layers of III-V materials, to convert a broad part of AM 0 solar spectrum [5]. Those type of solar cells typically have AM 0 efficiency around 30% in 3J configuration and even 32% in 4-junction (4J) configuration [6]. Their main drawback lies in their prices, roughly 2-3 orders of magnitude higher than a standard terrestrial silicon cell for instance; in addition, the Ge substrates used commonly for III-V cells, with a thickness in the 150µm range, are also relatively massive.

On the other hand, some terrestrial technologies have shown these last years significant performances improvements, exceeding efficiencies of more than 20%.

In this context, terrestrial solar cells are potential good candidates to address the cost and/or mass challenge, provided their performances and response to space radiations are acceptable and compatible with mission requirements. This paper provides a review on a set of terrestrial solar technologies. A radiation benchmark based on pertinent test approach is defined to evaluate state of the art terrestrial cell technologies (commercial or pre-commercial) such as perovskite (Pk) and silicon. The aim is to conclude on their capabilities to fly in a realistic space mission configuration (LEO, GEO, flexible arrays, etc.).

SOLAR CELLS REVIEWS

State of the art technologies

Laboratory efficiency records for solar cells are listed in the biannual publication from Green et al. [7]. III-V cells, as mentioned previously, are leading the efficiency race with record efficiencies of 47.1% for a 6-junction device under concentrated AM 1.5d spectrum, 39.2% for a six junctions under AM 1.5g spectrum, and more than 35% for a 4J device under AM 0 spectrum [START_REF] Siefer | Eur. Space Power Conf. ESPC[END_REF].

M ore interestingly for this study, other technologies (with lower efficiency though) have a strong potential in terms of mass and/or cost savings. This is the case for instance for c-Si and perovskite solar cells. Perovskites, with an absorber thickness in the few hundreds nm range, can bring significant mass saving; in addition, Pk cells are reaching 25.2% (0.1cm 2 ). Concerning c-Si, Kaneka holds record power conversion efficiency with 26.7% AM1.5G spectrum, for a 80 cm 2 IBC cells. Those lab efficiencies give indication of technology potential, but available commercial products have lower efficiency and may require developments for space compatibility (e.g. substrate, size, architecture, etc.).

Solar Cells Radiation Hardness

Solar cells, as opto-electronic devices, are susceptible to damage dose induced by the radiative space environment. The interaction mechanisms with electrons and protons produce displacement defects (points defects such as vacancies and intertistials, Frenkel pairs, complex defects) acting as recombination centers. The result is a reduced carrier lifetime and diffusion length, which impacts on cells performances. . It appears that this resistance is mostly due to rapid self-annealing mechanisms temperature-dependent [START_REF] Brus | Defect Dynamics in Proton Irradiated CH3NH3PbI3 Perovskite Solar Cells[END_REF]. Organic nature of Pk suggests ionization also plays a major role here inducing scissions of covalent links such as C-H and N-H, freeing H atoms contributing to the formation of recombination centers in the bandgap of the bulk material, but also passivating intrinsic or radiation defects.

To conclude here, common trends in radiation response of Pk and also some thin films technologies are: Electrons are penetrating particles with constant dose deposition with target depth but able to induce charging of dielectrics or insulating materials and inducing overheating of samples when large beam current is used during irradiation (large flux).

•

Protons range strongly depends on energy and mode of interaction; it leads to limited range and non-uniform dose profile with maximum of interaction at the end of the track (Bragg peak).

In case of solar cells (not shielded from radiation) representative energy ranges in a typical LEO-to-GEO space environment are 10-30M eV for electrons (few mm penetration depth) and 1-10M eV with protons (few tens of µm). Therefore, electrons can be easily used for irradiating solar cell assemblies (SCA i.e. with coverglass or encapsulation) whereas irradiating with low energy protons (the most "damaging") required bare solar cells (or ultra-thin encapsulation layers).

Regarding representativeness, solar cell on-board solar generator systems (SGS) are exposed to combined electron/proton with space flux defining the degradation/recovery kinetic ratio.

