Anton Pishchagin
email: anton.pishchagin@c2n.upsaclay.fr

Frank Glas
email: frank.glas@c2n.upsaclay.fr

Gilles Patriarche

Andrea Cattoni

Jean-Christophe Harmand

Fabrice Oehler

Dynamics of droplet consumption in vapor-liquid-solid III-V nanowire growth

We study experimentally and theoretically the consumption of the apical gallium droplet that mediates the self-catalyzed vapor-liquid-solid growth of GaP nanowires. Consumption is achieved after growth by providing only phosphorous and its progress is monitored ex situ in nanowire arrays fabricated by molecular beam epitaxy. We develop detailed calculations of the process, taking into account four channels of liquid gallium consumption. These include the formation of GaP using phosphorous delivered to the droplet by direct impingement or after re-emission from the substrate. We show that two other channels contribute significantly, namely the diffusion of phosphorous along the sidewalls and gallium back diffusion from the droplet. All currents are calculated analytically as a function of droplet geometry. Complementary experiments are performed to extract the two model parameters governing the diffusion currents. We then compute numerically the dynamics of the system exposed to a constant external phosphorous flux. Our quantitative model allows one to predict how droplet contact angle and radius change while operating blindly in a standard epitaxy chamber. Controlling these parameters is crucial for tailoring the crystal phase of III-V nanowires and fabricating quantum size structures.

INTRODUCTION

Nanowires (NWs) of III-V semiconductors, with diameters of a few tens of nanometers and lengths up to several micrometers, have remarkable physical properties which open large prospects of original applications. [START_REF] Krogstrup | Single-nanowire solar cells beyond the Shockley-Queisser limit[END_REF][START_REF] Frederiksen | Nanowire-aperture probe: Local enhanced fluorescence detection for the investigation of live cells at the nanoscale[END_REF][START_REF] Saket | Nanoscale electrical analyses of axial-junction GaAsP nanowires for solar cell applications[END_REF][START_REF] Haffouz | Single quantum dot-ina-rod embedded in a photonic nanowire waveguide for telecom band emission[END_REF][START_REF] Motohisa | Fundamental properties of semiconductor nanowires[END_REF] Many of these however require a precise control of the NW geometry. This is for instance the case in devices relying on quantum confinement, which can be obtained by inserting thin disks along the NW axis; in addition, lateral confinement may occur in very thin NWs. [START_REF] Kammhuber | Conductance quantization at zeromagnetic field in InSb nanowires[END_REF][START_REF] Barrigón | Synthesis and applications of III-V nanowires[END_REF] To produce III-V NWs, the vapor-liquid-solid (VLS) method 8 is often used. In this growth mode, the catalyst droplet located at the top of the NW acts as a reservoir of constituents which favors nucleation and feeds the growth of the NW. It also sets the NW diameter, and its composition in the case of alloys. Moreover, the contact angle of the droplet impacts the crystal structure of the NW. [START_REF] Glas | Why does wurtzite form in nanowires of III-V zinc blende semiconductors?[END_REF][START_REF] Jacobsson | Interface dynamics and crystal phase switching in GaAs nanowires[END_REF][START_REF] Panciera | Phase selection in self-catalyzed GaAs nanowires[END_REF] Therefore, controlling the droplet volume and geometry is crucial to obtain NWs with required dimensions and crystal structure.

For GaAs and GaP, with exciton Bohr radii of about 15 and 5 nm, respectively, lateral confinement typically occurs for NW diameters below 10 to 30 nm. This requires droplets with similar sizes. Unfortunately, forming such small droplets on the surface of the growth substrate is challenging. Nevertheless, VLS growth makes it possible to modify the droplet geometry by tuning the growth fluxes. In particular, in order to reduce locally the NW diameter, one can consume partially the droplet during growth. [START_REF] Priante | Stopping and resuming at will the growth of GaAs nanowires[END_REF][START_REF] Kim | Bistability of contact angle and its role in achieving quantum-thin self-assisted GaAs nanowires[END_REF] Self-catalyzed growth [START_REF] Jabeen | Self-catalyzed growth of GaAs nanowires on cleaved Si by molecular beam epitaxy[END_REF][START_REF] Colombo | Ga-assisted catalyst-free growth mechanism of GaAs nanowires by molecular beam epitaxy[END_REF][START_REF] Ramdani | Arsenic pathways in self-catalyzed growth of GaAs nanowires[END_REF][START_REF] Glas | Comparison of modeling strategies for the growth of heterostructures in III-V nanowires[END_REF][START_REF] Dubrovskii | Understanding the vapor-liquid-solid growth and composition of ternary III-V nanowires and nanowire heterostructures[END_REF][START_REF] Dubrovskii | Fundamental properties of semiconductor nanowires[END_REF] is a variant of III-V VLS growth, whereby the catalyst droplet contains only the NW elemental constituents, and actually a very large proportion of the group III species. [START_REF] Glas | Predictive modeling of self-catalyzed III-V nanowire growth[END_REF] It presents several advantages, such as a reduced risk of contamination of the NW by foreign impurities and the possibility to attain a stationary NW radius. [START_REF] Dubrovskii | Fundamental properties of semiconductor nanowires[END_REF][START_REF] Dubrovskii | Self-equilibration of the diameter of Ga-catalyzed GaAs nanowires[END_REF][START_REF] Tersoff | Stable self-catalyzed growth of III-V nanowires[END_REF] The method is particularly suited to control the NW geometry. Since the catalyst droplet contains no foreign atoms, its volume can be reduced at will. It can even be consumed completely in order to inhibit VLS growth in favor of vapor-solid (VS) growth, which is useful to form shells of controlled thickness. Without going to such extremes, the droplet diameter can be reduced to obtain very thin NWs. [START_REF] Kim | Bistability of contact angle and its role in achieving quantum-thin self-assisted GaAs nanowires[END_REF] In practice, the droplet volume is controlled by changing the ratio of the group III and group V fluxes. An excess input of group III inflates the droplet whereas an excess of group V reduces its volume by consuming stored group III atoms to form the III-V solid phase. This may change the droplet contact angle, the droplet radius, or both. There is thus a strong interest in understanding the dynamics of droplet consumption in order to control precisely the geometry and the crystal phase of the NW.

In the present work, we combine experiments and theory to clarify and tailor the mechanisms of droplet consumption. We develop a model which describes the evolution of a Ga catalyst droplet on top of a GaP NW. This model can easily be transposed to other self-catalysed III-V NWs. We consider the usual case of droplet consumption by providing only group V atoms. We deal with low-density NW arrays, where the shadowing by neighboring NWs can be neglected. We establish the mechanisms that empty the droplet and estimate their respective contributions to the consumption process, which are all given in analytical form. This allows us to predict the droplet evolution un-der group V exposure. This understanding of the droplet dynamics is particularly important since direct and real-time observation of these processes is not accessible in standard epitaxy systems; on the other hand, in situ studies do provide such data, but at the expense of a different NW environment. [START_REF] Jacobsson | Interface dynamics and crystal phase switching in GaAs nanowires[END_REF][START_REF] Panciera | Phase selection in self-catalyzed GaAs nanowires[END_REF]

EXPERIMENTS

Preparation of the patterned growth substrates

We prepared patterned growth substrates as follows. A 33 nm thick silica layer was formed on fully deoxidized intrinsic Si(111) wafers by chemical vapor deposition. The hexagonal pattern, which comprised several areas with pitches of 300, 400, 500 nm, 1 and 5 µm, was written in a polymethyl methacrylate (PMMA) mask over the silica. For each pitch, holes with diameters from 30 to 70 nm were then drilled in the silica layer using reactive ion etching by CHF 3 /SF 6 . However, only NWs grown from holes of diameter 50 nm were used in our quantitative analysis. The PMMA resist was removed by using acetone and isopropanol. Finally the silica was cleaned by an oxygen plasma. Immediately before introduction into the growth system, the substrate was etched with 1% HF for 30 s to obtain a completely deoxidized Si(111) surface at the bottom of the holes. The samples were outgassed before growth in a separate chamber at 600 • C and further outgassed in situ at 680 • C.

Nanowire growth

Self-catalyzed GaP nanowires were grown by molecular beam epitaxy (MBE) in a RIBER 32 machine on the patterned substrates, at 600 • C. Ga alone was first deposited for 2 min to form droplets in the holes. Ga and P 2 were then provided simultaneously for 20 min. The Ga flux was equivalent to a 2D growth rate of 0.144 nm s -1 for (100) GaP, as measured by reflection high energy electron diffraction (RHEED). The P 2 flux was adjusted as follows. Using RHEED, we first found the value F 0 corresponding to the transition between group-IIIlimited and group-V-limited growth on (100) GaP, where the effective atomic fluxes of both species are equal, as described previously for GaAs. [START_REF] Ramdani | Arsenic pathways in self-catalyzed growth of GaAs nanowires[END_REF][START_REF] Faktor | New method for III/V flux ratio calibration in MBE systems from arsenic pressure measurements[END_REF][START_REF] Rudolph | Direct observation of noncatalytic growth regime for GaAs nanowires[END_REF] For growth, we adjusted it to 1.3F 0 and kept the same Ga flux. The substrate was rotated (at a rate of 20 to 30 rpm) during growth and droplet consumption.

