Mélanie Canault
email: canaultmelanie@yahoo.fr

Rafael Laboissière
email: rafael.laboissiere@inserm.fr

Pascal Perrier
email: pascal.perrier@gipsa-lab.inpg.fr

Rudolph Sock

Development of Lingual Displacement Independence at Babbling Stage

In this study, we recorded jaw movements and the acoustic signal of 15 babies of 8 to 12 months of age during babbling in order to assess the hypothesis whereby tongue gestures would be more independent from mandibular ones with age.

Results corroborate our expectations. We have shown that increase in the amplitude of tongue gestures in the anterior/posterior dimension, in relation to vertical jaw movement, is noticeable in older babies. This reveals emergence of articulatory control in babies throughout the babbling stage

Introduction

Babbling (6-12 months) is a language development stage which is achieved in spite of relatively poor motor control abilities. The famous "bababa..." sequences, associated with this period, could be produced by mandibular activation only. This is the hypothesis advocated by MacNeilage in the Frame then Content theory [START_REF] Macneilage | The Frame/Content theory of evolution of speech production[END_REF], which is the theoretical framework of this study.

The mandible's influence on the production system at the babbling stage

The "Frame then Content" theory assumes that there could be a natural mandibular movement from which would emerge a specific and complex control for speech function. Speech would then be based on a "syllabic frame", generated by the alternation of vocal tract open-close phases, the closing phase giving a consonantal configuration and the opening phase a vocalic one. The "content" would in turn be congruent with the emergence of the independent control of any single vocal tract articulator, superimposed on the mandibular cycle. Babbling productions would result in a frame production, without content, and would depend on the intrinsic rhythm of mandibular oscillations. Accordingly, the jaw would be the only active articulator at this stage [START_REF] Green | The physiologic development of speech motor control: lip and jaw coordination[END_REF][START_REF] Green | The sequential development of jaw and lip control for speech[END_REF]. Consistent with this last assumption, Munhall & Jones's [START_REF] Munhall | Articulatory evidence for syllabic structure[END_REF] Optotrak measurements showed that the lips are not actively involved in the open/close phase of the vocal tract in babbling. Throughout the closing gesture, lower lip movements were found to be passively carried by the jaw thus pushing the upper lip upwards at contact. Throughout the opening gesture, the lower lip would simply move downwards under the mandible's influence. Hence, lip displacements seem to be initially a passive consequence of mandibular oscillations.

In this perspective, speech motor control abilities at the babbling stage, characterized by mandibular frame dominance and tongue passivity, have led Davis & MacNeilage [4, et al. 5] to assume three associative CV sequences to be limited to three associative patterns: central vowels associated with labial consonants within the "pure frame" (like in [ba]); front vowels associated with coronal consonants within the "fronted frame" (like in [dè]); back vowels with velar consonants within the "backed frame" (like in [gu]) .

Articulatory control emergence

Early in the babbling stage, the frame generated by mandibular oscillations is reduplicated. These successive repetitions of jaw phase alternations could in part reflect poor articulatory control. According to MacNeilage's theory, "content" could increase in a trend called "fronting", which would correspond to the first form of intercyclic variation. Thus, during a bisyllabic sequence, the first syllable would involve a "pure frame", which would be followed by a lingual movement implicating a "fronted frame" and giving utterances like /pate/. However, this type of variation cannot alone account for the emergence of content, or more exactly for that of articulatory control.

We assume that entry into mature articulatory patterns involves dissociation of articulatory movements within a single cycle, which means that articulators can follow different trajectories. Our aim is to observe how the independence of articulators, such as the tongue, will evolve with age. It is hypothesized that articulatory control emerges when babies are able to dissociate tongue and jaw movements. In this context, it is assumed that, as babies get older, they their tongue movements become decoupled from jaw oscillations, thus drifting away from typical "pure-frame" movements.

Method 4.1 Participants

Fifteen babies from 8 to 12 months of age were recorded. They reported no history of motor or perceptual disorders. Their distribution across the speech acquisition stage was as follows: 3 subjects of 8 months of age, 3 of 9 months, 3 of 10 months, 3 of 11 months and 3 of 12 months. All babies were born in Germany and were living with parents who exclusively spoke German to them.

Experiment

We observed the evolution of tongue-jaw correlations by simultaneous articulatory and acoustic studies. The kinematic signals were acquired with Optotrak [START_REF] Munhall | Articulatory evidence for syllabic structure[END_REF], a movement tracking system, which is, according to Green et al [START_REF] Green | Estimating mandibular motion based on chin surface targets during speech[END_REF], the only investigation technique available, reliable enough to study mandibular movements before 4 years of age. Optotrak signals allowed the capture of jaw movements in the vertical dimension. Acoustic signals were used to infer tongue displacements during lowering or raising of the mandible. The tongue is an articulator whose position cannot be detected by Optotrak. Its displacements can be indirectly inferred from a spectral analysis of the acoustic signal. Indeed, the second formant (F2) is suggested to be an acoustic indicator to determine lingual movements in the anterior-posterior dimension [START_REF] Fant | Acoustic Theory of Speech Production[END_REF].

Data processing

Jaw trajectories were segmented into simple movements according to displacements in the raising or lowering dimension. Within each simple jaw movement, F2 variations were segmented into monotonic segments, interpreted as individual tongue movements in the anterior-posterior dimension (see Figure 2). In order to assess the variation of tongue movement amplitudes, relatively to jaw movement amplitudes, the difference in Hz between F2, at movement onset, and F2 at movement offset (∆F2) was computed for each simple movement. The distance (in mm), covered by the jaw in the same temporal interval was also measured (∆jaw). Further, we determined the ratio of these two values (∆F2/∆jaw). The higher the ratio, the more pronounced the tongue movement would be, relative to the jaw. Inversely, the lower the ratio, the more predominant jaw movement would be. The average ratio was calculated for each subject, and the correlation between this ratio and age was estimated, in order to report on the progression of independence of tongue movement between 8 and 12 months. Our data concern motor control development of speech during a period going from reduplicated babbling to variegated babbling. Actually, results suggest that there is an increase in tongue movement amplitude in the anterior -posterior dimension of the vocal tract during this period. The ∆F2/∆jaw ratio shows a significant progression, with a correlation coefficient of R = 0.61 (p< 0.02).

Results

This suggests that the amplitude of the tongue movements in respect to the amplitude of jaw movements will increase with age. In addition, more and more lingual movements in the anteriorposterior dimension could be superimposed to the mandible's vertical displacements, with age.

Conclusion and discussion

This study aimed at giving an experimental support to MacNeilage's « Frame then Content » theory. MacNeilage defines speech as a frame on which content is superimposed. It means that human productions would result from the association of mandibular oscillations (frame) and other articulatory gestures (content). From an ontogenetic point of view, the baby must learn to superimpose this content on the mandibular frame in developing the ability of the other articulators, which, initially, only move under the mandible's influence.

Our results seem to support this hypothesis. Development of motor abilities for mature speech function goes through a phase during which other articulator displacements begin to be spatially dissociated from displacements imposed by the jaw, in order to associate content to the frame.

With age, babies increase their articulatory capabilities and especially lingual gestures. The amplitude of tongue movements in the anterior/posterior dimension of the vocal tract is quite small for the younger subjects (8 months). Gradually, however, the tongue begins to be more active and its movement patterns become independent of those from the jaw.

Nevertheless, it cannot be concluded that articulatory control has been acquired at this stage. Articulatory patterns must still be refined. A study by Nittrouer [START_REF] Nittrouer | The emergence of mature gestural patterns is not uniform: evidence from an acoustic study[END_REF], for example, shows that lingual gestures are constrained by external factors such as phonologic context, until the age of 7 years. Other investigations, which looked at lip behaviour in children, pointed out the fact that even if kinematic patterns are in average relatively similar to adult ones at the age of 4 or 5 [START_REF] Smith | Kinematic characteristics of postvocalic labial stop consonants produced by children and adults[END_REF], or even 6 [START_REF] Green | The physiologic development of speech motor control: lip and jaw coordination[END_REF][START_REF] Green | The sequential development of jaw and lip control for speech[END_REF], they still show remarkable variability [START_REF] Sharkey | Variability of lip and jaw movements in children and adults: implications for the development of speech motor control[END_REF]. Thus, in order to achieve mature patterns, articulators like the tongue, the lips or the velum must stabilize their trajectories.

Moreover, a question remains. Would our results be similar if we had chosen babies from languages with other characteristics, like Chinese (tone language) or Gambian Wolof (quantity language)? Actually, linguistic environment could influence the production system. Boysson-Bardies et al. [START_REF] Boysson-Bardies (de | A crosslinguistic investigation of vowel formants in babbling[END_REF] have, for example, shown in measuring formant values that differences between linguistic communities already appear in 10 month old babies.

