Baptiste Reyne
email: baptiste.reyne@ec-nantes.fr

Pierre-Yves Manach
email: pierre-yves.manach@univ-ubs.fr

Nicolas Moes
email: nicolas.moes@ec-nantes.fr

Nicolas Moës

Macroscopic consequences of Piobert-Lüders and Portevin-Le Chatelier bands during tensile deformation in Al-Mg alloys

Keywords: characterization, aluminium alloys, plasticity, Portevin-Le Chatelier, Piobert-Lüders, strain localization

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Introduction

At the onset of plastic yielding, a wide variety of metallic materials develop Piobert-Lüders (PL) bands [START_REF] Piobert | Expérience sur la pénétration des projectiles dans le fer forgé[END_REF][START_REF] Lüders | Uber die ausserung der elasticitat an stahlartigen eisenstaben und stahlstaben, und uber eine beim biegen solcher stabe beobachtete molecularbewegung[END_REF] associated with a peak in stress and a plateau on the hardening curves. Among these materials, some impure alloys subsequently exhibit the Portevin-Le Chatelier (PLC) effect [START_REF] Chatelier | Influence du temps et de la température sur les essais au choc[END_REF][START_REF] Portevin | Sur un phénomène observé lors de l'essai de traction d'alliages en cours de transformation[END_REF], which is an irregular hardening (or jerky plastic flow) combining stress drops (serrations) with a negative strain rate sensitivity (NSRS). The common feature of both of these behaviors is a heterogeneous plastic flow under an apparently homogeneous stress: thin localization bands, which are often described as propagating, serve to spread increments of plastic strain over the material domain. It is commonly accepted that PL bands and the PLC effect arise from strain aging micro-mechanisms associated with the pinning of dislocations by solutes [START_REF] Cottrell | Dislocation theory of yielding and strain ageing of iron[END_REF]. For instance, in the case of PLC in Al-Mg alloys, the diffusion of magnesium solutes enables the repetition of pinning leading to dynamic strain aging (DSA) [START_REF] Van Den | Theory of the effect of dynamic strain aging on mechanical properties[END_REF][START_REF] Mccormick | Theory of flow localisation due to dynamic strain ageing[END_REF] as opposed to static strain aging (SSA) for PL bands [START_REF] Antolovich | Plastic strain localization in metals: origins and consequences[END_REF].

Three types of PLC behavior are classically distinguished [START_REF] Lebyodkin | Spatio-temporal dynamics of the Portevin-Le Chatelier effect: experiment and modelling[END_REF] depending on temperature, plastic strain magnitude and strain rate, in addition to the material micro-structure. At high strain rates and low temperatures, type A bands nucleate smoothly and in spatial order associated with Lüderslike peak stress and plateaus. At low strain rates and high temperatures, type C bands grow in an uncorrelated manner [START_REF] Ait-Amokhtar | Kinematics fields and spatial activity of Portevin-Le Chatelier bands using the digital image correlation method[END_REF][START_REF] Chmelík | Investigating the Portevin-Le Châtelier effect by the acoustic emission and laser extensometry techniques[END_REF] and strong serrations are observed. An intermediate situation corresponds to type B, often referred to as hopping bands, which are spatially ordered but come with distinct stress drops. For both types B and C, it has been established that the nucleation of each band occurs along with a single serration [START_REF] Zdunek | Digital image correlation investigation of Portevin-Le Châtelier effect in an aluminium alloy[END_REF]. This classification of plastic instabilities in discrete categories poses a problem for the interpretation of transition and crossover regimes which remains to be resolved [START_REF] Yilmaz | The Portevin-Le Chatelier effect: a review of experimental findings[END_REF]. In the following, this issue is tackled by suggesting a continuum that allows for a smooth evolution from one type to another.

The quantitative assessment of plastic instabilities is mostly performed using tensile tests although recent investigations extend the technique to additional loading paths, such as simple shear [START_REF] Coër | Piobert-Lüders plateau and Portevin-Le Chatelier effect in an Al-Mg alloy in simple shear[END_REF][START_REF] Manach | Kinematics of Portevin-Le Chatelier bands in simple shear[END_REF], biaxial expansion [START_REF] Min | Spatio-temporal characteristics of plastic instability in AA5182-O during biaxial deformation[END_REF] or equi-biaxial deformation [START_REF] Cam | Calorimetric analysis of Portevin-Le Chatelier bands under equibiaxial loading conditions in Al-Mg alloys: kinematics and mechanical dissipation[END_REF]. In addition to stress drop distributions, the characterization of PL bands and the PLC effect essentially relies on specific kinematic measures. The band morphology of softening material is a common topic of research in the literature; the orientation of bands remains constant throughout tensile tests [START_REF] Chihab | The kinetics of the Portevin-Le Châtelier bands in an Al-5at% Mg alloy[END_REF][START_REF] Cai | Characterization of the deformation behaviors associated with the serrated flow of a 5456 Al-based alloy using two orthogonal digital image correlation systems[END_REF] while their width exhibits a positive strain rate sensitivity [START_REF] Ait-Amokhtar | Kinematics fields and spatial activity of Portevin-Le Chatelier bands using the digital image correlation method[END_REF][START_REF] Ait-Amokhtar | The dynamics of Portevin-Le Chatelier bands in an Al-Mg alloy from infrared thermography[END_REF][START_REF] Yuzbekova | Effect of microstructure on continuous propagation of the Portevin-Le Chatelier deformation bands[END_REF][START_REF] Cai | Characterization of the deformation behaviors associated with the serrated flow of a 5456 Al-based alloy using two orthogonal digital image correlation systems[END_REF]. Although the deformation mode has been rarely investigated in detail, it is known to correspond principally to simple shear [START_REF] Cai | Characterization of the deformation behaviors associated with the serrated flow of a 5456 Al-based alloy using two orthogonal digital image correlation systems[END_REF]. The strain increment carried by bands is found to increase monotonically with strain [START_REF] Kovács | Localized deformation bands in Portevin-Le Châtelier plastic instabili-ties at a constant stress rate[END_REF][START_REF] Renard | Characterisation of the Portevin-Le Châtelier effect affecting an austenitic TWIP steel based on digital image correlation[END_REF] sometimes with a linear trend [START_REF] Min | Effect of strain rate on spatio-temporal behavior of Portevin-Le Châtelier bands in a twinning induced plasticity steel[END_REF][START_REF] Bernard | Relationship between local strain jumps and temperature bursts due to the Portevin-Le Chatelier effect in an Al-Mg alloy[END_REF] and sensitive to strain rate [START_REF] Ziegenbein | Correlation of temporal instabilities and spatial localization during Portevin-Le Châtelier deformation of Cu-10 at.% Al and Cu-15 at.% Al[END_REF][START_REF] Klusemann | Thermomechanical characterization of Portevin-Le Châtelier bands in AlMg3 (AA5754) and modeling based on a modified Estrin-McCormick approach[END_REF]. Finally, the apparent velocity of bands propagation have been measured in several studies [START_REF] Abbadi | On the characteristics of Portevin-Le Chatelier bands in aluminum alloy 5182 under stress-controlled and strain-controlled tensile testing[END_REF][START_REF] Louche | Thermal observations associated with the Portevin-Le Châtelier effect in an Al-Mg alloy[END_REF][START_REF] Benallal | An experimental and numerical investigation of the behaviour of AA5083 aluminium alloy in presence of the Portevin-Le Chatelier effect[END_REF][START_REF] Klusemann | Thermomechanical characterization of Portevin-Le Châtelier bands in AlMg3 (AA5754) and modeling based on a modified Estrin-McCormick approach[END_REF][START_REF] Ranc | Experimental studies of Portevin-Le Chatelier plastic instabilities in carbon-manganese steels by infrared pyrometry[END_REF] and understood to accommodate the imposed kinematics [START_REF] Hähner | Spatiotemporal analysis of Portevin-Le Châtelier deformation bands: theory, simulation, and experiment[END_REF], as explained in section 3.2. While existing studies provide extensive information on the macroscopic kinematics aspects, interpretation of the results can be hindered by the scarcity of data points caused by the difficulty of their assessment, as well as the need to cover a wide range of parameter variability. Since sample size is one of the relevant parameters whose influence on PL and PLC bands remains to be thoroughly investigated, this aspect is addressed in the present study. To develop novel and original approaches, in addition to investigating the phenomenology, specialists in modeling and simulation require experimental studies and conceptual tools for validation and analysis at the scale of industrial application.