Droplet consumption

After growth, to consume the catalyst droplet, the Ga flux was abruptly switched off and the sample exposed to P 2 only. The atomic flux of phosphorous was then set to about 2.3 times the flux used during growth, i.e. 1.07 × 10 19 at m -2 s -1 . The experiment was terminated by closing all shutters and valves abruptly and switching off the substrate heater for rapid cooling. The duration of exposure to phosphorous was varied between 1 min and 3 min in order to study the progress of the catalyst droplet consumption. The NW arrays were observed by scanning electron microscopy (SEM) in a FEI Magellan system operated at 10 kV.

Before droplet consumption, our arrays of asgrown NWs are of high quality (Fig. 1(a)). Except for a small fraction (where we find 3D crystallites), all openings are occupied by single vertical NWs, which are slightly reverse-tapered, their radius varying from 40-45 to 55-60 nm from bottom to top (Fig. 1(a)). Table 1 indicates how the geometry of NWs and droplet vary with pitch. Importantly, no significant difference is observed between the largest pitches of 1 and 5 µm.

Figure 1(b) to (f) illustrates the droplet geometry after different times of consumption by exposure to phosphorus. The consumption rate is not the same for all pitches. In arrays with pitches of 500 nm and less, the droplets are consumed more slowly than in arrays with larger pitches. However, as was the case for the NW growth rate, we observed very little difference in consumption rate for pitches of 1 µm and larger (figures are given below). This indicates an influence of neighboring NWs in dense arrays and the absence of interaction in arrays with distant NWs. This can be related to the small inclination angle α = 17 • of the P source with respect to the substrate normal, which restricts shadowing to the close neighborhood of each NW. We will show that a significant amount of phosphorous reaches the droplet after being reemitted from the neighboring surfaces, so that the presence of the NWs close by could have a strong influence on this flux. The impact of the neighboring NWs, which was studied previously in the context of growth, [START_REF] Sibirev | Influence of shadow effect on the growth and shape of InAs nanowires[END_REF][START_REF] Oehler | Measuring and modelling the growth dynamics of self-catalyzed GaP nanowire arrays[END_REF] is out of the scope of the present work. Instead, we focus on large pitches and model a single NW isolated on its substrate.

Pitch (nm)

400 1000 5000

H N W (nm) 680 ± 21 725 ± 20 726 ± 22 R N W (nm) 50 ± 2 58 ± 3 60 ± 2 β ( • ) 138 ± 2 137 ± 2 137 ± 2
Nevertheless, using arrays with a high yield of vertical NWs presents several advantages. It insures that all NWs grow in the same conditions. A NW extracted at random for TEM examination is very likely representative of the ensemble and we are sure that it did not have any neighbor closer than the pitch, as necessary to employ our isolated NW calculations. Anyway, most measurements are performed with NWs still in position, using SEM images where the local environment is readily checked.

The droplet geometry is described by two parameters which may change over time, namely its contact angle β and its base radius. The evolution of the droplet can be divided into three stages corresponding to different regimes of variation of these parameters. Initially, β is around 137 • (Fig. 1(b) and Table 1). During consumption, as long as β remains larger than 90 • , the droplet keeps a base radius equal to the NW radius (Fig. 1(c)). This will be called stage I. Once the contact angle reaches β 90 • (Fig. 1(d)), the NW tapers via the cre-ation of sidewall facets tilted by angle η 47 • (Fig. 1(e)), a value close to that measured in situ by Panciera et al. for GaAs during droplet manipulation [START_REF] Panciera | Phase selection in self-catalyzed GaAs nanowires[END_REF] (this tapering is much more pronounced than during stem growth, and in the opposite direction). The droplet remains pinned to the edge of these facets, so that its base shrinks in a known fashion while the contact angle keeps decreasing (stage II). We did not observe any contact angle below 63 • . This value is close to the Young's angle β Y 65 • for a pure Ga liquid droplet on a GaP (111) surface. [START_REF] Sibirev | Surface energy and crystal structure of nanowhiskers of III-V semiconductor compounds[END_REF] After the droplet adopts the Young's contact angle (stage III), it depins from the tilted facets, its base diameter shrinks further until it finally vanishes (Fig. 1(f)). The tapering of the nanowire top end is clearly visible in Figure 1(e), whereas it is much reduced after complete droplet consumption (Fig. 1(f)). Reduced tapering and flat nanowire top are consistent with a transfer, at stage III, of the Ga of the vanishing droplet to the periphery of the top of the nanowire to form GaP by radial VS growth.

MODEL AND CALCULA-TIONS

Calculations of the various contributions to droplet consumption

To describe the dynamics of the droplet geometry during crystallization, we develop calculations taking into account four possible channels of droplet consumption under exposure to the sole group V species (Fig. 2). Three channels correspond to different currents of phosphorus to the droplet that consume gallium by forming solid GaP. Phosphorus atoms can indeed be delivered to the droplet by direct impingement of the beam (i), or after re-emission from the substrate (ii) or via surface diffusion of adatoms deposited on the substrate or on the sidewalls (iii). This third pathway is usually deemed ineffective for group V elements. Finally, the droplet may shrink due to back diffusion of Ga atoms down the NW sidewalls (channel (iv)).

To calculate the corresponding currents (number of atoms per unit time), we consider an axisymmetric NW isolated on an infinite substrate. The apical droplet is a spherical cap with contact angle β, radius R d and base radius R b = R d sin β and the NW stem a right circular cylinder with radius R N W and height H N W (Fig. 2). As long as the droplet remains pinned to the sidewalls, R b = R N W . The whole system is exposed to a P 2 molecular beam (at angle α), yielding an atomic P flux F e per unit area of substrate.

Direct group V impingement

Re-emission of group V (i) Glas has calculated the direct current I dir to a spherical cap droplet. [START_REF] Glas | Vapor fluxes on the apical droplet during nanowire growth by molecular beam epitaxy[END_REF] It depends on droplet geometry and on beam orientation via a certain function ε(α, β):

β α R d Group III sidewall diffusion R b H NW Group V sidewall diffusion
I dir = πR 2 b F e ε(α, β) (1)
(ii) Several authors have considered that both group III [START_REF] Oehler | Measuring and modelling the growth dynamics of self-catalyzed GaP nanowire arrays[END_REF][START_REF] Rieger | Ga-assisted MBE growth of GaAs nanowires using thin HSQ layer[END_REF][START_REF] Krogstrup | Structural phase control in self-catalyzed growth of GaAs nanowires on silicon (111)[END_REF] and group V species [START_REF] Ramdani | Arsenic pathways in self-catalyzed growth of GaAs nanowires[END_REF][START_REF] Glas | Predictive modeling of self-catalyzed III-V nanowire growth[END_REF] can be transferred to the NW sidewalls and to the droplet by re-emission of atoms initially landed on the substrate or on the neighboring NWs, a process sometimes called secondary adsorption. Ramdani et al. showed that As re-emission can contribute significantly to GaAs NW growth. [START_REF] Ramdani | Arsenic pathways in self-catalyzed growth of GaAs nanowires[END_REF] Here, for our isolated GaP NW, we consider re-emission of phosphorous from the substrate only. The absence of deposit on the mask indicates that all P species that reach it are actually re-emitted.

To calculate I r , we need to specify the a priori unknown angular distribution of re-emission.

We test two hypotheses, already considered for various purposes in the literature, namely Lambertian (cosine) distribution [START_REF] Oehler | Measuring and modelling the growth dynamics of self-catalyzed GaP nanowire arrays[END_REF][START_REF] Dalacu | Selectivearea vapour-liquid-solid growth of InP nanowires[END_REF][START_REF] Gibson | Model of patterned self-assisted nanowire growth[END_REF] and specular reflection. [START_REF] Ramdani | Arsenic pathways in self-catalyzed growth of GaAs nanowires[END_REF][START_REF] Oehler | Measuring and modelling the growth dynamics of self-catalyzed GaP nanowire arrays[END_REF] In the former case, the phosphorous species are re-emitted independently of their incidence angle. In the latter, they are reflected by the substrate at an angle equal to their fixed incidence angle α. These are two extreme cases: specular re-emission corresponds to a purely mechanical interaction with the substrate whereas a Lambertian distribution is expected for molecules having reached equilibrium with it. [START_REF] Wenaas | Equilibrium cosine law and scattering symmetry at the gas-surface interface[END_REF][START_REF] Comsa | Dynamical parameters of desorbing molecules[END_REF] In both cases, we assume that re-emission occurs at the point of incidence, thereby neglecting surface diffusion on the mask.

In the Lambertian case (superscript L), the current re-emitted, per unit area of substrate and unit solid angle, is π -1 F e cos θ. The analytical calculation of the total P current I L r re-emitted to the droplet is given in Supporting information S1. For β ≥ π/2, we derive three analytical approximations:

I L r,i = π 2 F e R 2 d (1 -cos β) 2 -I i (β) (2)
where the I i terms, given by Eqs. (S2.12), (S2. 16), (S2.17) for i = 1, 2, 3, are alternative corrections accounting for a partial blockage of re-emission by the NW stem. These approximations (all more precise than a previous proposal [START_REF] Gibson | Model of patterned self-assisted nanowire growth[END_REF] ) are discussed below. If β ≤ π/2, I L r is given exactly by Eq. ( 2) with I i = 0.

