David Rozen-Rechels
email: david.rozen-rechels@normalesup.org

Hugo Valls-Fox

Cheryl Tinashe Mabika

Simon Chamaillé-Jammes

Cheryl Tinashe Mabika

Simon Chamaillé- Jammes

Temperature as a constraint on the timing and duration of African elephant foraging trips

Keywords: activity rhythm, large herbivore, movement ecology, nycthemeral, savanna, surface water Water is a key resource for organisms living

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

passive cutaneous or respiratory water losses; Cain [START_REF] Cain Iii | Mechanisms of thermoregulation and water balance in desert ungulates[END_REF][START_REF] Gerson | The impact of humidity on evaporative cooling in small desert birds exposed to high air temperatures[END_REF][START_REF] Tieleman | Cutaneous and respiratory water loss in larks from arid and mesic environments[END_REF], changing skin permeability to limit cutaneous water losses [START_REF] Muñoz-Garcia | Metabolic rate, evaporative water loss and thermoregulatory state in four species of bats in the Negev desert[END_REF][START_REF] O'connor | Avian thermoregulation in the heat: efficient evaporative cooling in two southern African nightjars[END_REF], or even heterothermy (facultative hyperthermia by allowing body temperature to rise temporarily, [START_REF] Hetem | Variation in the daily rhythm of body temperature of free-living Arabian oryx (Oryx leucoryx): does water limitation drive heterothermy?[END_REF][START_REF] Hetem | Heterothermy in large mammals: inevitable or implemented?[END_REF][START_REF] Gerson | The functional significance of facultative hyperthermia varies with body size and phylogeny in birds[END_REF]. Behavioral adjustments also are used to reduce water losses, for instance by reducing activity or shifting to cover when ambient temperature becomes too high (Abdu et al. 2018;[START_REF] Fuller | Towards a mechanistic understanding of the responses of large terrestrial mammals to heat and aridity associated with climate change[END_REF]. These adjustments will become critical for the survival of organisms that may face increasing water scarcity in the future as a consequence of global changes in climate [START_REF] Field | Managing the risks of extreme events and disasters to advance climate change adaptation: special report of the intergovernmental panel on climate change[END_REF][START_REF] Mitchell | Revisiting concepts of thermal physiology: Predicting responses of mammals to climate change[END_REF][START_REF] Mckechnie | Physiological and morphological effects of climate change[END_REF].

Individual space-use strategies become critical when animals face water scarcity. Most large herbivores living in arid and semi-arid environments worldwide only can find drinking water in sparsely distributed water sources such as water pans [START_REF] Cain Iii | Mechanisms of thermoregulation and water balance in desert ungulates[END_REF][START_REF] Cornélis | Spatiotemporal dynamics of forage and water resources shape space use of West African savanna buffaloes[END_REF][START_REF] Espinosa | Landscape connectivity among remnant populations of guanaco (Lama guanicoe Müller, 1776) in an arid region of Chile impacted by global change[END_REF][START_REF] Gedir | Potential foraging decisions by a desert ungulate to balance water and nutrient intake in a water-stressed environment[END_REF][START_REF] Redfern | Surface-water constraints on herbivore foraging in the Kruger National Park, South Africa[END_REF][START_REF] Chapman | Searching in heterogeneous and limiting environments: foraging strategies of white-lipped peccaries (Tayassu pecari)[END_REF][START_REF] Valls-Fox | Resource depletion versus landscape complementation: habitat selection by a multiple central place forager[END_REF]). These pans are highly seasonal, and their location strongly constrains animal movement during the dry season [START_REF] Loarie | Fences and artificial water affect African savannah elephant movement patterns[END_REF][START_REF] Valls-Fox | Resource depletion versus landscape complementation: habitat selection by a multiple central place forager[END_REF]. Individuals must leave the vicinity of water to make foraging trips and then return to water. Prior research has focused on understanding how the distance between water and forage ultimately constrains the movements of individuals [START_REF] Cain Iii | The costs of drinking: comparative water dependency of sable antelope and zebra[END_REF][START_REF] Mtare | African elephants adjust speed in response to surface-water constraint on foraging during the dry-season[END_REF].

Environmental conditions during these foraging trips, and in particular temperature, also could constrain individual movements. This would be true particularly in environments where temperature already is generally high. Exposure to high temperatures and high water losses due to passive (respiratory water losses) or active evaporative cooling (e.g. panting, sweating; Robbins and Parker 2017) during foraging trips will make them costly for thermo-hydroregulation [START_REF] Rozen-Rechels | When water interacts with temperature: Ecological and evolutionary implications of thermo-hydroregulation in terrestrial ectotherms[END_REF]. We should therefore expect individuals to adjust the duration of the trips to the temperature they experience, with potential trade-offs for feeding. We also might expect, in places where a diel cycle in temperature is significant, that individuals account for these diel variations and adjust the timing of trips to minimize the risk of overheating and dehydration.

In this study, we test whether the temporal aspects of foraging trips of the African savanna elephant, Loxodonta africana (Cuvier, 1825), are influenced by environmental temperature.

Foraging trips between visits to distant water sources during dry season are well documented in elephants [START_REF] Mtare | African elephants adjust speed in response to surface-water constraint on foraging during the dry-season[END_REF][START_REF] Polansky | Elucidating the significance of spatial memory on movement decisions by African savannah elephants using state-space models[END_REF][START_REF] Shannon | The affects of artificial water availability on large herbivore ranging patterns in savanna habitats: a new approach based on modelling elephant path distributions[END_REF][START_REF] Thaker | Fine-scale tracking of ambient temperature and movement reveals shuttling behavior of elephants to water[END_REF][START_REF] Wato | Movement patterns of African elephants (Loxodonta africana) in a semiarid savanna suggest that they have information on the location of dispersed water sources[END_REF]. Their thermal physiology also is well understood. The elephants' mass and volume, and the absence of sweat glands, make it difficult for them to lose heat, increasing the risk of overheating [START_REF] Wright | Why do elephants flap their ears?[END_REF][START_REF] Wright | Do elephants need to sweat?[END_REF]. Biophysical studies highlighted anatomical and morphological adaptation in elephants favoring heat dissipation through ear flapping [START_REF] Koffi | The role of pinnae flapping motion on elephant metabolic heat dissipation[END_REF][START_REF] Phillips | Heat exchange by the pinna of the African elephant (Loxodonta africana)[END_REF][START_REF] Wright | Why do elephants flap their ears?[END_REF] or sufficient passive evaporative cooling [START_REF] Wright | Do elephants need to sweat?[END_REF] through cracks in the skin [START_REF] Lillywhite | Surface sculpturing and water retention of elephant skin[END_REF][START_REF] Martins | Locally-curved geometry generates bending cracks in the African elephant skin[END_REF]. Finescale behavioral adjustments such as shade-seeking, dust-bathing, or wetting, also could be critical for their physiology, especially under high water and thermal constraints when physiological adaptations are not suficient [START_REF] Kinahan | Ambient temperature as a determinant of landscape use in the savanna elephant, Loxodonta africana[END_REF][START_REF] Mole | Coping with heat: behavioural and physiological responses of savanna elephants in their natural habitat[END_REF][START_REF] Thaker | Fine-scale tracking of ambient temperature and movement reveals shuttling behavior of elephants to water[END_REF]. Overall, temperature-dependent physiological and small-scale behavioral adjustments generally are wellunderstood in elephants. What remains poorly known is whether other adjustments occur at larger scales, such as at the scale of entire foraging trips.

