Jean-Christophe Dupré

Delphine Jullien

Luca Uzielli

Franck Hesser

Lorenzo Riparbelli

Cécilia Gauvin

Paola Mazzanti

Joseph Gril

Gilles Tournillon

Danièle Amoroso

Jean-Christophe Dupre
email: jean.christophe.dupre@univ-poitiers.fr

Philippe Hazael Massieux

Pierre Stepanoff

Marina Bousvarou

Experimental study of the hygromechanical behaviour of a historic painting on wooden panel : devices and measurement techniques

Keywords: Wood, panel painting, hygromechanical behaviour, optical method, strain measurement, Moisture-induced strain, Highlights

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

Experimental study of the hygromechanical behaviour of a historic painting on wooden panel : devices and measurement techniques

Introduction

An exhibition planned in 2018 at the Fabre Museum of Montpellier intended to promote public understanding of art conservation practice and collaboration between museum and research actors [START_REF]Dans le Secret des oeuvres d[END_REF]. This project involved several research laboratories, curators of the Museum and restorers. This paper describes the initial part of this collaboration consisting in the assessment of the hygromechanical behaviour of a wooden panel painting, before and after its structural and pictorial conservation. Indeed such structures experienced frequent climatic variations during the several centuries of their existence, leading to deformations and cracks of the wooden panel that were transmitted to the paint layer [START_REF] Arends | Relating relative humidity fluctuations to damage in oak panel paintings by a simple experiment[END_REF][3] [START_REF] Hunt | Strains in gesso on painted wood panels during humidity changes and cupping[END_REF]. In the past, rigid frames and structures were used to avoid distortions; nevertheless such devices could introduce large mechanical stress leading to serious damage to the artwork. Specifically, the artwork studied in this project showed large damage produced by an inappropriate "cradling" intervention implemented in an unknown period, mainly consisting of several cross-beams glued on the back face of the panel. Modern conservation techniques try to prevent possible damage through flexible frames and structures. Their optimised design requires an improved knowledge of the hygromechanical behaviour of both the panel and the back frame designed and built on purpose [START_REF] Marcon | Mechanical study of a support system for cupping control of panel paintings combining crossbars and springs[END_REF][6] [START_REF] Gauvin | Experimental and numerical study of the hygromechanical behaviour of a wooden panel[END_REF].

The location of the artwork in the middle of a museum hall open to the public required the design and implementation of specifically build equipment: a climatic enclosure and a suitable optical measuring system. Furthermore, a continuous monitoring (several data per hour during three years) was necessary to follow the behaviour of the panel during the imposed climatic variations. The experimental set-up and the principle of the experimental techniques will be detailed in this paper, together with the first part of the experimental campaign. The data recorded to describe the hygromechanical behaviour of the panel are the temperature, the relative humidity, the variations of the panel weight and the deformations. The weight was determined using a balance placed inside the show case. Changes in the shape deformation and the panel strain due to the climatic variations, were observed using two methods: three sets of displacement transducers fixed on the back face of the panel measured local curvatures [START_REF] Uzielli | The Deformometric, Kit: a method and an apparatus for monitoring the deformation of, wooden panels[END_REF] while a non-contact optical technique, mark tracking, was used for the assessment of the entire surface of the panel [START_REF] Brémand | Valle Mesures en mécanique par méthodes optiques[END_REF][10] [START_REF] Gauvin | Image Correlation to Evaluate the Influence of Hygrothermal Loading on Wood[END_REF] [START_REF] Gauvin | Strain measurements during structural conservation treatment and the longterm monitoring of a 17th-century Dutch panel painting[END_REF]. The correlation between local and whole-field measurements will be verified. The following paper will cover the whole campaign, and address the effects of the original engaged frame, of the inappropriate "cradling" mentioned above, of the results of the conservation work, and of the flexible back frame added as a result of this study.

Research aim

In order to acquire extensive data on the hygromechanical behaviour of the studied panel painting we have developed an experimental set-up including: a showcase allowing humidity variations to be applied while keeping both the painted face and the back face of the panel visible to visitors of the museum; a balance for weight variation measurement; three sensors for local strain measurement (deformometric kits, DK); and 2 stereo-image acquisition devices for the whole-field shape variation and strain measurement on the two faces of the panel. The monitoring allows us to show the correlation between the various data obtained and to describe the behaviour of the structure composed of the panel and its engaged frame, submitted to a variation of hygrothermal conditions.

Material and methods

3-1. The wooden panel and its original frame

La Sainte Trinité couronnant la vierge is an oil-on-wood panel of the sixteenth century, anonymous, which can be attributed to Flemish or Spanish art (Figure 1 The entire back face of the panel and the crossbars is covered with a brown layer whose composition has been identified on a sample taken, by micro-chemical analyses completed with an analysis by Fourier Transform Infrared Spectroscopy. The material consists of a mineral component based on lead white (or ceruse) mixed with red earth (iron oxides) and an organic part of a lipid nature (oil). It seems that this layer is more of a paint than a wash. Finally, it is important to note the presence of other layers in the sample, including residues from preparatory layers, very thin, that can be identified with a sizing material. The state of the panel described previously is an outcome of a previous conservation intervention, that may be regarded as inappropriate; the presence of the glued cross-beams clearly produced the vertical cracks in the boards, the separation between the boards, the cupping of the panel (different in its upper and lower parts), and the severe damage areas present on the paint layers, not described here.

3-2. Climate showcase

The showcase is made of four plywood panels and two anti-glare glasses that allow pictures to be taken, with dimensions 2400 mm × 1700 mm × 320 mm. It is mounted on a storage cabinet in which the humidity generator, the display unit of the scale and the computer for data acquisition are placed (Figure 2). The CIC-PMCG unit (Preservatech trademark) is a humidity generator that uses ionic electronic membrane to control the relative humidity (RH) in the showcase in the range 17% and 60% (with an accuracy of +/-3%) at a temperature (T) between 0 and 40°C simply by drawing moisture necessary for microconditioning from the surrounding environment. 22 mm input and output silicone hoses allow for air distribution and recirculation. A RH sensor is placed in the showcase and connected to the unit to regulate the climate. A second independent sensor is placed inside the showcase and connected to the computer to continuously record RH and T. The equipment does not control the temperature, which therefore depends on the temperature of the Museum's hall where the showcase is placed.

3-3. Weight measurement and isostatic restraint of the panel

The weight variation of the panel is measured using a Sartorius industrial scale, model Combics type CAWIP-1-60ED-I, with a range of 60 kg, an accuracy of 2g and dimensions of the plate of 400 mm × 300 mm × 94 mm. The weighing system uses a strain gauge sensor. The instrumented tray is connected by a 3 m cable to the display unit, itself connected to the computer via an RS232 interface.

The panel rests on the weighing pan, contact being made through two sliding supports that allow it to cup freely (Figure 2). It is held standing vertically by means of a horizontal connecting rod, terminated by two ball joints. One of these ball joints is connected to a steel bracket screwed to the back of the panel, near the centre of its upper edge, while the other one is connected to a second steel support rigidly bonded to the top of the showcase with a threaded rod to adjust the vertical position. This mechanism allows the panel to be held vertically, totally free to deform (realizing this way an externally isostatic constraint), and without affecting the weight measurement.

(a) (b)

(4) (3) (2) (1)
Figure 2 : The apparatus in the museum: climate chamber, optical device and vertical positioning device

3-4. Local strain and cupping measurement

The panel is monitored with 3 Deformometric Kits (DKs) [START_REF] Uzielli | The Deformometric, Kit: a method and an apparatus for monitoring the deformation of, wooden panels[END_REF] glued at the back of boards 2 and 3: DK1 and DK2 are placed in the upper and lower parts of board 2 respectively, DK3 in the lower part of board 3, horizontally aligned with kit 2 (Figure 3-a). The locations of the DKs have been chosen on undamaged parts of the boards, crossing no wood cracks nor separations between the two columns, otherwise the instrumental reading of the DK would have taken into account simultaneously both the deformation of the support and the movements of the crack lips without the possibility of decoupling the two contributions. The DK is an instrument that allows the continuous local monitoring of the deformation dynamics of the wooden panel with respect to both the external forces applied and the hygroscopic coactions: in other terms, it allows to understand the reactivity of the panel, the evolution of the cupping over time, and under some hypotheses (detailed in [START_REF] Uzielli | The Deformometric, Kit: a method and an apparatus for monitoring the deformation of, wooden panels[END_REF], with the operating principles) the deformation of the panel in the proximity of the device. It consists (Figure 3-b) in measuring the distance a and b between the two columns by two displacement transducers. Knowing the vertical distances m and z, geometrical characteristics of each kit, it is possible to calculate the base dimension e where the columns are fixed. Assuming that the base line c and g are an arc of circle, it is possible to calculate their length and thus the circumferential strains and the cupping angle . Uncertainty is a function of geometric parameters. For example, we have obtained for DK1: a=168.2 mm, b=166.7 mm, m=70.5 mm, z=29.8 mm, which gives an uncertainty close to 0.02% in strain and 0.06° for the cupping angle. Although not all of the above assumptions are fully true in this case, however data resulting from DKs were very useful in monitoring the panel's distortions and especially their evolution over time.