In the specular case (superscript S), reemission is calculated using the method previously applied to the direct current [START_REF] Glas | Vapor fluxes on the apical droplet during nanowire growth by molecular beam epitaxy[END_REF] or as shown in Supporting information S2, which gives: 3 gives the variations of the direct and re-emitted currents calculated in the Lamber-tian and specular cases, as a function of the droplet contact angle β, for the P 2 beam incidence α = 17 • pertaining to our experiments, and for arbitrary incidence α = 45 • , for comparison. For Lambertian re-emission, corrections I 1 and I 2 (Eq. ( 2)) give very close results. This is manifest in the main panel of Fig. 3 but also in the insert, where we compare the absolute values of I 1 and I 2 as a function of contact angle. The closeness of these terms for any beta is very satisfying since, as shown in Supporting information S1, they yield an overestimate and an underestimate of the re-emitted current, respectively. Hence, the real current, which lies in between, is very well approximated by either. For specificity, we shall use I 1 . On the other hand, the insert shows that the correction may amount to more than 10% of the total for contact angles on the order of those encountered at the start of consumption, which makes it necessary.

I S r = F e R 2 d cos α                    β + sin β cos β (1 -2 sin α) -π 2 cos α sin 2 β for β ≥ π 2 ; π 2 -cos β sin 2 α -cos 2 β -sin 2 β cos α arccos (cot α cot β) -arcsin cos β sin α for π 2 -α ≤ β ≤ π 2 (3) with I S r = 0 for β ≤ π/2 -α. Figure
In Figure 4(a-c), the experimental variations over time of several geometrical parameters of the droplet (symbols) are compared to various calculations (lines). The measured droplet contact angle, radius and volume decrease more rapidly than those calculated by including only direct impingement (i) and reemission (ii), whether Lambertian or specular (broken curves). These two currents do not provide enough phosphorous to consume the droplet and the missing amount is significant.

This leads us to consider the two extra channels of Ga consumption mentioned above. The first one (iii) consists in a third P current into the droplet, due to migration up the sidewalls. Whereas NW growth models commonly take into account the surface diffusion of group III atoms, [START_REF] Dubrovskii | Diffusion-induced growth of GaAs nanowhiskers during molecular beam epitaxy: Theory and experiment[END_REF][START_REF] Harmand | Growth kinetics of a single InP 1-x As x nanowire[END_REF] that of the volatile group V species is usually neglected. [START_REF] Priante | Stopping and resuming at will the growth of GaAs nanowires[END_REF][START_REF] Kim | Bistability of contact angle and its role in achieving quantum-thin self-assisted GaAs nanowires[END_REF][START_REF] Ramdani | Arsenic pathways in self-catalyzed growth of GaAs nanowires[END_REF][START_REF] Dubrovskii | Fundamental properties of semiconductor nanowires[END_REF][START_REF] Scarpellini | Ga crystallization dynamics during annealing of self-assisted GaAs nanowires[END_REF] Several authors nevertheless discuss it [START_REF] Rudolph | Direct observation of noncatalytic growth regime for GaAs nanowires[END_REF][START_REF] Bauer | Position controlled self-catalysed growth of GaAs nanowires by molecular beam epitaxy[END_REF] and some even estimated As diffusion lengths up to hundreds of nm at usual growth temperatures. [START_REF] Krogstrup | Advances in the theory of III-V nanowire growth dynamics[END_REF] To obtain the phosphorous diffusion current (iii), we introduce a surface diffusion length λ V and simply assume that all atoms impinging the sidewalls within a distance λ V below the TPL are transferred to the droplet. This implies that H N W > λ V , which also excludes any contribu- tion from diffusion on the substrate. We thus only need to calculate the direct and re-emitted currents collected by the sidewalls.

The direct current is that intercepted by a vertical rectangle of width 2R N W and height λ V , namely I dir = 2F e R N W λ V tan α. In case of specular reflection, the re-emitted current is the same, which gives a total P diffusion current

I S dif = 4F e R N W λ V tan α (4)
For Lambertian re-emission, the calculation (Supporting information S3) is exactly the same as performed previously in the context of NW heating by Glas and Harmand [START_REF] Glas | Calculation of the temperature profile in nanowhiskers growing on a hot substrate[END_REF] and gives

I L dif = F e R N W λ V (2 tan α + π) (5)
The second extra consumption channel, non exclusive of the first one, does not involve phos-phorous, but back diffusion of Ga atoms out of the droplet (iv). To calculate this contribution, we use the transition state approach developed for NW growth by Krogstrup et al. [START_REF] Krogstrup | Advances in the theory of III-V nanowire growth dynamics[END_REF] The net group III current is the difference of the currents entering and leaving the droplet. The former scales with the density of Ga adatoms on the sidewalls, just below the TPL, and depends exponentially on their chemical potential (with respect to the transition state energy). However, due to the lack of external Ga supply during droplet consumption, density and hence chemical potential should be low. We thus consider only the reverse transition liquid → adatom. We show in Supporting information S4 that this back diffusion current can be expressed as:

I bd = 2πR b A(T ) exp µ GT k B T (6)
with µ GT a Gibbs-Thomson correction, to be evaluated at each step of the consumption process.

The droplet also suffers from desorption of its two constituents, with opposite effects on its consumption. However, Supporting information S5 shows that we can safely ignore these pathways in our calculations, at least for the present experiments.

Computation of droplet dynamics

The number dN V /dt = I dir +I r +I dif of P atoms entering the droplet per unit time is obtained from the previous calculations, with I r and I dif calculated either for Lambertian (Eqs. ( 2),( 5)) or specular (Eqs. ( 3),( 4)) re-emission. Assuming that these atoms are all used to form GaP, this consumes the same number of Ga atoms stored in the droplet, which volume thus decreases by dV i = dN V ω L Ga . In addition, dN III /dt = I bd Ga atoms leave the droplet per unit time by back diffusion, which reduces its volume by an extra dV bd = dN III ω L Ga . The droplet volume V d thus obeys equation

dV d dt = dV i dt (β, R b ) + dV bd dt (β, R b ) (7)
where we stress that all currents depend on the instantaneous geometry of the droplet, defined by contact angle β and base radius R b . However, a given decrease of droplet volume may be effected via a change of β or R d , or both, and our model does not prescribe which particular combination of these changes will actually occur. To lift this ambiguity, we use our experimental results which, as described above, allow us to divide the droplet consumption process into three main stages. During stage I, R b remains equal to R N W and V d decreases entirely via a decrease of β. Stage I ends when β reaches about π/2. Then (stage II), the NW starts tapering but the droplet remains pinned to the edge between tilted and top facets; we assume a fixed tapering angle η = 47 • (Fig. 1(e)). During this stage, R b and β both vary. After β reaches the Young's angle β Y , it remains fixed to this value but the droplet depins so that R b shrinks and its volume further decreases until vanishing (stage III). Once this is specified, our recursive procedure allows us to model self-consistently the evolution of the droplet parameters β and R d during consumption, according to Eq. ( 7). This succession of stages is not based only on our ex situ observations and is not specific to GaP. Indeed, Panciera et al., recently investigating the self-catalyzed growth of GaAs NWs by in situ TEM, observed the very same regimes when making the droplet swell or shrink by varying the V/III flux ratio 11 (these experiments were subsequently modelled, without accounting analytically for all pathways considered here [START_REF] Wilson | Modeling the dynamics of interface morphology and crystal phase change in selfcatalyzed GaAs nanowires[END_REF] ). Various ex situ observations had previously showed a tapered section near the top of the NW associated with a group-V-rich regime and a flat top facet after total droplet consumption, [START_REF] Priante | Stopping and resuming at will the growth of GaAs nanowires[END_REF][START_REF] Kim | Bistability of contact angle and its role in achieving quantum-thin self-assisted GaAs nanowires[END_REF]42,[START_REF] Ambrosini | Vapor-liquidsolid and vapor-solid growth of selfcatalyzed GaAs nanowires[END_REF] although others did not detect tapering. [START_REF] Scarpellini | Ga crystallization dynamics during annealing of self-assisted GaAs nanowires[END_REF] On this basis, we solve numerically Eq. ( 7) using the MATLAB environment, with a time step of 0.01 s. At each step k, the four currents contributing to droplet consumption are calculated by using our analytical expressions, evaluated for the instantaneous droplet geometry, defined by parameters β(k), R d (k). The droplet volume V d at step k + 1 is then computed and parameters β(k + 1), R d (k + 1) yielding this volume are selected depending on the current stage of the process (I, II or III), as ) and diffusion (I

L(S)
dif ) currents of P and of Ga back diffusion current (I bd ), calculated under assumptions of Lambertian (d) or specular (e) P re-emission from the substrate. discussed above. This process is repeated until the droplet vanishes (V d = 0). We discuss in Supporting information S6 in which measure these expressions, derived for a droplet pinned at the TPL of a cylindrical NW (as pertains to stage I), can still be used in altered geometries at stages II (NW tapering) and III (droplet depinning).

Determination of the model parameters

Our model includes two unknown parameters, namely the P diffusion length λ V (Eqs. (4), ( 5)) and prefactor A(T ) for Ga back diffusion (Eq. ( 6)). To estimate these parameters, we devised complementary experiments based on the following remarks. During consumption, the Ga atoms lost by the droplet can either generate an axial solid volume V ax by VLS growth, or diffuse to the sidewalls to form a radial volume V rad by VS growth (Fig. 5(g)). Since the droplet is the only source of Ga, V ax should correspond to the total phosphorous current I dir + I r + I dif arriving to the droplet and V rad to the Ga back diffusion current I bd .