We test the hypothesis that temperature influences the timing and duration of elephants' dry season foraging trips in Hwange National Park, Zimbabwe. In Hwange, elephants visit waterholes periodically (every 24h or 48h, sometimes 72h; [START_REF] Mtare | African elephants adjust speed in response to surface-water constraint on foraging during the dry-season[END_REF][START_REF] Valls-Fox | Resource depletion versus landscape complementation: habitat selection by a multiple central place forager[END_REF]. We chose not to include the rainy season because surface water is widespread and its availability does not constraint elephant movement as it does during the dry season [START_REF] Mtare | African elephants adjust speed in response to surface-water constraint on foraging during the dry-season[END_REF][START_REF] Valls-Fox | To drink or not to drink? The influence of resource availability on elephant foraging and habitat selection in a semi-arid savanna[END_REF]. We test the hypothesis that ambient temperature constrains the decision of continuing, or stopping a trip, and we predict that longer trips would be made under relatively colder conditions. Regardless of trip duration, the timing of elephants' visit to waterholes is usually concentrated around nightfall [START_REF] Valeix | Interference competition and temporal niche shifts: elephants and herbivore communities at waterholes[END_REF][START_REF] Valls-Fox | To drink or not to drink? The influence of resource availability on elephant foraging and habitat selection in a semi-arid savanna[END_REF], leading to the surprising observation that elephants travel at high speed under the afternoon's sun [START_REF] Mtare | African elephants adjust speed in response to surface-water constraint on foraging during the dry-season[END_REF][START_REF] Thaker | Fine-scale tracking of ambient temperature and movement reveals shuttling behavior of elephants to water[END_REF]. We test the hypothesis that this timing allows elephants to minimize the average temperature experienced during the foraging trip from and to water.

MATERIAL AND METHODS

Study area

The study was carried out in the eastern region of Hwange National Park, Zimbabwe (~26.9°E 18.8°S). The area is characterized by relatively level terrain (alt. 1000-1100 m asl) and the vegetation is typical of semi-arid savanna. Average annual precipitation is ca. 600 mm with high inter-annual variations [START_REF] Fritz | Spatial patterns of the NDVIrainfall relationship at the seasonal and interannual time scales in an African savanna[END_REF]. Rainfall is highly seasonal: about 80% of the annual rainfall occurs between November and April. Natural depressions and dams fill up with water during the rainy season and water thus is unlikely to constrain foraging during this season. In most of the park, there are no rivers, and those found in the north and south of the park only flow for a few days after heavy rains. Some pools keep water for longer, but as for all natural water pans, they gradually dry up during the dry season [START_REF] Fritz | Climate-driven fluctuations in surface-water availability and the buffering role of artificial pumping in an African savanna: Potential implication for herbivore dynamics[END_REF]. At the end of the dry season in the study area, surface water only can be found at artificial waterholes into which groundwater is pumped continuously. Water-dependent species such as elephants must undertake foraging trips to and from these waterholes [START_REF] Mtare | African elephants adjust speed in response to surface-water constraint on foraging during the dry-season[END_REF]. This creates local forage depletion near waterholes and, in the long-run, habitat change, i.e. a piosphere [START_REF] Andrew | Grazing impact in relation to livestock watering points[END_REF]). Here, vegetation cover increases with distance to water up to several kilometers away from these waterholes [START_REF] Fritz | Piosphere contribution to landscape heterogeneity: a case study of remote-sensed woody cover in a high elephant density landscape[END_REF]). In the study area, the locations are known of all artificial waterholes and large natural pans that retain water until at least June.

Thermal conditions across seasons

Data sampling was carried out during the 2013 dry season, from June 13th (when the elephants had settled in their dry season home-range) until October 23 rd , when the elephants dispersed again after the first significant storm. We focused on the elephants' foraging trips that occurred during three periods of the dry season as defined based on changes in water availability [START_REF] Valls-Fox | Resource depletion versus landscape complementation: habitat selection by a multiple central place forager[END_REF].

The first period covered the early cold-dry season (13 June to 7 July; mean daily temperature ± SE:

13.1 ± 0.4°C, from 105 water pans at the start of the period to 97 at the end). The following periods covered the mid-dry season (5 August to 10 September; 18.0 ± 0.3°C, from 72 to 63 pans), and the hot-dry season (11 September to 23 October; 23.7 ± 0.2°C, from 62 to 57 pans). We excluded the end of the cold-dry season because of the rapid decrease of the number of water pans during that period of time (from 92 to 73 pans; [START_REF] Valls-Fox | Resource depletion versus landscape complementation: habitat selection by a multiple central place forager[END_REF]. Cold-dry season was included as a matter of comparison with warm seasons during which we expect thermal constraints to be the highest (Supplementary Data SD1). At the same time, air temperature also was measured every hour at the Hwange LTER-CNRS weather station (26.952°E 18.731°S; Supplementary Data SD2). Whatever the season, temperatures were maximal around 14:00h -15:00h and reached up to 27.6°C during the cold-dry season, 32.3°C during the mid-dry season, and 38.1°C during the hot-dry season (Supplementary Data SD2).

Elephant movement data

In November 2012, 13 adult female elephants belonging to different family herds were equipped with GPS collars recording one location every 30 min (every 5 min from 11 October to 14 October).

We retained data from 8 collars for which the occasional failures in acquiring locations occurred when the elephant was too far away from water to have been able to reach water and be back at the next acquired location. This enabled us to reliably identify visits to water. Note that GPS collars were programmed to collect one location every 30 minutes and the average time spent by elephant family herds at a waterhole is 20 min. Trips were removed from the dataset if two conditions were fulfilled: (a) the gap lasted more than 1h and (2) the gap occurred when the elephant was sufficiently close to water for it to travel back and forth in a straight line at a speed below 1m.s -1 . By using a speed criterion, trips with small gaps in the GPS sequence occurring far away from waterholes were maintained in the dataset. An individual was considered to have visited a waterhole if its GPS track intersected a buffer of 200m radius, or if an individual could have reached water between two successive GPS locations based on its speed and direction (see [START_REF] Valls-Fox | Resource depletion versus landscape complementation: habitat selection by a multiple central place forager[END_REF] appendices for methods and validation). A foraging trip was defined as the movement path covered between two consecutive visits to a waterhole (see [START_REF] Valls-Fox | Resource depletion versus landscape complementation: habitat selection by a multiple central place forager[END_REF] for further information about the extraction of trips from trajectory data). During the 2013 dry season, we identified 901 trips. In this study, direct observations and camera trap records of the studied herds suggest that they were made of 5-17 individuals, typically comprising about 2-8 adult females and their immature offspring, and occasionally one or a few adult males.