3-5. Optical measurements

Several optical techniques have been used for mechanical studies of historic wooden panels. The fringe pattern profilometry technique (FFP) [9][18] gives the relief and out-of-plane variations of a panel. It is being used to measure the relief of Mona Lisa painting [START_REF] Brémand | Relief analysis of the Mona Lisa's wooden panel[END_REF] [START_REF] Mohen | Mona Lisa, inside the painting[END_REF]. More recently shearography [START_REF] Morawitz | Detection of transport and age induced damages on artwork: an advanced concept[END_REF][17] coupled with FFP has been used to study the changes and damage areas of an artwork: FFP gives global variations of the out-of-plane displacement while shearograms detect local defects such as bubbles, delamination and tunnels caused by wood worms. These techniques are too complex to be implemented in a museum for automatic readings during several months and with visitors around. In addition, surface strains cannot be evaluated by FFP that gives only the relief. Photogrammetry, used in cultural heritage studies for 3D reconstruction of an object by multiple views [START_REF] Aicardi | Recent trends in cultural heritage 3D survey: The photogrammetric computer vision approach[END_REF], was also difficult to implement in this case. It was finally decided to obtain the 3D coordinates of surfaces by methods based on a triangulation calculation with a stereoscopic vision system. Two techniques have been considered: stereo-correlation [START_REF] Colmars | Hygromechanical response of a panel painting in a church, monitoring and computer modeling[END_REF][14] [START_REF] Orteu | 3-D computer vision in experimental mechanics[END_REF] and stereo-mark tracking [START_REF] Brémand | Valle Mesures en mécanique par méthodes optiques[END_REF][10] [START_REF] Gauvin | Strain measurements during structural conservation treatment and the longterm monitoring of a 17th-century Dutch panel painting[END_REF]. Both give the coordinates and the displacement of the zones of interest by following particular marks on the surface -that is to say, a gradient of grey level. The first one uses the painting or the natural aspect of the wood as marks. The second one follows a series of markers placed on the surfaces. All tests were performed using DEFTAC3D, a homemade software which controls image acquisition and analysis, computing displacements and strains on the specimen surface. For the back face of the panel, only the second solution could be used because the optical appearance is uniform due to the brown coating. Furthermore, the shadow of the crossbars moved during panel movement and introduced errors in the correlation process. For the painted face, both techniques were tested and several images of the same panel condition were recorded and analysed. In this case, the expected displacements are zero so the standard deviation of the measured displacement can be used to compare the two methods and assess their performance (Table 1). For the painted panel La Sainte Trinité, DIC was not effective enough due to the low contrast, and dark or bright zones (Figure 4) gave a large error or decorrelation phenomenon (wrong results). By increasing the size of the subset (100x150 pixels 2 to 200x200 pixels 2 ) the standard deviation decreased thanks to the lower number of areas with a decorrelation phenomenon. A median filter eliminated these wrong results, dividing the uncertainty in z displacement by 10. However this procedure was difficult to implement in the other directions (x,y), so that the mark 1 2 3 tracking technique was finally preferred. It should be noted that the choice of method depends on the paint; for another painting such as Sainte Agnès (Figure 4), very contrasted with many details enhancing the correlation, DIC and mark-tracking techniques gave similar results, and a better accuracy than La Sainte Trinité. . The procedure used by DEFTAC3D consists in defining a subset around each mark and an intensity threshold in order to extract the mark from the background (the painting). The marks could be white or black; in this case, the white colour was chosen. This procedure is automatic, the intensity threshold being modulated when the brightness of the images changes during the test, e.g. due to a modification of floor lighting or surface condition.

Paintings

. Strain calculation

The strain can be calculated globally to visualize the strains on the panel surface, or locally to study, for example, the curvature (cupping) and local strain in a given direction.

 2  2 x Cx 2 Cy 2 Cx 1 Cy 1 X Y Z L 1 L 2  1  1 dx 1 dx 2 X Y Z N 2 1 X Z = 2 - 1 1 2 3 back face  1  2 +

Whole-field strain calculation (see appendix B)

The strains are calculated by a finite differences process on a subset defined by 4 marks, where the deformations are assumed homogenous (Figure 5-a). Two vectors (dX1, dX2) in the initial state and two vectors in the deformed state (dx1 , dx2) are defined. For each loading step, the normal 𝑁 ̅ to the surface, locally defined by the markers, is calculated. Following the process described in appendix B, the strain tensor locally defined in a referential (1,2) tangential to the surface is then calculated [9][10]. It gives the strain values in direction 1 and 2 and the shear strain (Figure 5-b). This process is repeated on the whole surface. In the studied case the direction 1 is close to the horizontal axis (X), so that in next sections, the deformation in direction 1 will be called horizontal strain.

Cupping and local strain calculation

This calculation is done with series of 3 marks aligned horizontally. Cupping angles  are obtained as shown in Figure 5-c. Considering a small variation of the angles, the local horizontal strains are obtained with the difference in distance of marks 3 and 1. It should be noted that front and back faces are defined using the same orientation axis, so that <0 corresponds to a concave deformation of the front face and a convex deformation of the back face ([8]).

Performance

The study shown in Table 1 was sufficient to compare methods but not to evaluate the uncertainty, which was assessed by applying out-of-plane displacements of the grid used for calibration in the range of -20 to +20mm with a 5mm step. Such displacements induce variations of grey levels and distortion and are another source of error that can disrupt results. The bias error between imposed and measured displacements resulted in a standard deviation of 0.03 to 0.06 mm in the 3 directions (Table 2). The expected strain being equal to zero in this case, its calculated standard deviation (0.01%) gave a direct estimate (Table 2). Assuming a confidence interval of 95%, the uncertainty, defined as twice the standard deviation, is 0.06, 0.08 and 0.12 mm for the 3 displacements, 0.02% for strain and 0.14° for cupping angle. Small white stickers were placed on both faces of the panel; round markers were cut out of Japanese paper and reversibly attached to the paint layer with a weak adhesive face (9x13 marks) (Figure 2). Sticky round labels were glued on the back face (Figure 3-a) allowing to assess the panel and/or the cross bars (studied grid 10x12 marks).

Four cameras were placed on the walls to record images of both faces (Figure 2). The painted panel is placed in the climate chamber with two anti-reflective glasses. The lighting is done by 4 LED strips in the left, right, top and bottom edges of the showcase. The optical deviations due to the thickness of the glass are taking into account in the calibration process.

Results

The campaign presented in this paper concerns the first study period corresponding to a stabilization of the relative humidity of the panel -engaged frame assembly maintained at 52% RH then at 63% RH. Temperature T is not controlled but stays at 23+/-3°C Figure 6: Evolution of temperature, relative humidity and mass of the panel-frame assembly.

4-1. Interpretation of weight measurement

Wood is a hygroscopic material: it absorbs and releases water to be in equilibrium with its environment. Figure 6 shows the evolution of the mass of the panel and its frame, according to the RH and T ambient conditions. From 7 September to 7 November 2016, the assembly made of the panel and its engaged frame was subjected to a constant RH of 52%. Starting from an initial mass of 31.980 kg, it has reached a stable mass of 31.910 kg after two months. Then the environment was set to 63% RH, and the mass stabilized at 32.088 kg after 3 months. The total mass of 32kg is distributed into 16 kg of softwood frame, 1 kg of metal pieces fixed on it, 4 kg of fir reinforcement, 1 kg of deformometric kits and 10 kg of oak panel. The relationship between the equilibrium moisture content (EMC) of the wood and the RH of the environment at a given T is classically represented in the literature by two hygroscopic equilibrium curves: adsorption and desorption isotherms, for increasing and decreasing RH respectively, thus introducing the hysteresis phenomenon. The moisture content (MC) of wood in a varying environment tends to reach an EMC placed between these two curves, according to a trajectory that depends on the history of climatic conditions. Varnier [START_REF] Varnier | Comportement thermo-hygro-mécanique différé des feuillus -Des sciences du bois à l'ingénierie[END_REF] proposed equations for these boundary curves based on a limited number of parameters:

𝑤 + (ℎ) = 𝑤 𝑠 . exp[𝜑 + .

ln ℎ . exp(𝛼 + ℎ) ]

(1)

𝑤 -(ℎ) = 𝑤 𝑠 . exp[𝜑 -. ln ℎ . exp(𝛼 -ℎ)] ( 2
)
where h is the RH value, 𝑤 + and 𝑤 -the EMC of the adsorption and desorption isotherms, respectively, 𝜑 ± and 𝛼 ± constants defining the shape of the isotherms, and 𝑤 𝑠 the fiber saturation point (FSP), i.e. the EMC reached by wood in a saturated environment (h=100%). The FSP depends on T according to :

𝑤 𝑠 = 𝑤 𝑠 0 -𝛽. 𝜃 (3
) where 𝜃 is the value of T expressed in °C, 𝑤 𝑠 0 the FSP at 0°C and 𝛽 a constant. According to Varnier [START_REF] Varnier | Comportement thermo-hygro-mécanique différé des feuillus -Des sciences du bois à l'ingénierie[END_REF] 𝑤 𝑠 0 and 𝛽 depend on the wood species while 𝜑 ± and 𝛼 ± can be given sets of values for all softwood species and for all hardwood species. Parameter estimates are given in Table 3 for each of our wooden parts: douglas for the frame, spruce (similar to fir) for the reinforcement, oak for the panel.

The temperature inside the climate showcase was influenced by the ambient temperature, lower in winter; we recorded an average value of 24°C and 21°C for the relative humidity levels of 52% and 63% respectively. Table 4 shows the expected values of EMC in adsorption (w + ), desorption (w + ) and mean value <𝑤 ± >, for the two considered environments, for each species, calculated from equations ( 1) and (2). The "total" line is calculated from the moisture contents obtained for each species, considering the proportion of the different types of wood, indicated in the last column.

Assuming that the initial mass corresponds to a MC of 11.3%, average of the mean values of the two considered states (10.2% and 12.4%), we can estimate the dry mass of wood of the panelframe assembly as m 0 =30/1.113=26.9 kg and thus calculate the mass corresponding to each EMC. The 2 kg mass of metal pieces and deformometric kits is kept constant. w + : adsorption EMC; w -: desorption EMC; <𝑤 ± > : mean EMC m + and m -: corresponding total weight compared with measured value.

Figure 7 illustrates how the mass of wood evolves, from its initial value of 30kg at intermediate RH (estimated at 57.5%), to the stabilized value at 52% RH and then at 63% RH. It does not reach the adsorption or desorption curves but follows their trends. We have measured a small increase of 0.6% of the mass of the panel-frame assembly, from 52 to 63% RH: this is much smaller than the 2.0% corresponding to the increase of adsorption curve on this interval. These measurements clearly show the error being made by an estimation solely based on the adsorption, desorption or even average curves for predicting a change in moisture content resulting from a given RH variation.

4-2. Relief measurement

3D coordinates of each marks have been represented on Figure 8-a. The relief of the panel was concave with an amplitude of 16 mm (Figure 8). The maximum of the curvature is located on the upper part of the panel especially on the two corners. Bilinear interpolation between these data allows us to view a mapping of the painting. The back face relief was also determined and gave similar results.

4-3. Deformation of the panel induced by relative humidity (RH)

4.3.1. Whole-field analysis This section analyzes the deformations of the panel, as provided by the collected data. A more thorough analysis will be provided in a future paper, with greater attention to conservation aspects. It should be however borne in mind that the deformations here considered are strongly influenced by the presence of the glued cross-beams, which can be seen as the result of an inappropriate intervention that strongly contributed to the separation and cracking of the boards, and to the damages of the paint layers.