We performed specific experiments, at the same temperature, to measure these volumes. To this end, we insert 5 Ga(As,P) marker layers (each grown for 10 s) separated by GaP segments (grown for 50 s) at the end of growth. After the growth of a similar final GaP segment, the droplet is totally consumed by exposing the system to P only. Individual NWs were studied by transmission electron microscopy (TEM) in a FEI Titan microscope operated at 200 kV. We recorded high-angle annular dark field (HAADF) images, where the Ga(As,P) alloy appears brighter than GaP, due to a higher average atomic number. The HAADF images clearly show the markers (Fig. 5(a-c)) but also reveal a 2 -3 nm-thick bright shell below the last marker (Fig. 5(c)), indicative of a small Ga(As,P) radial growth during axial marker growth. These thin lines extend down to the bottom of the NW (Fig. 5(c-e)).

The droplet consumption results in the growth of a top segment with length of about 4 to 4.5 R N W (Fig. 5(b)). Its radius is almost equal to that of the last Ga(As,P) marker (it only diminishes slightly at the very top due to shrinking of droplet base at the end of consumption). This implies that this top segment is grown in the VLS mode, without any significant radial VS growth, and thus corresponds to V ax . In addition, a GaP shell forms. Below the last marker, its inner border is clearly delineated by the thin Ga(As,P) shell formed before consumption. Panels (b) and (c)-(e) in Figure 5 show that the thickness of this outer shell varies from a few nm at the markers level to 13-15 nm at the NW foot. Its formation during droplet consumption (under P only) is confirmed by energy dispersive X-ray (EDX) analysis which clearly shows As-containing vertical traces corresponding to the inner Ga(As,P) shell, while no As is detected in the outer part of the shell (Fig. 5(f)). Note that a back-diffusion of Ga all the way down to the NW foot, i.e. along 1.4 to 1.6 µm, is compatible with estimates of Ga diffusion lengths of several microns during MBE growth of III-V NWs [START_REF] Dubrovskii | Fundamental properties of semiconductor nanowires[END_REF][START_REF] Krogstrup | Advances in the theory of III-V nanowire growth dynamics[END_REF][START_REF] Dubrovskii | Theoretical analysis of the vapor-liquidsolid mechanism of nanowire growth during molecular beam epitaxy[END_REF] but not with the short diffusion lengths reported for GaP NWs. [START_REF] Leshchenko | Tuning the morphology of self-assisted GaP nanowires[END_REF] An analysis of the volumes grown during droplet consumption shows that 96 ± 4% of the initial droplet volume V 0 is transformed into solid GaP. More precisely, we measure V ax = (0.53 ± 0.03) V 0 ω and V rad = (0.44 ± 0.05) V 0 ω (see Supporting Information S7), where ω = ω GaP /ω L Ga accounts for the fact that each Ga atom from the liquid yields a Ga-P pair (of volume ω GaP ) in the solid. Here, V 0 is obtained from the narrowly distributed contact angle β 0 measured on samples removed from the growth chamber immediately after growth, before droplet consumption (Fig. 1(b), Table 1).

Recovering as solid GaP nearly the exact amount of liquid Ga estimated to be present in the droplet before its consumption strengthens our estimate of V 0 . This confirms that no significant loss of Ga occurs during rapid postgrowth cooldown and that β 0 is actually the contact angle at the end of NW growth.

This experiment allows us to measure the value of prefactor A of Eq. ( 6). Namely, for back diffusion to provide the amount of Ga necessary to form volume V rad , we must have A = 6.85 × 10 8 at nm -1 s -1 at 600 • C.

As regards axial growth, neither Lambertian nor specular re-emission, together with the di-rect current, provide enough phosphorous to create the observed volume V ax by VLS growth. The direct and re-emitted P currents consume only 37% and 23% of V 0 (i.e. 70% and 43% of V ax ) in the Lambertian and specular cases, respectively. What remains of V ax has to be formed using phosphorous provided by sidewall diffusion. This requires phosphorous diffusion lengths λ V of 80 nm and 400 nm for Lambertian and specular re-emission, respectively.

The relative values of V ax and V rad must depend on the radius of the NW analyzed. However, parameters λ V and A are expected to depend only on temperature. We can thus now use the values quoted above to model selfconsistently the evolution of the droplet geometry at the same temperature, during the three stages of the consumption process, namely (I)

β ≥ π/2, R b = R N W , (II) β Y ≤ β ≤ π/2, with R N W and

RESULTS AND DISCUS-SION

The full curves in Figure 4(a-c) illustrate the evolution of droplet contact angle, radius and volume with time, when all three phosphorus pathways (direct impingement, re-emission, diffusion) are active, together with Ga back diffusion. It appears that, at variance with the calculations omitting diffusion, these four currents consume the right amount of Ga to account for our experimental data (symbols in Fig. 4(a-c)). During stage I, as prescribed by the experiments and taken as constraints in our calculations, the volume of the droplet can only change via a reduction of the contact angle, and during stage III via a shrinking of its base. At stage II, the droplet behavior is more complex since β and R b vary simultaneously.

It is interesting to analyze the droplet fractions consumed in the different possible ways. Figure 4(d,e) shows the evolution of each current with time during consumption. For large contact angles, at the beginning of consumption, the contributions from the four material pathways are of the same order. With decreasing contact angle, the phosphorous impingement currents (i,ii) diminish (re-emission even vanishes in the specular case), making Ga and P diffusion (which are β-independent except for weak small size effects at very small R b ) the most effective mechanisms for emptying the droplet. During stages II and III, Ga back diffusion diminishes due to the decrease of R b but P diffusion remains constant (see also Supporting information S6). Overall, with either Lambertian or specular reemission, the diffusion of both species accounts for around two thirds (63% and 76%, respectively) of droplet consumption. Ga back diffusion contributes significantly. The corresponding current (Eq. ( 6)) depends only on droplet base radius and temperature, whereas the phosphorous currents (Eqs. ( 1)-( 5)) all scale with external flux F e . Thus, increasing the phosphorous supply will increase the contribution of direct and re-emitted currents. In Figure 4(d,e), the currents are calculated for our already quite high experimental P flux (corresponding planar growth rate is about 0.44 nm s -1 ). Increasing e.g. this flux five times, Ga back diffusion still contributes significantly, for about 15% of the total. On the other hand, an accurate control of droplet geometry requires low consumption rates and, therefore, low phosphorous fluxes. Another option would be to reduce Ga back diffusion, which might be achievable by lowering temperature, but this requires a separate study.

Our model predicts accurately the consumption time needed to obtain a droplet with predefined geometry. Stopping the process at a very small base radius might be tricky however, since R b = R d sin β decreases rapidly when it gets small (Fig. 4, stage III), even though Ga is then mostly consumed via back diffusion (which decreases with R b ). Another difficulty in achieving a given droplet size might stem from the residual group V species that linger in the MBE chamber even after the closure of all valves and shutters. [START_REF] Priante | Abrupt GaP/GaAs interfaces in self-catalyzed nanowires[END_REF] We performed all calculations under two alternative re-emission hypotheses. As seen in Fig. 3, at least for group V beam incidence α below 45 • (which accounts for most MBE setups), specular reflection delivers a much lower current to droplets with large contact angle. Moreover, Lambertian re-emission operates until total consumption of the droplet. However, we cannot state which is the actual scheme, since our experiments can be fitted with both, albeit using very different P diffusion lengths. The value λ V 400 nm found for specular re-emission, about five times the Lambertian value, seems unlikely large. Since the specular re-emission currents depend on the source inclination angle whereas the Lambertian currents do not, performing experiments at different source angles might clarify this question.

CONCLUSIONS

In summary, we developed a model of the consumption of a group III droplet seating on top of a III-V NW when only group V atoms are provided. Our model is based on series of experiments on Ga droplets on top of self-catalyzed GaP NWs, exposed to P. We find that, beside the direct impingement of group V species and their re-emission from the substrate, group V diffusion to the droplet and group III back diffusion from the droplet, along the NW sidewalls, both contribute significantly to the consumption process and we established a general method to measure the parameters governing these two fluxes. We derived analytical expressions for all re-emitted and diffusion currents as a function of instantaneous droplet geometry, which we then used to model the decrease of the droplet volume over time. Our experimental data can only be correctly fitted if the four consumption pathways are included.

Our model allows one to predict the time needed to reduce the droplet to a given geometry, under given group V flux and starting from a known geometry. Controlling the droplet contact angle is key to selecting at will the crystal phase of III-V NWs 11 and fabricating crystal phase heterostructures. [START_REF] Spirkoska | Structural and optical properties of high quality zinc-blende/wurtzite GaAs nanowire heterostructures[END_REF][START_REF] Dick | Crystal phase engineering in single InAs nanowires[END_REF][START_REF] Akopian | Crystal phase quantum dots[END_REF] On the other hand, lateral confinement in radial heterostructures requires tailoring the droplet base radius. While dedicated in situ TEM experiments offer unprecedented opportunities to achieve such control in a single NW, it is highly desirable to attain the same objectives reproducibly and blindly in arrays of identical NWs grown on a crystalline substrate in a standard epitaxy equipment. Our model, which is generic at least for III-V NWs, grants such control, in particular by predicting precise timings for the two extreme stages of consumption, where one of the two geometrical parameters of the droplet (contact angle or base radius) varies while the other remains constant.