Actually, in spite of possible sociolinguistic variations, babbling productions can be hypothesized, according to MacNeilage, to be generated by universal motor constraints which would involve, for example, the dominance of reduplicated syllables, co-occurrence patterns and a preference for some sounds, regardless of the language: consonants [p, t, k, b, d, g, m, n, w, j] and vowels [a, ae, è, oe, e] are privileged [8, 12, 19, 20, 3, 1, 21 4, 5, 7…]. Moreover, these predilections would expand until the stage of first words [START_REF] Macneilage | The Frame/Content theory of evolution of speech production[END_REF][START_REF] Davis | Acquisition of serial complexity in speech production: a comparison of phonetic and phonological approaches in first word production[END_REF]. Furthermore, Boysson Bardies et al.'s data [START_REF] Boysson-Bardies (de | A crosslinguistic investigation of vowel formants in babbling[END_REF] show that, at 10 months, F2 mean values are comparable for English and French babies. For our discussion, standard deviation mainly matters, and it is stable between the two communities. This is not consistent with Rvachew et al. [START_REF] Rvachew | Developmental and cross-linguistic variation in the infant vowel space: The case of Canadian English and Canadian French[END_REF] who present data that show discrepancies for 20 Anglo Canadian babies vs. 23 Franco Canadian babies, from 10 months to 18 months of age. Actually, according to their results standard deviation increases for English and is stable for French, with age. It is then possible that differences found in F2 evolution could be related to specificities in vocalic inventories. However, these across-language disparities should essentially emerge after 12 months, and our data collection does not go beyond 12 months. Examining such results shows, nonetheless, an F2 variation of different degrees: the standard deviation varies from 130 mels to 245 mels for English, and from 157 mels to 175 mels for French.

Thus, increase in tongue displacements, which stands out in our study, is likely not related to the nature of the target language. We believe that some aspects of motor control would indeed adjust differently to specific linguistic requirements. More exactly, increase in tongue movements, related to the vertical displacements of the mandible, would be systematic, even though this phenomenon could be more or less pronounced as a function of the language.

Figure 1 :

 1 Figure 1: Segmentation of single tongue movements

Figure 2 :

 2 Figure 2: Detection of a change of F2 trajectory within a single jaw movement interval

Figure 3 :

 3 Figure 3: Evolution of ∆F2/∆jaw Jaw ratio with age On Figure 3, the mean ∆F2/∆jaw ratio for each baby is plotted as a function of age. Vertical bars represent standard errors. The line represents the linear regression of the ratio as a function of age.Our data concern motor control development of speech during a period going from reduplicated babbling to variegated babbling. Actually, results suggest that there is an increase in tongue movement amplitude in the anterior -posterior dimension of the vocal tract during this period. The ∆F2/∆jaw ratio shows a significant progression, with a correlation coefficient of R = 0.61 (p< 0.02).This suggests that the amplitude of the tongue movements in respect to the amplitude of jaw movements will increase with age. In addition, more and more lingual movements in the anteriorposterior dimension could be superimposed to the mandible's vertical displacements, with age.

Acknowledgments: This research was supported by grants from the Maison Interuniversitaire des Sciences de l'Homme-Alsace (MISHA), 2005-2008 (ACM) and AN-07-CORP-018-01-DOCVACIM, 2008-2011. Investigations were carried out at the Max Planck Institute for Human Cognitive and Brain Sciences of Munich.


Pierre Trontin
email: pierre.trontin@onera.fr

Stephane Vincent

Jean-Luc Estivalezes

Jean-Paul Caltagirone

Detailed comparisons of front-capturing methods for turbulent two-phase flow simulations

Keywords: capturing, VOF, TVD, level set, augmented Lagrangian, projection, CSF, ghost fluid

In the framework of numerical study of multiphase flows, different front-capturing methods are compared. Two different approaches dealing with the incompressibility constraint will be compared, too. Then, every technique is tested on several relevant test cases in order to make a comparison. The surface tension treatment is evaluated for each method and every front-capturing method is tested on a case where interface deformations have something in common with turbulent behaviour. Finally, every method is studied through a phase inversion problem, which is an unsteady test case. Front-capturing methods are tested on physical cases where Navier-Stokes and advection equations are coupled in a non-linear way.

INTRODUCTION

The objectives of the present work are to evaluate Navier-Stokes discretization and solvers as well as interface tracking methods dedicated to unsteady incompressible multiphase flows. This work aims at providing a synthetic and critical work on two-phase flow simulations in order to develop in the near future an original large eddy simulation (LES) numerical modelling of incompressible free surface flows. In the numerical study of multiphase flows, the way the interface is treated has crucial importance. Indeed, the understanding of local phenomena near the interface is impossible without an interface, which has been properly located in the flow field. Let u be the velocity, t the time, the density, the dynamic viscosity, p the pressure, g the gravity vector, S D = 1 2 (∇u+∇ t u) the deformation rate, a function that represents the position of the interface and T the surface tension force. Multiphase flows were calculated on a fixed Eulerian mesh in order to deal with unsteady, three-dimensional flows, with fragmentations and re-connections of the interface. A onefluid model is obtained [START_REF] Scardovelli | Direct numerical simulation of free surface and interfacial flow[END_REF], in which an advection equation for is introduced to describe the interface evolutions:

∇ •u = 0 (1a) *u *t +∇ •(u⊗u) +∇ •( pId-2 S D )-g+T = 0 (1b) * *t +u•∇ = 0 (1c)
In order to accomplish the purpose of this research, two home-made computational fluid dynamics libraries are used to solve the system (1a)-(1c). The first one, named Aquilon, is based on finite volumes with an augmented Lagrangian method for the treatment of incompressibility. The interface tracking is achieved by volume of fluid (VOF)-piecewise linear interface construction (PLIC) [START_REF] Youngs | Time-dependant multimaterial flow with large fluid distorsion[END_REF], VOF-total variation diminishing (TVD) [START_REF] Vincent | A one cell local multigrid method for solving unsteady incompressible multi-phase flows[END_REF] and Front Tracking [START_REF] Shin | Modelling three-dimensional multiphase flow using a level contour reconstruction method for front-tracking without connectivity[END_REF] methods. The surface tension is modelled by a CSF method of Brackbill [START_REF] Brackbill | A continuum method for modelling surface tension[END_REF]. Concerning the second library called Dyjeat, the incompressible flow solver is based on classical projection methods [START_REF] Chorin | Numerical solution of the Navier-Stokes equations[END_REF][START_REF] Temam | Sur l'aproximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires ii[END_REF] to verify the incompressibility constraint. In Dyjeat, the ghost-fluid method [START_REF] Fedkiw | A non-oscillatory eulerian approach to interfaces in multimaterials flows (the ghost fluid method)[END_REF] was used to deal with surface tension forces as well as density and viscosity jumps. The application of the ghost-fluid method is represented in Equation (1b) by the function T. To capture the interface level-set methods [START_REF] Osher | Fronts propagating with curvature dependent speed: algorithm based on Hamilton-Jacobi formulations[END_REF] are used in Dyjeat. In this work, every front-capturing method and every technique used to solve Navier-Stokes equations are taken from the literature. Each method passed the classical tests successfully (Zalesak rotating disk [START_REF] Zalesak | Fully multidimensional flux-corrected transport[END_REF], streamer test case [START_REF] Bell | A second-order projection method for the incompressible Navier-Stokes equations[END_REF], parasitic currents [START_REF] Couderc | Développement d'un code de calcul pour la simulation d'écoulements de fluides non miscibles[END_REF], etc.), and the drawbacks of every technique are well known. The originality of our approach is to test every front-capturing method on physical cases where Navier-Stokes and advection equations are coupled in a non-linear way. Front-capturing methods coupled with Navier-Stokes solvers will be studied on stiff unsteady physical problems.

NUMERICAL METHODS

The techniques dedicated to solve the Navier-Stokes equations are first considered. The velocity-pressure uncoupling can be computed with the augmented Lagrangian method. The standard augmented Lagrangian method was first introduced by Fortin and Glowinski [START_REF] Fortin | Méthodes de lagrangien augmenté. Application à la résolution numérique de problèmes aux limites[END_REF]. This predictor/corrector iterative method optimizes the solution by solving a velocity-pressure saddle point with an Uzawa algorithm [START_REF] Uzawa | Iterative method for concave programming[END_REF]. A flexible version of the augmented Lagrangian method is proposed in [START_REF] Vincent | An adaptative augmented Lagrangian method for three-dimensional multi-material flows[END_REF]. On the other hand, the velocity-pressure uncoupling can be carried out by a classical projection method, in its fully explicit formulation, as it has been accomplished by [START_REF] Chorin | Numerical solution of the Navier-Stokes equations[END_REF][START_REF] Temam | Sur l'aproximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires ii[END_REF].

Regarding the computation of the surface tension force (represented by T in (1b)) and the jump conditions at the interface, different methods were performed. One of the choices to calculate this force is by using the CSF method of BrackBill [START_REF] Brackbill | A continuum method for modelling surface tension[END_REF]. The method is based on the regularization of the surface tension force thanks to a regularized volume formulation, which gives an approximation to the original formulation of this surface tension force. The force per unit volume is spread on several mesh cells around the interface. To take into consideration the jumping behaviour at the interface directly and to remain closer to physics reality, there is the alternative of using ghost-fluid approach [START_REF] Fedkiw | A non-oscillatory eulerian approach to interfaces in multimaterials flows (the ghost fluid method)[END_REF]: it is a simple boundary treatment, which allows the incorporation of jump conditions into the discretization of the momentum equations.