Apart from dealing with questions on the microscopic mechanisms governing the PLC effect, this study aims to provide a global and coherent view on their macroscopic consequences that may be useful for new modeling approaches of this effect. For this purpose, tensile tests are performed on an Al-Mg alloy at room temperature over a wide range of imposed strain rates. By comparing two different sizes of samples, the analysis can be focused on the width of a band and explore the intrinsic nature of the usual variables of interest. The information thus obtained enables us to draw conclusions about the behavior of PL and PLC bands as macroscopic mechanical objects.

Experiments

Material

Experiments are conducted on rolled sheets of aluminum-magnesium alloy (AA5086-H111) with a nominal thickness of 0.8 mm (a thorough thermo-mechanical characterization of this material is available in [START_REF] Manach | Benchmark 3 Numisheet[END_REF]). The chemical compound are semi-quantitatively evaluated using scanning electron microscopy and energy-dispersive X-ray spectroscopy (EDS) on eight samples. They report 95.5(5) % aluminum and 4.5(5) % magnesium. Figure 1 provides insights on the material micro-structure using electron backscatter diffraction (EBSD). Measurements are conducted on polished samples before and after deformation, then posttreated with the MTEX library [START_REF] Hielscher | A novel pole figure inversion method: specification of the mtex algorithm[END_REF]. The average grain diameter is 16 µm. The material texture exhibits no notable anisotropy on any sample in spite of the rolled sheet forming process and applied deformation.

Experimental procedure

Two sets of tensile tests associated with distinct samples geometries and corresponding test apparatus are considered as illustrated in fig. 2. They are both cut using electrical discharge machining and kept at room temperature. Medium-size measurements are performed with a conventional geometry referred to as large (fig. 2a) tested with a Instron tensile machine using a 10 kN load cell. Results from smaller-sized specimens, referred to here as small samples (fig. 2b) allow us to distinguish the geometry effects from the material influence and to isolate the phenomenon at the scale of a band. Small samples are tested with both an Instron-10 kN and a MicroTest machine using a 2 kN cell to improve the accuracy of the force measurements under the lowest strain rates. This geometry is based on the study of [START_REF] Feng | Investigation of PLC band nucleation in AA5754[END_REF] and [START_REF] Klusemann | Thermomechanical characterization of Portevin-Le Châtelier bands in AlMg3 (AA5754) and modeling based on a modified Estrin-McCormick approach[END_REF] who characterized AA5754 at an identical scale by means of thermal radiation and strain gauge measurements.

All tensile tests are performed with the rolling direction aligned with the cross-head displacement, defining the axial basis vector e x in fig. 2. After setting the sample in the device, the grips are closed, thus inducing a pre-stress that is kept within the material elastic domain. A constant 3 -2 0 2

x (mm) t = 17.9 s t = 20.9 s t = 23.9 s t = 26.9 s t = 29.9 s

0 0.5 1 ε (%) -2 0 2 x (mm) 0 0.2 0.4 ε (% s -1 )
Figure 3: Snapshots of the strain norm (upper row) and strain rate norm (bottom row) for a small sample at nominal strain rate vc/Lc = 6.67 × 10 -4 s -1 during PL band nucleation and propagation. Each square represents a finite element used for DIC.

velocity denoted v c is then applied to the mobile cross-head until fracture of the sample. Each geometry is characterized by the initial length of its gauge zone L (60 mm large and 4.2 mm small) and by the initial total length between grips L c (100 mm for large and 10 mm for small). The specimens are tested at room temperature with several constant imposed velocities and a ratio v c /L c , referred to as the nominal strain rate, covering an interval from 10 -4 s -1 to 10 -1 s -1 . Samples are prepared with a random black and white painted pattern; a camera (100 mm macro lens) is set and adjusted in front of the sample. The tensile force signal is acquired and synchronized with images taken at a common variable rate ranging from 3 fps to 240 fps, which enables intermittent temporal refinements for the analysis of subtle events. Data gathering process and optical equipment are both managed with the Aramis system (Gom, Germany).

Post-processing

Displacement fields are computed from pictures using digital image correlation (DIC) and the dedicated software UFreckles [36] that outputs measurements in the Matlab matrix format. The images are discretized with ordered Q4 finite elements, allowing fields to be approximated as shown in fig. 3. The physical elements size varies from 130 µm to 200 µm for small samples and from 550 µm to 700 µm for large samples. For 1D studies, the results are gathered together on the line of nodes that is the closest to the axis of symmetry drawn as dashed lines on the upper-left graph. Gradients and rates are then computed by means of finite differences.

The Cauchy stress is assumed homogeneous over the gauge area in order to compare both geometries. It is taken equal to σe x ⊗e x with σ = F/A where F is the output force signal and A is the current cross-sectional area, computed using the assumption of small strains and isochoric deformation from DIC strain results. Contrarily, the strain field and its rate are strongly heterogeneous due to the occurrence of PL bands and the PLC effect, imposing a distinction between the global nominal strain u c /L c and local measures (where u c is the cross-head displacement). Moreover, it can be observed that the actual gauge zone elongation rate v/L (where v is the elongation rate of the gauge zone and L its length) is strongly sensitive to geometry and cumulative plastic strain: in the case of small samples, it diverges by up to 75 % from the nominal strain rate (averaged values can be compared in table 1a). Hence, it should be considered as an order of magnitude over the gauge area, which is only used as a test label. The local strain ε is computed as the linearized Green-Lagrange measure from digital image correlation.

Overview of one-dimensional graphical representations

Figure 4 shows a propagating behavior associated with the so called type A kinetics-different nominal strain rates are analyzed in section 3.4. Figures 4a and4c display the local stress vs. time and the local stress vs. strain, respectively. It should be noted that the virtual gauge zone, shown on the right hand side figures and centered at 43 mm, would have yield different values if taken elsewhere, as the strain at a given instant is uneven over the studied domain.

Figure 4b is the characteristic representation where the strain rate magnitude is mapped as a function of time along the axis of interest. This representation is widely used in the context of propagating waves and is applied to characterizing the PLC effect by means of acoustic emissions and laser extensometry [START_REF] Chmelík | Investigating the Portevin-Le Châtelier effect by the acoustic emission and laser extensometry techniques[END_REF], infrared radiation [START_REF] Louche | Thermal observations associated with the Portevin-Le Châtelier effect in an Al-Mg alloy[END_REF][START_REF] Feng | Investigation of PLC band nucleation in AA5754[END_REF] or kinematic fields [START_REF] Benallal | An experimental and numerical investigation of the behaviour of AA5083 aluminium alloy in presence of the Portevin-Le Chatelier effect[END_REF]; and used by [START_REF] Mazière | Numerical aspects in the finite element simulation of the Portevin-Le Chatelier effect[END_REF] to develop a numerical tool for band detection in finite element simulations. The dark patterns reflect an intense strain activity and correspond to the band location at each given instant. The numerical evaluation of the local strain rate requires the numerical derivation of the displacement field in both space and time. This latter step involves large uncertainties due to the varying acquisition frequency which, in the absence of quantitative information, justifies the normalization of strain rate magnitudes.