Due to the strong multimodality in trip duration (Fig. 1A), and as in previous studies [START_REF] Mtare | African elephants adjust speed in response to surface-water constraint on foraging during the dry-season[END_REF][START_REF] Valls-Fox | Resource depletion versus landscape complementation: habitat selection by a multiple central place forager[END_REF], we divided the trips into four categories named after their average values (Fig. 1A): trips that lasted less than 12 hours (4.5 hours in average in our data); 24 h long trips (12 -36 h long); 48 hours long trips (from 36 -60 h long); and 72 h (≥ 60 h). We focused on trips of the 24h, 48h, and 72h, categories, as we considered that trips lasting 12h or less were too short to be constrained by the risk of overheating or dehydration, or that adjustments would occur at a smaller scale than the one considered here. Ultimately, we analyzed data from 535 trips (Fig. 1A).

We analyzed how elephants timed their departure according to sunset by fitting the linear regression between the duration of the trip and time elapsed since sunset. Departure time was 0 hour if it occurred at sunset, positive if departure occurred within 12h after sunset and negative if departure occurred within 12h before sunset. Sunset time has been estimated for the mean coordinates of Hwange National Park (26.9°E 18.8°S) using the algorithms provided by the National Oceanic and Atmospheric Administration (NOAA) with the "maptools" package in R [START_REF] Bivand | maptools: tools for handling spatial objects[END_REF].

Testing whether departure time affects temperature experienced during the trips

We used departure times from waterholes, corrected by sunset time, as indicators of the timing of the trips. Note that the departure time of a trip usually is very close in time to the arrival time from the previous trip, as elephants do not stay long at waterholes (often < 30 min). Departure time was estimated using the timestamp of the first location record of the trip.

We computed the average temperature experienced during each trip as an indicator of thermal conditions. To determine the importance of departure time, we calculated the average temperature for shifted departure times. We shifted the departure time by -12h, -11h, …, +11h and repeated the computation of the average temperature. For each trip, we thus obtained the 'real' average temperature experienced, as well as 24 values of the average temperature that could have been experienced if the trip had started at a different time of the day (hereafter called an alternative trip).

We did not use the maximal temperature because in most cases-and because trip duration was large relative to the shifts imposed-the time of the maximum temperature experienced during the actual trip was included in the shifted trips, and there was therefore no difference between the maximum temperature experienced during the actual trip and the maximum temperature of any of the shifted trips. We modeled how the average temperature of alternative trips changed according to departure time using generalized additive mixed models. In these models, the average temperature experienced during the trip was the response variable and departure time a fixed predictor transformed using a cyclic cubic spline because departure time is a circular variable. The model fitted 9 splines, one for each trip type (24, 48, 72h) and season (cold-dry, mid-dry, hot-dry) combination. The identity of each elephant was included as a random effect on the intercept. For each trip type, season and hour of the day, we extracted the predicted average temperature experienced during the trip (Tpredict).

To test if there were more trips at times that allowed elephants to experience lower average trip temperature, we modeled the number of trip departure per hour as a function of Tpredict for that departure hour. In other words, we tested if hours with most departures also are hours with the lowest Tpredict. We did this by fitting a generalized linear model with a Poisson distribution for errors, for each one of the 9 predicted splines with the three-way interaction (temperature × season × trip type).

Testing whether temperature experienced early in the trip affects trip duration

For each trip, we calculated the average temperature during the first 12 hours. We considered that these measures could be good proxies of the thermal conditions that would influence the decision of returning to a waterhole and thus carrying out a 24h trip, or pursuing the trip and undertaking a longer trip (48h or more). We modeled the probability of carrying out a 24h trip (vs. a longer trip) according to two-way interaction of the average temperature during the first 12 hours, and the season, with a logistic regression using generalized linear models with a binomial error and the elephant identity as a random effect on the intercept. In the same way, we analyzed how average temperature during the first 24 hours of a trip would affect the probability of undertaking a 48 h trip v. a longer trip with another logistic regression. All statistical analyses were carried out using the R software version 3.4.4 (R Core Team, 2018) and the lme4 [START_REF] Bates | Fitting linear mixed-effects models using lme4[END_REF], and mgcv (Wood 2017) packages.

Ethical note

All necessary permits for the study were obtained from the appropriate agency

RESULTS

The general timing of trip departure is presented in Fig. 1B and1C. Most trips started around sunset, i.e. between 18:00 and 20:00, and very few in the late night or early morning, i.e. between 03:00 and 10:00 (Fig. 1B). The duration of trips was adjusted so that arrival and departure of the next trip occurred around sunset: when individuals left earlier (later) they undertook longer (shorter) trips (Fig. 1C, trip category × corrected departure time: F2,522 = 8.1, p = 0.0003; slope estimated for 24h trip types: -0.48 ± 0.06; for 48h trip types: -0.33 ± 0.10; for 72h or longer trips: -1.32 ± 0.23). This explains the clear multimodal distribution of trip duration roughly lasting 24, 48 or 72h (Fig. 1A).

Departure time selection according to potential thermal conditions

In the case of 24h and 48h trip types, trips starting at sunset or slightly after sunset are those for which the average temperature is the lowest (Fig. 2). Most departures occurred around sunset, i.e., between 15:00h -20:00h, throughout the dry season and for all trip types. The relationship between predicted temperature and hour of departure was not significant for 72h-long trips, but sample size was very limited (5 during the Cold-Dry season, 20 during the Mid-Dry, 6 during the Hot-Dry). We therefore excluded 72h-long trips from further analyses. Most trips departed at hours allowing lower experienced trip temperature as shown by the negative relationship between the number of trips observed to start at a specific time and Tpredict (Fig. 3). The relationship was significant for 24h and 48h trips throughout the dry season (Tpredict × season × trip type: χ 2 4 = 17.9, p = 0.0001; Fig. 3, details of the results in Supplementary Data SD3).

Probability of undertaking a longer trip according to temperature

The probability of undertaking a 24-hour trip rather than a longer trip increased when the average temperature during the first 12 hours of the trip was higher (χ 2 1,3 = 12.4, p = 0.0004), for all three periods of the dry season (temperature × season: χ 2 2,7 = 2.5, p = 0.29; season: χ 2 2,5 = 3.1, p = 0.21). The probability of undertaking a 48-hour trip rather than a longer one was significantly the lowest during the mid-dry season and highest during the hot-dry season (χ 2 2,4 = 7.4, p = 0.03; multiple comparisons provided in Supplementary Data S4), regardless of thermal conditions during the first 24h of the trip (temperature × season: χ 2 2,7 = 0.2, p = 0.93; temperature: χ 2 1,5 = 0.91, p = 0.34).