To deal with the interface Equation (1c), three front-capturing (Eulerian) methods were applied: the VOF technique with a PLIC [START_REF] Youngs | Time-dependant multimaterial flow with large fluid distorsion[END_REF], the TVD VOF approach [START_REF] Vincent | A one cell local multigrid method for solving unsteady incompressible multi-phase flows[END_REF] (without geometric reconstruction) and the level-set method [START_REF] Osher | Fronts propagating with curvature dependent speed: algorithm based on Hamilton-Jacobi formulations[END_REF]. In addition, a Lagrangian front-tracking method [START_REF] Shin | Modelling three-dimensional multiphase flow using a level contour reconstruction method for front-tracking without connectivity[END_REF] is presented in some cases. Hirt and Nichols [START_REF] Hirt | Volume of fluid (vof) methods for the dynamics of free boundaries[END_REF] were the first to propose the VOF technique in which, for each medium, a phase function or colour function is used to locate the different fluids and solids standing C = 0 in the outer media, C = 1 in the considered medium. The colour function is advected depending on the fluid velocity. With VOF-PLIC method the interface is defined by its slope and unit normal. The slope is calculated thanks to the colour function C gradients, and the position of the piecewise interface elements is determined in the normal direction to ensure the conservation of volume fraction in each cell. When analyzing the TVD schemes, they belong to VOF methods and are still based on the colour function C advected in the flow. Contrary to VOF-PLIC methods, there is no explicit interface reconstruction, and the colour function is calculated directly. With this intention, the TVD schemes [START_REF] Yee | Upwind and symmetric shock-capturing schemes[END_REF] were used to deal with noncontinuous aspects of the colour function and to solve the hyperbolic equation (1c). A technique dedicated to front-capturing approach is the level-set method, introduced by Osher and Sethian [START_REF] Osher | Fronts propagating with curvature dependent speed: algorithm based on Hamilton-Jacobi formulations[END_REF] and refined by Sussman et al. [START_REF] Sussman | A level-set approach for computing solutions to incompressible two-phase flow[END_REF]. A level-set function is defined as the normal distance function from the interface with its original value set to zero at the interface. This function is advected thanks to Equation (1c). The interface is associated with = 0. is a smooth function and provides a natural way to calculate the unit normal vectors at the interface and curvatures of the interface.

VALIDATIONS

To deal with Equations (1a) and (1b), two different techniques were used to compute the velocitypressure uncoupling: the augmented Lagrangian method and the classical projection method. Studies are made on the inviscid Taylor-Green vortex. Here, only the two-dimensional case was carried out [START_REF] Shu | Numerical convergence study of nearly incompressible, inviscid Taylor-Green vortex flow[END_REF]. Periodic boundary conditions on a square domain, with a [0, 2 ] 2 side length, were chosen. Numerical dissipation is studied: the error between the theoretical value of kinetic energy ( 2 ) and the one calculated is represented in Figure 1 for several mesh sizes. When using refined grids, both augmented Lagrangian method and projection method are equivalent and of second order. Hence, when capillary terms are not taken into consideration, both methods give the same results and will not be at the origin of the differences observed in the solutions when capillary terms will be taken into account. For the projection method a distinction is made about the way spatial discretization is carried out: fifth order weighted essentially non-oscillatory (WENO) schemes [START_REF] Jiang | Efficient implementation of weighted ENO schemes[END_REF] can be used in a conservative form [START_REF] Hu | Weighted essentially non-oscillatory schemes on triangular meshes[END_REF] (weno-c) or not (weno-nc).

Several test cases were performed to compare different techniques to solve Equation (1c). Firstly, two-dimensional Rayleigh-Taylor instability [START_REF] Chandrasekhar | The stability of superposed fluids: the Rayleigh-Taylor instability. Hydrodynamic and Hydromagnetic Stability[END_REF] in its linear form is studied. A heavy fluid is over a lighter one (density ratio = 1000), the two phases being separated by an interface. A small sinusoidal disturbance is initiated at the interface, and the resulting growing instability is studied. For each front-capturing method and for several surface tension forces, the growth rate n is calculated. The stability parameter represents the intensity of surface tension forces. This test case allows one to understand how the different front-capturing techniques behave when surface tension forces are the main driving forces. The results are presented in Figure 1. For the ghost-fluid level-set method, the growth rates calculated are very close to those given by the theory. However, differences can be observed for high corresponding to high surface tension forces, which can make calculations unstable. VOF-TVD schemes seem to be very efficient to deal with the capillary terms. With VOF-TVD schemes the interface is spread over two or three cells of the mesh. This is the reason behind the greater accuracy of VOF-TVD schemes with the CSF model. With VOF-PLIC methods the issue is stiff on the interface and the CSF model requires an artificial spreading of the interface, which can explain coarser results in Figure 1.

Another test case is the surface wave test case of Prosperetti [START_REF] Prosperetti | Motion of two superimposed viscous fluids[END_REF]: an initial sinusoidal perturbation is created in an interface separating two viscous fluids. The simulation is carried out without gravity. The surface tension force tends to make the interface oscillate. This oscillation is damped because of the viscosity diffusion. Results are shown in Figure 2. When using insufficiently refined grids, none of the front-capturing methods are able to capture the interface accurately. When using enough refined grids, the ghost-fluid level-set techniques appear to be very accurate to capture the interface. In contrast, several interface smoothing iterations are needed to obtain good results when using VOF techniques. VOF methods tend to be less efficient, when high surface tension forces are at stake and when fine meshes are used. The Rayleigh-Taylor and Prosperetti test cases evaluate the surface tension treatment more than the interface tracking. However, for the same CSF model, it has been demonstrated that the utilization of the TVD or the PLIC technique can induce significant differences.

The last studied test case is the dam break flow over a wet bottom. Numerical results can be compared with experiments [START_REF] Vincent | Numerical modelling of bore propagation and run-up on sloping beaches using Mac-Cormack TVD scheme[END_REF]. Here, the Reynolds number is 9000. The aim is to perform simulations on a test case where strong unsteady vortices of various scales interact with the interface, indeed mimic a pseudo-turbulent behaviour. The three front-capturing methods are compared with a Lagrangian front-tracking method [START_REF] Shin | Modelling three-dimensional multiphase flow using a level contour reconstruction method for front-tracking without connectivity[END_REF]. In Figure 1, the air/water-free surfaces given by each technique are represented at two different times. The VOF-TVD technique is accurate to deal with problems, where strong deformations with little scales of turbulence occur, even if it has been shown that this method diffuses the interface when a strong local shearing occurs [START_REF] Vincent | A one cell local multigrid method for solving unsteady incompressible multi-phase flows[END_REF]. With VOF methods, filaments that fragment into droplets appear. Even if the mass conservation for VOF-PLIC methods is accurate, these droplets are not relevant to physical features as previously observed by [START_REF] Lafaurie | Modelling merging and fragmentation in multiphase flows with SUPER[END_REF]. Level-set methods give accurate results, as do VOF-TVD techniques.

THE CASE OF PHASE INVERSION

In a closed square box, a two-dimensional phase inversion is studied [START_REF] Labourasse | Towards large eddy simulation of isothermal two-phase flows: governing equations and a priori tests[END_REF]. Initially a lighter phase (oil) is located in the lower left corner of the box (lower left quarter part of the box), the heavier one (water) filling the rest of the box. Under the action of gravity, the lighter phase moves upward, inducing complex stretching and tearing off the interface as well as strong unsteady vortex motions during the transient stage of the flow, looking like turbulent flows. Reynolds numbers are, respectively, 99 045 for the water phase and 891 for the oil phase. Strong deformations of the interface and instabilities appear. Such characteristics are found in turbulent flows. This problem is a stiff one and there is no reference solution. This test case offers a lot of configurations to study: varied interface structures, phenomena of coalescence, and break up. In Figure 3 are shown results about phase inversion on a 256×256 uniform Cartesian grid. Slight differences can be observed particularly near the left vertical wall, where VOF methods seem to generate unphysical small oil blobs. At a later time, as can be seen in Figure 3, larger differences are observed. Concerning the front-tracking method, the interface treatment on the wall seems different from the other methods. With VOF methods, filaments, which fragment into droplets, tend to appear. For level-set methods, problems of mass losses can appear. If macroscopic data are studied, Figure 3 (left) shows that every front-capturing method has the same behaviour in terms of kinetic energy with typical oscillations of 1 Hz.

CONCLUSIONS AND PERSPECTIVES

The relevant coupling between a front-capturing method and the jump conditions treatment at the interface depends on the studied case. To capture mean effects (Prosperetti test case) and an instability (Rayleigh-Taylor test case), level-set methods coupled with ghost-fluid technique seem accurate. The same conclusion can be drawn when using VOF-TVD techniques with a CSF approach. Coupled with CSF method of Brackbill, VOF-PLIC technique is appropriate to capture mean effects. However, difficulties are encountered when computing problems with instabilities. Hence, when turbulence is taken into consideration, VOF-PLIC method coupled with CSF approach is not the more accurate technique to use. When strong deformations of the interface appear (dam break, phase inversion) each method has its own disadvantages, and conclusions are drawn to characterize the pros and cons of each method in the turbulent cases. Future works will be dedicated to introducing LES models, improving front-tracking results and testing other surface tension models for VOF methods [START_REF] Vincent | An adaptative augmented Lagrangian method for three-dimensional multi-material flows[END_REF].