Figure 4d shows the kinematic representation partially used in [START_REF] Min | Effect of strain rate on spatio-temporal behavior of Portevin-Le Châtelier bands in a twinning induced plasticity steel[END_REF]: it consists of all the spatial strain distributions measured during the full range of the test, plotted successively as dotted lines. The time difference between each plot shown here is constant and equal to 4.17 µs, corresponding to the camera acquisition frequency. Had the strain remained homogeneous, only horizontal lines would be displayed. When a strain state persists in time, several lines become superimposed, yielding a thicker cluster of lines. On the contrary, transient states only occupy a space of the graph once. As a result, the kinematic behavior of the bands can be directly visualized. Even though time is not explicitly indicated, the variation of local axial strain with time can be understood due to the fact that strain at any given point can only increase since the deformation is essentially plastic and the test is monotonic. Then, for any given line, the subsequent state is represented by the line directly above. Using such a representation, the quality and quantity of the strain jump carried by each band can be assessed by looking at the difference between two persistent states; and its location evaluated graphically as detailed in section 3.2.

The first occurrence of Lüders bands (pointers p1) is associated with the spreading of a uniform strain increment (pointer p2) over the initially homogeneous distribution. Nucleation occurs at each extremity of the sample and a propagation trend continues until coalescence (pointer p3) at x ≈ 42 mm. Then the PLC effect takes over with several increments of increasing amplitude. The zone (x ∈ [40; 55]mm) where strain increments are seen to override each other in an irregular way coincides with a change in band orientation; this behavior is observed in most tests. The inherent nature of the strain increment in characterizing the PLC effect is clearly expressed here since the heterogeneities are maintained and enhanced after the onset of band growth. 4: Results for large sample with a nominal strain rate of 10 -1 s -1 . Figure 4a shows the evolution of stress vs. time. The time axis is in common with fig. 4b where the spatial distribution of strain rate is mapped at each instant-scalar values are normalized and range from 0 (white) to 1 (black). Figure 4c is the hardening curve where local strains are computed with a virtual gauge centered at x = 43 mm, shown here as highlighted zone ( ) on the right hand figures. Figure 4d displays the DIC axial strain measures in space at each captured instant. In figs. 4b and 4d, the common x axis is taken in the tensile direction and in the middle of the specimen. Drawings indicate locations in time and space corresponding to nucleations ( ), propagations ( ) and coalescences ( ); each can be found once on both figs. 4b and 4d. Finally, three strain increments are explicitly shown (blue arrows ). Pointers are used in text references.

Results and discussion

Hardening

The stress-strain curves of six tensile tests are presented in fig. 5, which is divided into two graphs according to the geometry of the samples (small or large). Results are plotted as disconnected points to emphasize the sudden changes of ε xx , which is arbitrarily measured in the middle of the sample over a single DIC element. NSRS is clearly observed since the average hardening values and serration amplitudes tend to increase with decreasing nominal strain rate.

The choice of strain measure has a decisive impact on the appearance and the clear representation of the consequent stress-strain behavior. By using a local strain measure, as opposed to global measures, we are able to obtain meaningful patterns. At low strains, a Lüders-like behavior is observed (fig. 5, zooms z1) after a yield limit of 145 MPa for most tests with an apparent continuity and no sudden stress drop, characteristic of the SSA contribution. Such a plateau is absent from two unique tests on small specimens above a nominal rate of 10 -2 s -1 where the yield stresses are 119.9 MPa and 115.7 MPa (fig. 5b andtable 1a). This behavior may be due to a pre-strain of the small sample during the experimental setup. At the highest nominal strain rates, the PLC effect is reproduced in a progression of repeated steps (elastic loading followed by plastic plateaus) until fracture. For the lowest nominal strain rates, stress-strain curves show a grouping of points in steep clusters (more clearly visible as vertical segments in fig. 5, zooms z2) that correspond to reversible elastic-like loading paths. The highest point of each cluster corresponds to the start of a strain increment (horizontal void) correlated with a serration (vertical drop), which is the characteristic behavior of type B and C bands [START_REF] Chihab | Héterogéneités macroscopiques de la plasticité de type sensibilite negative a la vitesse de deformation[END_REF]. The serrations amplitude increase with decreasing nominal strain rate and increasing strain, up to 20 MPa. The specimen size does not appear to have any influence on stress drops amplitude (see section 3.5). This effect is illustrated onfig. 5 where the isolated point chosen to evaluate the strain is more rarely subjected to localization; the small samples produce clearer patterns because the associated points are more often found in the localized domain. Indeed, by reducing the sample area, a higher spatial resolution and a tighter zone of events allow an accurate evaluation of the mechanical state leading to a more exhaustive characterization of hardening.

Table 1a presents a quantitative summary of the work-hardening results where a single test of each nominal strain rate is arbitrarily chosen for the sake of clarity. The yield stress is taken at a strain of 0.5 %. The average stress-strain curves for both sets of samples remain consistent in spite of changes in geometry and apparatus.

The fracture strain of small specimens is systematically higher than that obtained for large samples which may be due to the presence of fewer defects induced by their smaller volume. As can be seen in fig. 5b, this essentially extends the necking phenomenon but does not cause a further spread of the PLC effect. This difference becomes much higher when the small samples are tested on Instron-10 kN than those tested on MicroTest-2 kN, which suggests that a bias is introduced by the change of machine. It can be due to configuration of MicroTest-2 kN which clamps are mounted on its frame and guided by a rail; whereas Instron-10 kN clamps allow lateral motion, hence lessen lateral stresses. Although this difference does not affect axial results, the more intense stresses due to MicroTest-2 kN transverse stiffness can lead to an earlier fracture.

Apparent propagation or temporal distribution

Figures 4b and4d show a smooth wavelike propagation that, at first sight, would be observed for any test with nominal strain rates corresponding to type A or B. The characteristic representation (4b) allows us to measure subsequent bands locations (e.g. pointer p4) and hence compute an apparent wave velocity that was used by [START_REF] Klusemann | Thermomechanical characterization of Portevin-Le Châtelier bands in AlMg3 (AA5754) and modeling based on a modified Estrin-McCormick approach[END_REF] to compare simulations with experimental results This propagating velocity has been estimated in several studies [START_REF] Ait-Amokhtar | The dynamics of Portevin-Le Chatelier bands in an Al-Mg alloy from infrared thermography[END_REF][START_REF] Bernard | Relationship between local strain jumps and temperature bursts due to the Portevin-Le Chatelier effect in an Al-Mg alloy[END_REF][START_REF] Klusemann | Thermomechanical characterization of Portevin-Le Châtelier bands in AlMg3 (AA5754) and modeling based on a modified Estrin-McCormick approach[END_REF][START_REF] Benallal | Dynamic strain aging and related instabilities: experimental, theoretical and numerical aspects[END_REF][START_REF] Wang | Kinematic and thermal characteristics of Lüders and Portevin-Le Châtelier bands in a medium Mn transformation-induced plasticity steel[END_REF]. It is linked to the strain increment through a kinematic continuity condition [START_REF] Hähner | Spatiotemporal analysis of Portevin-Le Châtelier deformation bands: theory, simulation, and experiment[END_REF]. According to the Hadamard [START_REF] Hadamard | Leçons sur la propagation des ondes et les équations de l'hydrodynamique, Cours du collège de France[END_REF] relation, the continuity of a weakly discontinuous displacement field expresses (here in the 1D tensile case):

v = ε xx w (1)
where v is the gauge area elongation rate, ε xx the axial strain increment (fig. 4d) and w the propagating velocity; they are illustrated on fig. 6. Thus, bands propagate as fast as necessary to accommodate the imposed kinematics. Therefore, an accurate description of the strain increment (see section 3.5) inherently results in a good description of the apparent propagation and vice versa. The strain increments ε xx (steps on fig. 4d) and associated bands locations (dark patterns on fig. 4b) are monitored using the characteristic and kinematic representations with a prediction algorithm prediction implemented with Matlab, which are then verified and corrected manually point-wise. The apparent bands velocities w are computed using polynomial approximations of the locations in time. The right-hand side ( ε xx w) and the left-hand side (v) of eq. ( 1) are plotted in fig. 7 where strong correlation coefficients corroborate the above hypotheses and interpretation for both sample geometries. The indirect measurements deviations remain largely smaller than the orders of magnitude of the direct measurements. Indeed, they can be caused by post-treatment errors, by events occurring outside the gauge area or oscillations of the elongation rate.