DISCUSSION

Our study shows that temperature influences decisions about when to move, and for how long. This completes past studies that highlighted the impact of thermal conditions on activity levels and habitat selection [START_REF] Kinahan | Ambient temperature as a determinant of landscape use in the savanna elephant, Loxodonta africana[END_REF][START_REF] Van Beest | Temperature-mediated habitat use and selection by a heat-sensitive northern ungulate[END_REF][START_REF] Fuller | Towards a mechanistic understanding of the responses of large terrestrial mammals to heat and aridity associated with climate change[END_REF][START_REF] Mole | Coping with heat: behavioural and physiological responses of savanna elephants in their natural habitat[END_REF][START_REF] Thaker | Fine-scale tracking of ambient temperature and movement reveals shuttling behavior of elephants to water[END_REF]. We show that the timing and duration of elephant foraging trips are partly determined by temperature: most trips start at an hour that allows elephants to experience a lower average temperature during the trip. In addition, when the beginning of the trip is warmer, the trip is more likely to be shorter.

The general, and distinctive, timing of elephants' visits at waterholes around nightfall between 18:00 and 20:00, or sometimes a few hours earlier when elephant numbers at waterholes increases during dry years [START_REF] Valeix | Interference competition and temporal niche shifts: elephants and herbivore communities at waterholes[END_REF], at first appears counter-intuitive. To reach waterholes at the end of the day elephants walk at relatively high speed (Chamaillé-Jammes et al. 2013) under the afternoon sun. However, we show that this timing allows elephants to achieve lower average trip temperatures than other departure times. This arises because trip duration is rarely exactly 24h or 48h (Fig. 1): when departing at sunset, trips lasting less than 24h or 48h reduce the time spent at above-average temperature while traveling (late afternoon; Supplementary Data SD2); in such cases elephants could then carry out a short trip of a few hours, during which temperatures are less important, before leaving at sunset for another long trip; trips lasting more than 24h or 48h could have allowed elephants to forage more, or further away from water, while limiting their exposure to high temperatures because the extra-time is spent at below-average temperature (early night; Supplementary Data SD2).

Surprisingly, the coincidence of trip departure with sunset also was evident in the colddry period. If this specific timing emerged to avoid overheating, as we assumed, we would have expected it to be less marked, if present at all, during the cold-dry period. We are aware that our results cannot give a proper explanation to that result. We offer three hypotheses: first, there could be no cost associated with such timing. Although less beneficial, we suppose that a behavioral pattern would not change if it is not costly, which could thus lead to its establishment during the entire dry season. Second, solar radiation and temperature could remain a constraint during the cold dry period [START_REF] Wright | Why do elephants flap their ears?[END_REF][START_REF] Wright | Do elephants need to sweat?[END_REF]. Third, nights during the cold-dry season could be too cold, particularly close to water (temperature sometimes falls below 0°C; Valls-Fox 2015). In Hwange National Park, water pans often are located in vleis, i.e. depression in the landscape where humidity level is higher and vegetation that could stop the wind is sparse. Temperatures at night often are much lower in water pan areas than elsewhere. Therefore, it is possible that traveling to warmer woodlands at night would limit heat loss and thus reduce the costs of keeping warm for elephants in the cold-dry season, despite the large thermal inertia associated with their large body size.

Despite the fact that the timing of visits to waterholes reduces the average temperature experienced during the whole trip, it seems that it puts elephants at risk of overheating due to the final march towards waterholes undertaken in the afternoon heat. We argue that this risk may be lower than expected because elephants can quickly cool down at the waterhole by drinking, bathing, wallowing, or spraying themselves [START_REF] Dunkin | Climate influences thermal balance and water use in African and Asian elephants: physiology can predict drivers of elephant distribution[END_REF][START_REF] Mole | Coping with heat: behavioural and physiological responses of savanna elephants in their natural habitat[END_REF], thanks to the water retention properties of their skin structure [START_REF] Lillywhite | Surface sculpturing and water retention of elephant skin[END_REF][START_REF] Martins | Locally-curved geometry generates bending cracks in the African elephant skin[END_REF].

The timing of visits to waterholes described here is not specific to Hwange National Park. Visiting waterholes at nightfall appears to be common in elephant populations in southern and eastern Africa (Table 1). Some of these studies suggest that such timing is especially marked when temperature is high and during the hot-dry season. This supports our assertion that temperature is the underlying driver of this timing. Such general observation spanning several distant populations strongly suggests that this timing is not a "cultural" behavioral trait developed in isolation in Hwange National Park [START_REF] Fishlock | Elephant resource-use traditions[END_REF], but rather that it is a flexible behavior that can be rapidly adjusted, or a behavior under relatively strong selection pressure in these arid and semi-arid environments. Individuals that timed their trips on sunset might have survived better on average.

The absence of modulation of this pattern during the coldest season would argue for a selected behavior.

We also show that temperature similarly affects, beyond the timing of trips, the duration of these trips. For example, long foraging trips (48 h long or more) are avoided with increasing temperatures. These results could have important implications for the ecology of this population of elephants. First, if temperature reduces the duration of the trip, it limits the ability of elephants to forage far away from water [START_REF] Mtare | African elephants adjust speed in response to surface-water constraint on foraging during the dry-season[END_REF]. Resources are scarcer closer to water due to a higher density of elephants [START_REF] Fritz | Piosphere contribution to landscape heterogeneity: a case study of remote-sensed woody cover in a high elephant density landscape[END_REF], which implies that under high thermal constraints, individuals only would have access to a limited amount of foraging resources.

High temperature might then influence foraging behaviors. Constraints imposed by food distribution (i.e. strong forage depletion near waterholes) might force individuals to make long trips, which could explain why the 48h trips still persist during the hottest part of the dry season. We tentatively suggest that these 48h trips during the dry season may create a water debt, whereas 24h trips are probably less beneficial for foraging but maintain an adequate water balance. This study also ignores the potential role of very short trips (5 hours long in average, shorter than 12 hours) which could compensate long trips in terms of water balance and heat avoidance.

Finally, our results add to the literature about the cognitive capacities of elephants.

Previous studies have shown that elephants are able to memorize the locations of waterholes and navigate back to them without searching [START_REF] Polansky | Elucidating the significance of spatial memory on movement decisions by African savannah elephants using state-space models[END_REF][START_REF] Presotto | Spatial mapping shows that some African elephants use cognitive maps to navigate the core but not the periphery of their home ranges[END_REF][START_REF] Wato | Movement patterns of African elephants (Loxodonta africana) in a semiarid savanna suggest that they have information on the location of dispersed water sources[END_REF]. Here, we show, implicitly, that they integrate memorized spatial information with expected travel time, likely adjusting speed of travel, to arrive at waterholes near nightfall. Obviously, estimating the accuracy of this time-space integration is beyond the scope of this paper.