Figure 1 .

 1 Figure 1. From left to right: (a) Taylor-Green test case; (b) Rayleigh-Taylor test case; (c) dam break t = 0.24 s; and (d) dam break t = 0.42 s.

Figure 2 .

 2 Figure 2. Prosperetti test case. Left = 32×32 mesh; middle = 64×64 mesh; and right = 128×128 mesh.

Figure 3 .

 3 Figure 3. Left: time evolution of the kinetic energy of the oil phase; middle and right: interface locations at different times for several methods: front-tracking (solid), level set+ghost fluid (-), VOF-PLIC+CSF (..), VOF-TVD+CSF (-..-); middle: t = 0.795 s; and right: t = 2.355 s.

Copyright q 2008 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Fluids 2008; 56:1543-1549 DOI: 10.1002/fld


Pascal Perrier
email: pascal.perrier@gipsa-lab.inpg.fr

& Liang Ma

Speech Planning for V 1 CV 2 Sequences: Influence of the Planned Sequence

The paper studies the potential influence of the structure of a language (in terms of phonological units) on the anticipatory coarticulation. It is hypothesized that speech gestures are optimally planned and that the size of the planned sequence is influenced by language constraints. The status of the syllable is studied via simulations with a speech production model and experimental data.

Introduction

It has been often suggested that the control of speech production sequences involves an optimal planning process in the central nervous system, which uses internal representations ( [START_REF] Jordan | Motor Learning and the Degrees of Freedom Problem[END_REF], [START_REF] Kawato | Trajectory formation of arm movement by cascade neural network model based on minimum torque-change criterion[END_REF]) of the speech production apparatus ( [START_REF] Guenther | A theoretical investigation of reference frames for the planning of speech movements[END_REF], [START_REF] Perrier | Modeling the production of VCV sequences via the inversion of a biomechanical model of the tongue[END_REF]), in order to achieve goals in the acoustic, perceptual, and/or articulatory domain, while optimizing a speakeroriented criterion (often called "articulatory effort"). This hypothesis is the theoretical background of the current study. Our speech production model, called GEPETTO 1 , includes a motor control model and a biomechanical model of the vocal tract ( [START_REF] Perrier | Modeling the production of VCV sequences via the inversion of a biomechanical model of the tongue[END_REF]). In the motor control domain the perceptual objectives of speech production are regions of the acoustic domain, which are related to targets in the space of the motor control variables. Sequence planning consists in finding optimal targets within the regions associated with the phonemes of the sequence. Once the planning has been completed, movement is achieved by shifting the motor variables at a constant rate from a target to the next and by applying them to the biomechanical model. Thus, articulatory trajectories are the result of the interaction between the motor commands at targets, the timing of their variations and the physical properties of the biomechanical model. This paper studies for V 1 CV 2 sequences the impact of the nature of the planned sequences (the whole V 1 CV 2 sequence or the CV 2 syllable) on the articulatory trajectories. More specifically; we were interested in studying to which extent the phonological structure of the language could influence the kinematic characteristics of speech movements. In this context, this study focuses on the study of the potential influence of the syllable on planning. Simulations were run with three different hypotheses about the planned sequence, which account for different status of the syllable within the V 1 CV 2 sequence. Simulated coarticulation patterns are compared to patterns that were experimentally observed in speakers of French and Mandarin Chinese, two syllable-based languages in which the syllable is classically considered to have different strengths in the organisation of speech ( [START_REF] Ma | Anticipatory Coarticulation in Vowel-Consonant-Vowel sequences: A crosslinguistic study of French and Mandarin speakers[END_REF], [6] [7]).

Materials and method

Modeling

Biomechanical model

For the simulations a 2D biomechanical model of vocal tract was used, which is build around a biomechanical model of the tongue. This model includes the main muscles responsible for shaping and moving the tongue in the midsagittal plane: posterior and anterior parts of the genioglossus (GGP and GGA), styloglossus (STY), hyoglossus (HYO), inferior and superior longitudinalis (IL and SL) and verticalis (VER). Elastic properties of tissues are accounted for by finite-element (FE). Muscles are modeled as force generators that (1) act on anatomically specified sets of nodes of the FE structure, and (2) modify the stiffness of specific elements of the model to account for muscle contractions within tongue tissues. Curves representing the contours of the lips, palate and pharynx in the midsagittal plane are added and mechanical contacts between these contours and the tongue are modeled. The jaw and the hyoid bone are represented in this plane by static rigid structures to which the tongue is attached (more details are given in [START_REF] Payan | Synthesis of V-V Sequences with a 2D biomechanical tongue model controlled by the Equilibrium Point Hypothesis[END_REF] and [START_REF] Perrier | Influences of tongue biomechanics on speech movements during the production of velar stop consonants: A modeling study[END_REF]). The tongue model is controlled according to the λ model [START_REF] Feldman | Once more on Equilibrium Point Hypothesis for Motor Control[END_REF] that specifies for each muscle a threshold length, λ, where active forces start.

Tongue movements are generated from target to target by changing the λ commands at a constant rate of shift. The whole biomechanical model is coupled with a harmonic analogue of the vocal tract, which generates formant patterns from the 3D shape of the vocal tract

Learning the relations between motor commands and acoustics: a static forward model

The internal representation used in GEPPETO's optimal sequence planning corresponds to a static forward model which functionally describes the relations between the λ commands and the first three formant (F1, F2, F3) patterns at targets. To learn the static forward model, 8800 different simulations were generated, which describe a large variety of tongue shapes; including those for consonants. To do so, the λ space was randomly sampled according to a uniform distribution. Formant values were computed for each simulation. Neural networks based on Radial Basis Functions (RBF) have been used to learn the relation between the λ motor commands and the (F1, F2, F3) patterns produced at target, and the mean square error on the (F1, F2, F3) patterns was less than 3% (see details in [START_REF] Perrier | Modeling the production of VCV sequences via the inversion of a biomechanical model of the tongue[END_REF] and [START_REF] Ma | La coarticulation en français et en chinois : Étude expérimentale et modélisation Unpub[END_REF]).

From phonemes specification to motor commands: Influence of the planned sequence

The static forward model was used to infer from a sequence of phonemes an optimal sequence of motor commands. In this aim, for each phoneme, target regions were defined in the (F1, F2, F3) domain, and elaborated an inversion procedure to recover motor commands from the formant patterns. This inversion procedure associates the minimisation of a speaker-oriented criterion and an account for listener-oriented constraints. It aims at minimizing the global distance between the λ commands associated with the phonemes of the planned sequence while ensuring that the (F1, F2, F3) formant patterns remain within the target regions defined for these phonemes ( [START_REF] Ma | Anticipatory Coarticulation in Vowel-Consonant-Vowel sequences: A crosslinguistic study of French and Mandarin speakers[END_REF], [START_REF] Perrier | Modéliser le physique pour comprendre le contrôle: le cas de l'anticipation en production de parole[END_REF]). The features of the motor control model in GEPETTO are close to those that can be found in general human motor control models. However, as compared to typical human skilled gestures, speech gestures have an additional semiotic component that is determined by the language. To study the potential influence of this language-related semiotic component onto speech movements, articulatory trajectories were generated with our model according to whether the whole V 1 CV 2 sequence is planned (henceforth sequential planning model) or the CV 2 syllable only is planned (syllable planning model). In other words the above mentioned global distance is minimized either over the whole sequence or just over the CV 2 sequence.

Experimental data

To evaluate the simulated influence of the syllable strength in speech planning, simulations obtained with both planning models were qualitatively compared with experimental data collected from speakers of French and Mandarin Chinese. Speech material consists of 15 VCV nonsense words where the vowel was /a/, /i/ or /u/ and the consonant was /k/ or /t/. The words were uttered at a normal speech rate by three native French speakers and two native Chinese speakers. Each target word was embedded in a carrier sentence and each carrier sentence was repeated 10 times. The articulatory data were collected with an electromagnetic midsagittal articulograph (EMMA; AG100 Carstens Electronics). The four sensors glued on the tongue are called T 1 , T 2 , T 3 and T 4 , from the tongue tip to the tongue back (see [START_REF] Ma | Anticipatory Coarticulation in Vowel-Consonant-Vowel sequences: A crosslinguistic study of French and Mandarin speakers[END_REF], [START_REF] Ma | La coarticulation en français et en chinois : Étude expérimentale et modélisation Unpub[END_REF], [START_REF] Ma | Anticipatory Coarticulation in Vowel-Consonant-Vowel sequences: A crosslinguistic study of French and Mandarin Chinese[END_REF] for more details).

Results

Measured coarticulation patterns in French and Mandarin Chinese.