Supporting Information Available S1,S2: Calculation of the atomic current reemitted from substrate to droplet, in the cases of Lambertian and specular re-emissions. S3: Calculation of the atomic current re-emitted from substrate to NW sidewalls, in the case of Lambertian re-emission. S4: Calculation of gallium back diffusion. S5: Desorption of P and Ga from the droplet. S6: Using our analytical expressions of the atomic currents in case of NW tapering or droplet depinning. S7: Experiments with marker layers (PDF)

Figure 1 :

 1 Figure 1: SEM images of GaP NWs (from arrays with 1 µm pitch) after various times of droplet consumption. (a) General view of an array. The apical droplet immediately after growth (b) and after being consumed for 1 min (c), 2 min (d) and 2 min 20 s (e). Droplet contact angle β and tapering angle η of terminal section are indicated. (f) An array with totally consumed droplets.

Figure 2 :

 2 Figure 2: Schematics of the material currents contributing to the consumption of a droplet located on top of an isolated III-V NW. Here, R b = R N W .

Figure 3 :

 3 Figure3: Currents of group V species collected by the droplet as a function of its contact angle β: direct contribution (full curves) and re-emission in the specular (dashes) or Lambertian (dash-dots) cases. Direct and specularly re-emitted currents are given for the two incident beam angles α = 17 • (black) and α = 45 • (green). Lambertian re-emission is calculated within approximations (1) (loose dash-dots) and (2) (dense dash-dots). All currents are normalized by sphere section πR 2 d and material source flux F e . Inset: Variation with contact angle β of terms I 1 (Eq. (S2.12) with J 1 = 0, dashes) and I 2 (Eq. (S2.16), dots), which correct Lambertian reemission for stem blockage.

Figure 4 :

 4 Figure 4: (a-c) Variations of droplet contact angle β (a), radius R d (b) and volume V d (c) during droplet consumption. Symbols give the experimental values for pitches of 1 µm (squares) and 5 µm (triangles), averaged over several NWs. The curves show the results of calculations considering only direct impingement and reemission [specular (dashed) or Lambertian (dash-dotted)], or with phosphorous and gallium diffusion in addition (full curve). (d,e) Variations during droplet consumption of direct (I dir ), re-emitted (I L(S) r

Figure 5 :

 5 Figure 5: GaP NWs with Ga(As,P) marker layers inserted before droplet consumption. (a-e) HAADF TEM images. (a) A NW before droplet consumption. The markers appear brighter than GaP. (b) A NW after total droplet consumption. (c-e) Images of the areas indicated by the same letters in (b), showing the formation of a GaP shell along the whole NW. Dashed lines drawn at the left mark the interface between initial NW and shell. (f) Map of group V composition obtained by EDX spectroscopy over area (f) of panel (b), showing markers and the thin As-containing shell parallel to NW axis. (g) Schematics of the evolution of the NW during droplet consumption, resulting in simultaneous axial and radial growth, with markers shown as black lines and inner Ga(As,P) shell shown as red lines.

  R b decreasing according to tapering angle η, and (III) β = β Y , R b decreasing further. From now on, all calculations are carried out using input parameters corresponding to our growth conditions, with R N W = 60 nm.

Table 1 :

 1 Measured morphologies of selfcatalysed GaP NWs grown in arrays with various pitches. H N W : NW height, R N W : top NW radius, β: droplet contact angle.

Acknowledgement This research has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 722176 (INDEED network), from ANR, the French National Research Agency, within project "Engineering spins and photons from anisotropic dots in NWs" (ESPADON, grant ANR-15-CE24-0029-01) and from the French RENATECH network (Réseau français de nanofabrication). The authors also thank Federico Panciera (C2N) for sharing some of his unpublished data.


MS Rebai Soret

Ana-Maria Montes-Solano Msc

MSc Chiara Manzini

PhD Vsevolod Peysakhovich

PhD Eve Floriane Fabre
email: fabreeve@gmail.com

Pushing open the door to reality: On facilitating the transitions from virtual to real environments

Keywords:

The recent rise of virtual reality technology has led researchers to investigate how to adapt transitions to virtual environments. Transitions play a key role in facilitating the return to reality, which is of particular importance when the virtual world is far more agreeable than the real world. In the present study, the efficacy of a door transitionan almost "transparent" door falling out the top of the virtual environment and controlled by the userwas evaluated and compared to two basic transitions: a direct transition and a fading transition. Participants reported a strong preference for the door transition that was evaluated as being smoother, more controllable, and greatly facilitated the return to reality. Moreover, the results showed that the door transition triggered no greater sickness in participants than the two other types of transition.

Introduction

Transitions in virtual environments

The virtual reality technology has demonstrated its utility in countless application fields such as art [START_REF] Cavazza | Intelligent virtual environments for virtual reality art[END_REF], entertainment (e.g., [START_REF] Zyda | From visual simulation to virtual reality to games[END_REF], education [START_REF] Freina | Applied Ergonomics xxx (xxxx) 103535 education: state of the art and perspectives[END_REF], technical training [START_REF] Aoki | Virtual-reality-based 3D navigation training for emergency egress from spacecraft[END_REF][START_REF] Bhagat | A cost-effective interactive 3D virtual reality system applied to military live firing training[END_REF][START_REF] Labedan | Virtual reality for pilot training: study of cardiac activity[END_REF][START_REF] Seymour | Virtual reality training improves operating room performance: results of a randomized, double-blinded study[END_REF][START_REF] Wilson | Virtual environments applications and applied ergonomics[END_REF] or rehabilitation (for a meta-analysis, see [START_REF] Howard | A meta-analysis and systematic literature review of virtual reality rehabilitation programs[END_REF]. As transitions play an important role in the user experience [START_REF] Men | The impact of transitions on user experience in virtual reality[END_REF], the recent rise of virtual reality has led researchers to investigate how to adapt transitions to virtual environments to maximize the users' experience (e.g., [START_REF] Men | The impact of transitions on user experience in virtual reality[END_REF][START_REF] Oberdörfer | Effects of VE transition techniques on presence, illusion of virtual body ownership, efficiency, and naturalness[END_REF][START_REF] Zhang | Evaluating the effect of transitions on the viewing experience for VR video[END_REF]. Different types of transitions have been evaluated: direct/simple cut transitions [START_REF] Men | The impact of transitions on user experience in virtual reality[END_REF]; fading transitions (e.g., [START_REF] Jung | In limbo: the effect of gradual visual transition between real and virtual on virtual body ownership illusion and presence[END_REF][START_REF] Men | The impact of transitions on user experience in virtual reality[END_REF][START_REF] Zhang | Evaluating the effect of transitions on the viewing experience for VR video[END_REF], merging transitions where the virtual world is a replica of the real environment (e.g., [START_REF] Kijima | Transition between virtual environment and workstation environment with projective head mounted display[END_REF][START_REF] Okeda | Toward more believable VR by smooth transition between real and virtual environments via omnidirectional video[END_REF][START_REF] Valkov | Smooth immersion: the benefits of making the transition to virtual environments a continuous process[END_REF] and even vortex or teleportation transitions [START_REF] Men | The impact of transitions on user experience in virtual reality[END_REF]Steinicke et al., 2009aSteinicke et al., , 2009bSteinicke et al., , 2009c)). Some studies focused on how to improve transitions between the scenes of virtual reality movies (e.g., [START_REF] Men | The impact of transitions on user experience in virtual reality[END_REF][START_REF] Zhang | Evaluating the effect of transitions on the viewing experience for VR video[END_REF], while others investigated how transitionsfrom the real to virtual en-vironmentscould improve the sense of presence/immersion/conviction about reality [START_REF] Jung | In limbo: the effect of gradual visual transition between real and virtual on virtual body ownership illusion and presence[END_REF][START_REF] Okeda | Toward more believable VR by smooth transition between real and virtual environments via omnidirectional video[END_REF]Steinicke et al., 2009aSteinicke et al., , 2009c;;[START_REF] Valkov | Smooth immersion: the benefits of making the transition to virtual environments a continuous process[END_REF] or distance estimation (Steinicke et al., 2009b(Steinicke et al., , 2009c) ) in the virtual environment. However, the question of how to adapt the transitions to facilitate the return to reality has received little attention.

Leaving the virtual wonderland and returning to the harsh reality

This question is of particular importance when the virtual world is far more agreeable than the real world. In this case, the return to reality can be difficult for the user and trigger a backlash reaction that can totally dispel the positive effects of a virtual reality session (e.g., stress management session; [START_REF] Anderson | Relaxation with immersive natural scenes presented using virtual reality[END_REF][START_REF] Botella | Psychological countermeasures in manned space missions:"EARTH" system for the Mars-500 project[END_REF][START_REF] Nukarinen | Physiological and psychological restoration in matched real and virtual natural environments[END_REF][START_REF] Stetz | The receptiveness of stress management techniques by military personnel[END_REF][START_REF] Stetz | The effectiveness of technology-enhanced relaxation techniques for military medical warriors[END_REF]. A solution to prevent these drawbacks and maximize the efficiency of virtual reality sessions is to design efficient transitions that ease the come back to reality.

The transition may have specific characteristics to facilitate the return to the real world. First, the transition should be natural to the users. Second, the transition should not be invasive. Third, users should be in control of the transition, enabling them to decide when they are ready to leave the virtual environment. Fourth, the transition should not trigger higher levels of cybersickness in users than preexisting tran-sitions [START_REF] Davis | A systematic review of cybersickness[END_REF][START_REF] Nichols | Health and safety implications of virtual reality: a review of empirical evidence[END_REF]. In everyday life, human beings are used to open and cross doors to transit between different spaces, making the door a natural transition to implement in the virtual world. To limit its invasiveness, this door should appear at the end of the session (instead of being displayed all the time) and be almost transparent to limit the occlusion of the natural environment (i.e., partial occlusion effect; [START_REF] Zhai | The partial-occlusion effect: utilizing semitransparency in 3D human-computer interaction[END_REF]. To maximize their experience, users should be able to actively control 1) the door opening, thus the moment the real environment appears in the virtual scene and 2) the moment and the speed of their return to the real environment by actively crossing the door [START_REF] Gibson | The Ecological Approach to Visual Perception[END_REF][START_REF] Slater | Taking steps: the influence of a walking technique on presence in virtual reality[END_REF].