Certain conceptual problems arise from considering PLC bands as slow plastic waves. First, it is incompatible with the observation of serrations since an oscillating flow is inherently correlated with sudden kinematic changes: true propagation is frequently not smooth and the patterns of fig. 4b should be regarded as a finite collection of short horizontal segments rather than continuous lines. However, such an interpretation does not allow a unified characterization of the PLC effect since it is not be appropriate for describing type C kinematics that do not display propagating behaviors.

Because of the apparent propagating nature of the PLC effect at higher strain rates, the term band (in the singular) is often used to designate a volume within which the plastic strain rate suddenly increases, even when it travels over the material domain. In the present study, the term band refers to the individual event that takes place at a unique location. Therefore propagation is not taken into account and we consider rather the tendency of bands to nucleate side by side, even if they do so often enough to become indiscernible (type A). A propagating behavior is characterized here by subsequent nucleations that are spatially ordered.

Thus, a single description can be applied for both propagating (ordered) and non-propagating (disordered) behaviors. The property previously brought by the Hadamard relation is conserved and can be rephrased as follows: bands will nucleate as often as necessary to accomodate the imposed kinematics. Their global temporal behavior is adequately defined provided that there is an accurate description of the strain increment.

Morphology

The orientation of bands with respect to the tensile direction is assessed graphically on large samples strain rates maps. Small samples are excluded because of the shoulders proximity to any localization band. In accordance with previous studies [START_REF] Chihab | The kinetics of the Portevin-Le Châtelier bands in an Al-5at% Mg alloy[END_REF][START_REF] Zdunek | Digital image correlation investigation of Portevin-Le Châtelier effect in an aluminium alloy[END_REF][START_REF] Cai | Characterization of the deformation behaviors associated with the serrated flow of a 5456 Al-based alloy using two orthogonal digital image correlation systems[END_REF][START_REF] Yuzbekova | Effect of microstructure on continuous propagation of the Portevin-Le Chatelier deformation bands[END_REF], the angle of orientation ranges between 55 and 65 degrees. As reported in [START_REF] Cai | Characterization of the deformation behaviors associated with the serrated flow of a 5456 Al-based alloy using two orthogonal digital image correlation systems[END_REF], a shearing mode is systematically reported in the samples plane.

Using a method similar to [START_REF] Ait-Amokhtar | Kinematics fields and spatial activity of Portevin-Le Chatelier bands using the digital image correlation method[END_REF], the width of bands is measured on the axial strain rate results: after identifying the strain rate peak (localization band), the width b is assessed graphically at 10 % of the peak height (see fig. 6). Results are presented is table 1b where the strain range of each test is divided into four intervals: [0, 1] % for Lüders bands; then [START_REF] Piobert | Expérience sur la pénétration des projectiles dans le fer forgé[END_REF][START_REF] Ait-Amokhtar | Kinematics fields and spatial activity of Portevin-Le Chatelier bands using the digital image correlation method[END_REF] %, [START_REF] Ait-Amokhtar | Kinematics fields and spatial activity of Portevin-Le Chatelier bands using the digital image correlation method[END_REF][START_REF] Ait-Amokhtar | The dynamics of Portevin-Le Chatelier bands in an Al-Mg alloy from infrared thermography[END_REF] %, [START_REF] Ait-Amokhtar | The dynamics of Portevin-Le Chatelier bands in an Al-Mg alloy from infrared thermography[END_REF][START_REF] Benallal | An experimental and numerical investigation of the behaviour of AA5083 aluminium alloy in presence of the Portevin-Le Chatelier effect[END_REF] % to distinguish PLC bands at the beginning, middle and end of the test, respectively. Each width value is the mean of ten measurements taken in the associated range, rounded to a precision of 0.5 mm due to the lack of precision of the peak shape, and oscillations of the signal at its edges. It should be noted that the widths are measured in the reference configuration and not transported to the current configuration.

On large samples, the band width is equal to 2 mm at the lowest nominal strain rates (10 -4 s -1 ) and increases up to 5.5 mm at the highest rates (10 -1 s -1 ). Such values are qualitatively consistent with previous studies [START_REF] Ziegenbein | Correlation of temporal instabilities and spatial localization during Portevin-Le Châtelier deformation of Cu-10 at.% Al and Cu-15 at.% Al[END_REF][START_REF] Hähner | Spatiotemporal analysis of Portevin-Le Châtelier deformation bands: theory, simulation, and experiment[END_REF][START_REF] Ait-Amokhtar | Kinematics fields and spatial activity of Portevin-Le Chatelier bands using the digital image correlation method[END_REF][START_REF] Yuzbekova | Effect of microstructure on continuous propagation of the Portevin-Le Chatelier deformation bands[END_REF], suggesting a non linear monotonic increase of the bands widths with increasing strain rate. However, for small specimens and with the same method, this width is found to range from approximately 2 mm to 2.5 mm with no apparent sensitivity to rate and a higher level of confidence owing to the finer spatial resolution. Such a result has not yet been reported in the literature, and is further discussed in section 3.5.

Spatial distribution

To qualitatively assess the spatial distribution of localization bands, fig. 8 presents the kinematic representations of three different nominal strain rates (decreasing from top to bottom) applied to each of the two considered geometries (large in the left column and small in the right column). After a homogeneous increase of strain over the specimen, the first localization occurs for all samples x (mm)

ε xx (%) (e) 0 1 2 3 x (mm) (f) macro meso ε = 5 × 10 -2 s -1 ε = 5 × 10 -3 s -1 ε = 1 × 10 -3 s -1
Figure 8: Subsequent strain states for different apparent strain rates plotted for both large (left column) and small (right column) samples. Each row corresponds to an order of magnitude of global strain rate specified on the right axis. Figures 8a and 8b at a common yield stress of 145 MPa. The location of the first band is due to local imperfections and can hardly be predicted. The subsequent bands (PL) follow a propagating pattern until full coverage of the gauge zone. The strain increment they carry is a consequence of SSA and remains at a value of 1.0(1) % independently of the applied velocity and irrespective geometry. The DSA mechanism starts at higher strains, with repeated occurrences of the PLC effect in different ways depending on the nominal strain rate of the test. Figures 8a and 8b correspond to higher nominal strain rates and type A bands. The associated stress-strain curves are dominated by plateaus with a low number of serrations that are correlated with each first nucleation of an ordered set of bands. Nucleations are so frequent that they cannot be picked out in the DIC results. A clear propagating behavior is observed for most sets of bands, except in the annotated zone that corresponds, as mentioned in section 2.3, to the area with overlapping bands of opposite orientations. The second row (8c-8d) illustrates intermediate nominal strain rates corresponding to type B bands, where serrations become predominant. While the bands appear ordered in space as in type A, a kinematic difference can be observed in fig. 8c where intermittent persistent states are annotated. They reflect the hopping band trend associated with type B, expressed as a short break between two subsequent localizations which results in the superimposition of several measured strain states. This observation is consistent with the behaviors described in section 3.2: even though the propagating tendency (spatial order) is maintained, a lower imposed velocity implies a lower frequency of localization, rendering the events distinguishable. Figures 8e and8f are associated with lower nominal strain rates and type C bands where serrations are larger in magnitude. In such regimes, the propagating patterns are frequently broken which result in an apparently disordered scheme. By contrast, only the large specimens (fig. 8e) clearly exhibit the characteristic disordered pattern of type C bands, while the small samples conserve a type B propagation trend in spite of an identical nominal strain rate and similar gauge area elongation rates (table 1).