Technical limitations at accelerators forbid the irradiation on earth at space flux (much too low) and usual acceleration factors typically lie in the 10 3 -10 5 range. The expected space degradation/recovery ratio can thus not be simulated at ground. However, in-situ testing may overcome this difficulty by allowing annealing monitoring and more testing at incremental steps of fluence under vacuum.

Therefore, the test plan (see Figure 2) includes electron irradiation, in-situ dark and light I(V) at M IRAGE facility (Axel Lab. [START_REF] Duzellier | Evaluation of tri-junction solar cells response to electrons and protons of the JUICE specific environment[END_REF] [START_REF] Sicard | GREEN: the new Global Radiation Earth Environment model[END_REF]), as well as ex-situ complete caracterisations at CEA-LITEN, for both commercial Si and Pk cells .

Cells and Constraints

As mentioned above, two commercial technologies are selected for this first campaign: perovskite modules (few tens of cm 2 ), terrestrial silicon solar cells (few cm 2 cuts from large cells).

For each of these technologies, sample configuration is not adequate for space application and thus for radiation testing. For instance, the Pk samples are encapsulated; therefore, it forbids any low energy protons testing (limited penetration depth).

Temperature is also a critical parameter for the cells electrical performance and radiation response. Therefore, typical irradiation set-up includes thermal regulation of samples through backside contact with cooled/heated plate.

Again the flexible/encapsulated Pk sample does not allow good thermal contact with backside plate; in addition, polymer materials are well known to degrade under radiation with the formation of color centers. Thus Pk encapsulation degradation will limit the analysis of radiation data introducing absorption bands in LIV testing.

Regarding sample size, typical beams spot is limited (flux non-uniformity monitored on 14x14cm² here) i.e. large devices cannot be fully exposed at once and the need for data with good statistics implies cutting large coupons into several small ones for testing (Si cells).

EXPERIM ENTAL RESULTS

Irradiation test campaigns have been shortened due to the COVID19 lock down period, thus only limited 1M eV electron irradiation on Pk and Si cells could be performed so far. 1M eV electron testing is recommended by the standards and norms (equivalent fluence concept).

Next table details the irradiation and in-situ testing steps. During this electron test campaign, short and medium-term annealing at RT was also investigated. In-situ DIV/LIV (1AM 0) was performed at each step.

Table I: The different steps of the 1M eV electron test campaign

Next figure provides LIV curves for Pk module measured ex-situ under AM 0 spectrum in begin-of-life (BOL) and endof-life (EOL), here 6.8 10 15 e-/cm 2 .

As one can see, the degradation of the J sc is significant, while the V oc does not degrade and is even improved after completing the irradiation through self-annealing mechanism. The origin of the J sc degradation is at least partially related to the transmittance degradation of the polymer/barrier layers encapsulating: this hypothesis was verified through BOL/EOL measurements on independent polymer / barrier films, as shown in Figure 4. Absorption in visible wavelength is linked to scission/cross-linking of polymer chain (double-bonds creation) leading to formation of color centers (Fig. 4). It induces yellowing of the materials, whereas cross linking induces stiffening of the encapsulation until mechanical deformation.

Figure 5 shows evidence of rapid self-annealing occurring within few minutes after the end of irradiation. This observation confirms what is reported in [START_REF] Kawakita | In-situ measurement of degradation of Cu(In,Ga)Se/sub 2/ thin film solar cells during electron and proton irradiations[END_REF] and explains the great stability of Pk to radiation. Only in-situ measurements allow for monitoring such rapid self-annealing. The Silicon in-situ Ligth IV measurements on sample A1 are disclosed in Figure 6 below. Both I sc and V oc are gradually affected by radiation (FF is stable) and no short-term annealing is observed.