Results observed for experimental data are exemplified in Figure 1. In French, V 2 influences significantly the sensor positions of both V 1 and C, and in a way that is compatible with an anticipation strategy (Sensors of get V 1 and C get closer to those of V 2 . In Mandarin Chinese changes in V 2 did significantly affect sensor positions of C, but no significant consequence could be observed for V 1 . In summary, in our data, anticipatory coarticulation goes back beyond the limits of the CV 2 syllable in French while it is strictly limited to the syllable in Mandarin Chinese ( [START_REF] Ma | Anticipatory Coarticulation in Vowel-Consonant-Vowel sequences: A crosslinguistic study of French and Mandarin speakers[END_REF], [START_REF] Ma | La coarticulation en français et en chinois : Étude expérimentale et modélisation Unpub[END_REF], [START_REF] Ma | Anticipatory Coarticulation in Vowel-Consonant-Vowel sequences: A crosslinguistic study of French and Mandarin Chinese[END_REF])..

Simulations

Figures 2 and 3 plot the positions of 4 nodes located on the upper contour of the tongue model for velar consonant /k/ and vowel // in /kV 2 / sequences, where V 2 is either /i/, /e/, //, /oe/, // or /a/. The 4 nodes are located along the tongue contour approximately at the same places than the sensors in the articulatory data presented in section 3.1. Since GEPETTO does not include a modelling of the lips, it was not possible to simulate rounded vowels in the same way as unrounded vowels. Hence, in our simulation, vowel /u/ was replaced by vowel // that is also articulated in the velar region of the vocal tract and does not require rounded lips to be acoustically correctly produced.

Figure 2 shows the results obtained for the sequential planning model, while figure 3 shows the results for the syllable planning model. It is important to recall here that the planning model determines the λ commands at the successive targets of the sequence, and that the actual position reached for the different elementary sounds are the results of the combined effect of these λ values, of their timing and of the dynamics of the biomechanical tongue model (mass, stiffness, damping..). For all simulations the timing of the λ commands was the same: transition time between targets was set to 40 ms, and the hold duration at targets to 100 ms. It can be observed that sequential planning induces significant changes in tongue positioning that are consistent with anticipatory coarticulation and similar to those observed for the French speakers in the experimental study (Fig. 1). Syllable planning induces only slight changes, which are not consistent with anticipation (for example in /e/ context position is slightly backwards as compared to the /a/ context). These results are similar to those obtained for the Chinese speakers (Fig. 1). Both plannings generate variations of tongue positioning for /k/ consistent with anticipation. The variation is slightly larger though for the syllable planning. Again these results match well our experimental findings (Fig. 1).

Conclusion

Simulations carried out with a model of speech production accounting for optimal sequence planning and biomechanical characteristics are in good agreement with experimental observations of anticipatory coarticulation in V 1 CV 2 sequences. They show that considering the length of the planning sequence in relation to the structure of the language (here the status of the syllable) allows the replication of anticipatory coarticulation variations across languages.

Figure 1 :

 1 Figure 1: Variation of T 2 T 3 , T 4 positions of /u/(left) and /t/ (right) in /ut/V 2 sequence,, when V 2 varies( /i/:green line; /a/:solid line; /u/:dotted line); . Left: French speaker; Right: Chinese speaker Top: vowel /u/; Bottom: consonant /t/

Figure 3 :Figure 4 :

 34 Figure 3: Node positions at target in /kV 2 / sequences for the sequential planning model, where V 2 is either /i/ (green), /e (red)/, / / (magenta), /oe/ /cyan, // (black) or /a/ (black). The upper solid line represents the palate contour. Lips are on the left hand side. Top panel: Vowel //; Bottom panel: Consonant /k/

GEPPETO holds for "GEstures shaped by the Physics and by a PErceptually Oriented Targets Optimization"


L Prazakova

E Nolot

E Martinez

F Fillot

D Rouchon

N Rochat

M Bernard

C Sabbione

D Morel

N Bernier

A Grenier

A.-M Papon

M.-C Cyrille

G Navarro

Temperature Driven Structural Evolution of Ge-rich GeSbTe Alloys and Role of N-doping

Ge-rich GeSbTe alloys allowed overcoming temperature limitations of Phase-Change Memory technology. In this paper, we present a thorough investigation of the structural evolution and crystallization process of these alloys as a function of increasing temperature of annealing. We highlight the progressive rearrangement of the structure towards the demixing of Ge and GeSbTe phases. In particular, we show the stability of Sb-Te units and the development of Ge-Te bonds around these features. We observe the formation of a transient GeSbTe phase, which is driven by crystallization phenomena, leading to a gradual diffusion and expulsion of Ge. Therefore, the system moves towards the complete separation of Ge and Ge2Sb2Te5 stable phases. Furthermore, we investigate the effect of N doping in Ge-rich GeSbTe, which induces the formation of Ge-N bonds. Such features are demonstrated to be responsible for a delayed structural reorganization to higher temperatures, thus affecting the entire process of crystallization and phase separation in the alloy.

I.

Introduction

Phase-Change Memory (PCM) is considered among the most promising Non-Volatile Memory (NVM) technologies thanks to its excellent performances such as fast programming speed, high scalability, low power consumption, good data retention and multi-level storage capability. PCM's maturity is demonstrated by its recent commercialization for Storage Class Memory (SCM) applications [1][2][3] and by its manufacturability and proved reliability in embedded automotive applications [START_REF] Arnaud | IEEE Int. Electron Devices Meet. IEDM[END_REF][START_REF] Cappelletti | [END_REF] . PCM has definitely passed the step of being an emerging technology, already playing an important role in the NVM market [START_REF] Navarro | IEEE Int. Mem. Workshop IMW[END_REF] . PCM device functionality is based on the reversible change between an amorphous and a crystalline phase of a chalcogenide material, accompanied by the large contrast in resistance and optical reflectivity between the two phases. Among the chalcogenide phase-change materials, Ge2Sb2Te5 (GST225) is known as the most common reference compound for PCM whose structure and crystallization mechanism have been largely studied over the past years [START_REF] Kolobov | [END_REF][8][9][10][11][12] . However, GST225 has a relatively low crystallization temperature of about 150 °C that is not compatible with data retention requirements of high temperature applications (i.e. automotive applications) [START_REF] Cappelletti | [END_REF][START_REF] Raoux | 11th Annu. Non-Volatile Mem. Technol. Symp. Proceeding[END_REF][START_REF] Zuliani | [END_REF] . Owing to Ge enrichment in GeSbTe alloys, PCM definitely demonstrated the capability of a high thermal stability, fulfilling the strict requirements of embedded applications [START_REF] Zuliani | [END_REF][START_REF] Zuliani | IEEE 11th Int. Mem. Workshop IMW[END_REF] . These findings, combined with the proved benefit of N doping on retarding the crystallization to higher temperatures [START_REF] Privitera | [END_REF][17][18][19][START_REF] Cheng | Int. Electron Devices Meet[END_REF] , raised questions about the origins of such reliability improvements. Recent investigations of Ge-rich GeSbTe (GGST) alloys highlighted the segregation of a Ge phase and a GeSbTe phase at high temperature [START_REF] Sousa | Symp. VLSI Technol. VLSI Technol[END_REF] . Moreover, transmission electron microscopy (TEM) analysis during the thermal annealing was used to suggest a two-step phase transition process, consisting of the initial crystallization of the Ge in excess, followed by the crystallization of a GeSbTe phase [START_REF] Agati | [END_REF]23 . However, a complete and exhaustive structural analysis of Ge-rich GeSbTe evolution in temperature is still missing. In this work, we present the thorough investigation of the structural evolution of undoped and N-doped Ge-rich GeSbTe systems at increasing temperature. Thanks to the results coming from a wide set of complementary techniques, such as resistivity measurements, Raman spectroscopy, ex-situ and isothermal X-ray diffraction (XRD) analysis, Fourier-transform infrared spectroscopy (FTIR), transmission electron microscopy linked with energy-dispersive X-ray spectroscopy (TEM-EDX), we outline the evolution of the detected structural features until the crystallization of the layers. We highlight the importance and the stability of Sb-Te structural units along the evolution of the layer in temperature, combined with the structural rearrangement of Ge-Te bonds. Finally, we show how the same dynamic takes place in N-doped samples, but it is delayed to higher temperatures by the presence of Ge-N bonds, that play a key role on the outstanding thermal stability of Ge-rich GeSbTe alloys.

II. Experimental Methods

Amorphous 100 nm-thick layers of GST225 and GGST were deposited at room temperature on 200 mm Si (100) wafers by magnetron sputtering from pure Ge2Sb2Te5 target (for GST225 thin layers) and by co-sputtering from Ge and Ge2Sb2Te5 targets (for GGST thin layers) in Ar atmosphere. The nominal GGST composition considered for our study was obtained by combination of 45 % Ge and 55 % of GST225. Same Ge, Sb and Te relative content was targeted in N-doped samples. The N-doped Ge-rich GeSbTe layers (N-doped GGST) were prepared by reactive sputtering from the same targets with Ar/N2 gas mixture in the deposition chamber. GGST layers with two different N contents were obtained by varying the ratio between Ar and N2 gas flow during the film deposition (hereafter referred as GGSTN and GGSTN + for N2 flow of 2 sccm and 10 sccm respectively). The layers were protected by a 3.5 nm-thick carbon capping layer to prevent surface oxidation.