The usual view of a "stochastic" or "random" distribution of bands that do not overlap [START_REF] Chihab | The kinetics of the Portevin-Le Châtelier bands in an Al-5at% Mg alloy[END_REF] does not entirely cover what can be understood from the present experiments. Not only will two bands never nucleate successively at the same location, but type C bands tend to appear where the cumulative plasticity is minimal and thus follow an overall deterministic trend. As observed in classical plasticity, localization bands collectively tend to foster the homogeneity of strain. The kinematic trend becomes progressively ordered as the nominal strain rate increases-propagating patterns are first clearly observed at a nominal strain rate of 10 -3 s -1 . From a macroscopic point of view, the tendency of bands to nucleate next to each other is influenced by the plastic strain gradient magnitude. Indeed, the steep strain step inherently produced by each band has for consequence a local peak of strain gradient that always matches the band location in the case of propagating behaviors (this can be seen from the simplified representation given on fig. 6). The gradient influence during plastic instabilities is in agreement with the strain gradient plasticity framework, applied by several authors to modeling the PLC effect [START_REF] Zbib | A gradient-dependent model for the Portevin-Le Châtelier effect[END_REF][START_REF] Mazière | Strain gradient plasticity modeling and finite element simulation of Lüders band formation and propagation[END_REF]. Consequently, the macroscopic spatial distribution of PLC bands can be seen as a competition between the minimal magnitude of plastic strain that dominates at lower strain rates, and the plastic strain gradient that takes over at higher strain rates. Since PL bands always appear at the onset of plasticity, their systematic propagation trend is caused by the plasticity gradient influence alone.

Characterization of transient states

The PLC effect involves a double-scale problem both in space (specimen length and band width) and in time (test duration and nucleation time). While the spatial issue is better addressed by increasing images resolution, the acquisition frequency and quality are generally not high enough to accurately measure the kinetics of plastic instabilities during nucleation. Nevertheless, the localization effects can be characterized in terms of their outcome, by comparing initial and final states. Following this procedure, several studies have used the strain increment to characterize the consequence of a band [START_REF] Ziegenbein | Correlation of temporal instabilities and spatial localization during Portevin-Le Châtelier deformation of Cu-10 at.% Al and Cu-15 at.% Al[END_REF][START_REF] Kovács | Localized deformation bands in Portevin-Le Châtelier plastic instabili-ties at a constant stress rate[END_REF][START_REF] Renard | Characterisation of the Portevin-Le Châtelier effect affecting an austenitic TWIP steel based on digital image correlation[END_REF][START_REF] Bernard | Relationship between local strain jumps and temperature bursts due to the Portevin-Le Chatelier effect in an Al-Mg alloy[END_REF][START_REF] Min | Effect of strain rate on spatio-temporal behavior of Portevin-Le Châtelier bands in a twinning induced plasticity steel[END_REF][START_REF] Klusemann | Thermomechanical characterization of Portevin-Le Châtelier bands in AlMg3 (AA5754) and modeling based on a modified Estrin-McCormick approach[END_REF]. Using the kinematic representation, the difference of strain between initial and final states is measured at all possible instants on all of the tested specimens following the method described in section 3.2 (computer prediction and manual correction). In the case of disordered behaviors, the measurement is taken at the maximum increment, that is, in the middle of the band. The results are shown in fig. 9 as a function of the stress at nucleation time (peak value). A color bar indicates the instantaneous mean strain rate which is obtained from DIC results as the difference in velocity between the two edges of the gauge area. This method is applied to avoid the effects of geometry on the measured rates. A clearly consistent pattern can be noted because the scatter of points takes the form of a constitutive relation showing a monotonic evolution up to saturation associated with NSRS, which suggests that the strain increment is an intrinsic quantity that defines the action of a localization band. Even though the PL bands increment seems to be in continuity with the set of data points, it is always several times larger than the directly consecutive PLC bands. While such small values cannot be explicitly quantified, the difference can be readily observed on figs. 8a, 8c and 8e. A weak size effect is reported here since a strain increment scaling of ∼ 20 % is needed to achieve a quantitative match between the two distributions. In the literature, strain increments are usually reported as a function of cumulative plastic strain. The present results display the same NSRS when plotted as a function of the linearized Green-Lagrange measure. They agree with [START_REF] Klusemann | Thermomechanical characterization of Portevin-Le Châtelier bands in AlMg3 (AA5754) and modeling based on a modified Estrin-McCormick approach[END_REF] where strain increments are measured using strain gauges, and a quasi-linear dependence is reported with cumulative plastic strain below 3 %. Although strain increments have been reported to decrease with increasing strain rate [START_REF] Ziegenbein | Correlation of temporal instabilities and spatial localization during Portevin-Le Châtelier deformation of Cu-10 at.% Al and Cu-15 at.% Al[END_REF] this was not observed in [START_REF] Kovács | Localized deformation bands in Portevin-Le Châtelier plastic instabili-ties at a constant stress rate[END_REF].

In fig. 10, the stress drops distributions are presented for each test as box plots shown as a function of the mean strain rate. Serrations are post-treated directly after the measurement and the data are maintained as such without further treatment; hence subjectivity is avoided but noise and small oscillations result in an overestimation of the amount of the smallest drops and a necessary shift of fractile values. The results are obtained following the method introduced by [START_REF] Lebyodkin | Spatio-temporal dynamics of the Portevin-Le Chatelier effect: experiment and modelling[END_REF] for tensile tests, as reproduced experimentally in shear tests by [START_REF] Coër | Piobert-Lüders plateau and Portevin-Le Chatelier effect in an Al-Mg alloy in simple shear[END_REF] and numerically by [START_REF] Manach | Kinematics of Portevin-Le Chatelier bands in simple shear[END_REF]. In this approach, histograms are considered and characterized by the number of peaks and their location. In the present study, each corresponding histogram exhibits a single peak that tends to decrease with increasing strain rate, qualitatively matching with the results of [START_REF] Lebyodkin | Spatio-temporal dynamics of the Portevin-Le Chatelier effect: experiment and modelling[END_REF]. The upper extreme and fractile values decrease exponentially with increasing strain rate, smoothly linking type C serrations to type A plateaus. The lower bounds can hardly be analyzed. A weak or negligible influence of the sample geometry is reported as regards the strain increment. This indicates that the stress drop is not only a structural response but an inherent actor in the nucleation process: since the stress drop is independent of size, its maximal amplitude can be predicted along with the strain increment knowing the mechanical state before nucleation.

The information on stress drops completes the kinematic observations which allows us to carry out the following analysis. Considering the one-dimensional problem of a rod of length L under constant imposed relative strain rate v/L; let τ be the nucleation time, i.e. the duration taken by a band to nucleate or the total time during which the plastic strain rate is non-zero. The increment of length caused by a single nucleation can then be written

∆L = τ v dt = τ L 0 ( σ/E + εp ) dx dt (2)
⇐⇒ vτ = (∆σ/E)L + ∆ε p b ( 3
)
where b is an equivalent band width. When the nominal strain rate is kept constant, increasing the length (in the present experiments from 4.2 mm to 60 mm) has no significant influence on {∆σ, ∆ε p , b} (resp. figs. 9 and 10 and section 3.3): in order to satisfiy eq. ( 3) the nucleation time τ accommodates size variations by decreasing with increasing length. This would imply that, during nucleation, the material constitutive relation thereof links strain differentials dε p and stress differentials dσ with little or no implicit time dependence dt. Indeed, the same results are obtained for ∆σ and ∆ε p with both geometries even though the nucleation process is several times faster for large samples. This postulate holds for both PL bands and the PLC effect. Moreover, the above feature allows us to understand the length effect measured in bands width (see section 3.3).