The out-of-plane displacements of the two faces of the panel were plotted (Figure 9) for states A and B, i.e. after stabilization in the climatic chamber of the panel and after a 10% RH increase and stabilization, respectively (see Figure 6). In the first few days we observe a concave bending due to the decrease in the moisture content of the wood (Figure 9-a). After 40 days, no more change is observed (state A). The increase in RH results in a stabilized convex bending on state B. As the initial state was not a stabilized state of the panel, we have observed that the outof-plane displacement values are a small convex bending due to the 10% increase in RH. Taking state A as the new initial state, we can observe (Figure 9-b) the effect of the 10% RH increase with a maximum deflection of 1.5 mm.

Note: According to the fixation system described in previous section 3-3, the centre of the upper edge of the panel should show no out-of-plane displacement. In fact, the vertical threaded bar proved to be insufficiently rigid, and the horizontal connecting rod suffered variable out-ofplane displacements (Figure 9) under the action of the variable overturning moment, which was produced by the progressive horizontal displacement of the centre of gravity of the deforming panel. The strain fields of the painted front face and of the back face have been plotted for each of the 4 vertical oak boards, for which a continuous material has been assumed (Figure 9). We focus here on the horizontal strain E 11 because it corresponds to the radial or tangential direction of the material, perpendicular to the grain of the boards, which presents the most significant moisture-induced deformations. Relatively to the initial condition in September 2016, E 11 strain exhibits a global shrinkage during initial stabilization and a global swelling during the 10% RH increase (Figure 9-a). As with the visualization of the out-of-plane displacement, to observe the effect of +10% RH, state A was taken as the reference state (Figure 9 subjected to a swelling with an average strain of about 0.08%. A heterogeneous strain field is observed, especially on the back face; these heterogeneities, for example in the upper left corner of the panel, being related to the cracks observed on the back face (in yellow on Figure 9), and to the glued cross-beams possibly having produced them. In these areas a positive strain can be interpreted as the opening of a crack and a negative one as the closing of a crack. We have to note that in the back view, the pitch of the strain field is not regular because some subsets have been shifted to avoid the overlapping by the Deformometric Kits.

An increase of about 0.6% of moisture content between states A and B has been measured. According to the literature [23] the mean swelling coefficients of oak are 4.5% and 9.7% in radial and tangential directions, between dry and saturated states, with a fibre saturation point of 31%. Assuming a linear relationship between swelling coefficients and moisture content, we can roughly calculate that an increase of 0.6% of moisture content corresponds to a radial strain of 0.10%, and a tangential strain of 0.22%, in the case of unrestrained boards. Considering the orientation of the boards, we could have expected higher values of strain in board 4 (on the left edge), which is a tangential board, compared to boards 1 to 3 which are radial boards: on the contrary, we cannot observe a significant difference. Anyway, the observed horizontal strains, ranging from 0.0 to 0.1%, are obviously limited by the effect of the crossbars (which are glued on the boards with their longitudinal direction perpendicular to the longitudinal direction of the boards) and disturbed by the effect of the cracks in the upper parts of the boards 1, 2 and 3. The engaged frame may also contribute to restraint the deformation of the panel painting.

Local analysis

The local analysis is done using the 3 DKs placed on the back of the panel and giving locally and accurately the strain and the cupping angle. With the optical technique it is possible to obtain comparable values with a lower accuracy (uncertainty of 0.02% for strain and 0.14° for cupping angle, respectively 0.003% and 0.014° for the DKs). An average filtering (on 24 data) is applied to the results (grey points). Nevertheless, the instrumental readings taken with optical methods and with DK show a good agreement, both for the values and for their evolution over time (Figure 10). It should be noted that the same filtering can be used on the DK strain.

Conclusion

Several devices and techniques have been developed and used to study the hygromechanical behaviour of a wooden panel visible in situ in a Museum hall open to the public. First, an RHcontrolled showcase has been developed to control variations of the micro-environmental conditions surrounding the panel. It has been designed to be placed in a museum, with two glasses allowing the visitors to see both faces of the panel and also the use of optical techniques. A balance was included to measure the variations of panel weight. The DKs allowed us to follow accurately the local curvature and deformation on chosen zones and directions. They could be used continuously even if the panel was moved. The used optical technique was a non-contact and non-disturbing method even if in this case we had to put marks on the two surfaces. It provided global data (displacement and deformation) on the whole front and back faces of the panel and can be used locally too, even if the accuracy is lower than that of DKs. The combination of these techniques allows us to study the hygromechanical behaviour of a wooden panel painting. Mass measurement, global deflexion and strain with optical techniques, local strains with DKs are complementary. A study of the painting including the hygrothermal conditions, the effects of the frame and of the conservation, will be presented in a next paper.

F ̿ = [ F XX F XY 0 F YX F YY 0 F ZX F ZY 0 ] (A.4)
Each component of this tensor is expressed by the coordinates and displacements of the four marks. Then the 2D strain Green-Lagrange tensor 𝐸 ̿ located on the surface of the panel can be calculated in the referential [START_REF]Dans le Secret des oeuvres d[END_REF][START_REF] Arends | Relating relative humidity fluctuations to damage in oak panel paintings by a simple experiment[END_REF]. It represents the Lagrangian deformations assumed uniform in the area defined by the four marks [START_REF] Arends | Relating relative humidity fluctuations to damage in oak panel paintings by a simple experiment[END_REF]:

𝐸 ̿ =

  -a). The panel is presented in a softwood frame, 135 mm wide and 40 mm thick in average, linked with eight metallic fasteners distributed around the periphery of the panel (Figure1-b). Two metal plates with ring screwed in the upper part of the frame allow it to be fixed to the wall. The unframed panel is 1370 mm high and 980 mm wide; the thickness varies between 10 and 13 mm. It consists of four vertical oak (Quercus sp.) boards numbered from 1 to 4 from right to left, mostly separated (unglued) from each other (blue lines on Figure1-a). Vertical cracks have been detected (red lines on Figure1-a) on boards 1 to 3. The boards are quarter sawn (radial grain), except board 4 which is flat sawn (tangential grain), connected by seven horizontal crossbars of section 35 mm (width) by 15 mm (thickness) made of fir (Abies sp.) and glued onto the oak planks (Figure1-b). Additional vertical crossbars of same section of fir wood are nailed to them, thus forming half-lap joints. The vertical crossbars at the left and right edges of the back face are one piece, while the other four vertical crossbars are divided into six pieces.

Figure 1 :

 1 Figure 1 : Front face (a) and back face (b) of the panel

Figure 3

 3 Figure 3 : a) Position of the 3 deformometric kits b) schematic representation from [8]

Figure 4 :

 4 Figure 4 : Two examples of paintings: (left) La Sainte Trinité couronnant la vierge, 1516, oilon-wood panel, Montpellier, musée Fabre, D61.1.379 (Depository of the Emile Zola Central Media Library) (before the removal of protections) and (right) Le couronnement de Sainte Agnès entourée des scènes de sa vie, 1519, oil-on-wood panel, Montpellier, N° IOM3999, property of the diocesan association of Montpellier, classified as a monument on 2005/05/02

Displacements

  𝑈 ̅ = (U x , U y , U z ) are obtained by calculating the difference in position between two recorded images at different times or loading states. U z represents the out-of-plane displacement. a) stereoscopic device (b) Strain tensor calculation (deformed state) (c) Cupping and local strain calculations

Figure 5 :

 5 Figure 5: Mark tracking technique, schematic representation of triangulation process and principle of the calculation of the strain field and the local strain

Figure 7 :

 7 Figure 7: Measured mass as function of relative humidity, compared to adsorption and desorption curves calculated in table 4.

Figure 8 :

 8 Figure 8: Panel relief of the front face (Z values x10): a) 3D coordinates of the marks, b) a mapping view using ParaView software (bilinear polynomial interpolation and assumption of a continuous relief field).

  a) State A versus initial state b) State B versus state A Figure 9: shape deformation and horizontal strain of the front and back faces of the panel relative to the initial state (September 2016) or relative to the stabilised state A, view from the front face (cracks in yellow, joints between the boards in red)

  -b). The panel is mainly Shape

Figure 10 :

 10 Figure 10: Comparison between data obtained by the DK1 and the mark tracking method

Table 1 :

 1 Standard deviation of the 3 components of displacement, for DIC (with several subset sizes) and mark-tracking methods.

		Methods	𝜎 𝑥 (mm)	𝜎 𝑦 (mm)	𝜎 𝑧 (mm)
	La Sainte Trinité DIC (front)	0.2 (100x150)	1.98 (100x150)	0.94 (100x150)
			0.14 (200x200)	0.34 (200x200)	0.25 (200x200)
		mark tracking (front)	0.014	0.028	0.047
	Sainte Agnès	DIC	0.028 (150x150) 0.042(150x150) 0.045 (150x150)
		mark tracking (back)	0.029	0.040	0.055

Table 2

 2

	: Statistical results obtained during out-of-plane displacement test
		X direction	Y direction	Z direction
	Average displacement gap (mm)	-0.008	-0.008	-0.009
	Standard deviation of displacement gap	0.03	0.04	0.06
	(mm)
	Standard deviation of strain	1e-4	1e-4	Not measured
	Standard deviation of cupping angle	Not measured	0.07 °	Not measured
	3.5.4. Arrangement of the devices

Table 3 :

 3 Constants used to described sorption isotherms according to equation (3)[START_REF] Varnier | Comportement thermo-hygro-mécanique différé des feuillus -Des sciences du bois à l'ingénierie[END_REF]

			𝑤 𝑠 0 (%) 𝛽 (10 -3 )	𝜑 +	𝜑 -		𝛼 +	𝛼 -
	Douglas (frame)	29.4	1.02	0.820	0.761	1.435	0.988
	Spruce (fir reinforcement) 30.4	1.12
	Oak (panel)		33.4	1.08	0.849	0.852	1.647	1.088
	Table 4: Estimates of EMC and corresponding total weight
	T, RH		24°C, 52%		21°C, 63%			initial mass
		w + (%) w -(%) <𝑤 ± > (%) w + (%) w -(%) <𝑤 ± > (%)	proportion
	Douglas	8.7	11.7	10.2	10.7	14.2		12.4	53.3%
	Spruce	8.9	12.0	10.5	11.0	14.5		12.8	13.3%
	Oak	8.3	11.6	12.7	10.3	14.3		12.3	33.3%
	Total	8.6	11.7	10.2	10.6	14.2		12.4
		m +	m -	measured	m +	m -	measured
	Mass kg	29.3	30.1	29.9	29.8	30.8		30.1

Acknowledgement

The authors sincerely thank the Fabre Museum, its staff and all the involved professionals, for their dedication and for the support provided.

