D S Bechstedt

E Martin

A Barritt

Y Prévôt

Borensztein

C Hogan

O Pulci

P Gori

F Bechstedt

D S Martin
email: david.martin@liverpool.ac.uk

E E Barritt

A Curcella

G Prevot

Y Borensztein
email: yves.borensztein@sorbonne-universite.fr

J Zhao

H Liu

Z Yu

R Quhe

S Zhou

Y Wang

Optical properties of silicene, Si/Ag(111), and Si/Ag(110)

Optical properties of silicene, Si/Ag(111), and

Si/Ag(110)

I. INTRODUCTION

Silicene, the silicon-based counterpart of graphene represents an exciting new material merging the exceptional physical properties of graphene with the simplicity of integrating it in the already existing and largely developed silicon-based technology. 1-5 A field-effect transistor has been reported at room temperature. 6 However, there is also interest in silicene from a basic point of view because it is predicted to be a topological insulator which realises the quantum spin Hall phase effect. 7 Freestanding ideal silicene presents a buckled honeycomb structure (Fig. 1(a)). Like graphene, silicene possesses (in the absence of spin-orbit corrections) massless fermions at the K point of the Brillouin zone. When spinorbit interaction is taken into account a gap as small as 1.5 meV is created. 8 Silicon (in contrast to carbon) is not able to create pure sp 2 hybridization, hence the Si-Si bonds are somewhat intermediate between sp 3 and sp 2 . This means that silicon atoms in silicene are quite reactive. When silicene is deposited on a substrate, interactions between silicon and substrate atoms cause deviations from the ideal geometry of freestanding silicene. Experimental studies and ab initio density functional theory (DFT) calculations have shown that 1 monolayer (ML) of silicon atoms on a Ag(111) surface arranges in an apparently honeycomb structure (see Fig. 1(c)) but with a slight biaxial strain and 3 × 3 periodicity with respect to silicene. [9][10][11][12] It was found to be thermodynamically stable across a wide range of chemical potential in Ref. 11, and recently confirmed experimentally using x-ray diffraction. 13 .

Besides the famous (3 × 3)/(4 × 4) phase epitaxially grown on top of Ag(111), 9 other overlayer structures with √ 13 × √ 13, √ 7 × √ 7, and 2 √ 3 × 2 √ 3 siliceneinduced reconstructions of the Ag(111) surface have been realised by depositing almost 1 ML of silicon onto the silver substrate. [14][15][16] Their atomic geometries have been explored by different techniques (see collections in Refs. 1 and 11). There are also several studies of the occupied electronic states of silicene on different substrates using angle-resolved photoemission spectroscopy (ARPES). 1,9,17,18 Silicon deposition on Ag(110) instead gives rise to regular, ordered, submonolayer quantum wires. 19 Based on scanning tunneling microscopy (STM) and ARPES experiments it was suggested that these (flat) wires could be nanoribbons (NRs) of silicene. [20][21][22] Further studies combining STM, Si coverage measurements and DFT calculations ruled out all honeycomb-shaped models, however. 23 Instead, a pentamer chain model (Fig. 1(d)) was proposed for the nanoribbon structures 24 that satisfies DFT total energy calculations and high-resolution STM, core-level photoemission, and grazing-incidence xray diffraction experiments. 24,25 Further confirmation of a pentamer chain structure has recently been provided by photoelectron spectroscopy (XPS) and angle-resolved photoelectron diffraction (XPD) experiments, 26 as well as non-contact atomic force microscopy (nc-AFM) and tip-enhanced Raman spectroscopy (TERS). 27 Similar to Si/Ag(111), the Si/Ag(110) system thus consists of silicon adlayers strongly bonded to the Ag surface; nonethe-less there is little evidence to suggest that these structures retain any of the electronic features of a silicene-like layer, even when peeled off the substrate. 24 Less effort has been devoted to understanding the optical signatures of silicenelike phases, their general sensitivity to optical probes, and the role the substrate plays in the optical response. Cinquanta et al. 28 investigated the Si/Ag(111) surface using transient-reflectance optical spectroscopy and performed DFT calculations of the dielectric functions for various Si/Ag(111) phases, deducing a strong Si-Ag hybridization and a surprising lack of sensitivity to the interface geometry. Deeper analysis can be provided by surface-sensitive spectroscopies like reflectance anisotropy spectroscopy (RAS) 29 and surface differential reflectivity spectroscopy (SDRS). [START_REF] Chiaradia | Photonic Probes of Surfaces[END_REF] RAS has been successfully applied to the study of quasi-1D metal-semiconductor interfaces [START_REF] Chandola | [END_REF]32 , and should thus be appropriate for investigating the geometry of the highly anisotropic Si/Ag(110) nanoribbon system. Previously, SDRS has been measured by some of us on monolayer Si/Ag(110) 33 and multilayer Si/Ag(111) 34,35 . Comparison with ab initio calculations of freestanding silicene 36,37 found, in both cases, no evidence for silicenelike structures. Freestanding silicene is reported to exhibit a π-π interband peak located near 2 eV and an additional peak around 4 to 5 eV due to a σ-σ transition at the Γ point. A joint theoretical-experimental study of surface optical properties should therefore be a key approach for determining whether silicon layers grown on a silver substrate do in fact possess electronic properties identical or close to those expected for freestanding silicene, as well to differentiate between similar structural geometries.

The paper is structured as follows. In Section II we summarize the theoretical and experimental methodologies. Section III reports our calculated optical spectra for bulk and surface Ag, highlighting some of the problems to be addressed in calculations of this nature. In Sections IV and V we present and discuss experimental data measured on silver-supported silicene-like systems, namely Si nanoribbons on Ag(110) and 2D honeycomb sheets on Ag(111), respectively. These data are compared with ab initio calculations based on previously proposed structural models. Finally, in Section VI we discuss the optical spectra of freestanding silicene, in particular investigating the importance of many body effects on the optical response. The paper concludes with a summary and outlook.

II. METHODOLOGY

A. Surface spectroscopy RAS and SDRS are two experimental techniques that probe the surface contribution to the reflectivity. RAS measures the difference in reflectivity R for two perpendicular polarizations x and y of light in the plane of the surface. The isotropic contribution of the Ag substrate (bulk) cancels out, leaving a signal that is sensitive to anisotropic surface transitions:

∆R R RAS = R x Si/Ag -R y Si/Ag R . (1)
In the case of a Ag(110) substrate, we choose x = [1 10] and y = [001]. Experimentally, the RAS signal is deduced from the relative variation of the complex reflection amplitude r via ∆R/R ≈ 2Re(∆r/r), where R = |r| 2 . SDRS instead measures the difference in reflectivity between a clean surface and the same surface covered by an adsorbate layer. It is thus sensitive to all surface optical transitions (i.e., it can be used to probe Si/Ag(111), whose RAS signal is zero by symmetry); furthermore, it can be performed with polarized or unpolarized light. Thus, for unpolarized light on a Si/Ag interface 38 :

∆R R SDRS = R Si/Ag -R Ag R Ag . (2)
Generalization of this formula for polarized light is straightforward. In order to simplify the analysis of measured and computed RAS and SDRS spectra we make use of a three-layer model. 39,40 In this way, the dielectric response of the semi-infinite system is approximated by (1) a layer of bulk (here, bulk Ag) with complex dielectric function εb = ε b + iε b ; (2) an anisotropic surface layer of thickness d with dielectric tensor εαβ s (where the subscript indicates a Si/Ag interface or the clean Ag surface); and (3) a layer of vacuum. Frequency dependence of all ε terms is understood throughout. We make the approximation that d is unchanged with addition of Si. This allows us to decompose the SDRS and RAS into the real and imaginary parts of pure bulk and pure surface terms:

41 ∆R R RAS = 4ωd c [A • ∆ε SDA -B • ∆ε SDA ], ( 3
) ∆R R SDRS = 4ωd c [A • ∆ε SDD -B • ∆ε SDD ], (4)
where

A = Re 1 εb -1 = ε b -1 (1 -ε b ) 2 + (ε b ) 2 , B = -Im 1 εb -1 = ε b (1 -ε b ) 2 + (ε b ) 2 .
(

) 5
Here we have defined two complex quantities, the surface dielectric anisotropy (SDA) appearing in the RAS:

∆ε SDA = εxx Si/Ag -εyy Si/Ag , (6)
where the subscripts indicate the Si/Ag surface (a similar expression applies to the clean Ag surface), and an analogous term from SDRS that we call the surface dielectric difference (SDD):

∆ε SDD = εSi/Ag -εAg,s , (7)
the last term indicating the clean Ag surface. Possible polarization dependence of the SDD is understood.