The present study

In the present study, the efficacy (i.e., facilitation of the return to reality) of the door transition was evaluated and compared to two basic transitions: a direct transition and a fading transition (e.g., [START_REF] Men | The impact of transitions on user experience in virtual reality[END_REF]. The transitions were tested in a stress management environment to ensure that participants' wellbeing in the virtual environment would make their return to reality harder (i.e., natural scenes; [START_REF] Anderson | Relaxation with immersive natural scenes presented using virtual reality[END_REF][START_REF] Botella | Psychological countermeasures in manned space missions:"EARTH" system for the Mars-500 project[END_REF][START_REF] Nukarinen | Physiological and psychological restoration in matched real and virtual natural environments[END_REF][START_REF] Stetz | The receptiveness of stress management techniques by military personnel[END_REF][START_REF] Stetz | The effectiveness of technology-enhanced relaxation techniques for military medical warriors[END_REF]. There were three experimental runs (one per type of transition), in which the transitions were presented at the end of various nature scene videos. The efficacy of the transitions was assessed both subjectively with questionnaires and objectively measuring participants' cardiac activity. At the end of each run, participants had to fill both the French version of the cybersickness questionnaire [START_REF] Bouchard | Revising the factor structure of the simulator sickness questionnaire[END_REF][START_REF] Kennedy | Simulator sickness questionnaire: an enhanced method for quantifying simulator sickness[END_REF][START_REF] Kim | Virtual reality sickness questionnaire (VRSQ): motion sickness measurement index in a virtual reality environment[END_REF]) and a questionnaire designed to subjectively measure to what extent they felt in control, liked the transition, the transition helped them come back to reality, and to evaluate both the speed and the smoothness of the transition. Cardiac activity was found to be a reliable physiological measure of both stress (increased heart rate in reaction to stress; [START_REF] Annerstedt | Inducing physiological stress recovery with sounds of nature in a virtual reality forest-results from a pilot study[END_REF] and cybersickness (increased heart rate in response to sickness; [START_REF] Garcia-Agundez | Identifying cybersickness through heart rate variability alterations[END_REF][START_REF] Nalivaiko | Cybersickness provoked by head-mounted display affects cutaneous vascular tone, heart rate and reaction time[END_REF]. Since the present study aimed, inter alia, at 1) investigating the effect of watching nature scenes in virtual reality on participants' stress and 2) ensuring that the door transition does not trigger higher levels of cybersickness than usual transitions (i.e., direct and fading transitions), measuring participants' heart rate appeared as particularly adapted to the present experimental paradigm. In line with previous studies, we predicted that watching nature scene videos would relax participants and trigger a decrease in heart rate along the experiment [START_REF] Annerstedt | Inducing physiological stress recovery with sounds of nature in a virtual reality forest-results from a pilot study[END_REF]. In the case the door transition is a better solution than both the direct and the fading transitions, we predicted that participants would report that the door was more helpful to come back to reality compared to the other two transitions because they felt more in control of the transition and that the door transition would either trigger lower or comparable levels of cybersickness (cybersickness questionnaire and heart rate) than both the direct and the fading transitions.

Material & methods

Participants

Thirty-four participants (15 females; M age = 23 years old, SD = 2) from the ISAE-SUPAERO University of Toulouse in France participated in the present study. All had a normal or corrected-to-normal vision and reported no history of neurological or psychiatric disorders. They received no financial compensation for their participation in the study.

Ethics statement

The study was conducted in accordance with the Declaration of Helsinki (1973Helsinki ( , revised in 1983) ) and was carried out fulfilling ethical requirements in accordance with the standard procedures of the ISAE-SUPAERO. After being informed of their rights, all participants gave their written consent.

Material

Virtual reality apparatus

We used an HTC Vive Pro Head Mounted Display (HMD) with a resolution of 1440 × 1600 pixels per eye (2880 × 1600 pixels in total), a refresh rate of 90 Hz, and a field of view of 110°. The experiment was developed using the Unity 3D game engine supporting C# programming and the plugins needed for virtual reality (Open VR and Steam VR). A Dell Alienware 17 r4 © was used to support the head-mounted display, create and run the virtual reality environment. Vive SR plugging was used to accurately reproduce the real environment (i.e., stereoscopy and depth) through the use of the cameras placed on the front of the HTC Vive Pro.

Electrocardiography

A 3-electrode 360°eMotion Faros© ECG device was used to measure the cardiac activity of the participants during the experiment. The sam-pling frequency was 500 Hz and the ECG was used in "datalogger mode" and the raw data were stored in the Faros internal storage in European data format (EDF) files.

Transitions

Three different transitions were tested between the virtual environment (i.e., nature videos) and the filmed real environment (filmed by the camera of the HTC Vive device): 1) a direct transition, 2) a fading transition and 3) a door transition (see Fig. 1 and videos in supplementary materials). The direct transition consisted in displaying the filmed real environment directly after the end of the videos. The fading transition consisted in a smooth fading from the virtual environment to the filmed real environment. The door transition consisted in an almost "transparent" door (i.e., 3D modeled object) falling out the top of the virtual environment. Participants were given 10 s to open the door by pulling the trigger of the controller and come through the door before it closes. When the door opened the filmed real environment was displayed inside the door frame. A vortex effect was added to limit the sickness of the participants while crossing the door. After passing through the door, the latter disappeared so participants had to stay in the filmed real environment and could not come back to the virtual environment .

Experimental design

Twelve 360°high-quality (i.e., from 4K to 8K) videos of fixed natural landscapes were selected for the present study. 360°panoramas were particularly adapted to the present experiment as they were found to be a suitable environmental-simulation display associated with the highest sense of presence and the most accurate psychological responses compared to photographs and virtual environments, supposedly because of the deeper emotional response they trigger [START_REF] Higuera-Trujillo | Psychological and physiological human responses to simulated and real environments: a comparison between Photographs, 360 Panoramas, and Virtual Reality[END_REF][START_REF] Riva | Affective interactions using virtual reality: the link between presence and emotions[END_REF]. Each video lasted for 45 s and was accompanied by relaxing music. The 12 videos were presented three times: once in the direct transition run (i.e., direct condition), once in the fading transition run (i.e., fading condition) and once in the door transition run (i.e., door condition). The order of the conditions was counterbalanced between the participants.

Procedure

The present study was conducted in a quiet and almost empty experimental room at ISAE-SUPAERO. After signing the consent form, participants were equipped with three self-adhesive disposable electrodes they were given. After the electrodes were placed, the experimenter helped them plug the ECG device to the electrodes. Then, participants were asked to stand quietly for 2 min while their baseline cardiac activity was measured. After measuring the baseline, the experimenter helped the participants place the HTC Vive device on their head and explained them how to adjust the headset. The experiment started only after the experimenter ensured that the device was properly placed and that the participants felt comfortable.

The virtual environment was composed of one skybox (i.e., sky and background of the virtual environment) displaying 360°videos. Participants were placed in the center of the virtual environment and had a 360°view of the scene (i.e., 3 degrees of freedom). Participants were asked to watch the twelve videos in each of the three experimental conditions. The transition from the virtual environment to the filmed real environment started 30 s after the beginning of the video. For each transition, the volume of the background music was gradually decreased until it became zero when the filmed real environment was displayed. The microphone of the HTC Vive Pro was then used as audio input. In the control condition, the transition to reality was direct; in the fading condition, the transition to reality consisted in a 5-s fading; and in the door condition, participants had 10 s to open a door and cross it to come back to the filmed real environment. At the end of the transition, participants stayed in the filmed real environment for ~5 s. The following video started after a 2-s shutter transition consisting of a black virtual image that gradually fell in front of the virtual camera (the camera used to display the virtual environment to the player via the HMD) until a black screen was obtained. After each experimental run, participants were asked to take off the HTC Vive device and to fill the French version of the cybersickness questionnaire [START_REF] Bouchard | Revising the factor structure of the simulator sickness questionnaire[END_REF][START_REF] Kennedy | Simulator sickness questionnaire: an enhanced method for quantifying simulator sickness[END_REF] to subjectively measure to what extent transitions made participants sick. They were also asked to fill a subjective questionnaire that we created, in which they had to indicate to what extent 1) they felt in control of the transition; 2) the transition helped them come back to reality; 3) they liked the transition; and to evaluate both 4) the speed and 5) the smoothness of the transition.

After filling these two questionnaires, they put the VR headset back on their head and continued with the next experimental condition (i.e., run). After participants went through all three experimental runs, they were asked to fill the French version of the Dissociative Experience Scales (DES; [START_REF] Darves-Bornoz | Validation of a French version of the dissociative experiences scale in a rape-victim population[END_REF][START_REF] Frischholz | The dissociative experiences scale: further replication and validation[END_REF] and the fantasy scale from the Interpersonal Reactivity Index (IRI; [START_REF] Davis | Interpersonal Reactivity Index[END_REF][START_REF] Gilet | Assessing dispositional empathy in adults: a French validation of the Interpersonal Reactivity Index (IRI)[END_REF], two subjective questionnaires measuring the ten-dency to respectively dissociate from reality and fantasizei.e., the latter being defined as the tendency to imaginatively transpose oneself into fictional situations. Afterward, participants were debriefed and thanked for taking part in the experiment.