Funding:

This research work has been based on a formal joint agreement [Contract number 160574] between Montpellier Méditerranée Métropole (the Fabre Museum financing institution) and the Universities of Montpellier, Poitiers and Firenze.

Appendix A : Principle of the mark-tracking method

The first step consists in calculating the coordinates 𝐶 ̅ 𝐶1 and 𝐶 ̅ 𝐶2 of each mark in the referential of the two sensors (camera 1 and 2) (Figure A-1): [START_REF] Brémand | Valle Mesures en mécanique par méthodes optiques[END_REF][10] [START_REF] Bretagne | Recent developments of the mark tracking technique: application to strain field and volume variation measurements[END_REF] 𝐶 ̅ 𝐶𝑗 = (

i is the index of each pixel of (𝑥 𝑖 , 𝑦 𝑖 ) coordinates and 𝐼 𝑖 grey level. A subset is delimited around each mark defining the area of interest. 𝐼 𝑠 is an intensity threshold of the studied subset. This last defines whether a pixel belongs to the markers or is a part of the image background. These subsets are automatically defined, furthermore their intensity threshold can be modulated when the brightness of the images changes during the test (due to a change in the lighting of the floor, a change in the surface condition ...), for example, according to the average of the values of the subset.

The 3D coordinates 𝑋 ̅ = (𝑋, 𝑌, 𝑍) of the marks are given by:

With 𝐺 ̿ 1 , 𝐺 ̿ 2 the transformation matrix ( 1 ,  2 , L 1 , L 2 the magnifications and the positions of the cameras) and 𝑅 ̿ 1 , 𝑅 ̿ 2 the rotations (angular positions:

Calibration is required to obtain geometric parameters. It consists in solving formula (A-2) using data obtained from images of a grid of marks with known positions of points. A recording of several images for different grid positions allows to calculate the parameters and to identify a 3D polynomial function related to optical distortion We have to note that the calibrations of the two couples of camera are done in the same referential, the coordinates and displacements obtained are then in the same referential too (X,Y,Z)

Appendix B : Strain tensor calculation

The strains are calculated by finite differences on a subset defined by 4 marks. Two vectors (dX1, dX2) in the initial state and two vectors in the deformed state (dx1 , dx2) are calculated (Figure 5). For each loading step, the normal 𝑁 ̅ to the surface, locally defined by the markers, is calculated. It gives two angles (, ) defining the orientation of the normal both in the initial state and in the deformed state.

The gradient tensor of the transformation F ̿ [START_REF] Brémand | Valle Mesures en mécanique par méthodes optiques[END_REF][10] is obtained by solving the system dX i F ̿ dx i with i = 1,2:


Luis Tito De Morais

Jean Guillard

Monique Simier

Ibrahim Sow

Jean Raffray

Jean Jacques Albaret

Fish population surveys in estuaries : a comparison between acoustic at moored stations and purse seine surveys

come

Introduction

 2000). Scientific interest is increasingly focusing on the effects of major natural or human perturbations on aquatic ecosystems, yet in this field of research few studies have been conducted on estuarine systems, particularly in the tropics. There are very few estuaries or coastal lagoons that can be used as an example of an undisturbed ecosystem. To some extent, the Gambia River Estuary may be considered an exception. It is the last and only large estuary in the West-African sub-region not to have been affected by extensive and/or intensive human disturbances.

Three types of complementary data were simultaneously collected: acoustic data, biological data and environmental data. Echosounding was performed vertically during daytime from a moored position during 30 minutes along with purse seine surveys performed from a second boat (Albaret et al., 2004, Guillard et al., 2004). Acoustic biomass and fished biomass were log transformed and recorded as logSa and logBiom. Each numerical environmental variable was ranked into quartile classes. Within each variable class the correlation between logSa and logBiom was then calculated and the correlation coefficient significance was tested. Classes in which the correlation between logSa and logBiom was significant allowed to infer which environmental conditions favour or not the adequation between the two methods.

The following were the environmental conditions of best correlation between the two methods : 1. Depth >= 6.9 m (third quartile: R=0.49, p=0. The lack of correlation between acoustics and seining at depths lower than 6.9 m is probably related to the fact that acoustics is expected to be less performing in very shallow waters. The purse seine is expected to perform well in a depth range from 2 to 18 m.

Both methods perform well when turbidity is high. The visual stimuli of the boat presence, and possibly of the net towing at the begining of the seine haul is expected to be reduced when turbidity is high.

Salinity and temperature are corrected for bias during acoustic operations and it is unlikely that purse seine had different performances with regard to these two variables. We suggest that the better correlation observed in fresh water and at high temperatures than at high salinities and low temperatures was related to the species composition associated with each environmental conditions. At higher salinities and temperatures, most species are pelagic clupeids living in schools, and the probability of such schools being seen by the sonar is higher than that of a school being captured by the purse seine.

Fish show complex day/night behaviour patterns in relation to environmental variables, the combination of which may explain the fact that the best correlation was observed in the middle of the day. Yet current speed, turbidity, depth, salinity and thus species composition and behaviour are expected to play the greatest role (Krumme and Saint-Paul, 2003).

As a rule, the major source of bias and imprecision in acoustic abundance estimates of semi-demersal fish is detectability, defined here as the proportion of the true abundance of a target species within the ensonified volume (surface to bottom) that is detected by an echosounder and included in integration (Lawson and Rose, 1999). The purse seine catches as well as acoustic detections are subjected to environmentally induced variations. Both are submitted to variability related to species presence and fish habitat preferences. Variations in detectability are also caused by species composition and diel vertical movements. The patterns observed during this work reflect this complex interaction of environmental factors and fish behaviour.

  , UR RAP, CRH BP 171, 34203 Sète Cedex, France ; (d) ISRA,CRODT, BP 2241, Dakar Sénégal.tito@ird.sn, guillard@thonon.inra.fr, simier@mpl.ird.fr, sowibou1947@yahoo.fr, raffray@ird.sn, albaret@ird.snMaterial and methodsMaterial and methodsPosterPresented at the INTERNATIONAL CONFERENCE ON COASTAL ECOSYSTEMS: Poster Presented at the INTERNATIONAL CONFERENCE ON COASTAL ECOSYSTEMS: Towards and Integrated Knowledge for an Ecosystem Approach for Fisheries Towards and Integrated Knowledge for an Ecosystem Approach for Fisheries June 26 -29, 2006 Campeche, México June 26 -29, 2006 Campeche, México Throughout the world, estuaries are among the most modified and threatened environments (Blaber et al.

  004 and fourth quartile: R=0.47, p=0.007) 2. Transparency <= 0.2 m (first quartile: R=0.49, p=0.0018) 3. Null salinity (first quartile: R=0.58, p=0.00029) 4. Temperature >29.1 (fourth quartile 4, R=0.48, p=0.0049) 5. Oxygen <=76% (first quartile: R=0.53, p=0.001 and second quartile: R=0.63, p<0.000) 6. Time: best correlation in the middle of the day (between 10h AM and 1 PM) 7. Current speed: high current (Classes 2 and 3) 8. Field campaign: end of the dry season.

  Transparent cool salt water Purse seine and acoustic sampling correlation Albaret, J.J., M. Simier, F. S. Darboe, J.-M. Ecoutin, J. Raffray and L. Tito de Morais, 2004. Fish diversity and distribution in the Gambia Estuary, West Africa, in relation to environmental variables. Aq. Living Res., 17: 35-46. Blaber, S.J.M, Albaret, J. J and C. V. Ching, 2000. Effects of fishing on the structure and functioning of estuarine and nearshore ecosystems. ICES J. Mar. Sci., 57 : 590-602. Guillard, J., J.-J. Albaret, M. Simier, I. Sow, J. Raffray and L. Tito de Morais, 2004. Spatio-temporal variability of fish assemblages in the Gambia Estuary (West Africa) observed by two vertical hydroacoustic methods: Moored and mobile sampling, Aq. Living Res., 17: 47-55. Krumme, U. and U. Saint-Paul, 2003. Observations of fish migration in a macrotidal mangrove channel in Northern Brazil using a 200-kHz split-beam sonar. Aq. Living Res., 16: 175-184. Lawson, G.L. and G. A. Rose, 1999. The importance of detectability to acoustic surveys of semi-demersal fish. ICES J. Mar. Sci., 56 (3): 370-380.


Lipin Chen

Oliver Skibitzki

Laurent Pedesseau

Antoine Létoublon

Julie Stervinou

Rozenn Bernard

Christophe Levallois

Rozenn Piron

Mathieu Perrin

Markus Andreas Schubert

Alain Moréac

Olivier Durand

Thomas Schroeder

Nicolas Bertru

Jacky Even

Yoan Léger

Charles Cornet

Strong Electron-Phonon Interaction in 2D Vertical Homovalent III-V Singularities

Keywords: III-V semiconductor, 2D vertical homovalent singularity, carrier confinement, phonon confinement, electron-phonon interaction

Highly polar materials are usually preferred over weakly polar ones to study strong electron-phonon interactions and its fascinating properties. Here, we report on the achievement of simultaneous confinement of charge carriers and phonons at the vicinity of a 2D vertical homovalent singularity (antiphase boundary, (APB)) in an (In, Ga)P/SiGe/Si sample. The impact of the electron-phonon interaction on the photoluminescence processes is then clarified, by combining transmission electron microscopy, X-ray diffraction, ab initio calculations, Raman spectroscopy and photoluminescence experiments. 2D localization and layer group symmetry properties of homovalent electronic states and phonons are studied by first principles methods, leading to the prediction of a type II band alignment between the APB and the surrounding semiconductor matrix. A Huang-Rhys factor of 8 is finally experimentally determined for the APB emission line, underlining that a large and unusually strong electron-phonon coupling can be achieved by 2D vertical quantum confinement in an undoped III-V semiconductor. This work extends the concept of electron-phonon interaction to 2D vertically buried III-V homovalent nanoobjects and therefore provides different approaches for material designs, vertical carrier transport, heterostructure design on silicon and device applications with weakly polar semiconductors.