B. Experiment

Clean Ag(110) surfaces were prepared in UHV by repeated cycles of sputtering and annealing. Experiments were performed in an ultrahigh vacuum (UHV) environment with a base pressure in the 10 -10 mbar region. Xray photoelectron spectroscopy (XPS) was used to confirm the absence of contaminants and low energy electron diffraction (LEED) was used to monitor atomic order. Si was deposited via an Omicron Focus EFM3 evaporator with the Ag crystal at room temperature, and coverage was determined by a combined analysis of XPS and LEED data. This preparation process results in growth of 0.8nm wide single nanoribbons (SNRs), as confirmed by STM measurements, and is in accordance with previous STM/LEED analysis. 42 Optical access into the UHV chamber was via a lowstrain window. RAS experiments were performed on two different Ag(110) crystals and during Si deposition the same characteristic spectral changes were observed from each crystal. Completion of the first Si ML was confirmed by the changes of slope of the signal recorded at two photon energies as a function of evaporation time, as shown in Fig. 2(a). Optical measurements for double nanoribbons (DNRs), obtained at higher temperature, have been reported elsewhere and the experimental details are given therein. 33 The SDA for Ag(110) and Si/Ag(110) were obtained by combining the real (Re) and imaginary (Im) parts of the measured ∆r/r signal with A and B computed using standard dielectric function data 43 of bulk Ag, and then solving Eq. 3 for ∆R/R ≈ 2Re(∆r/r) and the corresponding equation for Im(∆r/r). As Im(∆r/r) is difficult to measure directly, Kramers-Kronig (KK) transforms of the measured Re(∆r/r) signal were performed. The limited spectral range of the RAS data (generally 1.5 to 5.5 eV) appears to be sufficient to generate an accurate KK transform for Ag(110). This is demonstrated in Fig. 3 where the experimentally measured Re and Im parts of the RAS response of an Ag(110) crystal in air are plotted (solid lines) for two sample temperatures (surface contamination is reduced at 570K). The measured Im part is compared to that calculated (dashed line) from a KK transform of the measured Re part. Here we use RAS data measured on a Ag(110) crystal in air 44 in order to avoid first-order strain effects on the measured Im part that occur under UHV conditions due to the optical access window. 29 As shown in Fig. 3, the shape of the calculated Im profile is in good agreement with the measured Im profile. We thus performed KK transforms on UHVmeasured (Re) RAS data on Ag(110) and Si/Ag(110) (specifically, to obtain the data in Fig. 10).

Deposition of Si on Ag(111) was performed at 515K and 600K. The quality of the surface and of the prepared phases were checked with LEED and with Auger electron spectroscopy. By comparing with previous LEED studies, 45 we estimate that the 515K phase is composed of about 30% (4 × 4) phase and 70% ( √ 13 × √ 13) phase, while the 600K surface is a majority of (2

√ 3×2 √ 3)R30 • .
As above, completion of the first Si ML was determined by the changes of slope of SDRS transients, shown in Fig. 2(b) for the case of Si/Ag(111) grown at 515K. The SDD were described by a sum of several Lorentzian functions for Si/Ag(111), therefore exactly fulfilling the Kramers-Kronig relations, and their parameters were obtained by fitting the experimental SDR spectra using Eq. 4. A complete description of the procedure is given in Ref. 33 for the detailed investigation of the Si/Ag(110) system. In this latter case, only one Lorentzian function was enough to reproduce the experiment.

C. Ab initio theory

Calculations were carried out using DFT in the local density approximation (LDA). 46,47 We use a planewave/norm-conserving pseudopotential framework as implemented in the quantum-ESPRESSO code. 48 Periodically repeated supercells containing symmetric slabs, or 2D layers, separated by vacuum regions were used to simulate the Si/Ag surfaces and silicene layers. We used a kinetic energy cutoff of 40 Ry and the LDA lattice constant of a 0 = 4.075 Å. For Si/Ag(111) we used a symmetric 7 layer slab of 4×4 periodicity (about 20 Å thick). For Si/Ag(110), 3 × 2 (SNRs) and 5 × 2 (DNRs) supercells were used containing slabs of 13 atomic layers (about 19 Å thick).

Optical properties were then calculated at different levels of theory (and corresponding computational effort) for different systems. For the Si/Ag slabs we use the simplest independent particle (IP) approach (equivalently, the RPA level without local field effects) based on the DFT eigenvalues, as implemented in the Yambo code 49 . Within DFT-IP, the imaginary part of the supercell (SC) dielectric function (i.e. slab plus vacuum region) is computed as:

Im [ε SC,αα s ] = 8πe 2 m 2 ω 2 AL k v,c |p α vc (k) + i[V NL , r α ]| 2 ×δ(E c (k) -E v (k) -ω) (8)
where A and L denote the cell area and height, respectively, and E c,v (k) are the DFT Kohn-Sham (KS) single particle eigenvalues. Dense k-point meshes of 12 × 12 × 1 for the Si/Ag(111) (4 × 4) cell and 16 × 32 × 1 for the Si/Ag(110) (3 × 2) cell were found to yield well converged spectra. The transition matrix elements contain the momentum operator p and a commutator term deriving from the nonlocal components of the pseudopotentials, V NL . 50 For Ag, the V NL term can imply a heavy computational penalty, especially for slabs containing many atoms, and is thus often omitted in ab initio calculations. 28 The same formula holds for bulk calculations, with A • L replaced by the volume V of the primitive cell, and was used to calculate ε b for bulk Ag. Surface dielectric functions ε s can be derived from the supercell ε SC s by appropriately accounting for the presence of two equivalent surfaces and renormalizing to d. It holds that:

51 d ∆ε SDA = d (ε xx Si/Ag -εyy Si/Ag ) = L 2 (ε SC,xx Si/Ag -εSC,yy Si/Ag ), (9)
d ∆ε SDD = d (ε Si/Ag -εAg,s ) = L 2 (ε SC Si/Ag -εSC Ag,s ). ( 10
)
Since the surface layer thickness d is not well defined, only quantities like d ε or d ∆ε are accessible from Eqs. 9 and 10, and d ∆ε can be compared with the experimental one.

The DFT-IP scheme has been widely used to compute surface optical spectra of semiconductors, especially when used in conjunction with a simple "scissors" shift to correct the (underestimated) DFT-LDA eigenvalues. This scheme is not easily applicable to metallic systems. Furthermore, many-body effects may be especially important in low dimensional systems. For this reason we calculate the electronic and optical properties of ideal freestanding silicene including many-body effects by following a standard three-step procedure. The first step consists of a DFT calculation of the KS eigenstates and eigenvalues, as before. Secondly, independent quasiparticle (IQP) corrections to the KS states are computed within the GW approximation, [START_REF] Bechstedt | Many-Body Approach to Electronic Excitations[END_REF] where G is the single particle Green's function and W the screened Coulomb interaction. In the final step, the Bethe-Salpeter equation for the optical response is solved which accounts for excitonic and local field effects. [START_REF] Bechstedt | Many-Body Approach to Electronic Excitations[END_REF] The GW calculations were performed in the usual oneshot (G 0 W 0 ) approach, applying a 50 × 50 × 1 (90 × 90 × 1) k-point mesh for the screened (exchange) part of the self-energy and the plasmon-pole approximation for the screening dynamics. 300 bands have been used for the screening. The Coulomb interaction between the sheets of the superlattice was cut. For the BSE calculation, 50 × 50 × 1 k-points, four filled valence and five empty conduction bands were included. The dp4exc code was used 53 .

III. AB INITIO CALCULATIONS OF SILVER

Equations 3-5 show that the RAS and SDRS depend on a delicate interplay between the optical properties of the surface/adlayer and that of the substrate. It has been noted elsewhere 40 that Ag systems present a particularly complicated case due to the forms of A and B, and thus analysis and computation of RAS and SDRS require care. In the following we examine in turn the optical response of bulk and surface Ag.

A. Bulk Ag

Experimental data [START_REF] Palik | Handbook of optical constants of solids[END_REF] for εb is shown in Fig. 4(a). The real part crosses zero close to 3.9 eV, which also marks the onset of interband transitions seen in the imaginary part. The reflectivity R (inset) is sharply peaked at 3.9 eV. The A and B terms, shown in panel (c), are particularly sharp, in contrast to many other semiconductors and metals. 40 Calculations of εb , A, B, and R are shown in Fig. 4(b) and (d). To account for intraband contributions, we add a simple Drude term to the interband part represented by Eq. 8:

εD (ω) = - ω 2 D ω(ω + iη) (11)
where ω D = 9.48 eV is the Drude plasma frequency [START_REF] Marini | [END_REF] and we set η = 0.133 eV. 43 There are considerable discrepancies with respect to the experiment. Firstly, the computed ε b is redshifted by about 1 eV, and overestimates the intensity. The onset of absorption thus occurs at about 3.0 eV, rather than near 3.9 eV where the bulk plasma frequency occurs. The importance of the Drude term is demonstrated in the figure for ε b . The decrease of reflectivity at 3 eV is also less sharp and less deep than the experimental data at 3.9 eV. The inclusion of V NL terms are shown to be critical in the case of bulk Ag, strongly modifying the intensity and lineshape of both ε b and ε b . Last, the A and B terms are 3-4 times weaker than the experimental ones, are redshifted, and lack sharpness. These results are nonetheless typical of what is possible within DFT-LDA. To obtain an improved agreement with experiment, quasiparticle corrections are needed, as demonstrated by GW calculations of the silver reflectance spectrum in Ref. 55. Simple scissors-like corrections are not possible in this case. Hence, all spectra in the rest of this paper will necessarily appear redshifted with respect to experiment by about 0.9 eV. Moreover, the features corresponding to A and B will appear also less sharp in the calculated spectra with respect to the experimental ones.

B. Ag surface

The surface optical spectra of Ag(110) have been thoroughly studied in the past both experimentally [56][57][58] and theoretically using dipolar models 59 and ab initio LMTO methods. 60,61 Here we revisit the RAS calculation in order to demonstrate the level of agreement with experiment for the clean Ag surface expected using our planewave/pseudopotential approach, to demonstrate some important technical approximations, and to illustrate the spectral decomposition in terms of surface and bulk contributions. These technical details are equally relevant for Ag(111).

The in-plane components of the computed dielectric tensor of the Ag(110) slab is shown in Fig. 5(a). As in the bulk case, the V NL term has a huge contribution to the slab ε αα Ag,s and its inclusion is crucial for obtaining the correct amplitude and lineshape. The differences between the xx and yy components are clearly enhanced. Panel (b) shows the corresponding RAS spectra. Following Monachesi et al. 61 we add a Drude term to the bulk ε b via Eq. 11 but not to the surface ε αα Ag,s as it is expected to (mostly) cancel out in the SDA. The RAS spectrum obtained from a full calculation including both V NL and the Drude component is indicated as (1) in the figure. It compares favourably with the spectrum reported by Monachesi et al, except for a small energetic shift.