This study lacks considerations of the micro-habitats used by individuals during their trips. By shifting their trajectories to cooler micro-habitats (more shade, thicker vegetation), individuals might be able to buffer the effects of heat [START_REF] Huey | Predicting organismal vulnerability to climate warming: roles of behaviour, physiology and adaptation[END_REF]. By doing so, individuals might efficiently avoid overheating during their afternoon race to water. Such behavior might mitigate and help to understand a significant part of the variability in the pattern described herein (Fig. 1B). A description of the thermal micro-habitats landscape would be useful to estimate the availability and use of temperature-buffering opportunities, as would be the use of accurate recordings of actual temperature experienced by elephants (for instance using black bulbs on collars; [START_REF] Fuller | Adaptation to heat and water shortage in large, arid-zone mammals[END_REF]). In the context of global warming, there is an urgent need to understand the effect of temperature on animals. Movement is a key aspect of temperature regulation, and how individuals adjust their movement strategies to temperature fluctuations has rightly become a subject of interest [START_REF] Fuller | Towards a mechanistic understanding of the responses of large terrestrial mammals to heat and aridity associated with climate change[END_REF][START_REF] Sears | Configuration of the thermal landscape determines thermoregulatory performance of ectotherms[END_REF][START_REF] Rakowski | Thermal refuge affects space use and movement of a large-bodied galliform[END_REF]. This effort should be pursued, and future work should address how temperature affects linkages between time and space in animal movement, as movement is by definition a complex multi-scale process.

Figures legends

Coefficients

(

  Zimbabwe Parks and Wildlife Management Authority, permits 23(1)(c) (ii)17/2009; 23(1)(c) (ii) 01/2010; 23(1)(c) (ii)05/2011). Permit applications are reviewed by an ad hoc committee that considers ethical and animal welfare issues. Immobilization and collaring was carried out specifically for this study by an experienced personnel who is granted authorization to immobilize and collar elephants by the Veterinary Services of Zimbabwe. All operations were carried out under the supervision of a Zimbabwe Parks and Wildlife Management Authority ranger. Each collar weighed approximately 13 kg, less than 0.01% of animal body weight.

Fig. 1 .

 1 Fig. 1.-A) Distribution of trip durations (in hours; excluding trips shorter than 12 hours). Black is for 24h trips, dark gray is for 48h trips and light gray is for 72h or more longer trips. B) Distribution of trip departure time, corrected by sunset time, i.e., the difference to 0 calculates the number of hours to or since sunset, for each trip type. C) Trip durations (in hours) as a function of the departure time. Points are for each trip, black and grey lines are for predicted relationship between the duration of the trip and the corrected time of departure for each trip duration category with a linear mixed model with the elephant identification as a random effect (trip category × corrected departure time: F2,507 = 7.7, p = 0.0005). Red lines are showing the 24 hours, 48 hours, and 72 hours, trips. The shaded square shows the night time period.

Fig. 2 .

 2 Fig. 2.-Predicted variations of mean temperatures experienced during trips (upper panels), across all possible hours of departure (difference to sunset), for each for each trip type (24h, 48h, 72h) and each period of the dry season (Cold-dry, Mid-dry and Hot-dry). Estimates were obtained from generalized additive models (upper panels), and should be compared with the distribution of counts of actual departures for each hour of the day (lower panels; Fig. 3). Temp is for temperature. Plain lines are mean predicted temperatures, dashed lines are 95% confidence intervals. The significance of smooth-terms (difference to 0 which is a linear relationship) from generalized additive models are indicated with symbols: NS = non-significant, † p < 0.10, * = p < 0.05, ** p < 0.01, *** p < 0.001. The number of actual trips n in each case are indicated in each histogram.

Fig. 3 .

 3 Fig. 3.-Number of trips in relation to Tpredict, for each trip type (24h, 48h, 72h) and each period of the dry season (Cold-dry, Mid-dry and Hot-dry).

  Figure 1

  Multiple comparisons of the probability of realizing a 48 hours trip over a longer one according to the season. Estimates and p-values are extracted from a Tukey's multiple comparison tests (multcomp library in R,[START_REF] Hothorn | Simultaneous inference in general parametric models[END_REF]

	Supplementary Data SD4 Comparison	Estimate	SE	Z value	P-value
	Hot-dry vs. Cold-dry	Estimate 0.86	SE 0.60	Z value 1.4	P-value 0.32
	Intercept Mid-dry vs. Cold-dry	12.4 -0.45	1.9 0.51	6.6 -0.88	< 0.0001 0.65
	Average temperature experienced Tpredict Mid-dry vs. Hot-dry	-0.9 -1.31	0.2 0.51	-5.9 -2.58	< 0.0001 0.03
	Hot-dry season	3.0	2.7	1.1	0.28
	Mid-dry season	6.0	3.0	2.0	0.04
	48h trip type	19.5	6.3	3.1	0.002
	T × Hot-dry season	0.3	0.2	1.9	0.06
	T × Mid-dry season	-0.03	0.2	-0.2	0.87
	T × 48h trip type	-1.6	0.5	-3.1	0.001
	Hot-dry season × 48h trip type	-15.0	8.9	-1.7	0.09
	Mid-dry season × 48h trip type	29.1	13.1	2.2	0.03
	T × Hot-dry season × 48h trip type	1.4	0.6	2.4	0.02
	T × Mid-dry season × 48h trip type	-1.2	0.8	-1.4	0.15

ACKNOWLEDGEMENTS

We thank the Director General of the Zimbabwe Parks and Wildlife Management Authority and the Research Council of Zimbabwe for providing the opportunity to carry out this research. Funding was provided by grant SAVARID ANR-11-CEPS-003 and LANDTHIRST ANR-16 CE02-0001-01 of the French 'Agence National de la Recherche'. This work was carried out within the framework of the Zone Atelier Hwange-Hwange LTSER (www.za hwange.cnrs.fr) and under the auspices of the Research Platform ''Production and Conservation in Partnership'' (www.rp-pcp.org). We thank R. Reyna-Hurtado, A. Shrader, and two anonymous reviewers, for their comments.

DATA AVAILABILITY STATEMENT

The datasets analyzed during the current study are available from the corresponding author on reasonable request.

AUTHORS' CONTRIBUTIONS

DRR and SCJ designed the study, which was facilitated by CTM. HVF collected and prepared the data. DRR analyzed the data and led the writing of the manuscript, with significant contributions from all authors.

SUPPLEMENTARY


F Leroy
email: leroy@cinam.univ-mrs.fr

D Landru

F Cheynis

O Kononchuk

P Müller

S Curiotto

Kinetics and coupled dynamics of dewetting and chemical reaction 1 in Si/SiO 2 /Si system 2

We report on the observation of a coupling between the dewetting of a Si layer on SiO 2 induced by surface/interface energy minimization and the etching between both materials due to the Si+SiO 2 -→2 SiO ↑ g reaction. In the limit of a thin SiO 2 layer (≤ 10 nm) sandwiched between a

Si layer and a Si handle wafer, the front of Si dewetting and the front of SiO 2 etching coexist in a narrow region. The interplay between both phenomena gives rise to specific morphologies. We show that extended Si fingers formed by dewetting are stabilized with respect to Rayleigh Plateau type instability over tenth of microns thanks to a localized etching of the SiO 2 layer. The break up of this structure occurs abruptly by an unzipping process combining dewetting and etching phenomena.

We also put in evidence that Si rings are created with a thin SiO 2 layer in the center. These processes are thermally activated with an activation energy of 2.4±0.5 eV and 4.0±0.5 eV respectively for dewetting and the etching reaction. All these results highlight the respective roles of wetting and etching in Si/SiO 2 /Si system dynamics and could be a stepping stone for the development of advanced processes based on Silicon-On-Insulator technology.