interaction is commonly quantified with the so-called Huang-Rhys factor S, whose maximum value may reach 100 with alkali halides. [START_REF] Leung | On the Luminescence Quenching of F Centres in Alkali Halides[END_REF] On the other hand, group-II-VI, III-V or IV semiconductors, have been widely used in photoelectric device applications due to their excellent optical and/or transport properties. When these bulk materials are pure and undoped, the electron-phonon interaction remains generally weak, reflected by quite low Huang-Rhys(S) factor (e.g. 0.0033 for InAs [START_REF] Bissiri | Optical Evidence of Polaron Interaction in InAs/GaAs Quantum Dots[END_REF] and 0.035 for CdSe [START_REF] Gindele | Phonon Interaction of Single Excitons and Biexcitons[END_REF] ), as the chemical bonds are either covalent (group IV) or slightly polar (group III-V or II-VI). Effective enhancement of the electron-phonon interaction was successfully obtained by using spatial confinement or carrier localization effects. [START_REF] Heitz | Enhanced Polar Exciton-LO-Phonon Interaction in Quantum Dots[END_REF] A. Alkauskas et al. comprehensively and deeply discussed the electron-phonon interaction in III-V semiconductors defects. [START_REF] Alkauskas | Tutorial: Defects in Semiconductors-Combining Experiment and Theory[END_REF] Especially, punctual antisite defects were found to greatly enhance the electron-phonon interaction. [START_REF] Fockele | Arsenic Antisite Defects in Al x Ga 1x As Observed by Luminescence-Detected Electron-Spin Resonance[END_REF] M. Kang et al. discovered Holstein polaron in surface-doped layered MoS 2 semiconductor. [START_REF] Kang | Polaron in a Valley-Degenerate Two-Dimensional Semiconductor[END_REF] Electron-phonon coupling was also investigated in many different localized systems such as nanoscale core-shell structures, [START_REF] Yu | Engineering Acoustic Phonons and Electron-Phonon Coupling by the Nanoscale Interface[END_REF] graphene and InAs double quantum dot (DQD) systems, [START_REF] Roulleau | Coherent Electron-Phonon Coupling in Tailored Quantum Systems[END_REF] WSe 2 /hBN heterostructure, [START_REF] Jin | Interlayer Electron-Phonon Coupling in WSe 2 /HBN Heterostructures[END_REF] or graphene/Monolayer h-BN structure. [START_REF] Brar | Hybrid Surface-Phonon-Plasmon Polariton Modes in Graphene/Monolayer h-BN Heterostructures[END_REF] In this work, we demonstrate strong electron-phonon interactions in a 2D III-V singularity, which combines both phonon and charge carrier confinements. The nanostructure is composed of a vertical atomically-thin In-rich Indium gallium phosphide ((In,Ga)P) antiphase boundary (APB), where the homovalent bonds drastically change the local polarity and charge distribution in the crystal, leading to efficient phonon confinement and localized holes wavefunctions. It is furthermore surrounded by a Ga-rich (In,Ga)P barrier enabling the quantum confinement of carriers. The unusual electron-phonon coupling strength measured in these buried and non-oxidized III-V vertical singularities provides many perspectives to understand the physics of the electron-phonon interaction in semiconductors.

RESULTS AND DISCUSSION

APBs are commonly formed during the epitaxy of Zinc-Blende III-V semiconductors on a group IV substrate in the diamond phase (e.g. silicon (Si) or Germanium (Ge)). It originates from the two different ways for the III-V crystal to fit the group IV substrate orientation. [START_REF] Lucci | Universal Description of III-V/Si Epitaxial Growth Processes[END_REF] As a consequence, two domains with different phases may grow on the same substrate, separated by wrong III-III or V-V bonds, inside the III-V matrix, as illustrated in Figure 1a. At first, APBs might be considered as detrimental non-radiative defects, comparable to grain boundaries in other polycrystalline materials. But we aim at demonstrating in the present work, that their topology is fundamentally different in nature, as they do not contain any dangling bonds, and respect the lattice ordering. The insertion of a local translational symmetry breaking, III-III(V-V) bond also adds 2 free holes (2 free electrons) in the semiconductor. However, unlike doping, APBs extend in the form of vertical 2D planes (at least locally), that can emerge at the sample surface. Theoretically, the APB composition may range from a pure vertical III-III APB to a pure V-V APB, resulting in these two extreme cases to a large excess of charges released in the lattice. But stoichiometric APBs (with equal numbers of III-III and V-V bonds within the same APB), as illustrated in Figure 1a, are more likely to form due to their relatively low formation energy resulting from the charge compensation effect. 19 1c and Figure 1d, respectively. The sample is composed of three main layers: a Si substrate, a 760 nm-thick Si 0.433 Ge 0.567 buffer layer and a 210 nm-thick InGaP III-V layer (Figure lb) with a nominal In content of 30%. The last epitaxial layer was grown at relatively high growth temperature (500°C) and low growth rate, to enhance non-equilibrium kinetic effects during the growth of the metastable (In, Ga)P alloy. Especially, In atoms are well-known for their ability to efficiently migrate at the surface of InGaP semiconductors due to their low binding energy to the substrate. In this sample, APBs are propagating almost vertically until the surface (boundary between dark grey and clear grey in Figure 1d), giving rise to 2D vertical homovalent singularities. The 2D vertical homovalent singularities shown as random honeycomb-like lattice at the surface (black lines in Figure 1c) separate the different domains, as illustrated in Figure 1b.

Elemental mapping by an energy-dispersive X-ray (EDX) system in a scanning transmission electron microscope (STEM) was employed to analyze local chemical composition in the sample. Figure 1e presents the cross-sectional bright field image of the sample along the [110] direction. The black line in the middle represents one APB. Figure 1f-1i show the corresponding EDX mapping images of indium (Figure 1f), gallium (Figure 1g), phosphorus (Figure 1h), and silicon (Figure1i). Figure 1j-1l show the plane view EDX mapping images of indium (Figure 1j), gallium (Figure 1k), and phosphorus (Figure 1l). Additional STEM and EDX images are given in the supplementary materials (Figure S1 and Figure S2). First, almost pure InP surface quantum dots (QDs) are evidenced in Figure1c (black circular areas) and in Figure 1j, arising from demixion due to the non-equilibrium growth conditions used. [START_REF] Yuan | Interplay Effect of Temperature and Excitation Intensity on the Photoluminescence Characteristics of InGaAs/GaAs Surface Quantum Dots[END_REF] Removal of these surface QDs will be discussed hereafter. Second, a preferential incorporation of In in the close vicinity of the antiphase boundary singularity is observed, together with an In-rich phase at the surface where the singularity emerges. Additionally, the use of X-Ray diffraction (see the supplementary materials), combined with EDX analysis allows the determination of In contents in the sample. The In composition inside the various domains (the largest part of the (In,Ga)P crystal) amounts to about 18%. On the contrary, it is hard to determine precisely the In content of the In-rich (In,Ga)P alloy close to the antiphase boundary singularity, but from EDX contrast, we deduce that the local content is larger than 60%, suggesting that the APB structures at the atomic scale are closer to InP-based APB rather than GaP-based APB. Finally, the In-rich phase observed at the vertical of the APB (where it emerges) is composed of pure InP. At the III-V/Si interface, intermixing is not observed. The origin of In accumulation at the APB level rather than Ga is therefore generally connected to the formation of an InP nanostructure at the surface where it emerges, to feed progressively the APB during the growth.

In accumulation and InP nanostructure formation are the consequences of stress and electrostatic interactions induced at the surface where the APB emerges, and the favored migration of In atoms. A sketch of a possible growth mechanism consistent with these experimental observations is indicated in the supplementary information part (Figure S3). Overall, this preferential indium incorporation leads to the presence of a quantum confinement for carriers around the 2D homovalent singularities.

We demonstrate in the following, that the 2D homovalent APB singularities are interesting nano-objects with original optical, vibrational or electronic properties due to their very specific atomistic structure and the quantum confinement effects afforded by the surrounding In-rich local environment. For this purpose, we especially design a procedure to carefully remove the other nano-objects. Therefore, In-rich surface QDs were removed by Chemical Mechanical Polishing (CMP). The Scanning Electron Microscopy (SEM) measurement and Photoluminescence (PL) experiments performed before and after the CMP (Figure S4 and Figure S5) show the effective suppression of these surface nanostructures, including especially the disappearance of a low energy peak on the PL spectrum after CMP. As described previously, APBs are composed of III-III or V-V bonds, [START_REF] Rubel | Formation Energies of Antiphase Boundaries in GaAs and GaP: An ab Initio Study[END_REF][START_REF] Tea | Theoretical Study of Optical Properties of Anti Phase Domains in GaP[END_REF] which induce a deficiency or excess of electrons. Therefore, it is expected to behave as acceptor or donor-like centers. [START_REF] Rubel | Formation Energies of Antiphase Boundaries in GaAs and GaP: An ab Initio Study[END_REF] One of the first consequences of the intrinsic APB structure is that inversion symmetry, which is absent in the bulk III-V zinc-blende lattice is restored locally (Figure 2a). This local structure entails specific symmetry properties as shown in the supplementary information part. In order to better understand and analyze the vibrational and electronic properties in the system, phonon and band structures need to be clarified. Phonon and electronic band structure calculations were performed using Density Functional Theory (DFT) for InP supercells containing two stoichiometric APB planes (called hereafter APB-supercell) (Figure 2a). For comparison, the corresponding calculations were also done for a reference InP supercell structure without APB (called hereafter bulk-supercell) (Figure S8). A symmetry analysis was performed for the electronic states and phonon modes of APB supercells of various sizes at the  point using the Pnnm space group or the p2/m11 layer group relevant respectively for the APB supercells or extrapolated for a single APB singularity (see supplementary information part).

Electronic bands were calculated along different k-paths (Z(0,0,0.5))-Г(0,0,0)-U(0.5,0,0.5); R(0.5,0.5,0.5)-Г(0,0,0)-S(0.5,0,0.5)), where the axis x, y, z of the reciprocal space correspond to the [001], [1-10], [110] crystallographic directions, based on Heyd-Scuseria-Ernzerhof (HSE) hybrid functional. The band structure plot of the APB-structure is shown in Figure 2b, where the states are weighted by their spatial localization at the APB plane.