Omitting the V NL term in the SDA produces curve (2). As expected, the intensity is greatly reduced. However, the overall lineshape is not considerably different from the full spectrum (1). Thus, omission of V NL from the SDA in computing the RAS may be a viable option, due to cancellations occurring in Eq. 3. On the other hand, omission of V NL from the bulk ε b yields a qualitatively incorrect spectrum, as shown by (3). Last, curve (4) demonstrates that inclusion of a Drude term in ε b is crucial for the RAS, and as noted previously, 61 even changes its sign. Clearly, the message here is that ε b must be com- puted to the best extent possible, and that V NL has to be included, at least for the bulk, and preferentially also for the surface.

The computed RAS are now compared with experiment in Fig. 6. In (a), we report data for a 'pure' single terraced Ag(110) surface prepared by repeated annealing to 1000K, and on the standard prepared surface prior to Si deposition. Peak P1, visible in the former data, is a true surface-state transition. As discussed in Ref. 58, peak P2 is associated with sample roughness, and should thus be absent from our computed spectra. All reported spectra in the literature show a sharp peak P3 with magnitude ranging from 0.012 to 0.100, 57,58,62 lying close to the bulk plasma frequency of silver. Thus both P1 and P3 should be accessible to theory.

The calculations in panel (b) reveal that our RAS spectrum using 256 k-points is well converged. Using a thicker slab (17 layers) reveals that the features at 2.4 eV and 3.4 eV are spurious. Thus, we succeed in reproducing well the P1 peak (the optically active states lie close to the Fermi level, and thus experience weak quasiparticle corrections), as well as the main P3 peak. The latter is redshifted by 0.9 eV for reasons discussed earlier, and the intensity is somewhat underestimated. There is also an incorrect feature near 3.8 eV. These discrepancies can be traced back to the poor description of the bulk reflectivity in Fig. 4.

IV.

SILICON NANORIBBONS: Si/Ag(110)

We now extend our study of the optical response of Ag(110) to the Si/Ag(110) nanoribbon (NR) system. As noted in the introduction, several structural models have been proposed, with the best being the pentamer chain model shown in Fig. 1(d) (being the most thermodynamically stable, and in closest overall agreement with experiments). To illustrate optical sensitivity to local geometry, we also consider the zigzag chain model proposed in Ref. 23 and shown in Fig. 1(d). As the NRs constitute a quasi-1D system, we can use both RAS as well as polarization-dependent SDRS to analyse the surface.

Using the same convergence parameters as before for the clean Ag(110) surface, the SDRS (Fig. 7) was computed for both models and for two light polarizations parallel to (x) and perpendicular to (y) the nanoribbon direction. These spectra are compared to previously published SDRS data 33 for the double nanoribbon-covered surface. As in the case of clean Ag(110), the intraband contribution to the SDD is neglected.

The experimental data [Fig. 7(a)] consists of a derivative-like resonance around the bulk plasma frequency of Ag, confirming the substrate origins of the SDRS signal. A slightly broader and larger amplitude profile is observed for the parallel component with respect to the perpendicular one. Our computed SDRS spectra (panels (b) and (c)) yield similar derivative-like lineshapes, with the usual redshift and reduced intensity. We can tentatively distinguish between the two models by considering the polarization dependence. The pentamer chain model, like the experiment, shows a lower intensity for the y polarization across the full spectral range. The opposite occurs for the zigzag chain model. This polarization dependence suggests that RAS should be a more useful technique for studying the Si/Ag(110) system. Fig. 8(a) compares the measured RAS of the clean Ag(110) surface (standard preparation) with the signal obtained after Si deposition until full coverage formation of single nanoribbons. Si deposition induces strong changes in the RAS. The main negative peak is weakened and redshifted by 0.1eV and a broad negative signal appears below it in the 2.4 to 3.7eV range. Furthermore, the spectrum becomes positive above 4eV, so that the overall signal has a derivativelike lineshape. RAS calculations are shown in panel (b) for the pentamer chain (SNR and DNR) and zigzag (SNR only) models. In contrast to the SDRS in Fig. 7, RAS clearly enhances the small structural differences between the two models. The pentamer model reproduces the main features of the experimental RAS. More precisely, it reproduces the redshift of about 0.1eV in the main negative peak and the broad negative tail below it. The change in sign above 3eV is also evident. These features are mostly missing from the zigzag model. It is also notable that the signal for SNR and DNR reconstructions are practically identical, at least below 3.5 eV. Moreover, the agreement with experiment for Si/Ag(110) is overall better than for the clean Ag(110) surface thanks to the removal of the positive peak P2. As explained above, P2 arises from local roughness such as vacancies or step edge defects induced by the ion bombardment procedure used to clean the Ag surface. However, it has been shown that the formation of (double) Si nanoribbons is accompanied by an important reconstruction of the Ag surface whereby two of every five Ag rows are removed. The ejected Ag atoms diffuse on the surface to form new Ag terraces. 63 Such reorganization of surface atoms could therefore "repair" the surface and remove the local defects induced by ion bombardment. The good agreement between the calculated and experimental RAS thus constitutes further evidence for the pentamer chain model of the Si/Ag(110) interface. The changes observed in the RAS signal with addition of Si can be understood by examining the calculated SDA (∆ε SDA ) for the clean and Si-covered surfaces in conjunction with the A and B terms plotted in Fig. 4(d). The SDA, and the SDA multiplied by A and -B, are shown in Fig. 9. Recall that the RAS is related to the sum of the latter quantities via Eq. 3. The ∆ε SDA terms appear relatively broad and featureless in comparison to the sharper A and B terms. For the specific case of Ag substrates, the SDA can therefore be understood as a weighting factor of the A and -B terms in forming the composite RAS signal. In the clean surface, ∆ε SDA is almost zero around 3 eV. Thus the RAS (shown in Fig. 8(b)) is largely dominated by the sharp B term, peaked at 3 eV, weighted by the positive ∆ε SDA . For the Si/Ag(110) surface, both real and imaginary parts of the SDA contribute to the RAS around 3 eV in equal amounts. In particular, the A term now gives rise a negative component (solid line, panel (d)) with a peak at 2.9 eV and a broad tail below this. This explains the small 0.1 eV redshift observed in the RAS upon addition of Si as well as the appearance of the broad tail. The ∆ε SDA term has an opposite sign to that of the clean surface: when multiplied by -B it gives rise to a positive peak at 3 eV. Summing the two components thus gives rise to the derivativelike RAS signal of Si/Ag(110).

Our analysis is supported by experimental extraction of the SDA from the measured RAS following the procedure outlined in Sec. II B. Fig. 10 shows ∆ε SDA for the clean surface annealed to 1000K (corresponding to the RAS in Fig. 6(a), solid curve) and for the 1 ML Si/Ag(110) SNR interface. Data is available only within the range of the measured RAS signal (1.5-5.0 eV). Furthermore, for Si/Ag(110), both the RAS and B terms are close to zero below about 2.4 eV, making inversion of Eq. 3 unreliable. Hence, the extracted SDA signal below 2.4 eV has been omitted from Fig. 10(b). In spite of these restrictions, the experimental SDA show general good agreement with the theoretical data shown in Fig. 9(a) and (b). For the clean surface, ∆ε SDA clearly shows a fea- ture at 1.7 eV that explains the surface state peak P1 in the RAS, as previously noted. 57 In the Si/Ag(110) case, the two components contribute with the same magnitude around the experimental plasma frequency (3.9 eV), in agreement with the theoretical prediction (theoretical plasma frequency equal to 3 eV). Moreover, taking into account the 0.9 eV shift between experiment and theory, the crossing points of ∆ε SDA and ∆ε SDA occur at consistent energies. On the other hand, the intensity at the crossing point differs between theory and experiment, and agreement diverges further at lower energies. There are several possible reasons for these discrepancies. On the theory side, this includes lack of consideration of intraband anisotropy in Ag(110), which can be modified upon formation of Si nanoribbons, as well as omission of many body effects on the lineshape. On the experimental side, the possible presence of anisotropic optical transitions at energies higher than the present energy range could give rise to a positive or negative constant contribution to ∆ε SDA when the KK transform is performed. In spite of these considerations, analysis of the SDA and A and B terms yields a consistent and almost thorough explanation of all features observed in the experimental and theoretical RAS spectra of clean and Si-covered Ag(110).

V. EPITAXIAL SILICENE: Ag(111):Si

We now move to the case of a single 2D silicon sheet adsorbed on Ag(111), which we refer to as "epitaxial silicene" after Vogt et al. 9 SDRS spectra measured for a coverage of 1 ML of silicon are presented in Fig. 11(a) for two different growth temperatures. They are characterized by a single main oscillation around 3.8 eV and are zero below 2 eV. A Lorentzian fit to the 1 ML data, obtained using the procedure described in Sec. II B, matches the data perfectly below 5eV. A half-monolayer spectrum is also reported for growth at 515 K. It exhibits an additional feature at 3.6 eV that is related to the excitation of surface plasmons on Ag due to the roughening of the surface for this coverage.

As noted in Sec. II B, the 515K surface is a mixture of 30% 4 × 4 phase plus 70% √ 13 × √ 13 phase, while the 600K surface is dominated by a 2 √ 3 × 2 √ 3R30 • phase. The similarity between the experimental spectra for different temperatures is reflected in the similarity between the computed dielectric functions for the various phases reported in Cinquanta and coworkers. 28 Thus in computing the SDRS we consider only a single system, the classic (4×4) phase. Its structural model, shown in Fig. 1(c), was proposed by Vogt et al. 9 and found to be stable across a wide range of Si chemical potential. 11 The computed SDRS is shown in Fig. 11(b). Its lineshape and intensity are in reasonable agreement with experiment, although the energy of the negative peak clearly exhibits a redshift of about 0.7 eV. As noted previously, this redshift derives from the neglect of many-body effects and the use of purely interband surface dielectric functions.