The evolution of main parameters with fluence shows that P max degradation curve is "driven" by I sc evolution (Figure 7). Figure 9 provides RF(Voc) comparison for 1M eV electron fluence between benchmark samples and "space" technologies. Firstly, comparing RF(V oc ) for PK and Si samples, it is interesting to observe sample starts degrading at much higher fluence (>>10 15 #/cm²) but exhibits V oc drop of similar amplitude at total fluence. Secondly, benchmark radiation data clearly show that no optimized Si technology still exhibits acceptable EOL RF(Voc) while the "extreme" resistance to radiation of PK technology is confirmed to be due to self-healing mechanisms.

Lastly, it is very likely that on-board spacecraft (electron orbit) no degradation at all would be observed on Pk due to the much lower flux in orbit leading to real-time/concurrent compensation of degradation by self-annealing (similar kinetics of mechanisms).

CONCLUSIONS AND PERSPECTIVES

This work is a first step to determine the viability of terrestrial solar cells in a space radiative environment. 1M eV electron testing have been performed on commercial Pk modules and Si cuts showing great stability of Pk due to self-annealing mechanisms and gradual degradation of Si samples with fluence. M ore testing (with protons, or combined protons/electrons) is planned to complete this study. This benchmark will be the basis for ranking of technologies relatively to typical orbits and mission and the opportunity to define further investigation on most promising cells (understanding of degradation mechanisms, recommendations for flight operation conditions…).

  Radiation data on thin films solar cells technologies are reported in the literature from decades [9]-[17][21]. Bätzner et al. in 2004 provided a comparison between different technologies (Figure 1) based on the displacement damage formalism (fluence multiplied by material specific Non-Ionizing Energy Loss parameter).

Figure 1 :

 1 Figure 1: Electrons/Protons degradation curves for different technologies [14]. Efficiency remaining factor (RF) versus damage dose Pk cells are also resistant to electrons and protons showing great stability [15][16]. It appears that this resistance is mostly due to rapid self-annealing mechanisms temperature-dependent[START_REF] Brus | Defect Dynamics in Proton Irradiated CH3NH3PbI3 Perovskite Solar Cells[END_REF]. Organic nature of Pk suggests ionization also plays a major role here inducing scissions of covalent links such as C-H and N-H, freeing H atoms contributing to the formation of recombination centers in the bandgap of the bulk material, but also passivating intrinsic or radiation defects.

•

  Stable response up to large 1M eV electron fluence (10 16 -10 18 #/cm²)•Degradation with low energy protons (50-300keV, fluence >10 12 -10 13 #/cm²) when peak of damage is localized near junction and interfaces•Self-healing mechanisms leading to partial or complete annealing (thermally and photo stimulated)3. RADIATIONS TEST PLAN3.1 Radiation Test ApproachRadiation testing of samples (electronics) requires adequate configuration depending on radiation species: •

Figure 2 :

 2 Figure 2: Test sequence with dark and light I(V) steps (DIV and LIV)

Figure 3 :

 3 Figure 3: Ex-situ Light I(V) @AM 0 of Pk modules (107D sample) in BOL and EOL (6.8 10 15 1M eV e -/cm 2 ). Note that the Pk was irradiated with its terrestrial encapsulation

Figure 4 :

 4 Figure 4: Degradation of transmittance in % of PK encapulation films due to 1M eV electrons. Increased absorption with increasing fluence in the visible range.

Figure 5 :

 5 Figure 5: Self-annealing at room temperature under vacuum after the end of irradiation (fluence 6.8 10 15 1M eV electrons/cm², 107D sample)

Figure 6 :Figure 7 :

 67 Figure 6: Light I(V) measurements in-situ during each electron irradiation steps on commercial terrestrial silicon cells (A1 Si sample)

Figure 8 :

 8 Figure 8: EQE data on A3 Si sample (EOL ex-situ characterization)

Figure 9 :

 9 Figure 9: Comparison of RF(Voc) for PK and Si samples with "conventional" space technologies (radiation figures from product datasheets). Typical equivalent fluence are shown for LEO, GEO and M EO orbits.

  6. ACKNOWLEDGM ENTThis work has been supported by the Centre National d'Etudes Spatiales (CNES).