The color map from blue to red underlines the increase of localization effect of the states at the APB. Figure S9 shows the band structure of the reference bulk supercell with a direct band gap of 1.40eV. For a clear comparison, the Valence Band Maximum (VBM) and the Conduction Band Minimum (CBM) of the bulk-supercell were marked in Figure 2b, shown as the horizontal black dotted lines. Both structures show band folding effect due to the construction of the supercell. As compared to the bulk, the APB structure does not affect much the nature of the CBM while it introduces two localized states at the top of the VB, shifting the VBM upward (by roughly 0.5eV) and thus reducing the band gap. These 2D VB electronic states belong to A g and B g irreducible representation (IR) in a layer group representation (see supplementary part for more details). Figure 2c shows the planar averages of the partial charge densities of the VBM and CBM integrated parallel to the APB. The VBM partial charge density clearly reveals localization of carriers on the APB plane and the density drop between APBs, in good agreement with the weighted band structure represented in Figure 2b. Conversely, the charge density of CBM slightly decreases at the APB location, indicating an overall type-II band alignment between the APB singularity and the bulk (schematically shown in Figure 3c).

Phonon dispersions of the APB-supercell and the reference bulk-supercell (InP) are then computed and shown in Figure 2d and Figure S10, respectively, where R(0.5,0.5,0.5), Г(0,0,0) and U(0.5,0,0.5) are the high symmetry points of the first Brillouin zone. In both cases, the phonon dispersions also show band folding effects due to the construction of the supercell. From the known bulk phonon dispersions, we identify the contributions of underlying InP acoustic (low frequency) and optical (high frequency) phonon branches (see supplementary information for the illustration of band folding effects). We may notice that the computed bulk phonon frequencies are a little smaller than the experimental ones, [START_REF] Lindsay | Ab Initio Thermal Transport in Compound Semiconductors[END_REF] which is an expected consequence of the generalized gradient approximation (GGA) that overestimates lattice constants and underestimates the energies of vibrational modes. [START_REF] Haas | Construction of an Optimal GGA Functional for Molecules and Solids[END_REF] Comparing the phonon dispersions of the bulk (Figure S10) and APB-structure (Figure 2d), it can be clearly observed that the APBsupercell introduces several new flat phonon branches in the phonon dispersion gap, positioned at around 5.3THz, 5.9THz, 7.8THz, 8.0THz, 12.6THz, marked by orange, blue, magenta, green and purple dot lines, respectively (Figure 2d). These phonons correspond at the  point respectively to the Ag, Bu, Au, Bu, Ag irreducible representations of the layer group for a single APB (see supplementary informations). Figure 2e-g show the partial vibrational density of states (PVDOS) of the "bulk-like" In-P bond, In-In APB bond and P-P APB bond (encircled by black, red and green dotted lines in Figure 2a), respectively, which reveals that the new flat phonon branches mainly result from the APB singularity. Moreover, the localized phonon with relatively low frequency (around 5.3 THz) mainly comes from the vibration of the In-In APB bonds and the other localized phonons mainly correspond to the vibration of the P-P APB bonds. The vibration behavior of the five new phonon modes at the Γ point (corresponding to the orange, blue, magenta, green and purple dots in Figure 2d) were extracted. The corresponding movies were put in the supplementary material and the schematic images are shown in Figure 2h, Figure 2i, Figure S13a, Figure S13b and Figure S13c, respectively, where the arrows represent the vibration directions and amplitudes of the main atoms involved. We can see that the five new phonon modes are mainly localized at the APB plane singularity, which is consistent with the vibrational PVDOS calculated before.

Spatially-and spectrally-resolved Raman measurements were performed on the sample after CMP and the results are shown in Figure 2j. The Raman peaks 2, 3, 4, 5, 6, 7, correspond respectively to Ge-Ge bonds, [START_REF] Ravaux | Effect of Rapid Thermal Annealing on Crystallization and Stress Relaxation of SiGe Nanoparticles Deposited by ICP PECVD[END_REF] GaP transverse optical (TO) phonons, [START_REF] Peternai | Investigation of Graded In x Ga 1-x P Buffer by Raman Scattering Method[END_REF] InP longitudinal optical (LO) phonons, [START_REF] Peternai | Investigation of Graded In x Ga 1-x P Buffer by Raman Scattering Method[END_REF] GaP LO phonons, [START_REF] Peternai | Investigation of Graded In x Ga 1-x P Buffer by Raman Scattering Method[END_REF] Ge-Si bonds, [START_REF] Ravaux | Effect of Rapid Thermal Annealing on Crystallization and Stress Relaxation of SiGe Nanoparticles Deposited by ICP PECVD[END_REF] and Si-Si bonds, [START_REF] Ravaux | Effect of Rapid Thermal Annealing on Crystallization and Stress Relaxation of SiGe Nanoparticles Deposited by ICP PECVD[END_REF] and the InP TO phonons [START_REF] Peternai | Investigation of Graded In x Ga 1-x P Buffer by Raman Scattering Method[END_REF] should give some contribution to the signal around 303cm -1 . The Raman peak 1 is relatively broad and weak, but its central frequency (around 200cm -1 , i.e. 6 THz) shows a reasonable agreement with the Ag Raman active mode with frequency around 5.3 THz localized at the APB calculated previously. In order to further confirm the contribution of the five localized phonons to the Raman signal, the Raman spectrum of the five localized phonons at point was calculated and extracted, shown in Figure S14. We thus confirm numerically that only the Ag localized phonons with frequency around 5.3 and 12.6 THz give a contribution to the Raman spectrum. Therefore, the Raman peak 1 in the experimental data is attributed to the Ag localized vibration with theoretical frequency around 5.3 THz. The Raman signal of the experimental data in the range of 400-500cm -1 should contain the contribution from the second Ag APB localized phonon with a theoretical frequency around 12.6 THz, but it is most probably hidden by the contributions related to the other parts of the sample. The hyperspectral mapping in the inset displays the spatial distribution of the Raman peak 3 of GaP TO (green area) and Raman peak 1 (red area) vibration modes. The clear observation of remaining red and green area in the spatial superposition of the two vibrational modes indicate that the two phonon vibrations do not originate from the same region. Based on the EDX images, we know that there are two main structures in the InGaP layer (after CMP): the main In-poor phase (InGaP with 18% In) and the In-rich phase located around the 2D APB singularities. Therefore, we attribute peak 3 observed in the Raman spectrum to lattice vibrations inside the In-poor domains away from the APB, while peak 1 comes from phonons localized at the APB homovalent singularities. The signature of the localized phonons (peak 1) in Raman experiments is relatively weak because of the small volume fraction of APBs. But this does not entail a low oscillator strength. Based on the structural investigations, the (band structure and phonon dispersion) calculations and Raman measurements, we can conclude that the 2D APB singularities simultaneously bring in both carrier and phonon localization in the same region of the sample, which are the basic ingredients to create uncommon carrier-phonon interaction effects. The existence of an unexpected low-frequency localized Raman-active optical mode at about 6 THz is in particular consistent with first-principles predictions.

Temperature dependent (15300K) PL and room temperature ellipsometry measurements were performed on the sample after CMP. A Tauc-Lorentz model with two oscillators was used to fit the ellipsometry data (Figure S15a).

The extracted refractive index (n), extinction coefficient (k) and absorption spectrum are shown in Figure S15b and Figure S15c. The absorption spectrum was shifted at higher energy by 66 meV to account for the Varshni dependence of the bandgap. [START_REF] Varshni | Temperature Dependence of the Energy Gap in Semiconductors[END_REF] Therefore, low temperature absorption spectrum and PL are both given in Figure 3a.

In the PL spectrum, one broad PL peak is observed between 1.8 and 2.1eV. In the absorption spectrum, one peak between 3.5 and 4.0eV can be observed, with a similar shape than the one usually reported for GaP, [START_REF] Aspnes | Dielectric Functions and Optical Parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 EV[END_REF] indicating that the absorption spectrum mainly comes from the In-poor phase. But the absorption curve starts from the high energy side of the PL around 2.1eV, which is smaller than the expected bandgap of the In-poor phase In 0.18 GaP at low temperature (which should be around 2.32eV). [START_REF] Zhang | InP-GaAs Photodiodes Tailored for Specific Wavelength Range[END_REF] This absorption tail can result from the alloy fluctuation of InGaP matrix or another part of the material with a lower bandgap (i.e. the In-rich phase with the APB singularity). Another important feature of the PL spectrum is the presence of several small peaks on the top (inset of Figure 3a), separated by approximately the same energy (24±2 meV, 5.8±0.5 THz, 193.6±16.1 cm -1 ), which shows the contribution of phonons in the PL process. The small peaks are referred to as phonon replicas. In fact, a phonon energy around 24 meV is much smaller than the optical phonons of both GaP and InP, while it is in fair agreement with the energy of phonons localized around APB planes, predicted theoretically and observed in Raman spectroscopy. The observation of these phonon replicas further shows that a specific PL signal results from the APB singularity region. Besides, the APB-localized phonons dispersion curves of Figure 2d are very flat, which can facilitate phonon-assisted emission.

Figure 3b displays the power-dependent PL spectra, from which it can be observed that the whole spectrum (including small peaks and the broad contribution) remains proportionally unchanged with increasing pumping power, which further indicates the broad PL peak contains and only contains multi-phonon replicas. Figure S16 displays the logarithm plot of the integrated PL intensity versus excitation power and it shows super-linear to linear power dependency behavior, which is related to acceptor or donor-like effect of the APB [START_REF] Bimberg | Bound Exciton Luminescence in Epitaxial Sn-Doped Gallium-Arsenide[END_REF][START_REF] Hellmann | Low-Temperature Anti-Stokes Luminescence Mediated by Disorder in Semiconductor Quantum-Well Structures[END_REF] (for the details see the supplementary materials).

From the previous band structure calculations, the general mechanism of the PL resulting from the 2D homovalent singularity is schematically represented in Figure 3c. After illumination, the excited electrons in the conduction band recombine with the holes localized in the APB plane and leads to PL emission. This general picture is further confirmed by the temperature dependent PL shown in Figure S17, where the main activation energy found is 200 meV. This represents the detrapping of the localized holes in the APB 2D states to extended 3D states of the In-rich phase. The mechanisms of electron-phonon interaction leading to the phonon replicas in the PL spectrum are analyzed first following the simplified Franck-Condon approach (Figure 3d). The configuration coordinate diagram shows the potential well vs the normal mode coordinate (Q) and the dotted horizontal lines represent oscillator states. [START_REF] Alkauskas | Tutorial: Defects in Semiconductors-Combining Experiment and Theory[END_REF] In this illustration, the potential well is ideally considered as harmonic so that the energy difference between two nearby oscillator states are the same and equal to the phonon energy.