These spectra are re-analysed in terms of the surface dielectric difference ∆ε SDD (see Eq. 7) by inverting Eq. 4 in order to remove the influence of the bulk A and B terms following the process detailed in Sec. II B. Results for d • ∆ε SDD are presented in Fig. 12(a) for the two growth temperatures. Both spectra are dominated by a broad peak between 3 and 4 eV, and their similarity again demonstrates that the influence of the actual mixture of silicene phases is weak. The theoretical SDD spectra (real and imaginary parts) for the (4 × 4) epitaxial silicene overlayer are reported in panel (b). They are in good agreement with the experimental curves, both in intensity and position. Also shown in the figure are the imaginary parts of the dielectric functions for the bare silver surface d • ε Ag,s and for the Si/Ag surface d • ε Si/Ag = d(ε Ag,s + ∆ε SDD ). These data demonstrate that the most pronounced peak in d • ∆ε SDD near 3.5 eV is due to the silicene overlayer. Fig. 12(c) and(d) shows the SDD components multiplied by the A and -B terms: their sum explains the final SDRS lineshape shown in Fig. 11.

These analyses demonstrate that the main SDRS spectral features of Si/Ag(111) can once again, like the Si/Ag(110) RAS, be traced back to the Ag(111) substrate via the bulk silver A and B terms (Eq. 5). The negative peak at 3.7 eV in the (experimental) SDRS comes from the negative A peak multiplied by d • ∆ε SDD , whereas the positive peak at 4.1 eV in the SDRS comes from the -B peak multiplied by d • ∆ε SDD (see Eq. 4). It is interesting to note that, while the agreement between theory and experiment is only reasonable for the whole SDRS signal (compare Fig. 11(a) and (b)), and even somewhat poor for the two main components (Fig. 12(c) and (d)), the comparison for the overlayer itself, after removal of the bulk contribution, is excellent (Fig. 12(a) and (b)). In other words, the optical signal of an epitaxial silicene overlayer on a silver substrate can only be deduced by performing a decomposition of the SDRS spectrum in terms of the SDD, as the lineshape of the SDRS is dominated by bulk silver features.

VI. FREESTANDING SILICENE

Finally, we consider the optical properties of silicene itself. Freestanding, honeycomb silicene (Fig. 1(a)) is characterized by a calculated Si-Si distance of a = 2.23 Å, a sheet buckling of ∆ = 0.45 Å, and a Fermi velocity of the electrons of about 0.53×10 6 m/s within DFT-LDA, and 0.65×10 6 m/s after inclusion of quasiparticle effects in the HSE06 approximation. [START_REF] Matthes | Silicene[END_REF] As discussed in the previous section, when grown epitaxially on Ag(111) as a (3 × 3) overlayer the silicon atoms rearrange as a symmetric distribution of flat and outward buckled Si atoms (Fig. 1(c)).

For normal incidence optical properties of an isolated silicene sheet are computed in a similar way as those for surfaces. The 2D objects are simulated by a superlattice arrangement of the silicene sheets. In the limit of independent particles, a formula similar to Eq. 8 de- The inset highlights the extrapolated data from 0-0.12 eV (dots). The spectra are renormalized to the DC optical conductivity σ0 = e 2 /4 .

scribes the optical absorption. Since the thickness L in Eq. 8 has to be identified with the superlattice period, the quantity LIm[ε(ω)] is independent of the lattice constant L of the artificial superlattice. The optical conductivity σ = -iωLε(ω)/4π is, however, a better welldefined quantity to characterize the optical properties of two-dimensional objects. For freestanding silicene, its real part (normalized to the DC quantum optical conductivity σ 0 = e 2 /4 ) is displayed in Fig. 13(a) in three different approximations for the many-body effects characteristic in excited states. The spectral variation for vanishing frequencies ω → 0 are not displayed because of the need of too many k-points in the many-body calculations and the possible appearance of new spectral features of the excitonic insulator phase. [START_REF] Jérome | [END_REF] The k-point sampling is crucial. 37 Too few k-points lead to optical spectra with an artificial fine structure. 66 Since the perturbative treatment of the quasiparticle corrections only influences the energy eigenvalues, the spectrum in the GW-IQP approximation computed starting from the DFT-LDA eigenfunctions and eigenvalues is mainly blueshifted by about 0.8-1.0 eV. The most important peaks related to van Hove singularities at the Γ and M points in the BZ 67 appear at higher photon energies. To include excitonic effects the Bethe-Salpeter equation (BSE) for the optical response function 52 is solved. The included screened Coulomb attraction between excited electrons and holes leads to a spectral redistribution resulting mainly in redshifts of the GW spectra. Quasiparticle and excitonic effects tend to cancel each other in two dimensions. As a consequence the DFT spectrum is widely recovered.

The high-energy peak at about 4 eV is hardly influenced, while the low-energy peak at about 1.5 eV is slightly reduced in intensity. Fig. 13(a) shows that the calculated DFT-IP/RPA optical response of silicene is in qualitative and quantitative agreement with the results obtained in the full threestep procedure. Although excitonic effects are indeed important-as one can deduce by comparing the GW-IQP and the excitonic (GW-BSE) spectra-they eventually cancel out almost completely. This provides partial justification for our neglect of excitonic effects in the surface-adsorbed silicene systems discussed previously.

The effect of the structural modification of a silicene layer by a substrate is illustrated in Fig. 13(b). In addition to the IP spectrum of freestanding silicene, calculated with a denser k-point grid, the figure also displays the corresponding spectrum for "peeled-off" silicene (Fig. 1(b)). This corresponds to the 3×3 silicon overlayer epitaxially grown on a 4×4 Ag(111) surface, but peeled off the substrate such that its atomic geometry is conserved. The lower symmetry with respect to freestanding silicene gives rise to a gap of the order of 0.3eV. 10,11 Our results are in good agreement with previous calculations also performed at the IP level. 28 In this peeled-off silicene layer, the two main peaks discussed above are broadened and reduced in intensity. The main feature around 4 eV thus appears at a slightly higher energy than the peak found in the dielectric function of epitaxially-grown silicene (Fig. 12(b)). Quite dramatic modifications however appear in the lowenergy region. A new double-peaked structure appears, because of the disappearance of the Dirac cones at the K points. The opened gap gives rise to an absorption edge at around 0.3 eV. The situation for ω → 0 is totally different for the freestanding honeycomb silicene. In the latter, due to the linear bands in the Dirac cones at the BZ boundary at K and K the real part of the conductivity exhibits a plateau governed by the Sommerfeld fine structure constant. 37,67 These cones have to be sampled with an unusually dense k-point set. 37 These calculations illustrate how optical spectra yield fingerprints of the presence or destruction of the Dirac cones associated with a pure silicene layer. However, it is important to note that the fingerprints of absorption in the infrared range cannot give conclusive results concerning silicene grown on a silver substrate since the reflectivity of silver is close to 100% in the infrared and almost unchanged with the presence of silicene. 33

VII. SUMMARY AND CONCLUSIONS

We have presented a joint experimental-theoretical study of freestanding silicene and silicenelike phases grown on silver surfaces using optical techniques. First, we have outlined how surface differential reflectance spectroscopy and reflectance anisotropy spectroscopy can be re-interpreted in terms of two quantities, the surface di-electric anisotropy and surface dielectric difference, which yield more direct information about the response of the silicon adlayer. The optical response of bulk Ag and clean Ag(110) were computed at the independent particle level using a DFT-pseudopotential approach. Common approximations and technical difficulties that arise in such calculations were discussed and resolved.

Following this, we presented RAS and SDRS measurements of the Si/Ag(110) nanoribbon system and compared with calculations for two proposed structural models. We found that the pentamer chain model yields results in good agreement with the measured data. This constitutes a further rejection of a hexagonal silicenelike geometry in the Si/Ag(110) system. [23][24][25] In spite of the many structural similarities, the zigzag chain model yielded poor agreement with experiment. RAS was found to be more sensitive than SDRS in this respect. Our analysis also revealed that the RAS and SDRS of Si/Ag(110)-or indeed, of any system with a silver substrate-largely derive from the response of bulk Ag. In order to extract direct information about the interface itself, a decomposition into the SDA or SDD is required. This was further demonstrated for the case of epitaxial silicene in the (3 × 3)/(4 × 4) Ag(111) geometry. In this case, optical absorption occurs at an energy (3.7 eV) close to the peak in the reflectivity of the Ag substrate (3.9 eV), showing that interpretation of optical reflectance measurements must be handled with extreme care.

Finally, we computed the optical spectra of freestanding silicene, with and without many-body corrections.

Such higher order effects are shown to cancel out, suggesting that independent particle calculations are adequate for describing silicenelike systems. When the silicene geometry is deformed following epitaxial growth on a Ag substrate, it becomes semiconducting and the distinct optical signal of the Dirac cones is destroyed. Our results thus provide further confirmation that the optical properties of freestanding silicene are not preserved when deposited on a silver substrate.

In conclusion, we have demonstrated that well-known surface-sensitive optical spectroscopies combined with appropriate ab initio calculations can help to understand the electronic and structural properties of 2D crystals grown on substrates. Our joint theoretical-experimental approach lead to novel results, i.e. clear optical fingerprints of epitaxial silicene in the (3 × 3)/(4 × 4) phase and destruction of its Dirac cones, as well as independent confirmation of the pentamer chain reconstruction of the Si/Ag(110) surface.

We have also presented a detailed theoretical approach for computing and analysing RAS and SDRS of 2D overlayers on substrates. We envisage that this approach can be further developed and applied as a non-invasive means for studying current and emerging nanostructured materials of technological relevance.

  FIG. 1. Geometries of (a) freestanding silicene and (b) silicene peeled off the Ag(111) substrate, where it is grown as (c) epitaxial silicene. (d) Si/Ag(110) single and double nanoribbons: pentamer chain and zigzag chain models. Blue and green balls represent up and down atoms of buckled silicon; grey is silver.