Comparing small and large specimens at equal nominal strain rate, the wider bands observed in large specimen are in fact subjected to a higher instantaneous local strain rates arising from a shorter nucleation time. The commonly accepted concept of band width increasing with strain rate is thus validated and can partly explain the gauge length sensitivity. While experimental data does not argue against this explanation, a large increase in acquisition frequency and accuracy is required, as well as a more exhaustive set of length values, to provide empirical evidences and draw further conclusions. Finally, table 1b indicates when two bands are observed simultaneously. Two PL bands are displayed at the same time in all large specimens tested with a nominal strain rate above 5 × 10 -3 s -1 , and all small samples above 1 × 10 -3 s -1 (e.g. fig. 3). Two coexisting PLC bands are observed in all large specimens above 5 × 10 -2 s -1 (e.g. fig. 8a) at low strain levels, while never reported in small samples. The higher the strain rate, the longer the coexistence persists, and no more than two coexisting bands are ever displayed at any one time. These observations suggest the existence of a maximal local strain rate beyond which a band cannot grow, being lower for PL than for PLC bands. The fact that several PLC bands are never found in small samples is consistent with the above observation: a smaller length implies slower nucleations and a smaller associated strain rate. The coexistence of bands is often described in experimental studies, but no interpretations have been found in the literature.

Conclusion

The Portevin-Le Chatelier effect and Piobert-Lüders bands are investigated in an Al-Mg alloy at room temperature. A macroscopic interpretation is proposed which integrates the common discrete categories (A, B and C type bands) into a continuous description while distinguishing spatial (disordered and ordered trends, respectively driven by the plastic strain magnitude and its gradient) from temporal factors (nucleation frequency, extrinsic to the material behavior and governed by imposed kinematics). The key results of the present investigations are as follows.

i. Plastic strain increments are inherent to the nucleation of PL and PLC band. They are linked to stress at nucleation through a constitutive relation that expresses a negative strain rate sensitivity with no significant size sensitivity. ii. The serrations distributions follow an overall decreasing trend with increasing strain rate and individual serrations show a monotonic increase with increasing strain. The development of serrations shows a small to negligible size sensitivity. Consequently, they can also be predicted without using transient differential equations.

Although the time refinement presented here does not exhaustively assess the nucleation process, a number of hypotheses are proposed by combining experimental evidence with a 1D kinematic model.

iii. The nucleation time and the strain rate carried by each band accommodate the size changes: the longer the sample, the faster the band evolution. iv. There is an inherent limit to the bands strain rate, being lower for PL than for PLC bands, which explains the occurrence of several bands at the same time.

Figure 1 :

 1 Figure 1: Electron backscatter diffraction results on AA5086 post-treated with the MTEX [34] toolbox. The computed grains boundaries are superimposed with bands contrast on fig. 1a. Figure 1b gives a histogram of the grains equivalent diameters.

Figure 2 :

 2 Figure 2: Geometries referred to as large (2a) and small (2b). Dimensions are given in mm.

Figure

  Figure4: Results for large sample with a nominal strain rate of 10 -1 s -1 . Figure4ashows the evolution of stress vs. time. The time axis is in common with fig.4bwhere the spatial distribution of strain rate is mapped at each instant-scalar values are normalized and range from 0 (white) to 1 (black). Figure4cis the hardening curve where local strains are computed with a virtual gauge centered at x = 43 mm, shown here as highlighted zone ( ) on the right hand figures. Figure4ddisplays the DIC axial strain measures in space at each captured instant. In figs. 4b and 4d, the common x axis is taken in the tensile direction and in the middle of the specimen. Drawings indicate locations in time and space corresponding to nucleations ( ), propagations ( ) and coalescences ( ); each can be found once on both figs. 4b and 4d. Finally, three strain increments are explicitly shown (blue arrows ). Pointers are used in text references.

Figure 5 :Figure 6 :

 56 Figure5: Cauchy stress vs. linearized Green-Lagrange strain curves on large (fig.5a) and small (fig.5b) samples, obtained with a DIC gauge located arbitrarily at the center of the specimens with the width of one finite element. Colors are associated with nominal strain rates specified in the legend. The same envelop curves are added to evaluate the influence of sample size on stress amplitudes.

Figure 7 :

 7 Figure 7: Gauge area elongation rate (mm s -1 ) for all results showing an apparent propagation-direct and indirect measurements are plotted with correlation coefficient R. Both direct and indirect measurements and prediction are obtained by post-treatment of the DIC results (see section 3.2).

  Figure8: Subsequent strain states for different apparent strain rates plotted for both large (left column) and small (right column) samples. Each row corresponds to an order of magnitude of global strain rate specified on the right axis. Figures8a and 8b(type A) as well as figs. 8c and 8d (type B) show spatially ordered patterns; while figs. 8e and 8f (type C) display a disordered behavior-see section 3.4. The fracture location is indicated with a vertical line.

1 )Figure 9 :Figure 10 :

 1910 Figure 9: A constitutive relation at the scale of the localized zone. The strain magnitude increment is measured as illustrated in fig. 4. The stress measure is taken at the onset of localization, before its drop. Two identical envelope curves are added for comparison.

Table 1 :

 1 Quantitative summary of experiments. Geometry: large (large) or small (small) specimens. Device: Instron-10 kN (Ins.); MicroTest-2 kN (Mic.). Nominal strain rate vc/Lc. The average strain rate v is the mean value of the measured gauge zone elongation rate v divided by the gauge zone length L. Work-hardening: yield stress σy and fracture strain ε f xx . Morphology: bd c is the averaged width (measured according to fig.6) in the interval εxx ∈ [c, d] in percents; b1 0 corresponds to PL bands while the rest are PLC. The marker ( * ) indicates the observation of two coexisting bands at several instants in the given strain range.

			10 -3 s -1	MPa %		mm mm mm mm
	large Ins.	0.1	0.1	139.3	25.7	2	2	2	2
		0.5	0.5	139.0	30.5	2.5 2.5 3	3
		1.0	1.1	138.3	35.5	4	4	4.5 4.5
		5.0	5.4	142.4	32.5	4.5 4.5 4.5 4.5
		10	10.9	139.2	35.3	5.5 5	5	5
		50	50.9	140.9	38.3	5 * 5	5	5
	100 5.5 small Mic. 89.2 142.7 38.4 0.2 0.1 147.6 38.2 2	2	2	2
		0.3	0.4	147.4	41.6	2	2	2	2
		0.7	1.0	143.2	40.9	2	2	2	2
	small Ins.	1.0	1.0	133.2	44.9	2	2	2	2
		10	9.3	119.9	64.7	2 * 2	2	2
		50	56.5	138.0	57.1	2 * 2	2	2
		100	152	115.7	71.0	2 * 2	2	2

* 5 * 5 * 5.5

Acknowledgment

This research is supported by the Brittany region. The authors thank A. Jegat, A. Magueresse and H. Bellegou for their substantial involvement in the experimental investigations; and J. Réthoré for advice and permission to use his software [36]. M.S.N. Carpenter post-edited the English style and grammar.

Data availability

The raw/processed data required to reproduce these findings are available to download from zenodo.org [START_REF] Reyne | AA5086 characterization in tension at several constant strain rates and room temperature using DIC with occurence of the Portevin-Le Chatelier effect[END_REF].