Beyond the localization effect related to the 2D homovalent singularity itself, the APB is embedded in an Inrich region surrounded by In-poor regions, which further brings an additional quantum confinement effect. Therefore, we expect a large number of localized electrons at the vicinity of the singularity. During absorption of the laser pump, the incoming photons can excite the electrons into the conduction band (CB) and change the filling of the APB states. Based on the classical Franck-Condon approximation, [START_REF] Stoneham | Theory of Defects in Solids: Electronic Structure of Defects in Insulators and Semiconductors[END_REF][START_REF] Lax | The Franck-Condon Principle and Its Application to Crystals[END_REF][START_REF] Markham | Interaction of Normal Modes with Electron Traps[END_REF] this optical transition takes place instantaneously. Meanwhile, the ions are slow, and their position do not change when the electronic state changes.

After losing the electrons, the lattice near the nanostucture relaxes to a new equilibrium position, through which the electrons relax to the bottom of the potential well of the conduction band of the 2D structure [START_REF] Alkauskas | Tutorial: Defects in Semiconductors-Combining Experiment and Theory[END_REF] (the dotted green curves in Figure 3d). Then the excited electrons will recombine with the holes in different localized vibration states (v=0,1,2…), giving the photoluminescence, shown as the multicolor emission lines in Figure 3d, which correspond to the phonon replicas. The interaction between the electrons and phonons has usually to be strong to exhibit such quantum effects, which is consistent with the co-confinement of the electrons and phonons in the same region. The magenta emission line from the bottom of the conduction band potential well to the ground vibration state (=0) corresponds to the zero phonon line (ZPL). At low temperature, the photoluminescence intensity I n of the n-th emission line follows the Poisson distribution: [START_REF] Malm | Effects in the Luminescence of CdS[END_REF] (1)

Where S is the Huang-Rhys factor which describes the magnitude of the electron-phonon coupling, and n the number of phonons generated in the transition. Moreover, the luminescence phonon wing is characterized by the relation: E n =E ZPL -nE ph (E ZPL and E ph corresponding to the energy position of the zero phonon emission line and the energy of phonon, respectively).

The broad PL was fitted based on the equation above. The phonon replicas were fitted by Gaussian functions with full width at half maximum (FWHM) of 26.5meV and a phonon energy of around 24 meV was used. Note that Lorentzian functions did not allow to fit the phonon replicas correctly. The Gaussian broadening observed is mainly considered as the consequence of the inhomogeneous broadening effect due to the composition inhomogeneity or the different distances between the APBs. [START_REF] Alkauskas | Tutorial: Defects in Semiconductors-Combining Experiment and Theory[END_REF] The broadening effect due to acoustic phonons shall amount only to a few meV range, [START_REF] Besombes | Acoustic Phonon Broadening Mechanism in Single Quantum Dot Emission[END_REF] which can be neglected in the present study. In addition, the energy difference between two nearby phonon lines in the low energy part of the spectrum becomes a bit smaller gradually, indicating that the potential well is slightly anharmonic. Anyway, this observation doesn't impact the conclusions given here. Figure 3e shows the experimental data and the theoretical fitting achieved by the Franck-Condon principle. Accurate fitting of the experimental curve was only obtained with a S parameter of 8 and a ZPL at 2.097eV.

To our knowledge, a Huang-Rhys factor of 8 is considerably larger than those found usually for undoped bulk III-V and II-VI semiconductors, even with confinement of carriers such as in QDs or QWs (0.015 for InAs/GaAs QD; 10 0.3 for InGaN/GaN QW; 36 0.36-0.7 for CdSe QDs; [START_REF] Norris | Size Dependence of Exciton Fine Structure in CdSe Quantum Dots[END_REF] 1.25 for InP/GaInP QD [START_REF] Odnoblyudov | Polaron Effects in Quantum Dots[END_REF] ). It indicates the presence of unusual strong electron-phonon interaction in the 2D In-rich vertical singularity due to (i) the double quantum confinement by the vertical quantum well, and (ii) the simultaneous confinement of electrons and phonons in the same region (as shown in Figure 3f). In addition, time-resolved PL was measured and fitted by a model designed for type II band alignements [START_REF] Mourad | Determination of Valence-Band Offset at Cubic CdSe/ZnTe Type-II Heterojunctions: A Combined Experimental and Theoretical Approach[END_REF] (Figure S18). The good fitting and the observed long lifetime (within the µs order of magnitude) are consistent with the theoretical picture of a type II band alignment (as shown in Figure 3c). It indicates that confined holes in the APB play a major role in the enhancement of the electron-phonon interaction.

Finally, we shall discuss the possible microscopic origins of the observed strong coupling regime between localized carriers and phonons. Raman scattering measurements coupled with PL replica characterization and localized phonon simulations point toward a mechanism involving both 2D A g even localized phonon modes and APB localized VB electronic states. Therefore, a specific optical deformation potential mechanism is the most probable process to explain the experimental observations. [START_REF] Braun | Spectroscopic Determination of the Optical Deformation-Potential Constant in Semiconductors[END_REF] The observation of phonon replica is a signature of a strong electron-phonon interaction, which is consistent with the microscopic computation of a large electron phonon coupling matrix elements for the first localized non-polar A g mode (vide infra). However, the second localized A g mode is also predicted to exhibit a strong coupling to the same confined valence state, despite the absence of corresponding discrete signatures on top of the PL envelope. Therefore, other aspects beyond our theoretical description and simplified APB model structure are likely to be important as well, including phonon-phonon interactions or lattice disorder. The Raman scattering experiment (Figure 2j) indeed shows that the first lowfrequency localized mode already exhibits a broader signature than extended lattice modes. We may thus infer that such broadening is even more important for the other localized modes, leading only to shallow contributions to the envelope of the PL spectrum. In addition, another classical electron-phonon coupling mechanism should be also considered for odd (polar) modes, that is the Fröhlich interaction. The theoretical study predicts that the APB polar phonon modes shall be located at a sizable energy above the lowest APB A g even phonon mode, and therefore shall not be good candidates to explain the observed phonon replica. These localized polar modes are nevertheless likely to be coupled to localized VB electronic states. Therefore, we rely on theoretical calculations to further investigate the electron-coupling processes induced by the new localized phonon modes around the APB structure. For that purpose, we calculated electron-phonon interaction (EPI) matrix elements ( ) for both polar and non-polar-localized modes using state of the art DFT-based microscopic theory [START_REF] Giustino | Electron-Phonon Interactions from First Principles[END_REF][START_REF] Verdi | Electron-Phonon Vertex from First Principles[END_REF][START_REF] Poncé | School on Electron-Phonon Physics from First Principles[END_REF] (for the complete definition of see the supplementary materials part).

Table S4 lists the electron phonon interaction matrix elements | | related to the coupling at the point between the A g localized non-polar phonon modes and, the bottom of the conduction band (m=n=CBM) or the top of the valence band (m=n=VBM). We can find that the EPI matrix elements are large and consistent with a strong deformation potential interaction between the two Ag localized phonon modes and the localized VBM electronic state. On the other hand, Figure S19 shows the variation of the EPI matrix element for the polar-localized phonon modes as a function of q coupled to the same electronic states. Consistently with the symmetry analysis, the matrix elements vanish at the  point (q=0). They may exhibit an increase at long wavelengths, q → 0 (Figure S19a), although these variations exhibit as well significant deviations from the classic analytical Fröhlich model (Figure S19b-d). More, the matrix elements correspond to sizeable numerical values (Figure S19) on the same order as the ones for non-polar modes at the  point (Table S4), thereby suggesting that the coupling to the localized polar modes is important for optoelectronic properties, and also playing a role for hole transport. This can shed some light on the recent experimental observation of APBs benefiting to carrier transport at room temperature. [START_REF] Cornet | Chapter 28 -GaP/Si-Based Photovoltaic Devices Grown by Molecular Beam Epitaxy[END_REF][START_REF] Alqahtani | Photoelectrochemical Water Oxidation of GaP 1-x Sb x with a Direct Band Gap of 1.65 EV for Full Spectrum Solar Energy Harvesting[END_REF] Indeed, APBs are planar structures, not point defects and therefore, vertical transport in the APB planes can take place. In the present work, APBs can be assimilated to effective quantum wells forming planar conduction channels for carriers.

Considering the recent researches that allow controlling both lateral and vertical extensions of APDs, [START_REF] Lucci | Universal Description of III-V/Si Epitaxial Growth Processes[END_REF][START_REF] Guillemé | Antiphase Domain Tailoring for Combination of Modal and 4¯ -Quasi-Phase Matching in Gallium Phosphide Microdisks[END_REF] more investigations are needed to characterize the nature and the strength of the electron-phonon interaction processes in such homovalent singularities.

CONCLUSION

In conclusion, the local change of chemical bonds polarity at the atomic scale in a weakly polar III-V crystal, positioned at the heart of a quantum confined vertical nanostructure enabled the simultaneous confinement of charge carriers and phonons at the vicinity of the 2D homovalent singularity. This situation led to a strong enhancement of the electron-phonon coupling, as testified by a large experimental Huang-Rhys factor and discussed in the framework of optical deformation potential and Fröhlich interaction. This extends the routes toward the understanding of electron-phonon interactions and gives different horizons for material designs or device applications with weakly polar semiconductors.

MATERIALS AND METHODS

Sample growth:

The preparation of the studied In 0.3 GaP on SiGe/Si sample contains two main processes. The First step is the growth of a relaxed SiGe buffer layer on Si substrate. [START_REF] Skibitzki | Lattice-Engineered Si 1-x Ge x -Buffer on Si(001) for GaP Integration[END_REF] The HR800 system is a high-resolution spectrometer fitted with a confocal microscopy system coupled to different lasers. Our experiments were performed in "confocal mode" with a 532 nm diode laser as excitation source and, to avoid sample heating, an optical density filter was used.