To perform the measurements of sheet resistance in temperature (RvsT), 100 nm-thick layers of GST225, undoped and N-doped Ge-rich GeSbTe with similar process parameters were deposited on SiO2 substrates and protected by a 10 nm-thick SiN capping layer. The ex-situ annealing was performed for the duration of 5 minutes, if not specified otherwise in the text, under an inert N2 atmosphere. Four-point probe technique was used for RvsT measurements, with fixed heating rate of 10°C/min. Raman spectra of as-deposited and annealed samples were measured at room temperature with a 532 nm laser diode excitation source (Renishaw InVia) in a range of 100 -1000 cm -1 . The intensity of the laser beam was maintained at low level to avoid the changes in Raman spectra due to thermally induced structural modifications by absorption of high laser power densities. The acquisition time and number of scans were tuned to achieve a high signal to noise ratio. X-ray diffraction (XRD) data were obtained with a two-circle diffractometer (PANanalytical Empyrean) using the Cu Kα radiation (λ = 1.5406 Å). The diffraction angles were in the range from 22° to 56° (2θ) with 0.01° steps at room temperature.

III. Results

In this section, we first report on difference in crystallization temperature of undoped and N-doped GGST thin layers. After, we investigate the structural evolution of GGST thin layer, particularly by Raman spectroscopy and XRD, and finally, we analyze the effects of N-doping on the structural evolution of these alloys.

A. Resistivity-vs-Temperature Measurements

RvsT measurements performed on GeSbTe alloys are shown in Fig. 1 and highlight the main resistivity drops of the layers in temperature. High resistivity amorphous films undergo the amorphous-to-crystalline phase transition at the crystallization temperature with a more or less sharp decrease in resistivity, related to segregation and crystallization of a low resistivity GeSbTe phase. For GST225, used as a reference for our analyses, two transitions at the temperatures of 160 °C and 330 °C can be observed for the cubic (fcc) and hexagonal (hex) phase transition, respectively 24,25 .

GGST layer features a double step transition with the first drop at 300 °C and a second one slightly below 350 °C, which will be deeply investigated in the following. On the contrary, N-doped GGST layer shows a single transition at about 390 °C, confirming the higher temperature stability showed in previous works [START_REF] Sousa | Symp. VLSI Technol. VLSI Technol[END_REF]26 . Higher resistivity of the crystalline state after the annealing in N-doped GGST with respect to GGST highlights the reduced progress of the segregation and the crystallization in the alloy due to N doping.

B. Structural Evolution of GGST as a function of Temperature

Raman spectroscopy and XRD measurements were performed to investigate the evolution of GST225, GGST and N-doped GGST structures with increasing temperature. Raman spectra of GST225 (Fig. 2), which is here used as the reference material, were compared to those of Ge-rich GeSbTe layers. The Raman spectra of amorphous as-deposited (AD) GST225 is dominated by a broad feature covering the frequency region between 100 cm -1 and 190 cm -1 , formed by overlapping bands at 110 cm -1 , 124 cm -1 and 154 cm -1 . A low intensity band at ~ 220 cm -1 can also be identified. The main peak at 154 cm -1 can be assigned to the stretching modes of Sb-Te vibrations in SbTe3 pyramidal units 27,28 . Considering the analogy with Ge-S vibration modes in GeS2 glasses 29 , the contribution of the vibration of Ge-Te tetrahedral units at about 160 cm -1 could also be possible, however this contribution is not visible due to much lower polarizability of Ge-Te bonds with respect to Sb-Te bonds 11 . Te-Te stretching mode, also possibly present in this frequency range [30][31][32][33] , is highly unlikely in GST225 27,28 . Indeed, previous studies by extended X-ray absorption fine structure (EXAFS) show no homopolar Te-Te bonds in this alloy 34,35 . The peaks at 110 cm -1 , 124 cm -1 and 220 cm -1 can be assigned to the different vibrational modes of Ge-Te bonds present in tetrahedral and defective octahedral structures as observed in amorphous GeTe 9,11,36 . Below 190 cm -1 we mostly find vibrations of defective octahedra, whilst weaker features at high wavenumbers above 190 cm -1 can be assigned to Ge in tetrahedral sites 11 . In more detail, the peak at ~ 124 cm -1 is assigned to the A1 vibration mode of corner-sharing tetrahedra GeTe4-nGen (n = 1, 2) and the peaks at 110 cm -1 and ~ 220 cm -1 are assigned to the A1 and F2 vibration mode of GeTe4 tetrahedral units, respectively 27,37 .

In the spectrum of GST225 annealed at 250 °C the peak at 154 cm -1 (SbTe3 units) remains stable, therefore characterizing even the cubic crystalline phase of the material 11,28,38 . Moreover, a new peak at 174 cm -1 appears, while the intensity of the peaks in the range 100 -140 cm -1 (i.e. Ge-Te modes) begin to decrease. At higher annealing temperatures, the peak at 174 cm -1 further increases at the expense of the peak at 154 cm -1 (SbTe3 units) which gradually disappears. This new peak was associated to the vibrations of Sb-Sb bonds in (Te2)Sb-Sb(Te2) units where the Sb-Sb bond is connected to four Te atoms 32 . This progressive change between the peaks assigned to different Sb-Te units is evidence of the ongoing development of GST225 structure from fcc to hex crystalline phase with increasing annealing temperature. The Raman spectrum of as-deposited GGST (Fig. 3) can be divided into three main parts: I) a main peak at 154 cm -1 assigned to the stretching mode of SbTe3 pyramidal units, already evidenced in GST225; II) features at low wavenumbers (below ~ 150 cm -1 ) that correspond to the Ge-Te vibration modes, in agreement with previous analysis of GST225; III) features at higher wavenumbers in the range of 190 -300 cm -1 which can be assigned to amorphous Ge (a-Ge) in tetrahedral sites. This broad feature is formed by two main peaks at ~ 272 cm -1 and ~ 230 cm -1 which are assigned respectively to the TO and LO vibrational modes of amorphous Ge (a-Ge) [39][40][41][42] . The peak at 154 cm -1 (i.e. vibration of SbTe3 units), contrary to what was observed in GST225, does not significantly change either in position nor in full width at half maximum (FWHM) up to the annealing temperature of 400 °C. Ge-Te part of the spectra evidences the evolution up to 335 °C, after which it starts to be similar to the spectra of amorphous as-deposited and crystalline fcc GST225 (Fig. 2). These findings already suggest the absence of a cubic-to-hexagonal transition even at high temperature 32 . In the a-Ge part of the spectra, we observe a gradual development of TO and LO modes with increasing annealing temperature, until the new peak at 297 cm -1 , assigned to Ge crystalline phase (c-Ge), appears in the spectrum at 335 °C. Such temperature is particularly low for observing Ge crystallization if compared with that of an elemental a-Ge layer, normally reported to be 480 °C -530 °C43-46 .

In order to follow the evolution trends of the above-mentioned features in GGST with temperature, we computed the sum of the peaks relative areas, obtained from the fitting of the spectra. We considered: for Ge-Te vibrational modes the peaks at 110 cm -1 and 124 cm -1 ; for a-Ge modes the peaks at 220 cm -1 and 270 cm -1 ; for c-Ge the peak at 297 cm -1 . The results were normalized with respect to the area of Sb-Te vibrational modes (main peak at 154 cm -1 and small contribution at 174 cm -1 ), which remain stable in all studied temperatures. The results are shown in Fig. 4 as a function of annealing temperature. The following evolutions can be highlighted:

T < 300°C  Ge-Te modes, present in the amorphous as-deposited layer, initially decrease with the annealing temperature, reaching the minimum value at 300 °C. At the same time, a-Ge modes slightly increase in intensity, reaching the maximum value at 250 °C; T > 300°C  Ge-Te modes involved in the ordering process of the layer (i.e. crystallization of a GeSbTe phase) begin to increase after 300 °C, reaching an almost stable intensity after 375 °C;  Simultaneously with the intensity increase of Ge-Te modes, the a-Ge modes gradually disappear, turning into the sharp peak of crystalline Ge. The c-Ge peak first appears at 335 °C and increases in intensity up to maximum annealing temperature. We performed XRD analysis to further investigate the development of the crystalline phases in GGST (Fig. 5). Well-defined diffraction peaks are observed starting from the XRD pattern at 350 °C. The characteristic peaks of the fcc GST225 crystalline phase coexist with the peaks of the Ge cubic phase, which increase in intensity with the annealing temperature up to 450 °C. The XRD pattern at 335 °C features a broad band reaching the maximum at ~ 30.5° (2θ), that can be further recognized in the XRD pattern at 350 °C as a broad shoulder of the GST225 [200] main peak. Several other small peaks can be identified at 350 °C, but they disappear at higher annealing temperatures together with the above-mentioned broad band at ~ 30.5°. The presence of these features highlight a transitional step of reorganization through which the system passes before the appearance of GST225 and Ge crystalline phases. The crystallites sizes were calculated from the Scherrer's law for [220] Bragg peak of GST fcc phase and for [111] Bragg peak of Ge cubic phase (Table 1). GST phase shows an almost stable grain size at all the temperatures, whereas the Ge grains almost double in size from 350 °C to 450 °C. Table 1: Crystallites sizes calculated by Scherrer's law for GST and Ge phases from the XRD pattern of annealed GGST in Fig. 5.