I. INTRODUCTION

Wetting of liquids on solids in reactive systems is of great importance with many industrial applications such as soldering or adhesion [1]. The kinetics of reactive wetting is affected by a number of factors like interfacial reactions, diffusion of constituents or dissolution of the substrate [2 and 3]. Under reaction the contact line dynamics can lead to complex behaviours such as oscillatory phenomenon of spreading and contraction [START_REF] Ohya | Oscillation of wettability of molten Cu islands on SiO 2[END_REF][START_REF] Ichinokawa | Behaviors of small molten metal islands on several substrates[END_REF][6][START_REF] Wachsmuth | SiO gas emission and triple line dynamics of small silicon droplets on quartz[END_REF], formation of reaction rings [START_REF] Saiz | Wetting and strength issues at Al/alpha-alumina interfaces[END_REF] or even droplet motion [START_REF] Curiotto | Self-propelled motion of Au-Si droplets on Si(111) mediated by monoatomic step dissolution[END_REF][START_REF] Curiotto | In-plane Si nanowire growth mechanism in absence of external Si flux[END_REF][START_REF] Curiotto | Surface-dependent scenarios for dissolutiondriven motion of growing droplets[END_REF]. For example, the reaction-mediated spontaneous drift of millimeter-scale solid-state camphor particles on the surface of water has been known for several centuries [START_REF] Nakata | Spontaneous dancing of a camphor scraping[END_REF]. In solid systems only scarce studies have explored the coupling between chemical reactions and wetting dynamics. For instance in metallic systems the alloying driving force can induce the self-propelled motion of solid Sn islands onto a Cu surface [13]. In the context of metal/oxide or semiconductor/oxide systems, solid state wetting properties may also be affected by interfacial redox reactions. For instance in the Si/SiO 2 couple, that plays a key role in the perspective of future devices based on Silicon-On-Insulator (SOI) technology [START_REF] Bollani | Templated dewetting of single-crystal submillimeter-long nanowires and on-chip silicon circuits[END_REF][START_REF] Naffouti | Complex dewetting scenarios of ultrathin silicon films for large-scale nanoarchitectures[END_REF][16][START_REF] Trautmann | Dewetting of patterned solid films: Towards a predictive modelling approach[END_REF], wetting and reactivity properties of the interface have been largely studied. Under moderate annealing (∼ 1100-1300 K) SOI dewetting occurs by edge retraction (see Fig. 1 and [18][START_REF] Nuryadi | Formation and ordering of self-assembled si islands by ultrahigh vacuum annealing of ultrathin bonded silicon-on-insulator structure[END_REF][START_REF] Nuryadi | Thermal agglomeration of single-crystalline Si layer on buried SiO 2 in ultrahigh vacuum[END_REF][START_REF] Legrand | Formation of silicon islands on a silicon on insulator substrate upon thermal annealing[END_REF][START_REF] Legrand | Thermally assisted formation of silicon islands on a silicon-on-insulator substrate[END_REF][START_REF] Bussmann | Dynamics of solid thin-film dewetting in the silicon-on-insulator system[END_REF][START_REF] Cheynis | Dewetting dynamics of silicon-on-insulator thin films[END_REF]), the expelled silicon accumulates in a receding rim that exhibits a capillary instability giving birth to elongated Si structures (called Si fingers). These fingers are in turn destabilized and periodically form 3D Si islands by a beading mechanism similar to a Rayleigh-Plateau instability. The driving force for this dewetting process arises from the surface/interface free energy gain. In solids mass transport is mediated by surface diffusion [START_REF] Mullins | Theory of thermal grooving[END_REF][START_REF] Wong | Periodic mass shedding of a retracting solid film step[END_REF][START_REF] Wang | Sharp interface model for solid-state dewetting problems with weakly anisotropic surface energies[END_REF] whereas hydrodynamics dominates in liquid films [START_REF] Reiter | Dewetting of thin polymer-films[END_REF][START_REF] Mukherjee | Instability, self-organization and pattern formation in thin soft films[END_REF][START_REF] Bhandaru | Ordered Alternating Binary Polymer Nanodroplet Array by Sequential Spin Dewetting[END_REF][START_REF] Dhara | Transition from Spin Dewetting to continuous film in spin coating of Liquid Crystal 5CB[END_REF]. This makes that the contact line with the substrate is particularly sensitive to the effect of the disjoining pressure in solid thin films whereas surface diffusion is much less affected [START_REF] Ashwani | Disjoining-pressure-induced acceleration of mass shedding in solid-state dewetting[END_REF]. Considering high temperature regimes (∼ 1300 K) Si and SiO 2 solids are also known to react and form volatile SiO ↑ g molecules. This is perfectly illustrated when a SOI film is completely dewetted at 1000 K, then annealed at 1330 K: the reaction leads jointly to the consumption of the 3D Si islands and to the etching of nanopits in the SiO 2 layer [33 and 34].

In this article we analyze the combined effects of etching reaction and dewetting on SOI films in the high temperature regime. Their interplay gives complex front dynamics: (i) (time t 1 ) that leads to beading and formation of a 3D Si island at its extremity (time t 2 ∼t 1 +120 s). This process repeats periodically (time t 3 ∼t 1 +240 s).

(b) (a) SOI t 1 t 2 t 3 t 2 t 3 1 m
formation of extended Si fingers stabilized by lateral etching, (ii) Si fingers break up by an unzipping mechanism and (iii) formation of Si rings with a thin SiO 2 layer in the center.

The etching and dewetting fronts dynamics are studied experimentally in situ and in real time by low energy electron microscopy (LEEM) and ex situ AFM measurements.

II. METHODS

The SOI wafers are originally fabricated at SOITEC (Bernin, France). They are cleaned and prepared in Ultra High Vacuum (UHV) conditions as described in Ref. [START_REF] Bussmann | Thermal instability of silicon-on-insulator thin films measured by low-energy electron microscopy[END_REF]. The studied thickness is about 30 nm for the Si layer and 8 nm for the buried oxide layer (BOX) of SiO 2 .

Such thin structures are highly sensitive to Si layer dewetting and etching reaction between Si/SiO 2 under thermal annealing. In the temperature range ∼ 1300 -1400 K, a front of dewetting of the Si layer forms spontaneously onto a defect at the surface/interface and is followed by an etching reaction front. Their motion and morphology are recorded in situ and in real time (1 s per image) by low energy electron microscopy (LEEM) in the tilted bright field mode (electron energy: 4 eV). The characterization of the coupling between the etching and dewetting fronts dynamics is completed by ex situ analysis of the surface morphology by atomic force microscopy (AFM, PSIA-XE 100). (1.5±0.1 µm period) occur whereas slightly more disordered ones can be observed when the front recedes in the [110] direction (Fig. 2(c)). A similar observation is obtained for Si(001) thin layer dewetting onto SiO 2 at lower temperature (1200 K) when etching reaction is negligible. The [100] front forms regular fingers by front edge instability as described by [START_REF] Leroy | Dynamics, anisotropy, and stability of silicon-on-insulator dewetting fronts[END_REF].