J Dupuis

E Fourmond

D Ballutaud

N Bererd

M Lemiti

Optical and structural properties of silicon oxynitride deposited by Plasma Enhanced Chemical Vapor Deposition for photovoltaic applications

Keywords: SiON, XPS, FTIR, ERDA, Surface passivation, Solar cells

We present an overview of the properties of silicon oxynitride material (SiON) deposited by Plasma Enhanced Chemical Vapor Deposition (PECVD) for photovoltaic applications. SiON films were deposited using silane (SiH 4 ), ammonia (NH 3 ) and nitrogen protoxide (N 2 O) as precursor gases in a low frequency PECVD. Varying the gas flow mixture leads to a whole range of SiON layers starting from the silicon oxide to the silicon nitride with unique stoichiometries and properties. Thanks to spectroscopic ellipsometry measurements we have confirmed the suitability of SiON for antireflection coating layers due to the range of the refractive indexes attainable. SiON structure was analyzed by X-ray photo-electron spectroscopy. We have thus highlighted the critical role of oxygen behavior on the SiON network and the progressive replacement of nitrogen by oxygen atoms when the oxygen precursor increases. The type of chemical bonds present in Si-ON layers was also investigated by infrared spectroscopy. The SiON layers also contain a non-negligible amount of hydrogen which might be useful for passivation applications. The behavior of hydrogen content was thus analyzed by elastic recoil decay analysis and desorption characterization. A typical rapid thermal annealing was performed on the SiON samples in order to simulate the solar cells contact annealing and to investigate its impact on the dielectric film properties. It was found that hydrogen becomes weakly bonded to the films and strongly decreases in quantity with the annealing. The surface passivation effect is presented in the last part of this paper. The trend before and after a rapid thermal annealing showed opposite results which could be explained by the high porosity of the layers and the formation of Si-O bonds.

INTRODUCTION

Silicon nitride (SiN) and silicon oxynitride (SiON) are widely used in the microelectronic field as in Si-based large-scale integration circuit technology or in optoelectronic devices. In the photovoltaic field, the refractive index of the amorphous hydrogenated form of SiN (SiN x :H) was found to be ideal as it causes very low absorption in the solar spectrum range and excellent passivation properties on the silicon surface and within the silicon bulk in the case of multi-crystalline material [1]. For that reason, in the previous decade, silicon nitride has become a standard to realize the front antireflection coating of industrial solar cells. Plasma enhanced chemical vapor deposition process (PECVD) is currently one of the preferred deposition method for the SiN films due to a lower thermal budget than the other CVD processes and a high amount of hydrogen in the layer.

At the present time, the SiON stays a suitable material for optoelectronic devices and integrated circuits such as waveguides or thin-film transistors [2,3,4]. But until recently, this material was not a serious candidate to compete with SiN for photovoltaic applications.

The situation might yet change. The amorphous hydrogenated form of the SiON dielectric (SiO x N y :H) presents some similar aspects to SiN: it can be deposited at low temperature by PECVD, it exhibits low absorbance and an adjustable refractive index below 1.5 and up to 3.0 [5,6] by changing the precursor gas flow ratio during the deposition process. Thus, these properties can be suitable for photovoltaic industry especially for the antireflection multi-layers coatings by adjusting carefully the optical index and the thickness of the film [7]. Multi antireflection layers can increase the short circuit current more than two percent for cell under air which may be used for high efficiency or specific module technology [START_REF]Proceedings of the 20 th European Photovoltaic Solar Energy Conference[END_REF]. With the use of SiON, multi antireflection layer can be performed in the same reactor at relatively low temperature (< 400 °C). The passivation effect of SiON is also under investigation to look for an alternative to the actual aluminium back surface field, which is responsible for high constraints on the back side of the thin silicon solar cells. From this point of view, a layer of SiN can be used but its passivation effect could be limited due to its high positive fixed charge density [7]. On the other hand, stack structures consisting of SiN and/or silicon oxide layers (abbreviated SiO afterwards) are a promising way to optimize the rear surface passivation without the use of high temperature process [START_REF]Proceedings of the 23 rd European Photovoltaic Solar Energy Conference[END_REF][START_REF]Proceedings of the 22 nd European Photovoltaic Solar Energy Conference[END_REF][START_REF]Proceedings of the 22 nd European Photovoltaic Solar Energy Conference[END_REF]. Finally, the low SiON refractive index make this layer suitable to act as a rear surface reflector for infrared photons which are less absorbed in the silicon.

Although a lot of studies have been done on the SiON material deposited by PECVD, the microelectronics and photovoltaics objectives are not completely similar. For that reason, the optimization of the SiON films will be different in both cases.

This work aims to study the optical, structural and electrical properties of SiON deposited by PECVD on silicon substrates for solar cells applications. Firstly, the optical properties of the layers deposited in our PECVD reactor will be presented. Secondly, we will investigate the structure of these layers by X-ray photo-electron spectroscopy, Fourier transform infrared spectroscopy and elastic recoil decay analysis measurements with a special attention to the hydrogen content of our films. Finally, we will study the passivation properties using minority carrier lifetime measurements, in order to show whether the PECVD SiON is a suitable material for passivation purposes.

EXPERIMENTAL DETAILS

SiON layers were deposited with a mixture of ammonia (NH 3 ), pure silane (SiH 4 ) and nitrous oxide (N 2 O) as precursor gases in a semi-industrial Low Frequency PECVD reactor (LF-PECVD). The reactor was developed by SEMCO-Engineering and presents a vertical configuration chamber (figure 1).

We chose to keep the silane gas flow constant at 25 sccm, while varying both NH 3 and N 2 O gas flows in order to keep the total gas flow constant. Different SiON stoichiometries were obtained by varying the "Ox" ratio, defined as:

3 2 2 NH O N O N Ox  
The Ox ratio is also an indicator of the oxygen and nitrogen content of the SiON layers: Ox = 0.00 corresponds to a SiN layer deposition, whereas Ox = 1.00 gives a SiO layer. This ratio will be used in the following as the main indicator to identify our samples.

A total of five different SiON layers, including a SiN and a SiO samples, were elaborated on <100> float zone 2 inches p-type silicon wafers with both sides polished and a resistivity of 4-7 ohm.cm. The gas flows parameters for each sample are summarized in the table 1.

A spectroscopic ellipsometer (Jobin Yvon UVISEL) was used to obtain the optical indexes of the SiON layers, using the Tauc-Lorentz model [START_REF] Jellison | [END_REF]. The composition and the structure of the SiON films were analyzed by XPS (X-ray Photo-electron Spectroscopy) and ERDA (Elastic Recoil Detection Analysis) characterizations. In both cases, the measurements were made deep enough in the layers to avoid carbon or oxygen outside contaminations.

The XPS measurements were carried out in a VG Esclalab 220iXL system, with a base pressure of 5.10 -10 torr, and using an AlK source (1486.6 eV) X-ray monochromatized radiation. The energy measurements were made with a Thermo Electron hemispheric analyzer in transmission mode. The spectra were obtained with a detector using six channeltrons put in series. The pass electron energy was 20 eV with a 0.1 eV pitch. The spectra resolution is 0.3 eV. The samples surface were etched using an Ar beam of 3 keV with a current density of 4 µA/mm 2 applied during 1 minute. The energy levels of XPS were calibrated with Au single crystal. The spectra were processed using the VG Eclipse Datasystem. The background contribution was included in the fitting process, using the Shirley method [13].

The ERDA characterizations were performed on the 4 MV Van de Graaff accelerator of the Nuclear Physic Institute of Lyon using 1.7 MeV kinetics energy alpha particles.

To study the hydrogen bonding environment we have used infrared transmission measurements. We have operated a Fourier-Transform infrared spectrometer (FTS60 A, Bio-Rad Inc.) associated with a Deuterated Triglycine Sulfate detector operating in the spectrum range of 1.6 to 20 micrometers to characterize the SiON samples.