C. N-doping Influence on Structural Evolution of GGST as a function of Temperature

Raman spectra of as-deposited and annealed GGSTN are shown in Fig. 6. Highly disordered structure of GGSTN + resulted in very noisy Raman spectra (thus not reported here). However, the spectra were still usable for main peaks recognition and deconvolution, which is discussed later in this section. The spectra of as-deposited and annealed N-doped layers feature the same vibrational modes recognized in GGST (Fig. 3), but the previously observed evolutions are shifted towards higher temperatures. The c-Ge peak at 297 cm -1 , for example, does not appear until 450 °C. The same feature analysis as reported in Fig. 4 for GGST (integrated intensities obtained from the fitting of the spectra and normalized with respect to intensity of Sb-Te modes) was also performed on GGSTN and GGSTN + . The evolution trends for Ge-Te, a-Ge modes are compared in the three layers in Fig. 7. For the sake of clarity, no distinction is done for Ge-Te modes before and after the detected minimum intensity, which we still attribute to the end of reordering of amorphous layer and the beginning of a GeSbTe phase crystallization. Ge-Te modes reach such minimum intensity at a temperature that increases with the N content, in particular at 300 °C, 350 °C and 400 °C for GGST, GGSTN and GGSTN + respectively. The same trend is observed for the temperature at which the maximum intensity of a-Ge modes is reached (i.e. 250 °C, 350 °C and 375 °C for GGST, GGSTN and GGSTN + respectively). Moreover, the following abrupt decrease of a-Ge modes intensity is more pronounced in the case of both N-doped GGST layers with respect to GGST. This is likely related to the crystallization of the Ge phase retarded at higher temperatures due to the N doping. Indeed, the speed of crystal growth increases with the temperature at which the nucleation takes place. In N-doped GGST samples, it leads to a faster disappearance of a-Ge modes whereas their evolution in GGST is more gradual due to its beginning at lower temperatures.

T (°C)

GGST GGSTN GGSTN + Fig. 7: Comparison of the evolution in temperature of Ge-Te (a) and a-Ge (b) modes obtained from Raman spectra in GGST, GGSTN and GGSTN + . Dashed vertical lines highlight the trends inversion for both types of the modes, significant of structural transitions that are delayed to a higher temperature, the higher the nitrogen content.

XRD measurements on GGSTN samples are shown in Fig. 8. GGSTN + samples, however, do not show the diffraction peaks up to more than 500 °C (not reported). The first diffraction peaks in GGSTN appear at 375 °C. These diffraction peaks might correspond to the GST225 fcc phase, however their positions are significantly shifted with respect to database data (ICDD PDF No. 00-054-0484). The presence of nitrogen and the effect of annealing may induce stress and change in the lattice parameter resulting in the shift of the peak positions. However, it was previously observed that N-doping slightly increases the lattice parameter of GST fcc phase with an expected shift of the peaks at lower 2θ angles 47 , which is contrary to what we observe in our spectra. The origin of such shift may be attributed to the crystallization of a transitional GeSbTe phase with Ge content higher than in GST225 (called G + GST). Indeed, the 375 °C XRD pattern is compatible with several phases with stoichiometry close to Ge3Sb2Te6 (GST326) (ICDD PDF No. 04-019-5066; 01-084-5074; 01-085-2822; 01-084-5063). N doping reduces the mobility of Ge in the alloy, which leads to the delay of the demixing process of Ge and GeSbTe phases to higher temperatures. As a result, the nucleation and growth rate of transitional G + GST phase is enhanced. Therefore, the transition step is more evident in N-doped samples. In the XRD pattern at 400 °C, the GST225 fcc peaks are well identified, with the presence of the broad band at ~ 30.5°, previously highlighted in GGST at 350 °C.

The diffraction peaks of Ge crystalline phase appear only at 450 °C. The crystallites sizes were estimated as before for [220] Bragg peak of GST fcc phase and for [111] Bragg peak of Ge crystalline phase (Table 2), confirming the delayed nucleation and growth of the identified phases. Table 2: Crystallites sizes calculated by Scherrer's law for GST and Ge phases from the XRD pattern of annealed GGSTN in Fig. 8.

N-doped GGST layers were further investigated by FTIR spectroscopy to support the previous results of Raman and XRD analysis. It is known that in N-doped GGST alloys, nitrogen tends to principally bond with Ge, forming thus the Ge-N bonds [48][49][50][51][START_REF] Navarro | IEEE 8th Int. Mem. Workshop IMW[END_REF][START_REF] Nolot | [END_REF] . A considerable charge transfer from Ge to N produces strong IR absorption bands related to the Ge-N bond structure well detectable by FTIR spectroscopy. IR spectra of both GGSTN and GGSTN + are shown in Fig. 9. In order to understand the impact of the presence of Sb and Te in GGST layers, we also prepared and analyzed N-doped single-element Ge thin layers (hereafter referred as GeN and GeN + ) with the same thickness and with the N incorporation close to N-doped GGST compositions. In both Ge and GGST layers, the main absorption band centered at ~ 700 cm -1 is assigned to the in-plane asymmetric stretching vibration of Ge3N skeletal group 39 . In GeN + and GGSTN + spectra, a second contribution at higher wavenumbers (750 -830 cm -1 ) appears, forming the large shoulder to the main absorption band. This second contribution is also ascribed to Ge-N stretching vibrations, but shifted to the higher wavenumber (with respect to the main peak at ~ 700 cm -1 ). The shift is the result of the inductive effect of higher nitrogen content, which is creating different chemical environment around the Ge atoms 39 . The increasing temperature does not affect N-doped Ge layers, where the main broad band of Ge-N vibration remains stable in position and FWHM. On the contrary, a significant shift of up to ~ 40 cm -1 (at 450 °C) to the higher wavenumbers is observed in GGSTN spectra as the annealing temperature increases. A similar shift is also observed in the spectra of GGSTN + , but reduced in size to ~ 10 cm -1 . As reported before, the shift to higher wavenumbers is due to a gradual change of the Ge and N atoms arrangement, in particular correlated to the impoverishment in Ge around the main Ge-N vibration. The trend is particularly evident in GGSTN where the crystallization of the layer is more advanced with respect to GGSTN + in the range of temperatures of our analysis. The comparison of almost unchanged spectra of GeN and GeN + with spectra of GGSTN and GGSTN + , reveals the effect of the ongoing crystallization of a GeSbTe phase on the nucleation of Ge and consequently on the perturbation of Ge-N system.

IV. Discussions and Complementary Experiments

Combining all the previous results from Raman, XRD and FTIR analysis in section III, we can finally highlight the main structural evolutions of Ge-rich GeSbTe alloys as a function of the annealing temperature. The as-deposited GGST sample features amorphous structure (XRD analysis, Fig. 5), which is usually associated with high level of disorder. Raman spectroscopy, however, reveals the vibration modes of structural Sb-Te units, which can be considered as the basis of the structure of GeSbTe alloys. It is important to note that these Sb-Te structural units remain stable from amorphous as-deposited samples up to samples annealed at high temperatures (Fig. 3).