In the case of a [110] front, as there are two equivalent directions for the fingering instability ([100] and [010]), the competition between both degrades the long range order [23 and 24]. As the SOI dewetting fronts recede (via fingers formation), the underlying SiO 2 BOX layer is exposed to vacuum (Fig. 2(b)). This free BOX layer shows triangular structures, the base pointing towards the SOI layer and the tip pointing in the direction of the Si handle wafer. We can infer that the edges of the triangles correspond to the reaction front between the remaining BOX layer and the Si handle wafer. As the front recedes in a steady state, the decay of the BOX occurs by a constant etching reaction rate (Si+SiO 2 -→2 SiO ↑ g ) localized at the Si/SiO 2 /vacuum triple-line. To evaluate the activation energies of SOI dewetting E d and etching reaction E r we have studied the effect of the sample temperature on both kinetics (Fig. 3(a)-(b)). As the temperature decreases from 1370 K to 1300 K the fronts velocity v f decreases from 53±5 nm.s -1 to 18±3 nm.s -1 , the extension of the free BOX layer W increases from 0.9±0.1 µm to 2.3±0.5 µm and the disappearance time t d of the free BOX layer increases from 20±1 s to 125±20 s. The SOI front velocity v f is only driven by SOI dewetting kinetics and can be written as v f ∼ e -E d kT assuming it is thermally activated.

From the ratio of the velocities v f at 1370 K and 1300 K, the dewetting activation energy is estimated as E d =2.4±0.5 eV that is in perfect adequation with previous SOI dewetting studies [START_REF] Bussmann | Dynamics of solid thin-film dewetting in the silicon-on-insulator system[END_REF] that show that Si surface diffusion is the dominant mechanism of mass transport mediating the dewetting process. The etching reaction activation energy E r is not related to the reaction front velocity. Indeed the reaction occurs at the Si/SiO 2 /vacuum tripleline and thus starts when the BOX is exposed to vacuum. Therefore the etching reaction activation energy has to be evaluated from the disappearance time t d ∼ e

Er kT of the free BOX layer. Measurements of t d at 1370 K and 1300 K provide an estimate of E r = 4.0 ± 0.5

eV. This is also in adequation with the activation energy reported by [START_REF] Leroy | Nonequilibrium diffusion of reactive solid islands[END_REF] from temperature dependent measurements of Si island decay kinetics onto SiO 2 . At last we have also measured the width W of the exposed BOX layer with respect temperature. It is related both to dewetting and etching reaction activation energies as

W = v f × t d ∼ e
Er -E d kT

. We measure that E r -E d = 2.1 ± 0.6 eV. The large difference between the activation energies of Si dewetting and etching reaction makes that the width W of the free BOX layer decreases strongly with temperature as observed experimentally. At last let us note that despite the difference between both activation energies, the dewetting and etching fronts move at the same velocity (i.e. at the Si layer dewetting velocity, see supplementary material S1). This is due to the fact that the etching reaction occurs only when the BOX layer is exposed to vacuum, i.e. after the dewetting front passage. Then it takes a time t d for the BOX layer to be completely etched which can be seen as a delay time for the etching front to progress behind the dewetting front.

This evaluation of the activation energies can also be completed with the quantitative analysis of the rate of etching reaction and dewetting front velocity. From the linear decrease of the BOX layer with time (triangular shape) the reaction rate ν reac = dN dt at the Si/SiO 2 contact line can be estimated (where N is the number of SiO 2 entities in the oxide layer).

We calculate therefore ν reac ≈ 3.2 × 10 3 s -1 per SiO 2 entity at the contact line at 1370 K and ν reac ≈ 5 × 10 2 s -1 per SiO 2 entity at 1300 K (oxide layer thickness: 8 nm). This result compares to previous report [START_REF] Leroy | Nonequilibrium diffusion of reactive solid islands[END_REF] on the reaction rate of Si islands onto SiO 2 (3 × 10 2

s -1 per atom) in a slightly lower temperature regime. Concerning the dewetting velocity of SOI, Cheynis et al. [START_REF] Cheynis | Dewetting dynamics of silicon-on-insulator thin films[END_REF] have shown that in the temperature range [1000 K -1200 K] v f ≃ 5.3×10 12 h 3 kT e -2.0/kT nm.s -1 where h is the SOI film height expressed in nm and kT is given in eV. Assuming this expression for a 30 nm thick film at 1370 K and 1300 K we obtain respectively v f =74 nm.s -1 and v f =31 nm.s -1 which gives the correct order of magnitude of the kinetics, the overestimation arising probably from a slightly too low activation energy in the modeling.

Beyond the description of the energetics of SiO To analyze the morphology of these fronts combining dewetting and etching, figure 4(a) shows a typical AFM image. We can clearly distinguish the SOI layer (turquoise) and the Si fingers (yellow and red). The AFM image shows also the SiO 2 BOX layer (blue); it appears as extremely flat areas located in between Si fingers close to the SOI dewetting front. They have the same shape as those observed by LEEM (triangular structures in 2(c)). We can also see from AFM that some Si fingers are unstable and split laterally into two branches exposing a small SiO 2 BOX layer (∼500 nm) in between (elliptic shape) as the one measured by LEEM. From the combination of both methods, a scenario of the process is proposed (fig. 4(b)-(c)) based on the combined effects of SiO 2 BOX etching and wetting/dewetting of the SOI layer. The scenario involves four steps labelled (i) to (iv) that can be observed also by AFM (fig. 4(a)) as time lag is related to the spatial position with respect to the front.

(i) First, a Si finger is formed by SOI dewetting on the SiO 2 BOX layer. This process is well known and arises from surface/interface energy minimization that kinetically destabilizes the receding front [37 and 38]. (ii) The Si finger formation results in the occurrence of a triple line between the freshly exposed SiO 2 BOX layer, the Si finger and vacuum. This contact line is very active for SiO 2 etching compared to SiO 2 dissolution through the SOI layer. Indeed, as shown by [START_REF] Sudoh | Interfacial reaction of Si islands on SiO 2 during high-temperature annealing[END_REF], the limiting mechanism for SiO layer is locally destabilized and this event suddenly generates a free SiO 2 layer that seems to detach and propagate at high velocity (210±10 nm.s -1 ) in the direction opposite to the front.

To understand this process we have performed an ex situ analysis of the surface morphology by AFM. BOX stripes. This analysis of the front dynamics is completed with a quantitative study of the energetics of the process. We show that dewetting and etching reaction are thermally activated with an activation energy respectively of 2.4±0.5 eV and 4.0 ±0.5 eV. To conclude, these results propose a general picture of the dynamics of Si/SiO 2 /Si interfaces at high temperature in the limit of a thin SiO 2 layer (≤ 8 nm). We believe these results may initiate new approaches to fabricate specific structures based on SOI technology [42 and 43] and to prevent SOI dewetting processes by encapsulation approaches.

V. SUPPLEMENTARY MATERIALS

See supplementary materials for the complete movies of the dewetting and reacting processes.