Results

Post-experimental debriefing

All participants indicated that they enjoyed taking part in the experiment and that watching the videos relaxed them. All indicated that they preferred the door transition to the two other types of transition. They found that coming back to reality was easier with the door transition because they felt more in control compared to the two other types of transition. They also indicated that they liked that the door was almost transparent because it limited the disturbance and facilitated the return to reality. Overall, the VR runs did not trigger cybersickness symptoms in participants, with the exception of five participants who reported feeling a bit dizzy and having some difficulty to focus at the end of the experiment.

Subjective questionnaire

The effects of the type of transition and the runs were investigated for each scale. As the data were not normally distributed (Shapiro tests: p s < .05), a 3 (Transition Type [Direct, Fading, Door]) one-factor Friedman's ANOVA and a 3 (Run [1st run, 2nd run, 3rd run]) one-factor Friedman's ANOVA were conducted on the participants' answers. Wilcoxon signed-rank tests with a Bonferroni-adjusted alpha level of 0.017 (0.05/3 comparisons) were conducted as post-hoc tests (see Fig. The type of transition [X 2 F (2) = 2.00, p = .37] and the run [X 2 F (2) = 5.43, p = .07] main effects did not reach significance.

Smoothness. Participants were asked to indicate "

To what extent did you think the transition was smooth?" from 1 = not at all to 5 = very much. The results showed a significant effect of the transition type [X 2 F (2) = 15.84, p < .001] with the door transition perceived as smoother (M = 3.62, SD = 1.04) than for the fading transition (T = 66.50, z = 2.94, p < .01; M = 2.88, SD = 1.01) and the direct transition (T = 35.00, z = 3.83, p < .001; M = 2.24, SD = 1.16). No significant difference in smoothness between the fading transition and the direct transition was reported by the participants (T = 95.50, z = 2.25, p = .025). The analysis revealed no significant effect of the run [X 2 F (2) = 0.12, p = .94].

Cybersickness questionnaire

The effect of the type of transition and the run was investigated for the mean perceived cybersickness and for each scale independently. As the data were not normally distributed (Shapiro tests: p s < .05), a 3 (Transition Type [Direct, Fading, Door]) one-factor Friedman's ANOVA and a 3 (Run [1st run, 2nd run, 3rd run]) one-factor Friedman's ANOVA were conducted on the participants' answers. Wilcoxon signed-rank tests with a Bonferroni-adjusted alpha level of 0.017 (0.05/3 comparisons) were conducted as post-hoc tests (see Table 1).

Mean perceived cybersickness. The analysis revealed an effect of run [X 2 F (2) = 6.76, p = .034], but Wilcoxon signed-rank tests revealed no significant differences after alpha level correction (first run: M = 0.30; SD = 0.31; second run: M = 0.38; SD = 0.34; third run: M = 0.42; SD = 0.50).

Fatigue. The analysis revealed an effect of run [X 2 F (2) = 10.71, p < .01] with an increased fatigue perceived after the third run (M = 0.56, SD = 0.86) than after the first run (T = 6.00, z = 2.59, p < .01; M = 0.24, SD = 0.61; see Fig. 3). The fatigue perceived after the second run (M = 0.41, SD = 0.70) was not significantly different than the fatigue perceived after the first run (T = 7.50, z = 1.47, p = .14) and the third run (T = 18.00, z = 1.33, p = .18).

Headache. The analysis revealed a significant effect of run [X 2 F (2) = 11.10, p < .01] with a greater headache perceived after the third run (M = 0.53, SD = 0.83) than after the first run (T = 0.00, z = 2.67, p < .01; M = 0.21, SD = 0.59; see Fig. 3). The perceived headache after the second run (M = 0.32, SD = 0.59) was not significantly different than headache perceived after the first run (T = 7.00, z = 1.18, p = .24) and the third run (T = 0.00, z = 2.02, p = .04).

Heart rate analysis

As the data were normally distributed (Shapiro tests: p s > .05), a 4 (Run [Baseline, 1st run, 2nd run, 3rd run]) one-factor ANOVA and a 4 (Transition [Baseline, Direct, Fading, Door]) one-factor ANOVA were conducted on the heart rate measurements. HSD post-hoc tests were conducted. The results showed a significant effect of run [F (3, 99) = 5.56, p < .001, ηp 2 = 0.17] with lower heart rates observed during the third run (M = 80.07 bpm, SD = 11.14, p < .05; see Fig. 4) than during the baseline (M = 83.42 bpm, SD = 14.25) and the first run (M = 83.24 bpm, SD = 12.90, p < .05). The heart rate was also lower during the second run (M = 79.98 bpm, SD = 13.90, p < .05) than during the baseline and the first run (M = 83.24 bpm, SD = 12.90). The heart rates observed during the baseline (M = 83.42 bpm, SD = 14.25) and during the first run (M = 83.24 bpm, SD = 12.90) were not significantly different (p = .99). The heart rates observed during the second run (M = 79.98 bpm, SD = 13.90) and the third run (M = 80.07 bpm, SD = 11.14) were not significantly different either (p = 1.00). The heart rate during the door run was the lowest (M = 79.95 bpm, SD = 13.23) compared to the baseline, the direct transition run (M = 81.97 bpm, SD = 13.24) and the fading transition run (M = 80.15 bpm, SD = 14.24) but the effect of transition type failed to reach significance [F (3, 99) = 2.42, p = .07, ηp 2 = 0.07] .

Correlation analysis 3.5.1. Correlations between the IRI and DES scales and the cybersickness and subjective scales

The analysis of the IRI fantasy scale and the DES results revealed that participants showed some tendencies to fantasize (M = 3.29 [from 1 to 7], SD = 0.71), but not to dissociate from reality (M = 13.45 [from 1 to 100], SD = 11.51). We investigated whether the tendencies to fantasize and to dissociate from reality could be correlated to the results of both the subjective questionnaire and cybersickness questionnaire. We predicted that the tendencies to fantasize and to dissociate from reality may be positively correlated to the difference in control, helpfulness, likeability, and smoothness between 1) the door transition and the fading transition; and 2) the door transition and the direct transition. As we had specific predictions on the results and the data were not normally distributed, we conducted one-tailed Spearman correlation tests. The analysis revealed that the tendency to fantasize was positively correlated to 1) the difference in smoothness rating between the

N C O R R E C T E D P R O O F
door transition and the fading transition (r s = 0.296, p < .05) and 2) the difference in likeability rating between the door transition and the direct transition (r s = 0.301, p < .05; see Table 2).

We also investigated whether the tendencies to fantasize and to dissociate from reality were correlated to the difference in perceived fatigue, the difference in perceived headache and the difference in mean perceived sickness between the third run and the first run. As we had no specific predictions regarding the results and the data were not normally distributed, we conducted two-tailed Spearman correlation tests. The analysis revealed that the tendency to fantasize was not significantly correlated to the difference in perceived fatigue (r s = 0.57, p = .37), the difference in perceived headache (r s = 0.21, p = .11) or the difference in general sickness (r s = -0.53, p = .38) between the third run and the first run. The analysis also revealed that the tendency to dissociate was not significantly correlated to the difference in perceived fatigue (r s = -0.07, p = .35), the difference in perceived headache (r s = -0.04, p = .40) nor the difference in general sickness (r s = 0.04, p = .40) between the third run and the first run.

Correlations between the heart rate and the mean perceived cybersickness

We investigated whether 1) the heart rate was correlated to the mean cybersickness as a function of both the type of transitions and the run; and 2) whether the difference in heart rate between the third run and the first run was correlated to the difference in perceived fatigue, the difference in perceived headache and the difference in mean perceived sickness between the third run and the first run. Based on previous studies, we predicted that the heart rate may be positively correlated to cybersickness symptoms. As we had specific predictions on the results and the data were not normally distributed, we conducted onetailed Spearman correlation tests. The heart rate and the mean cybersickness were not correlated as a function of the transition type (direct: r s = -0.03, p = .43; fading: r s = -0.21, p = .12; door: r s = -0.19, p = .13) or the run (1st run: r s = -0.14, p = .22; 2nd run: r s = -0.09, p = .31; 3rd run: r s = -0.15, p = .20). The difference in mean heart rate between the third and the first runs was not significantly correlated to the difference in perceived fatigue (r s = -0.003, p = .49), the difference in perceived headache (r s = 0.05, p = .40), and the difference in mean perceived sickness (r s = 0.03, p = .44) between the third run and the first run.