FIG. 2 .

 2 FIG. 2. Variation of the optical signal for two photon energies as a function of evaporation time: (a) RAS spectra of Si/Ag(110) and (b) SDRS spectra of Si/Ag(111). Dashed lines indicate full completion of the Si overlayer.

3 .

 3 Experimental RAS of Ag(110) in air at two temperatures. Plotted are the real and imaginary parts of ∆r/r (measurements) as well as the imaginary part computed using a Kramers-Kronig transform of the measured real part.

FIG. 4 .

 4 FIG. 4. Dielectric function of bulk Ag. Left panels: experiment, right panels: theory. (a) Data from Palik. 54 (b) Full calculations of ε b , ε b . Also shown: ε b without the Drude term (dashed line); ε b , ε b without the V NL term (dotted lines). Panels (c) and (d): A and B terms. Insets: reflectivity.

  . (a) Clean Ag(110) surface dielectric function times d with (upper) and without (lower) the nonlocal commutator term V NL (Eq. 8). Solid blue lines: x = [1 10]. Dashed red lines: y = [001]. (b) Influence of V NL and Drude term (Eq. 11) on the computed RAS. (1) Full calculation, including V NL in εαα Ag,s and εb , and a Drude term in εb . (2) As (1), without V NL in εαα Ag,s . (3) As (1), without V NL in εαα Ag,s and εb . (4) As (3), with no Drude term in εb .

FIG. 6 .

 6 FIG. 6. RAS of clean Ag(110). (a) Experimental data on a high-quality surface annealed at 1000K (solid black line, scaled ×5) and on the present Ag surface before Si deposition (blue dashed line). (b) Calculations for a 13-layer slab using 82, 144, and 256 k-points, as well as for a 17-layer slab with 144 k-points (dotted). The horizontal line indicates the zero of the Y -axis in each case; note the difference in Y -scale between the two panels.

FIG. 7 .FIG. 8 .

 78 FIG. 7. SDRS of Si/Ag(110) for polarization parallel (x = [1 10], dashed black lines) and perpendicular (y = [001], solid red lines) to the nanoribbons. (a) Experiment (DNRs, Ref. 33). (b) Theory: pentamer chain model (DNRs). (c) Zigzag model (SNRs). X and Y scales are the same in each panel.

FIG. 9 .

 9 FIG. 9. Calculated SDA for clean Ag(110) and the Si/Ag(110) single nanoribbon system. Panels (a) and (b): components of d ∆εSDA. Panels (c) and (d): as (a) and (b), but including the A and -B prefactors as they appear in Eq. 3. X-and Y-scales are the same for (a) and (b), and for (c) and (d), respectively.

FIG. 10 .

 10 FIG. 10. Experimental SDA for (a) clean Ag(110) (corresponding to post-anneal data) and (b) with Si nanoribbons deposited at RT. Kramers-Kronig transforms have been used to extract these data (see Sec. II B).

FIG. 11 .

 11 FIG.11. SDRS of Si/Ag(111): (a) Experimental measurements at 515K for 0.5 ML (dashed black line) and 1.0 ML (solid black line ) and at 600K for 1.0 ML (dot-dashed red line). The Lorentzian fit to the 1.0 ML 515K data is superimposed (blue dots). (b) Computed spectrum for the (4 × 4) model (corresponding to 1.0 ML coverage).

FIG. 12 .

 12 FIG. 12. Surface dielectric difference (SDD) spectra of Si/Ag(111). The colour scheme is consistent with Fig. 9. (a) Experimental data at 515K and 600K (imaginary part only, blue dot-dashed line), showing the influence of the growth temperature on the phase purity. (b) Computed SDD spectra for the 4 × 4 structure (solid red and black dashed curves). Also shown are the imaginary parts of the slab dielectric function for the clean (Ag,s: dot-dashed magenta line) and Sicovered surface (Si/Ag: green dots). Panels (c) and (d): as (a) and (b), but including the A and -B prefactors as they appear in Eq. 4. X-and Y-scales are the same for (a) and (b), and for (c) and (d), respectively.

3 FIG. 13 .

 313 FIG.13. Real part of the optical conductivity of a silicene sheet computed at (a) different levels of theory: DFT-IP/RPA (black line); GW-IQP (blue dashed line); GW-BSE (red dashdotted line); and (b) for different geometries, within DFT-IP: freestanding (black line), recalculated using a dense k-point grid; and peeled-off the Ag(111) substrate (red dashed line). The inset highlights the extrapolated data from 0-0.12 eV (dots). The spectra are renormalized to the DC optical conductivity σ0 = e 2 /4 .

ACKNOWLEDGMENTS

CH, OP and PG acknowledge supercomputing support from CINECA through the ISCRA initiative. OP thanks the EU for funding through the HORIZON2020 MSCA RISE "CoExAN" (GA 644076).


Guillaume Loup
email: guillaume.loup@univ-lemans.fr

Sébastien George
email: sebastien.george@univ-lemans.fr

Iza Marfisi
email: iza.marfisi@univ-lemans.fr

Audrey Serna
email: audrey.serna@insa-lyon.fr

A Visual Programming Tool to Design Mixed and Virtual Reality Interactions

Keywords: Mixed and Virtual Reality, immersive interactions, script generator, sharing expertise, game engine, multiplatform

devices are now more accessible. However, developing MVR applications is still complex for the majority of developers, because it requires specific expertise. For the past few years, several packaged solutions offered to assist developers who are non-MVR experts. These solutions rarely offer full freedom to create specific interactions adapted to the context. We therefore propose a new MVR tool named MIREDGE (MIxed and virtual REality Development tool for Game Engine). Its interface allows visual programming of MVR interactions. This solution aims at allowing developers to capitalize, re-use, share and associate interaction algorithms. It also takes into account software and hardware compatibility in order to compose new algorithms. The specific architecture of MIREDGE provides opportunities for MVR and non-MVR developers to collaborate to meet a common need: writing efficient MVR interaction algorithms. MIREDGE Editor was evaluated by 31 MVR and non-MVR developers. Results shows that MIREDGE Editor seems effective and efficient particularly for non-MVR developers.

INTRODUCTION

The general public has lately become particularly interested in Mixed and Virtual Reality (MVR) interactions and several Head Mounted Displays 1 (HMDs) are now available and affordable. However, even though the demand for new applications and games that can be played with these technologies is high, still very few developers have the specific MVR skills [START_REF] Häfner | Teaching Methodology for Virtual Reality Practical Course in Engineering Education[END_REF].

The implementation of a realistic virtual environment remains a complex process for developers. In recent years, the use of tools dedicated exclusively to virtual reality is limited and developers have decided to use mainly video game development environments [START_REF] Trenholme | Computer game engines for developing first-person virtual environments[END_REF]. These environments are reliable and easy to use, with good perfor-mances. They are inexpensive and allow users to create extensions that improve the interface themselves. In many cases, developers also share projects with documentation and source code so that other users can create new content. These game engines make low-cost virtual reality more accessible. Hilfert and König [START_REF] Hilfert | Low-cost virtual reality environment for engineering and construction[END_REF] consider that these game engines are sufficient to allow non-developers creating immersive virtual environments. Despite this, there are still many prerequisites to create an immersive application with interactions adapted to specific user's needs. Even if some game engines allow to develop applications without knowing a programming language, mastering the logic of programming remains essential. Our approach is based on the assumption that a developer, without training in MVR but assisted by a tool based on the knowledge of MVR experts, is able to develop an immersive application adapted to the user's needs.

Although a developer and virtual reality developer may have different skills and various design approaches, their communities are influencing each other and they are beginning to use common tools such as Unity3D [START_REF] Zyda | From visual simulation to virtual reality to games[END_REF]. So, it may be relevant to consider that the same tool could meet the expectations of both communities. One priority of the non-MVR developer community is to simplify the implementation of interactions. Ideally, this simplification makes development more accessible without restricting the range of possibilities. Concerning the community of MVR developers, their priority is to optimize their process of writing interaction algorithms. This optimization should make it possible to write their solution faster, while ensuring reliable and efficient results.

This paper aims at proposing an approach and evaluating a tool -named MIREDGE Editor -to design and code immersive interactions based on algorithms already considered to be efficient. Furthermore, this solution becomes more attractive if its tools are free software and its compatibility with peripherals is important.

In the next section, we will discuss the pros and cons of different existing MVR development solutions. Section 3 describes MIREDGE principles. The evaluation of MIREDGE Editor is detailed in section 4. Finally, the limitations of the tool and its future evaluations are discussed in sections 5 and 6.

RELATED WORK

Today, a large number of tools allow writing MVR interaction algorithms. Some of them are independent environments, while others are dedicated to particular game engines [START_REF] Kreylos | Environment-Independent VR Development[END_REF]. Moreover, some are intended for MVR developers and others for non-MVR developers. In order to understand the variety of existing tools, we proposed to classify them into four categories:

 Development platforms dedicated to MVR  Game engines with MVR manufacturers' libraries  Game engines with middleware  Game engines with assistance tools For each of these categories, we highlight their advantages and disadvantages regarding the following criteria [START_REF] Ritter | Overview and Assessment of Unity Toolkits for Rapid Development of an Educational VR Application[END_REF]:

 Usability: can non-MVR developers easily use the tool?  Script capitalizing: is it possible to capitalize scripts written by MVR developers?  Collaboration: does the tool allow MVR and non-MVR developers to collaborate in order to create scripts? [START_REF] Sowe | Understanding knowledge sharing activities in free/open source software projects: An empirical study[END_REF]  Script re-use: is it possible to re-use scripts written during previous projects?  Devices compatibility: when will the tool be compatible with new devices?  Cost.