  FIG. 1. (a) Low energy electron microscopy image of the dewetting of a SOI film (∼20 nm thick) at 1160 K. (b) sketch of the dewetting mechanism: a Si finger destabilizes by a lateral undulation

  FIG. 2. (a) Sequence of two LEEM images of a thin SOI layer (30 nm) onto a BOX layer (8 nm) at 1370 K. The SOI dewetting front and the etching front Si/SiO 2 advance in the [100] direction (See Supplemental Material S1 at [URL will be inserted by publisher] for the complete movie). The Si handle wafer is on top of the image and the SOI layer is at the bottom. Dotted circles: SiO 2 layers moving opposite to the dewetting/etching front. The linear defects in the SOI layer (bottom right part of the image) occur due to remaining lateral temperature gradients during annealing. They have no influence on the fronts dynamics. (b) Close view of the area of coexistence of the dewetting front (black arrow) and reaction front (dashed arrow): The exposed SiO 2 layer has a bright contrast with a triangular or elliptical shape. Si fingers are formed in between triangular SiO 2 layers. (c) Same as (a) for an advancing front in the ⟨110⟩ direction.

Figure 2 (

 2 Figure 2(a) shows two LEEM images of the SOI (30 nm)/BOX (8 nm)/Si handle wafer during solid phase etching and dewetting at 1370 K. The SOI layer exhibits a black/white contrast coming from the (1×2)/(2×1) surface reconstructions. The SOI dewetting front appears as an undulating grey line (fig. 2(b)) that separates the SOI layer and the underneath SiO 2 BOX layer (bright contrast). The fronts recede in a steady state at a constant velocity

FIG. 3 .

 3 FIG. 3. (a) LEEM image of a SOI layer (30 nm) onto a BOX layer (8 nm) at 1300 K (See Supplemental Material S2 at [URL will be inserted by publisher] for the complete movie). The SOI dewetting front and the etching front Si/SiO 2 (middle) advance in the [110]. (b) Close view of the fronts: Si fingers onto SiO 2 layer are visible (black arrows) as well as circular holes in the Si layer (black dotted circles) exposing SiO 2 .

  2 etching, figures 2(b) and 3(b) show also very specific structures that highlight a complex interplay between the dynamics of dewetting and etching. This interplay occurs because the timescale for the formation of fingers and 3D islands by dewetting is comparable to the timescale for the consumption of the BOX layer. We will focus on three main structures: (i) SiO 2 BOX layer of elliptic shape located in between two free BOX triangles and separated by Si (dotted ellipse in fig.2(b), at 1370 K). (ii) Elongated free BOX structures crossing the surface from time to time in the direction opposite to the dewetting front (dotted circles in fig.2(a)) with a large velocity (> 100 nm.s -1 ). (iii) SOI islands with a ring shape and exposing a circular BOX layer in the middle (see fig.3(b) at 1300 K). To understand all these structures we will describe in the following part the main stages of their formation and propose different scenarios with coupled etching and dewetting phenomena. B. Coupled dynamics of dewetting and etching a. Steady state elliptic shape BOX structure Figures 2(a)-(b) show LEEM images of a dewetting/reaction front moving along the [100] direction. The regularly spaced triangular BOX structures separate Si fingers that are short and perpendicular to the dewetting front. Some Si fingers are prolonged by BOX elliptic structures (dotted ellipse in fig. 2(b)) that are stable during the steady motion of the fronts (See complete movie S1 at [URL will be inserted by publisher]).

FIG. 4 .

 4 FIG. 4. (a) AFM image of the surface morphology of the front. Si fingers from the SOI layer separated by triangular shape BOX layers are visible. (i) to (iv) address the different steps of Si finger evolution (see scenario in (c)). (b) Scheme of the surface morphology considering elliptic holes (top view). (c) Scenario in four steps of the Si finger evolution: (i) Si finger formed by SOI layer dewetting and simultaneous SiO 2 BOX etching at the contact line. (ii) Complete lateral etching of the SiO 2 layer and contact between the Si finger (from SOI) and the Si handle wafer. Simultaneous lateral progression of the reaction front and Si mass shedding from the center of the finger. (iii) Splitting of the finger into two fingers and occurrence of new etching fronts with the free BOX. (iv) Complete etching of the inner SiO 2 BOX layer and rewetting of the SOI layer onto the Si handle wafer. (i)-(iv) are also sketched on AFM image in (a). (v) Scenario of direct BOX layer encapsulation (without finger splitting).

  2 etching is the diffusion of dissolved O atoms created at the Si/SiO 2 interface. When O atoms reach the Si surface they combine to Si atoms and create volatile SiO ↑ g molecules. The diffusion time is therefore minimized when O atoms are directly formed at the triple line [33, 34, and 39]. The local etching thins locally the SiO 2 BOX layer (∼8 nm) until the Si fingers meet the Si handle wafer. (iii) This has two consequences: (1) thermodynamically the Si finger tends to spread laterally on the Si handle wafer thanks to perfect wetting. (2) Kinetically the newly formed lateral etching front forces the finger to progress laterally. This enlargement of the fingers is visible in LEEM (fig. 3(b)) and AFM images (fig. 4(a)). This forced lateral spreading gives rise to a destabilization of the finger: it splits laterally in two parts with the occurrence of a newly exposed SiO 2 BOX layer in the middle. (iv) This SiO 2 layer is in turn the place for preferential etching at the triple line. When this SiO 2 layer in the middle is completely etched, the two Si fingers meet again and form a flattened structure that encapsulates the remaining SiO 2 BOX layers that are protected against further fast etching. When the splitting in two parts of the Si fingers does not occur, no elliptic SiO 2 layer is formed and another scenario with direct encapsulation of one SiO 2 BOX stripe occurs (see (v) in fig. 4(c)). This last scenario is clearly put in evidence in the unzipping process of Si fingers as detailed in the following. b. Unzipping of Si fingers Figure 5(a) shows a sequence of LEEM images at 1370 K. We can observe a local anomaly at the reaction front edge: the triangular SiO 2 BOX

Fig. 5 (FIG. 5 . 2 FIG

 552 FIG. 5. (a) LEEM image sequence of Si/SiO 2 BOX front at 1370 K. Black dashed circles show the occurrence of a defect at the front that generates the linear propagation of a new front of SiO 2 BOX layer decomposition in the direction opposite to the dewetting front. (b) Scheme of the unzipping scenario of SOI finger with encapsulated SiO 2 . The finger is destabilized at the front side. This event allows for the lateral dewetting of Si and splits the finger into two parts. This process progresses all along the finger over tenth of microns (unzipping process). Simultaneous etching of the newly exposed SiO 2 BOX layer.(c) AFM image (16×10 mum 2 ) showing the morphology of this unzipping process (black dashed areas). Inset: profile of a silicon finger hollowed out in the middle (black line): Si lateral rim, trenches in the the SiO 2 layer at the contact line with Si and flat area of BOX in the middle.

ACKNOWLEDGMENTS

This work has been supported by the ANR grants LOTUS (ANR-13-BS04-0004-02) and HOLOLEEM (ANR-15-CE09-0012)