DFT calculations: Band structure and phonon calculations were performed with the density functional theory (DFT) [START_REF] Kohn | Self-Consistent Equations including Exchange and Correlation Effects[END_REF] by combining the Vienna Ab initio Simulation package (VASP), [START_REF] Kresse | Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set[END_REF][START_REF] Kresse | Efficient Iterative Schemes for ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set[END_REF] VASPKIT package, [START_REF] Wang | A Pre-and Post-Processing Program for VASP Code[END_REF] and PHONOPY package [START_REF] Togo | First Principles Phonon Calculations in Materials Science[END_REF] codes. DFT calculations are performed using the plane-wave projector augmented wave (PAW) method [START_REF] Blöchl | Projector Augmented-Wave Method[END_REF][START_REF] Kresse | From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method[END_REF] as implemented in VASP code. The standard generalized gradient approximation (GGA) parameterized by Perdew-Burke-Ernzerhof (PBE) [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] were used for structure optimization and phonon calculation, and the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional [START_REF] Paier | Screened Hybrid Density Functionals Applied to Solids[END_REF][START_REF] Heyd | Hybrid Functionals Based on a Screened Coulomb Potential[END_REF][START_REF] Heyd | Efficient Hybrid Density Functional Calculations in Solids: Assessment of the Heyd-Scuseria-Ernzerhof Screened Coulomb Hybrid Functional[END_REF] was chosen for the band calculation, with energy cutoff of 500eV. A Monkhorst-Pack 4x1x6 grid [START_REF] Monkhorst | Special Points for Brillouin-Zone Integrations[END_REF][START_REF] Pack | Special Points for Brillouin-Zone Integrations"-A Reply[END_REF] of k points was set on the geometry optimization step and the structures were relaxed until the Hellmann-Feynman forces on the atoms were less than 10 -4 eV/Å. The symmetry information and Raman spectrum of the localized phonons around APB were extracted through the phono3py [START_REF] Togo | Distributions of Phonon Lifetimes in Brillouin Zones[END_REF] package codes. The symmetry properties of electronic states were calculated and extracted based on metaGGA (TB-mBJ) [START_REF] Tran | Accurate Band Gaps of Semiconductors and Insulators with a Semilocal Exchange-Correlation Potential[END_REF] potential by Quantum Espresso (QE) package codes. [START_REF] Giannozzi | A Modular and Open-Source Software Project for Quantum Simulations of Materials[END_REF][START_REF] Giannozzi | Advanced Capabilities for Materials Modelling with Quantum ESPRESSO[END_REF] Electron-phonon interaction matrix element calculations based on the local-density approximation (LDA) and the Quantum Espresso (QE) code. [START_REF] Verdi | Electron-Phonon Vertex from First Principles[END_REF][START_REF] Poncé | School on Electron-Phonon Physics from First Principles[END_REF]

Figure 1 .

 1 Figure 1. Structural characterizations of the InGaP/SiGe/Si sample. a, Sketch representing the atoms arrangement in an APB. b-d, Schematic image (b) as well as plan view (c) and cross-sectional (d) STEM images of the studied InGaP/SiGe/Si sample. e, Cross-sectional bright-field (BF) STEM image of the InGaP/SiGe/Si platform. The black line in the middle and the hump on the surface corresponds to the APB and surface nanostructure, respectively. f-i, Cross-sectional EDX elemental mapping images of indium(f), gallium (g), phosphorus(h) and silicon(i). j-l, Plan-view EDX mapping images of indium(j), gallium(k), phosphorus(l). Two kinds of In-rich nanostructures are observed: pure InP surface nanostructures and 2D In-rich vertical quantum wells (QWs) surrounding the APB singularities.

Figure

  Figure 1b is a schematic representation of the InGaP/SiGe/Si sample's structure. Experimental scanning transmission electron microscopy (STEM) plan-view and cross-sectional images are shown in Figure 1c and Figure

Figure 2 .

 2 Figure 2. First principle simulations of electronic band structure and localized phonons for a model APB and experimental Raman spectrum a, The 32 atoms APB-supercell (APB in InP matrix) used for DFT band structure and phonon calculations. b, Calculated electronic band structure of a 48 atoms APB-structure, weighted by the spatial localization of the wave functions at the APB interface. Layer group irreducible representations (IRs) at  point are indicated. c, Partial charge density of the VBM and CBM at the Γ point for a 48 atoms supercell, integrated in the planes parallel to APBs. The dotted line corresponds to the APB plane. d, Phonon dispersions of 32 atoms APB-structure. The phonon modes highlighted by orange, blue, magenta, green and purple dotted lines correspond to additional localized modes related to APB planes. They are labelled according to layer group IRs at  point. e,f,g, Partial vibrational (phonon) density of states of the middle InP atoms, In-In APB atoms and P-P APB atoms, corresponding to the atoms encircled by the black, red and green dotted lines respectively in Figure 2a. h,i, Schematic images of vibration behaviors of the first Ag APB localized phonon mode around 5.3 THz and the Bu APB localized phonon mode around 5.9 THz at Γ point according to layer group IRs, corresponding to the orange and blue dots in Figure 2d, respectively. j, Experimental Raman spectrum. The Raman peaks 2, 3, 4, 5, 6, 7, correspond respectively to Ge-Ge bonds, GaP transverse optical (TO) phonons, InP longitudinal optical (LO) phonons, GaP LO phonons, Ge-Si bonds and Si-Si bonds. The Raman peak 1 shows a good corresponding to the 5.3 THz phonon localized at the APB calculated previously. The inset shows the plane-view spatial distribution on the sample of the Raman peaks 1 (around 200cm -1 , i.e. 6 THz) and 3.

Figure 3 .

 3 Figure 3. Electron-phonon coupling. a, Photoluminescence and absorption spectra at low temperature (15K). The inset corresponds to the PL spectrum in high magnification. b, Power-dependent Photoluminescence at 15 K. c,d, Mechanism of the Photoluminescence with a spatial representation (c) or within the electron-phonon interaction configuration coordinate point of view (d). e, Experimental data (grey dots) and theoretical fitting (red line) of the broad PL peak based on the Franck-Condon model. The small multicolored peaks correspond to the distinct phonon replicas contributions. f, Schematic plot of the 2D vertical In-rich structure, embedding APB planes with strong electron-phonon interaction.

Experimental measurements:

  The Scanning Transmission Electron Microscopy (STEM) high-resolution imaging and Energy Dispersive X-Spectroscopy (EDX) were obtained by FEI Tecnai Osiris TEM tool, operating at 200 kV with implemented energy-dispersive x-ray (EDX) detector. TEM lamellas were prepared by milling and undercutting processes using a Zeiss NVision 40 focused ion beam operating at up to 30 kV. The InGaP/SiGe/Si samples were characterized by X-ray diffraction (XRD) on a 4 circles Brucker D8 Diffractometer. A Bartels asymmetric Ge (220) monochromator was used for both line scans and reciprocal space maps. The detection is ensured by a Lynxeye TM , 1 dimensional position sensitive detector (PSD) allowing a collection angle of 2.6° over 2θ. 1% H 3 PO 4 solution was used for the Chemical Mechanical Polishing (CMP). The SEM images were obtained by using a JEOL JSM-7100 scanning electron microscope. Ellipsometry measurements were performed at room temperature in the 1.5-5 eV photon energy region. To fit the measured ellipsometry spectra, a Tauc-Lorentz model including two oscillators was used to describe InGaP optical contants, and the SiGe buffer layer was considered as a known alloy. The power-dependent PL was designed with the excitation power from 24 mW to 0.24 mW at 15K by using a 405 nm laser. The temperature-dependent PL was performed from 15 K to 100 K through a helium bath closed cycle cryostat with an excitation density of 24 mW by using the 405 nm laser. The laser spot size of the 405 nm laser is around 10 μm on the sample. The time-resolved PL was measured at 15K by a Q-switched 355 nm pulse laser at an excitation intensity of 560 mW/cm 2 (pulse duration:7ns, repetition rate:5kHz). The signals were filtered by two different bandpass filters of 600 and 800 nm. The fluorescence lifetime was determined by time-correlated single photon counting. Raman image was obtained with a HR800 micro-Raman spectrometer (HORIBA Scientific).

  a growth rate of 0.1ML/s, followed by a 0.27ML In deposition at the same growth rate (0.1ML/s), and then by a 4s growth interruption. Finally, a 200nm-thick In 0.3 GaP layer is grown at 500°C in the conventional continuous MBE growth mode and at a growth rate of 0.14ML/s on the MEE layer.

	A 760nm Si 0.433 Ge 0.567 layer was grown at 550°C
	and 80 Torr reactor pressure on one clean Si(001) wafer misoriented by 4 o towards the [110] direction with a
	reduced pressure chemical vapor deposition (RPCVD) system. Then SiGe was annealed in-situ at 1000°C for 5 mins
	under H

2 flow for relaxation. The second step is the regrowth of In 0.3 GaP on SiGe/Si pseudo-substrate, which contains two growth modes: Migration Enhanced Epitaxy (MEE) and traditional Molecular Beam Epitaxy (MBE).

The first 10nm InGaP layer was grown with the MEE growth mode. One MEE cycle consists in a first 0.63ML Ga deposition at

ACKNOWLEDGMENTS

This research was supported by the French National Research Agency ANTIPODE Project (Grant No. 14-CE26-0014-01), Région Bretagne. Lipin Chen acknowledges the China Scholarship Council (CSC) for her Ph.D financial support (No. 2017-6254). The authors acknowledge RENATECH (French Network of Major Technology Centers) within Nanorennes for technological support and thank the SIR platform of ScanMAT at University of Rennes 1 for technical assistance for the Raman measurements. DFT calculations were performed at Institut FOTON and the work was granted access to the HPC resources of TGCC/CINES/IDRIS under the allocation 2019-A0060906724 made by GENCI. Jacky Even acknowledges the financial support from the Institut Universitaire de France.

ASSOCIATED CONTENT Supporting Information

The Supporting Information is available free of charge at … Additional scanning transmission electron microscopy (STEM) images; Sketch of the APB vertical growth; Scanning electron microscopy (SEM) and Photoluminescence (PL) of the reported sample before and after chemical mechanical polishing; X-Ray diffraction and Reciprocal Space Mappings (RSM); Reference density functional theory calculations for bulk InP; Symmetry analysis of the APB supercell electronic and vibrational properties;

Notes

The authors declare no competing financial interest. All images in figure graphics (including the TOC graphic) are original and created by the authors.