Development Platforms Dedicated to Mixed and Virtual Reality

The oldest development platforms fully dedicated to MVR allow programming interactions and staging 3D scenes via a single interface as illustrated in Figure 1. Such platforms were developed 30 years ago, when virtual reality was mainly associated with military, entertainment or education needs.

Pros. The programming interface is often designed to accommodate different levels of expertise. For example, the most popular platforms, Virtools and Eon studio, offer visual programming [START_REF] Yingyan | Design and Implementation of Interactive 3D Scenes Based on Virtools[END_REF]. To give MVR developers more freedom, Virtools also allows them to script their own programming blocks.

Cons. These platforms have a high acquisition cost and are therefore intended for a limited number of specialized developers. Furthermore, it is often necessary to wait or even pay for the platforms to be compatible to new software and hardware devices.

.

Game Engines with MVR Manufacturers' libraries

Ten years ago, only a few game studios had the means to purchase game engines. Today, the new generation of game engines, such as Unity3D and Unreal Engine, are less expensive or even free [START_REF] Eberly | 3D game engine design: a practical approach to real-time computer graphics[END_REF]. These real-time 3D engines have begun to satisfy the general public and have been used to create many popular games on smartphones and game consoles [START_REF] Juul | A Casual Revolution: Reinventing Video Games and Their Players[END_REF]. To facilitate the work of developers, famous manufacturers such as Oculus and HTC Vive offer libraries for these game engines.

Pros. Most of the new libraries are free and allow direct access to the MVR hardware (Figure 2.). The libraries allow interacting with the most popular MVR and common devices (e.g. HoloLens, HTC Vive, Kinect, joystick, mouse). Moreover, manufacturers provide access to low-level information coming from the hardware allowing developers to write custom algorithms.

Cons. The use of these libraries requires to understand specific and technical instructions that are not easy for non-MVR developers. For example, setting the helmets "parallax" or understanding how to find the arm orientation among the data provided by the Kinect (player id, articulation names, angle radiant…).

Game Engines with MVR Middleware

MVR middlewares ensure the transfer of data between a wide range of devices and the final application.

Pros. The main advantage of middlewares is to unify the different exchange protocols required by each device. All the MVR interactions can be implemented uniformly, without direct communication with the drivers (Figure 3). The best example is VRPN (Virtual Reality Peripheral Network) [START_REF] Stelzer | Expanding VRPN to Tasks in Virtual Engineering[END_REF]. This middleware offers a simple and efficient method of sharing device information with useful messages through a server client architecture. Other middleware, such as CaveUDK, also offer high level interface to facilitate the use of complex devices that are not managed by game engines [START_REF] Lugrin | CaveUDK: a VR game engine middleware[END_REF]. MiddleVR [START_REF] Koenig | Introduction to Low-Cost Motion-Tracking for Virtual Rehabilitation[END_REF], associated with Unity3D, also offers an accessible configuration interface. This solution has already been adopted by many MVR developers. Finally, it should be noted that, as independent applications, middleware offers a wide range of compatible devices.

Cons. Manipulation libraries require knowledge of innovative devices that is too complex for non-MVR developers. Furthermore, if developers wish to re-use their interaction algorithms, they have to duplicate them and manually transfer them from one project to another.

Game Engines with MVR Assistance Tools

The term "MVR assistance tool" refers to all the libraries and other tools added to the development environment to simplify development of MVR interactions. Unlike the manufacturers' libraries, these tools offer a higher level of design, closer to the interactions than to the hardware (Figure 4). The Reality-based User Interface System (RUIS) [START_REF] Takala | RUIS: A Toolkit for Developing Virtual Reality Applications with Spatial Interaction[END_REF] has been available for several years and has been the subject of several publications.

Pros. RUIS is cost-free and intended for non-MVR developers. It offers a set of components that are imported directly into the game engine such as Unity3D. These components can easily be added to a 3D scene to configure a set of predefined MVR interactions. It works with several types of devices: position trackers (e.g. Kinect, Razer Hydra, PlayStation Move) and display systems (e.g. Oculus DK2).

Cons. The tools only offer a set of predefined interactions for each device and are not intended to create new custom interactions. Let us note that this classification encompasses the most common tools but not all of them. For example, it does not include MASCARET, a framework design for research [START_REF] Chevaillier | Semantic modeling of Virtual Environments using MASCARET[END_REF]. MASCARET is original in the sense that it allows non-MVR experts to describe MVR interactions based on Unified Modeling Language (UML). The framework also has the specificity of perceiving the avatar of the player and all the virtual object of a scene (e.g. table, cup, pen, paper…) as agents. The purpose of this architecture is to trace the users' activity and not to offer powerful interactions with several devices. We note that most of the tools require knowledge of MVR hardware and are therefore not easy to use for non-MVR developers. Only the MVR assistance tools offer the means to customize some basic MVR interactions. The existing tools also offer very little means of capitalizing and re-using scripts. Only the dedicated platforms offer the possibility of adding new blocks of scripts to a common library which facilitates the re-use of scripts within the community. Finally, all of the existing tools also have one major limitation. When a new MVR device placed on the market, the developers have to wait several months, and sometimes pay, for the tool to be upgraded to the next version or for the manufactures to release a library compatible with their game engine. Considering the high demand for MVR applications using the latest devices, this delay is a real concern for companies.

Hybrid solution

In order to help developers who have no training in MVR, several tools have been designed. These tools are based on the concept of reusability and device abstraction for MVR frameworks [START_REF] Steed | Some useful abstractions for re-usable virtual environment platforms[END_REF]. The interfaces of these tools propose to connect graphical building blocks [START_REF] Tramberend | Avocado: a distributed virtual reality framework[END_REF]. To be compatible with a large number of MVR devices, it is recommended to use a specific development system architecture [START_REF] Blach | A highly flexible virtual reality system[END_REF] with entitycomponent [START_REF] Fischbach | Semantic Entity-Component State Management Techniques to Enhance Software Quality for Multimodal VR-Systems[END_REF].

To combine all of the above features, Figueroa et al. [START_REF] Figueroa | Intml: A dataflow oriented development system for virtual reality applications[END_REF] propose the Interaction Techniques Markup Language (InTml) to facilitate the collaboration of two communities: VR graphic designers and VR developers. VR graphic designers are trained in User Experience and are usually not developers. InTml represents the interaction algorithm as a dataflow, allowing MVR designers to understand the logic of the chosen algorithm. This dataflow is then automatically transformed into C++ or Java scripts and allows VR developers to exploit it in their projects. To describe VR interactions, InTml is hardware-independent, component-based and uses formal models. New components can be created by MVR developer. This type of solution could facilitate fast prototyping [START_REF] Knott | Data-flow oriented software framework for the development of haptic-enabled physics simulations[END_REF].

The limit with InTml, is that its dataflow representation is intended for VR graphic designers, who are not developers. The representation is therefore very simplified because VR graphic designers have neither the ability nor the need to program the interaction. This tool is therefore not suited for developers, who need to compose their own interaction algorithm. To meet this need, new interfaces, such as Blueprints [START_REF] Sewell | Blueprints Visual Scripting for Unreal Engine[END_REF], let non-VR experts program interactions with dataflow. However, these interfaces are limited to a single development environment and to a small number of devices.

MIREDGE APPROACH

As we have discussed above, none of the existing tools meet the needs of the non-MVR developers, such as usability, re-use, capitalization and cost-free. Therefore, we propose a hybrid solution including the advantages of each kind of tool.

System description

Based on the concept of interaction modeling in a virtual environment [START_REF] Pellens | Conceptual modelling of behaviour in a virtual environment[END_REF] and on the above-mentioned solutions, we propose MIREDGE, a MIxed and virtual REality DEvelopment tool for Game Engines (Figure 5). The main goal of this tool is to allow MVR and non-MVR developers to re-use interaction algorithms available in a library, to visually program new ones, and generate the corresponding script for the chosen game engine.

Capitalizing, Sharing and Evolution: a Community based Tool

A new tool providing the source code is more attractive for a developer community. A virtual reality platform, named OSVR, demonstrated that open source could enable collaboration between communities as diverse as academia and industry [START_REF] Boger | OSVR: An open-source virtual reality platform for both industry and academia[END_REF]. Consequently, MIREDGE is open-source to offer transparency and freedom.

One of the main limitations of the existing MVR tools, described in the first part of this paper, is the fact that they are only compatible with a limited number of MVR devices. As shown in Figure 6. MIREDGE offers the possibility for MVR developers to create new components for the algorithms as soon as new devices are released with the MIREDGE Creator tool. These new components can be rated by other developers to offer a guarantee of reliability [START_REF] Plonka | Knowledge transfer in pair programming: An in-depth analysis[END_REF], and integrated to the other blocks in the MIREDGE Library. Manufacturers of new technologies can also create new blocks to facilitate the use of their devices.

3.3

Ease of use: visual programming MIREDGE Editor allows non-MVR experts to write MVR algorithms by creating visual flowcharts of blocks [START_REF] Myers | Taxonomies of visual programming and program visualization[END_REF] (Figure 7.). Despite the simplistic aspect of these blocks, this kind of interface is adapted to developers' logic and allows writing a large number of algorithms [START_REF] Resnick | Scratch: Programming for All[END_REF]. Each method is represented by a block containing a text and an icon. There are three block categories:

 The first category of blocks (blue blocks) are specific methods for interacting with MVR devices. These methods are used to transmit execution commands to devices and to collect information about their properties, such as the vertical nodding Oculus detection block.  The second category (yellow blocks) are logical elements. These allow developers to add conditions as well as repetitions, such as IF or WHILE blocks. This category is essential to allow the creation of custom algorithms while remaining simple for non-MVR developers.  The third category (green blocks) allows developers to refer to variables, classes and methods that already exist in the scripts of the project.