Discussion

The relaxing effect of watching natural scenes in virtual reality

During the debriefing, participants declared that they found the natural scene videos relaxing. Moreover, the analysis of the cardiac activity results showed a significant decrease in the heart rate during the runs. Taken together, these results suggest that watching natural scenes in virtual reality lowered participants' stress level, confirming the re- Soret et al. Applied Ergonomics xxx (xxxx) 103535 sults of previous VR studies (e.g., [START_REF] Anderson | Relaxation with immersive natural scenes presented using virtual reality[END_REF][START_REF] Liszio | The Relaxing Effect of Virtual Nature: Immersive Technology Provides Relief in Acute Stress Situations[END_REF][START_REF] Nukarinen | Physiological and psychological restoration in matched real and virtual natural environments[END_REF]. While participants reported greater levels of perceived fatigue and headache at the end of the third run than at the end of the first run, the perceived fatigue, headache and mean cybersickness remained low during the whole experiment (i.e., a maximum of respectively 0.56, 0.53 and 0.42 observed in the third run, on a scale of 0-3). These results show that the present experimental paradigm triggered low levels of cybersickness. No significant correlations between heart rate and perceived fatigue, headache, and mean cybersickness were found as a function of the run, suggesting that participants' cybersickness might have been too low to trigger significant heart rate modulations. While the heart rate was found to be a suitable physiological measure of cybersickness in extreme experimental paradigms (e.g., rollercoaster; [START_REF] Nalivaiko | Cybersickness provoked by head-mounted display affects cutaneous vascular tone, heart rate and reaction time[END_REF], the results of the present study suggest that it may not be the case for experimental paradigms that trigger low levels of cybersickness, such as ours.

U N C O R R E C T E D P R O O F R.

Comparing the door transition to the direct and the fading transitions

All participants indicated, both in the subjective questionnaire (i.e., likeability scale) and the post-experimental debriefing, that they had a strong preference for the door transition. The analysis of the subjective questionnaire results revealed that participants found the door transition smoother and of greater help to come back to filmed reality than both the direct and the fading transitions. The results of the subjective questionnaire also revealed that participants felt more in control of their return to the filmed real environment with the door transition than with the two other types of transitions. During post-experimental debriefing, participants explained that the greater "helpfulness" of the door transition was due to this greater control compared to the two other transitions. They also indicated that they liked that the door was almost transparent (i.e., partial occlusion effect; [START_REF] Zhai | The partial-occlusion effect: utilizing semitransparency in 3D human-computer interaction[END_REF], because it limited the disturbance of the door and facilitated the return to reality. Taken together these results suggest that both limiting the invasiveness of the transition and making the users control the transition facilitated the return to the filmed real environment.

Interestingly, participants' preference for the door transition compared to the direct transition was positively correlated to their tendency to fantasize. The latter was also positively correlated to greater perceived smoothness of the door transition compared to the fading transition. These results suggest that the door transition may be particularly adapted to individuals who tend to imaginatively transpose themselves into fictional situations and therefore might show greater difficulties to come back to reality.

The cybersickness symptoms reported after the door transition run were not significantly different from those reported after the fading transition and the direct transition runs. Consequently, the door transition seems not to have triggered higher levels of cybersickness in participants than the two transitions that are most frequently used in virtual reality [START_REF] Nalivaiko | Cybersickness provoked by head-mounted display affects cutaneous vascular tone, heart rate and reaction time[END_REF]. Taking together these results demonstrate that the door transition might be a suitable solution to facilitate the transition between the virtual and the real environment (i.e., filmed real environment in our case).

Finally, no difference in heart rate was found as a function of the transition type, and no significant correlations between the ratings of the cybersickness questionnaire and the heart rate were found as a function of the transition type. These results once again suggest that the heart rate may not be the most suitable physiological measure of cybersickness in the type of paradigm that was used in the present study.

Limitations and future work

While the results of the present study are encouraging some limitations should nevertheless be acknowledged. We found no correlation between heart rate measurements and the levels of cybersickness reported by participants in the cybersickness questionnaire, either as a function of the run or the transition type. We assume that heart rate measurements may be adapted to assess cybersickness in extreme virtual environments (e.g., rollercoaster; [START_REF] Nalivaiko | Cybersickness provoked by head-mounted display affects cutaneous vascular tone, heart rate and reaction time[END_REF], but not in virtual environments that do not trigger high levels of cybersickness, such as ours. To definitively confirm that the door transition does not trigger more cybersickness than the two other transitions, the present study could be replicated using more sensitive physiological measurements such as galvanic skin responses, electroencephalography (EEG), or electrogastrography (EGG) for instance (for a review, see [START_REF] Rebenitsch | Review on cybersickness in applications and visual displays[END_REF]. Moreover, further research is now necessary to evaluate the efficiency of the door transition 1) on individuals living and working in extreme environments (e.g., battlefields or the International Space Station); and 2) using other types of virtual stress management techniques, like remote social interactions and/or interactions with social virtual agents for instance [START_REF] Wu | Maintaining psycho-social health on the way to Mars and back[END_REF].

Implications for VR design

Participants reported that they liked that the door appeared at the end of the session in a non-invasive way. Consequently, we would recommend limiting the invasiveness of the transition to maximize the user experience in the virtual world. They also reported that being in control of the transition was the main reason why the door transition was the more helpful to come back to reality. Therefore, we would recommend allowing users to control the transition between the virtual and the real environments to facilitate their return to reality.

Fig. 1 .

 1 Fig. 1. Illustration of the door transition (up), the fading transition (middle), and the direct transition (down).

Fig. 2 .

 2 Fig. 2. Illustration of the effects of transition type on the sensation of control, helpfulness, likeability, and smoothness.

  2). Control. Participants were asked to indicate "To what extent did you feel in control of the transition?" from 1 = not at all to 5 = very much. The results showed a significant effect of the transition type [X 2 F (2) = 24.82, p < .001] with a greater control felt for the door transition (M = 3.76, SD = 1.13) than for the fading transition (T = 30.00, z = 3.57, p < .001; M = 2.47, SD = 1.33) and the direct transition (T = 11.00, z = 4.08, p < .001; M = 2.15, SD = 1.28), but not between the fading transition and the direct transition (T = 65.50, z = 1.19, p = .24). The analysis revealed no significant effect of the run [X 2 F (2) = 0.14, p = .93]. Helpfulness. Participants were asked to indicate "To what extent did the transition helped you come back to reality?" from 1 = not at all to 5 = very much. The results showed a significant effect of the transition type [X 2 F (2) = 19.33, p < .001] with a greater helpfulness felt for the door transition (M = 3.65, SD = 0.98) than for the fading transition (T = 68.00, z = 2.91, p < .01; M = 2.88, SD = 1.17) and the direct transition (T = 39.50, z = 3.59, p < .001; M = 2.44, SD = 1.11), but not between the fading transition and the direct transition (T = 81.50, z = 1.96, p = .05). The analysis revealed no significant effect of the run [X 2 F (2) = 1.14, p = .56]. Likeability. Participants were asked to indicate "To what extent did you like this transition?" from 1 = not at all to 5 = very much. The results showed a significant effect of the type of transition [X 2 F (2) = 11.42, p < .01]. Participants liked better the door transition (M = 3.56, SD = 1.28) than the fading transition (T = 41.00, z = 2.78, p = .01; M = 2.74, SD = 1.21) and the direct transition (T = 58.50, z = 3.29, p < .001; M = 2.41, SD = 1.16). No significant difference in likeability between the fading transition and the direct transition was reported by the participants (T = 99.50, z = 1.44, p = .15). The analysis revealed no significant effect of the run [X 2 F (2) = 0.70, p = .71]. Speed. Participants were asked to indicate "To what extent did you think the transition was fast?" from 1 = not at all to 5 = very much. U N C O R R E C T E D P R O O F R. Soret et al. Applied Ergonomics xxx (xxxx) 103535

Fig. 3 .

 3 Fig. 3. Illustration of the effect of run order on fatigue and headache. Error bars represent standard errors.

Fig. 4 .

 4 Fig. 4. Illustration of the heart rate as a function of the run order. Error bars represent standard errors.

U

Table 2

 2 Correlations between the DES, the IRI fantasy scale and the subjective questionnaire.

	DOOR -FADING		Control Helpfulness Likeability Smoothness
	Dissociative Experience Scale IRI fantasy scale	R Spearman p (one-tailed) N R Spearman p (one-tailed) N	-.000 .499 34 .249 .077 34	-.049 .391 34 .236 .089 34	-.0655 .356 34 .272 .060 34	-.188 .143 34 .296* < .05 34
	DOOR -DIRECT		Control Helpfulness Likeability Smoothness
	Dissociative Experience Scale IRI fantasy scale	R Spearman p (one-tailed) N R Spearman p (one-tailed) N	.118 .254 34 .176 .160 34	.060 .367 34 .200 .128 34	.022 .452 34 .301* < .05 34	-.068 .351 34 .255 .072 34
	DOOR -FADING		Control Helpfulness Likeability Smoothness
	Dissociative Experience Scale IRI fantasy scale R R Spearman p (one-tailed) N Spearman p (one-tailed) N	-.000 .499 34 .249 .077 34	-.049 .391 34 .236 .089 34	-.0655 .356 34 .272 .060 34	-.188 .143 34 .296* < .05 34
	DOOR -DIRECT		Control Helpfulness Likeability Smoothness
	Dissociative Experience Scale IRI fantasy scale R R Spearman p (one-tailed) N Spearman p (one-tailed) N	.118 .254 34 .176 .160 34	.060 .367 34 .200 .128 34	.022 .452 34 .301* < .05 34	-.068 .351 34 .255 .072 34

Fullness of head X 2 F (2) = 1.60, p = .21 X 2 F (2) = .91, p = .63

Blurred vision X 2 F (2) = .65, p = .72 X 2 F (2) = 3.14, p = .21 Dizzy eyes open

Dizzy eyes closed X 2 F (2) = 1.14, p = .56 X 2 F (2) = .07, p = .96

Stomach awareness X 2 F (2) = 1.83, p = .40 X 2 F (2) = 1.13, p = .57 Burping X 2 F (2) = .88, p = .65 X 2 F (2) = .50, p = .78

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.apergo.2021.103535.