The initial increase of the temperature up to 300 °C results in a first reorganization step, characterized by the decrease of Ge-Te modes and simultaneous enhancement of a-Ge modes (Fig. 4). Indeed, the breakage of unfavorable bonding in mixed GeSbTe units (e. g. GeSbTe3, Ge2SbTe2 or GeSb2Te2 54,55 ) and the rearrangement of GeTe4-nGen (n=0, 1, 2, 3, 4) tetrahedral units may occur in originally amorphous disordered system, both resulting in reduction of the Ge-Te modes. As a consequence, the overcoordinated Ge atoms in the mixed units are liberated, increasing the intensity of a-Ge modes. This is in agreement with previous investigations on amorphous GeTe alloys 37 , based on the random bonding model 56 , in which the combination of the different tetrahedra complex units depends also on the layer stoichiometry. The observed reorganization at low temperatures is also present in N-doped layers (Fig. 7); however, the reorganization process is prolonged up to a higher temperature due to the delay induced by N doping. The structural evolution is more significant at annealing temperatures above 300 °C. At this temperature, the Ge-Te modes evidence the minimum value (Fig. 7) related to the end of the first reorganization step. Higher annealing temperatures evidence the progressive increase of Ge-Te modes, which indicates the gradual rearrangement of Ge-Te bonds around Sb-Te features inside the crystalline GeSbTe phase. The crystalline GeSbTe phase then further nucleates and grows in the layer. On the contrary, disappearing of a-Ge modes at temperatures above 300 °C is associated with the reorganization of Ge structure and with the consequent nucleation and growth of Ge cubic phase (Fig. 3 and Fig. 5). N doping leads to the formation of Ge-N bond, affecting the mobility of Ge atoms. As a result, the demixing of GeSbTe and Ge phases as well as the process of nucleation of a GeSbTe phase are delayed to higher temperature. XRD analyses on both GGST and GGSTN samples showed the appearance of an intermediate structural evolution step at ~ 30.5° (2θ) (at 350 °C for GGST in Fig. 5, and at 400 °C for GGSTN in Fig. 8). Combining the results from GGST and GGSTN, we can suggest the formation of a transient phase (G + GST), which features higher Ge content with respect to standard GST225. Evidence of such double step crystallization can be already found in RvsT measurement of GGST in Fig. 1. In addition, the G + GST transient phase can even grow, as observed in GGSTN (Fig. 8) if the temperature and the duration of the annealing are high enough. To confirm the hypothesis of transient G + GST phase, we performed isothermal XRD measurements for the duration of 70 hours (Fig. 10). The temperature of the isothermal annealing was kept at ~ 300 °C, i.e. the temperature at which the first changes in XRD spectra are observed in Fig. 5 for GGST. The aim was to sufficiently slow down the entire mechanism and therefore to achieve the clear sequence of the different phases appearing in the spectra. The G + GST broad band appears in the spectra after about one hour of annealing. After only few hours, the [200] main peak of GST225 cubic phase starts to increase. The intensity of G + GST peak then decreases progressively as the intensity of the GST [200] peak increases. The gradual expulsion of Ge from G + GST continues in favor of the crystallization of more stable GST225 phase. This is rather in agreement with previous observations on a crystallization-induced segregation in Te-rich GeSbTe materials 57 . More than 30 hours of annealing are required to initiate the growth of Ge crystals, when Ge is finally accumulated on the grain boundaries outside of GeSbTe crystalline regions. The presence of GeSbTe crystalline interfaces likely induces the heterogeneous nucleation of Ge, followed by the rapid growth of Ge crystallites. The rapid growth of Ge crystalline phase overtakes the crystallization dynamics of the system and limits the further development of GeSbTe crystals (i.e. crystallite size of GST225 remains constant with temperature, as shown in Table 1). Heterogeneous nucleation of Ge from the neighbor seed crystal allows Ge to crystallize at the temperatures lower than at elemental a-Ge layers, as observed in Fig. 3. The main compositional steps of the GeSbTe phase developed in GGST layer in temperature are evidenced in Fig. 11. The Ge over Te ratio in GGST samples approaches 2:1. GST225, however, lies on the line between Sb2Te3 and GeTe where Ge over Te ratio is close to 1:1. As the Ge mobility increases in temperature, the local organization of the structure around the stable Sb-Te features drives the system locally towards a gradual expulsion of Ge, giving rise to a G + GST transient phase. The nucleation and growth of this G + GST transient phase then continues to feed the demixing process. The red circle in Fig. 11 highlights the region around GST326 in which possible transient phases can be found. Following this evolution, Ge-Te features evolve until a stable configuration of GST225 is reached (saturation observed in Fig. 4). We performed the TEM-EDX images on GGST samples (Fig. 12), in order to follow the demixing process in the alloy. The image of as-deposited (AD) layer indicates the perfect homogeneity of the prepared amorphous alloy. An elemental migration is already visible at 300 °C, which correspond to the end point of the first reorganization step, as observed by Raman spectroscopy (Fig. 3 and Fig. 4). The migration becomes more evident at 380 °C where the Ge-rich and Sb/Te-rich regions are already clearly separated. Formation of such regions evidences the demixing process of Ge and GeSbTe phase described above. Separated Ge-rich regions confirm the XRD findings (Fig. 5), where the already developed Ge crystalline phase is observed around this temperature. The phase separation is fully completed at 450 °C where the perfectly formed Ge and GeSbTe crystalline phases can be distinguished. Yellow squares in Fig. 12 highlight a region with GeSbTe grain. The crystallization growth of separated Ge and GeSbTe phases dominates the system at this temperature (crystallite sizes in Table 1).

Fig. 12: TEM-EDX analyses of GGST samples: amorphous as-deposited (AD) and annealed at 300 °C, 380 °C and 450 °C. Ge, Sb and Te cartographies highlight the ongoing demixing process.

As mentioned above, N doping retards the Ge diffusivity due to the formation of Ge-N bonds (Fig. 9) and delays the appearance of a GeSbTe crystalline phase to higher temperature. Besides, the nucleation rate and the growth speed increase with the temperature. Therefore, the G + GST phase can develop clear peaks in XRD spectra before the final transition towards a more stable GST225 phase (at 375 °C in Fig. 8). Continuous expulsion of Ge during the formation of the GST225 phase leads to the coexistence of crystalline GST225 and G + GST surrounded by Ge in excess. Ge crystalline phase appears only after the full development of the GST225 phase, which is clearly observed in GGSTN samples (development of c-Ge peak at 450 °C in Fig. 8). Indeed, the important role of N-doping in the delay of Ge crystallization is confirmed by FTIR results (Fig. 9), which highlight the gradual reduction of Ge atoms involved in Ge-N features. Ge-N bonds (EGe-N ~ 2.65 eV) are stronger than Ge-Ge (EGe-Ge ~ 1.94 eV) 39 and require higher annealing temperature for breaking. As discussed in section III, the shift of the peak energy of dipole vibration at higher wavenumbers, is associated with the change of Ge and N environment (Ge-N in different bonding configurations), in particular with an impoverishment in Ge 39 around the Ge-N bonds. The liberated Ge is then progressively involved in the crystallization process of a Ge cubic phase. Moreover, the presence of Te atoms in the environment of Ge-N bonds may also affect the IR shift presented in Fig. 9 and should be a subject of another study. The overall review of the steps of the structural evolution of GGST and GGSTN as a function of annealing temperatures is shown in Fig. 13.

V. Conclusions

In this work, we presented a thorough investigation of the structural evolution of undoped and N-doped Ge-rich GeSbTe phase-change materials with annealing temperature. Thanks to a wide set of techniques, such as Raman and FTIR spectroscopy, XRD, TEM-EDX, we observed the stability of the Sb-Te structural units in these alloys at increasing temperature and the gradual structural rearrangement of Ge-Te bonds around these units. We deeply investigated the mechanism of crystallization of GGST starting with the crystallization of a GeSbTe transient phase with higher Ge content than GST225 phase (G + GST) and consequent progressive expulsion of Ge. The system moves towards a complete separation of Ge and GST225 phases. After the GeSbTe stable phase is reached, the GeSbTe grains serves as a seeds for heterogeneous nucleation and crystallization of the Ge phase. Nitrogen in the as-deposited N-doped GGST layer leads to the formation of Ge-N bonds and reduces the Ge mobility. As a result, the process rearrangement of Ge-Te bonds and the global crystallization dynamic of the layer are delayed. Indeed, Ge-N bonds present in the layer affect the entire demixing process of Ge and GST225 phases, leading to the outstanding stability of N-doped Ge-rich GeSbTe materials at high temperatures.

Fig. 1 :

 1 Fig. 1: RvsT measurements for GST225, GGST and N-doped GGST thin layers. Dashed lines indicate the main resistivity transitions observed in the different alloys.

Fig. 2 :

 2 Fig.2: Raman spectra of amorphous as-deposited (AD) and annealed GST225 (from 250 °C up to 400 °C). Vertical lines at 154 cm -1 and 174 cm -1 highlight main Sb-Te features.

Fig. 3 :

 3 Fig. 3: Raman spectra of amorphous as-deposited (AD) and annealed GGST. Vertical lines show the position of the vibrational modes of SbTe3 units (154 cm-1 ) and crystalline Ge (297 cm-1 ).

Fig. 4 :

 4 Fig.4: Intensity evolution of Ge-Te, a-Ge and c-Ge modes from Raman spectra in GGST starting from as-deposited (AD) up to an annealing temperature of 450 °C.

Fig. 5 :

 5 Fig. 5: XRD pattern of amorphous as-deposited (AD) and annealed GGST up to 450 °C.Indexation is performed from database data (ICDD PDF No. 00-054-0484 and 00-004-0545).

Fig. 6 :

 6 Fig. 6: Raman spectra of amorphous as-deposited (AD) and annealed GGSTN. Vertical lines show the position of the vibrational modes of SbTe3 units (154 cm-1 ) and crystalline Ge (297 cm-1 ).

Fig. 8 :

 8 Fig. 8: XRD pattern of amorphous as-deposited (AD) and annealed GGSTN up to 450 °C.Indexation is performed from database data (ICDD PDF No. 00-054-0484 and 00-004-0545).

Fig. 9 :

 9 Fig. 9: FTIR spectra of amorphous as-deposited (AD) and annealed N-doped Ge and GGST.

Fig. 10 :

 10 Fig. 10: Isothermal XRD measurements at ~ 300 °C on GGST showing the development of GST225 and Ge crystalline phase (black and violet dashed lines, respectively). A transient G + GST phase (red dashed line) is detected before the appearance of GST225 phase.

Fig. 11 :

 11 Fig. 11: Ge-Sb-Te ternary diagram highlighting GST225 and GGST compositions. Red circle indicates the region (around GST326) of the transient G + GST phase that can give rise to start of partial crystallization in GGST as observed in XRD analyses.

Fig. 13 :

 13 Fig. 13: Diagram summarizing the main features highlighted in this work related to the structural evolution of GGST (black, bottom bars) and GGSTN (red, top bars) with annealing temperature.

Acknowledgments

This work has been performed with the help of the NanoCaracterization Platform of Minatec the financial support of the "Recherche Technologique de Base" program. It has been partially supported by the European 783176 WAKeMeUP Project, financed by European commission, French government and Auvergne-Rhône Alpes Region.

Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.