The developers can connect these blocks with two types of links. The first type of links (pink arrows) defines the order in which the block will be executed. The second type of link (yellow arrows) allows to transmit variables from the output of one block to the input of another block. For example, in Figure 8, the algorithm defines that, when fingers are detected by the LeapMotion device, the Answer method of QuizzManager script within the game engine project will be called. To manage the LeapMotion device, a blue block had to be placed in the initialization sequence. To manage the detection, a blue block is placed in the continuous sequence. This block has two output parameters, one boolean determining if the detection is correct, another indicating the number of fingers detected. Thus the link with the yellow condition block allows to filter according to the quality of the detection status. Finally, the green block represents a specific method from one of the existing scripts of the game engine project.

A generic script translator

Once the developers have designed their MVR interactions with blocks in MIREDGE Editor, they are translated into source code [START_REF] Biernacki | Clock-directed modular code generation for synchronous data-flow languages[END_REF]. For example, if the developers are using Unity3D, MIREDGE converts the dataflow to Javascript and C# code. The generated scripts are automatically sent to the project chosen by the developer and linked with others resources. The developer can then modify these scripts in their development environment. This feature also has a pedagogical value. Indeed, it gives the non-MVR experts the possibility to read the generated code thanks to the comments.

MVR is an area in which devices, languages and game engines appear every year. It therefore offers a solution that can adapt to this constant renewal of technology. In order to transform the graphical entities into lines of code for different game engines, we consider the algorithms produced under MIREDGE as models. Moreover, all these models are derived from the meta-model presented in Figure 9. The main rule is that each graphic block is mapped to different sets of code lines. These lines allow users to declare or use libraries, methods or variables. They can be attached to one or more devices. There may be variations of the same block in different languages and for different engines.

EVALUATION OF MIREDGE EDITOR: AN EXPLORATORY STUDY

Objective

The study described here aims at evaluating the effectiveness and efficiency of MIREDGE Editor (i.e. the part of MIREDGE the most used by the two communities), both for MVR and non-MVR expert developers. We wanted to verify that non-MVR experts would be able to use MIREDGE Editor easily and develop the required interactions in the allotted time. We also wanted to ensure that MVR experts would not be inconvenienced by MIREDGE Editor and would be inclined to contribute to the community-based features that we wish to promote.

Participants

We asked a panel of developers to add several MVR interactions in an existing project with MIREDGE Editor. The first group of fifteen participants (aged from 21 to 27, mean=22, SD=1.5), qualified as the non-MVR expert group, trained to develop serious games but without MVR interactions. The second group consisted of sixteen other participants (aged from 21 to 27, mean=24, SD=1.8) trained to develop MVR applications, qualified as the MVR expert group. The participants came from two backgrounds: the 15 non-MVR participants were in bachelor of serious games, and the 16 MVR participants were in master of virtual reality. In each background, students were selected by the pedagogical supervisor based on their programming grades (i.e. students with the highest grades participated in the study).

Participants of both groups were evenly distributed in the two following experimental conditions:  With MIREDGE Editor: the developers used MIREDGE Editor to implement the required interactions and export them to Unity3D (eight non-MVR experts and eight MVR experts)  Without MIREDGE Editor: the developers used the Unity3D game engine and existing libraries to implement the required interactions (seven non-MVR experts and eight MVR experts). We choose this game engine because it is currently the most used in the game industry and it is the tool that the MVR experts where trained on.

Equipment and measures

Each participant had a PC with Unity v5 and access to Internet. Two MVR devices were available: the head mounted display Oculus Rift DK2, and the Leap Motion controller. This combination offers very specific interactions [START_REF] Hilfert | Low-cost virtual reality environment for engineering and construction[END_REF]. The device drivers were already installed, and the SDK included in the Unity project.

We measured efficiency and effectiveness using indicators from digital tracks. After completing the task, participants had to list positive feedback and negative feedback (i.e. areas for improvement) regarding MIREDGE Editor.

Tasks

Figure 10. Capture of the interface related to task 1

The participants had one hour to implement three MVR interactions for an existing project. We explicitly asked them to implement each interaction one after the other because the tasks were increasingly difficult. The existing project consists of a scene where the player is surrounded by four avatars. Each avatar has a series of questions to ask the player (Figure 10). We asked the developers to implement three MVR interactions for the player to interact with these avatars:  The first interaction to implement is answering yes or no by shaking the head. This interaction uses the gyroscope of the head mounted display and parameters such as the duration and magnitude of the movements.  The second interaction to implement allows the players to choose one proposition out of four by holding up the corresponding number of fingers. This interaction uses the Leap Motion controller and parameters related to the duration and the inclination of the fingers.  The last interaction to implement allows the players to change interlocutor by simply facing another avatar and pointing it with their finger. This interaction uses a combination of data coming from the HMD and the Leap Motion.

Developers without MIREDGE Editor had a library containing methods for detecting head and finger movements. Their final production was a script directly written in C # in MonoDevelop editor. Likewise, developers using MIDEGE Editor had access to blocks corresponding to each of the methods of this library. In the MIREDGE Editor workspace, they had to connect the available blocks to define sequences. Finally, they had to launch the script generation procedure that directly sent the result to Unity. All the participants could test their script as soon as they wanted in order to make the necessary modifications.

Data analysis

This exploratory study included only 31 participants, and involved appropriate statistics. For categorical variables (e.g. effectiveness measured by successful/unsuccessful task completion [START_REF] Loup-Escande | Effects of Stereoscopic Display on Learning and User Experience in an Educational Virtual Environment[END_REF]), we used Cramer's V2 to estimate the magnitude of the association between two categorical variables [START_REF] Cramér | Mathematical Methods of Statistics (PMS-9)[END_REF]). For numerical variables (e.g. efficiency measured by duration), we used descriptive statistics (i.e. mean, SD, min, max).

Results

Before the experimentation, an inspection of the tool was carried out by an ergonomic expert. It consisted in "reviewing MIREDGE Editor's interface to verify that it meets a set of ergonomic criteria" [START_REF] Nogier | Ergonomie du logiciel et design web -4e éd[END_REF] [START_REF] Baccino | Mesure de l'utilisabilité des Interfaces[END_REF]. The recommendations helped us improve MIREDGE Editor before the main experimentation. To comply with this protocol and adapt to the availability of users and equipment, it was necessary to conduct all the experiments during only one week. Despite these constraints, no problems have been encountered and all the data generated by the participants could be taken into account in this results of effectiveness and efficiency.

Effectiveness

Our main indicator for measuring effectiveness is the percentage of successfully accomplished tasks (i.e. implementation of three MVR interactions). Table 2 shows the number of users who were able to complete zero, one, two or all three of the tasks for each group. We observe that none of the tasks were either too easy or too difficult because they were all be completed by at least one person and never by everyone for each experimental group (MVR experts/non-experts combined with/without MIREDGE Editor). In order to determine if the use of MIREDGE Editor significantly helped the developers to accomplish their tasks, we used the Cramer's V2 rate 2 . The calculations give a score of 0.14, which shows an intermediate association between the experimental group and the number of tasks performed by participants. In addition, we calculated the Relative Deviation 3 (RD), that measures the association between modalities of two variables (e.g. MVR experts without MIREDGE Editor for 1 performed task) [START_REF] Knott | Data-flow oriented software framework for the development of haptic-enabled physics simulations[END_REF]. As depicted in Figure 11, it reveals positive attractions between: 2 Cramer's V2 estimates the magnitude of the association between two categorical variables [START_REF] Cramér | Mathematical Methods of Statistics (PMS-9)[END_REF]. It is calculated by dividing phi2 by phi2 max. Phi2 is the average deviation in the table, while Phi2 max is the smallest dimension in the table minus 1. Cramer's V2 lies between 0 and 1. The association is conventionally considered as strong when V2 > 0.16, as weak when V2 < 0.04, and as intermediate between the two scores [START_REF] Wolf | L'Analyse Statistique des Données en Psychologie (Statistical data analysis in psychology -translated by authors[END_REF]. 3 Relative Deviation (RD) is calculated on the basis of a comparison between observed and expected frequencies (i.e. those that would have been obtained if there was no association between the two variables), according to the following formula: RD = (observed data -theoretical data) / theoretical data. There is attraction when RD is positive, and repulsion when it is negative. By convention, we retain only RD with absolute terms > 0.25. First of all, this data shows that non-MVR experts managed to accomplish one task without MIREDGE Editor whereas they accomplished two with the tool. This show that MIREDGE Editor somewhat helped them. In addition, two tasks seem like a good score, considering that MVR experts managed to accomplish 2 to 3 task in the same given time with their usual tools (Unity3D).


The data also shows that MVR experts had difficulty completing the first task with MIREDGE Editor. This could be explained by the difference between their practice of this tool and their automatisms acquired on the tool usually used. Changing habits over such a short duration is very difficult. Also, we would like to emphasize the fact that we strictly followed the experimentation protocol and therefore did not intervene during the experimentation, even when the developers seemed to be struggling with the tool. Helping them would certainly have increased their rate of success but we wanted to reproduce real conditions.

Efficiency

Completing a task successfully is interesting but, completing it quickly is just as important. We therefore measured the time necessary to develop each MVR interaction. The start time corresponds to the entry of the first instruction or the placement of the first block. The end time corresponds to the last action necessary for the algorithm to be functional for this task. Tables 3 and4 show the data to compare tasks 1 and 2. The data in the tables correspond to the completion time of these tasks in minutes and seconds. We observe that the MVR experts complete the first task faster without MIREDGE Editor, whereas the non-MVR experts complete it faster with MIREDGE Editor. In short, the non-MVR experts are more efficient with the tool, whereas the MVR developers are more efficient without the tool. For the second task, non-MVR experts are still more efficient with MIREDGE Editor. More interesting: MVR experts, who have gotten used to MIREDGE Editor's interface, are also more efficient with MIREDGE Editor, than those using Unity.

Feedback

For users, MIREDGE Editor should have a functionality to identify algorithmic errors. Indeed, a block can be created without any connection to other blocks. Although this will not cause errors in the generated script, it may cause confusion. A connection checker could be to better assist the user. Concerning the positive points, the flowbased programming representation was appreciated by the MVR experts. Here are some of the comments we collected during the experimentation: "the block programming is simpler to visualize than code", "I linked the simplicity of the terms in the tool and the explanation of the input and output variables". Non-MVR experts, on the other hand, emphasized the simplicity of the interface: "the interface was easy to understand and the blocks easy to manipulate", "the tool is easy to use", "the tools facilitate the creation of interactions".

DISCUSSION

In order for the results to be relevant for a time limited to an hour, we had to provide all participants with equivalent resources and an identical goal. Indeed, in the experimentation without MIREDGE Editor, the developers were provided directly with the libraries containing high-level functions adapted to the context. However, in reality, developers have to conduct considerable research to find these functions in previous projects, forums or documentation. Concerning experiments with MIREDGE Editor, we asked developers to program the entire algorithm. Normally, MIREDGE Editor also allows sharing and thus re-use of existing algorithms. We can therefore assume that the task could have been carried out far more efficiently with access to an algorithm database.

Since the MIREDGE Editor training sessions were short and only theoretical, we can assume that longer term experiments could demonstrate greater efficiency and effectiveness of this tool. That is why improving the form and content of application training remains one of our main objectives.

Thus, the concept of reengineering is a process used by developers. As InTml [START_REF] Figueroa | Intml: A dataflow oriented development system for virtual reality applications[END_REF], if a developer modifies a script generated by MIREDGE Editor, this will not affect its graphical representation of the algorithm. Consequently, each time a script is generated, the changes made in the text editor will be overwritten. Assuming that these modifications are usually simple customizations, we suppose that MIREDGE Editor can avoid being confronted with this situation.

About debugging, this is necessary whenever errors can be made. Using visual programming, thanks to the logic of the meta-model and various restrictions rules of the interface, the goal is to prevent errors. These limits are partially linked to the fact that MIREDGE is an independent application. Therefore, considering MIREDGE as a development environment plugin is an option that needs to be studied. In addition, the current block library only contains a limited number of blocks. When the MVR experts will add blocks it will be necessary to implement filters to help developers quickly find the right. These filters could be based on the type of action, such as moving a 3D object, selecting an area or changing the view. We can also take into account the hardware and software that the developers want to such as the game engine, the input device (e.g. mouse, Kinect, Leap Motion) and the output device (e.g. TV screen, augmented reality glasses, the mounted display).

Finally, even if the experiment was carried out on a very limited number of interactions, the meta-model must theoretically allow a wide range of interactions to be coded. It would thus be interesting to study a larger variety of interaction algorithms such as selection, navigation and manipulation [START_REF] Weidig | Classification of VR interaction techniques, based on user intention[END_REF] [START_REF] Jr | 3D User Interfaces: Theory and Practice[END_REF]. Another question worth asking is whether visual programming will always be as efficient for more advanced interactions [START_REF] Wonner | Bubble Bee, an Alternative to Arrow for Pointing out Directions[END_REF] or for specific devices such as Brain Computer Interfaces [START_REF] Mercier-Ganady | Can We Use a Brain-computer Interface and Manipulate a Mouse at the Same Time?[END_REF].

CONCLUSION

Today, developers who are experts in MVR and those who are not experts in MVR often work with the same programming tools but using different methods. Yet, these communities could greatly benefit from each other in order to rapidly produce powerful MVR applications. Indeed, MVR experts have the knowledge to create specific MVR algorithms for new devices and non-MVR experts can produce large quantities of applications that re-use and combine these algorithms. Our approach therefore consists in proposing MIREDGE that responds to this goal by allowing these two communities to collaborate.

MIREDGE has two main advantages. First of all, it allows non-MVR experts to create MVR interactions, without any specific MVR knowledge, by combining blocks with graphical programming. These blocks contain scripts written by MVR experts and allow to interact with MVR devices. MIREDGE offers a library of blocks that can be enriched by experts when new devices appear. The second advantage of MIREDGE is the fact that it is interoperable with any game engine. Indeed, the tool is based on a meta-model that allows to convert the programming blocks into fully editable script for any game engine.

To validate the contributions of this tool, experiments have showed a gain in efficiency and effectiveness especially for non-MVR developers. New experiments will be conducted on a larger scale to confirm compatibility with maximum interactions, game engines and devices. Also, a study will be done to evaluate all the conditions required so that MVR experts are ready to share their knowledge and so that non-MVR experts are ready to integrate new MVR devices with an assistant such as MIREDGE.

Figure 1 .

 1 Figure 1. Structure of development platforms dedicated to virtual reality

Figure 2 .

 2 Figure 2. Structure of Game Engines with MVR Manufacturers' libraries

Figure 3 .

 3 Figure 3. Structure of Game Engines with MVR Middleware

Figure 4 .

 4 Figure 4. Programming interactions in Game Engines with MVR Assistance Tools

Figure 5 .

 5 Figure 5. MIREDGE: visual programming and script generation, a hybrid solution

Figure 6 .

 6 Figure 6. Process for community development of immersive interaction in MIREDGE

Figure 7 .

 7 Figure 7. Example of connected blocks in the MIREDGE interface

Figure 8 .

 8 Figure 8. Example of an algorithm in MIREDGE

Figure 9 .

 9 Figure 9. Overview of MIREDGE Immersive Interaction Meta-model

Table 1 .

 1 Analysis for each category of tools.

		Dev. platform				Game engine with…
		dedicated to
		virtual reality		MVR Manufactur-	MVR Middleware	MVR Assistance
				ers' libraries			Tools
	Usability	Requires		Requires knowledge	Requires knowledge	Easy for intended
		knowledge	of	of MVR hardware	of MVR hardware	use, difficult for
		MVR hardware						custom use
	Script	Requires packag-	Requires packaging	Only the authors of	Only	the	tool
	capitalizing	ing and placing it	and placing it in an	the tool can share	authors can share
		in an online store	online store
	Collabora-	In many cases	Difficult for non-	Difficult for non-	Possible but in a
	tion	with visual pro-	MVR experts to re-	MVR experts to re-	predefined bounda-
		gramming		use the work of	use the work of	ry
				MVR experts	MVR experts
	Script re-use	A list of blocks is	Search,	duplicate	Search,	duplicate	A list of compo-
		available		and rewrite scripts	and rewrite scripts	nents is available
	Devices	Requires upgrad-	As fast as the manu-	Requires upgrading	Requires upgrading
	compatibility	ing and sometimes	facturer can
		paying
	Cost	Usually expensive More and more are	Free or very expen-	Usually free
				free		sive
	Examples	3dvia studio		Unity3D		VRPN		RUIS
		Eon Reality studio	Unreal Engine with	MiddleVR		ARToolkit, FreeVR,
		Virtools		SDK				#FIVE

Table 2 .

 2 Number of users who completed tasks

	Group	0 Task	1 Task	2 Tasks 3 Tasks Total num. of
						participants
	MVR experts	1	1	3	3	8
	without MIREDGE
	MVR expert	4	2	1	1	8
	with MIREDGE
	non-MVR experts	2	4	1	0	7
	without MIREDGE
	non-MVR experts	2	2	4	0	8
	with MIREDGE
	Total number	9	9	9	4	31

  Main attractions based on RD values between the experimental groups and the number of tasks performed by participants

	MVR experts without MIREDGE Editor and 2 or 3 finished tasks (resp.
	RD=0.29 and RD=0.91)
	 MVR experts with MIREDGE Editor and 0 finished task (RD=0.72)
	 non-MVR without MIREDGE Editor and 1 finished task (RD=0.97)
	 non-MVR experts with MIREDGE Editor and 2 finished tasks (RD=0.72)
	MVR experts without MIREDGE	0 task
	MVR experts with MIREDGE	1 task
	non-MVR experts without MIREDGE	2 tasks
	non-MVR experts with MIREDGE	3 tasks
	Figure 11.

Table 3 .

 3 Duration in seconds to perform task 1

	Group	Mean	Min	Max	Standard deviation
	MVR experts	22min 7s	12min 24s	33min 07s	09min 12s
	without MIREDGE
	MVR experts	30min 18s	17min 39s	42min 56s	17min 53s
	with MIREDGE

Table 4 .

 4 Duration in seconds to perform task 2

	Group	Mean	Min	Max	Standard deviation
	MVR experts	10min 35s	04min 45s	23min 51s	06min 59s
	without MIREDGE
	MVR experts	04min 44s	02min 26s	07min 47s	02min 45s
	with MIREDGE
	non-MVR experts	06min 16s	06min 16s	06min 16s	4
	without MIREDGE
	non-MVR experts	03min 06s	01min 55s	04min 26s	01min 13s
	with MIREDGE

It is impossible to calculate the deviation because there is only one value for this group.

ACKNOWLEDGMENTS

This work was funded by the French Research Agency (ANR-13-APPR-0001, JEN.lab project). The authors want to thank all the participants for their key contributions.

SHORT BIO

Guillaume Loup obtained his PhD in Computer Sciences from Le Mans University. He is interested in the implementation of 2D/3D interactions in real-time, multiplatform implementation and the integration of devices for interacting with virtual environments. His area of expertise is the design of virtual reality-based games.

Sébastien George is a Full Professor in Computer Science from Le Mans University. His research deals with the field of Technology Enhanced Learning. He is interested in interactions and communications with context as a central issue: learning context, context of learners or tutors, context for knowledge and skills building.

Iza Marfisi is an Associate Professor in Computer Science from Le Mans University. Her research interests are in the domain of Technology Enhanced Learning and include the exploration of innovative educational techniques such as Serious Games for education.