The loss of hydrogen in the SiON layers due to thermal treatment has also been investigated in more details with Temperature Programmed Desorption (TPD) measurements.

The characterization process consists to put the sample under vacuum and to apply a slow temperature ramp. The quantity of hydrogen that exodiffuses from the layer under such a treatment is then measured by mass spectrometry.

Finally, we have studied the surface passivation properties of our layers by measuring the minority carrier lifetime (MCL), using photoconductance decay (PCD) measurements by a WCT-100 Photoconductance Tool from Sinton Consulting [14]. SiON layers of 70 nm have been deposited on both sides of float-zone polished 1-10 ohm.cm silicon wafers, n-type and p-type (<100> oriented). The high quality of the silicon wafer implies that the effective lifetime measured depends essentially on the surfaces recombination velocity, since the bulk minority carrier lifetime is superior to 3 milliseconds in this case.

OPTICAL PROPERTIES

The refractive indexes and the thicknesses results are summarized in the table 2. The refractive index incertitude is ± 0.02 and the thickness ± 2 %. The values are in agreement with the literature [15,16,17,18]. As previously discussed [6], the absorption coefficient k remains lower than 10 -3 for wavelengths above 300 nm. For that reason, front solar cells applications as antireflection coatings are possible.

The increase of the Ox ratio, and consequently the N 2 O flow, entails lower refractive indexes. According to Mattson et al. [16], the refractive index is controlled by the oxygen specific volume, in other words by the Si-O electron density bonds. The replacement of the nitrogen atoms by the oxygen atoms induces a slight increase of the bond angle of the Si-O-Si bridges, and results in a lesser Si-O electron density, which decreases the refractive index. The refractive index of the Ox = 1.00 layer is still above the value observed for SiO 2 , since the layer has not the same stoechiometry and contains hydrogen, as it will be shown in the following.

STRUCTURAL PROPERTIES

Most of the XPS results has been already published in a previous study [6]. In this section, we will combine the XPS and the ERDA results to establish the complete stoichiometry of the dielectrics layers.

ATOMIC COMPOSITION

The SiON chemical compositions are plotted on the figure 2. The incertitude was taken to ± 2 % for the ERDA results, according to the approximate density of the layers, and to ± 4 % for XPS results because of some variations in the composition depending on the depth of the analysis within the layer.

The main change in the composition from Ox=0 to Ox=1 comes from the oxygen and the nitrogen contents. As expected, a higher N 2 O flow during the process leads to an increase in the oxygen incorporation within the layer. Moreover the plot highlights the fact that the relative oxygen content is almost opposed to the nitrogen one, while silicon and hydrogen contents do not vary notably. This trend suggests a replacement of the nitrogen atoms by the oxygen atoms during the increase of the Ox ratio. This replacement is partly due to the higher oxygen precursor concentration during the deposition process, but also to a more thermodynamic stability of the Si-O bond (4.7 eV) compared to the Si-N bond (3.7 eV) [START_REF] Darwent | National Standard Reference Data Series[END_REF]. This tendency has been previously observed for SiON layers deposited by PECVD with no ammonia in the precursor gazes [15,[START_REF] Alayo | [END_REF].

The amount of hydrogen within the layers is in accordance with other authors [15,18] and does not vary significantly between the samples (13 % -18 %), except for the SiO layer (4 %). This notable drop of concentration can be explained by the low hydrogen content of the precursor's gases, since no ammonia is used in that case. Naskar noticed the same phenomenon for SiON samples based on N 2 O and SiH 4 when the flow of SiH 4 becomes low [15].

XPS PEAK DECOMPOSITION

The XPS analysis does not only give the atomic composition of a material but brings also information about the bonding environments within the layer.

Although our materials are amorphous, non-stoichiometric and contain a lot of hydrogen, a microscopic order is always observed within the layer. Two models are commonly used to describe this order: the random mixture model (RMM), and the random bounding model (RBM) [21]. Both models are based on the silicon-centered tetrahedrons with in-plane triply coordinated nitrogen as bonding structures. For the RMM, the bonding structure of the SiON consists of a random mixture of silicon, nitrogen and oxygen, where stable phases like Si 3 N 4 and SiO 2 prevail. In the RBM, the structure is controlled statistically by the nearest nitrogen and oxygen atoms bonded randomly to the silicon tetrahedrons.

SILICON 2p ELECTRON CONFIGURATION PEAKS

The 2p electron configuration of the silicon has been analyzed to investigate the degree of organization of the SiON matrix, and to study its change with the progressive replacement of nitrogen by oxygen atoms. The associated XPS peak is located near an electron binding energy of 100 eV. The peaks and the Gaussian fits for the five samples are presented on the figure 3 and the table 3.

A shift occurs when the oxygen concentration increases in the layer. This shift is particularly obvious when the SiN film and the SiON films are compared. Usually, a shift in the electron binding energy can be attributed to a charge transfer caused by the atoms electronegativity [22]. The electronegativities of silicon, hydrogen, nitrogen and oxygen are respectively 1.74, 2.20, 3.07 and 3.50, considering the Allred and Rochow scale [23]. Thus, the Si-O and Si-N bonds have both a strong ionic behavior and consequently, the shift can be mainly attributed to the energy difference between these two bonds.

Every peak exhibits a nearly-gaussian profile, independently of the stoichiometry. This tends to prove that the film structure is dominated by a single amorphous phase as suggested by the RBM. But the change of the full width at half maximum (FWHM) between the samples reveals some dispersions on the bond frequencies, and thus points out structural disorders and different local bonding environments [24]. This indicates that the layer could contain some local specific environments within the matrix (like for instance the silicon nanocrystals for silicon-rich SiN as reported by [25]), or a more various bonding environment due to oxygen incorporation.

To analyze the cause of the shift and the FWHM variation, XPS peaks are decomposed according to the reference data from [7], [21] and [22]. The table 4 presents the results of the decomposition for the five samples. The uncertainties on the peak contributions are ± 3 %. Note that we did not choose to introduce hydrogen environment in the database because it would have involved too many possible chemical species with similar electron binding energy. The hydrogen will be analyzed further by the decomposition of the XPS nitrogen 1s peak configuration.

The decomposition of the SiN sample, presented in the figure 4, is in accordance with previous work [7]. The layer is however richer in silicon than the reference silicon nitride Si 3 N 4 (The N/Si ratio is 0.75 compared to 1.33). The silicon bonding environment thus reveals a high contribution of the Si-N 4 species (Si 3 N 4 ) with a silicon-rich contribution.

Unsurprisingly, the bonding environment tends to become oxygen-rich while increasing the Ox ratio. This point is evident on the decomposition of the Si(2p) global peak, with the disappearance of the species based on nitrogen. More interesting is the high contri- The strong change in the matrix with the incorporation of oxygen is probably due to its high reactivity with the silicon. As it was already mentioned, this reaction is thermodynamically preferred to any others. This may explain the high contribution of the oxygen-based environment despite the relatively low oxygen content (near 20 % on figure 2). The disappearance of the nitrogen environment when Ox increases is slow and follows the decrease of the atomic nitrogen contribution in the film (figure 2), as the table 4 and figure 4 tend to prove.

NITROGEN 1s ELECTRON CONFIGURATION PEAKS

Contrary to silicon, N-O bonds are not thermodynamically privileged compared to N-H or N-Si (2.1 eV against 4.0 and 3.7 eV respectively [7] [START_REF] Darwent | National Standard Reference Data Series[END_REF]). Thus, to analyze the hydrogen content through the study of the nitrogen peak N(1s) is easier than with the Si(2p) peak.

Unfortunately, the nitrogen composition varies significantly with the Ox ratio and the decomposition becomes harder for the nitrogen-poor films. Thus, we have chosen to focus on the general trend of the peaks.

As for the silicon, the nitrogen peaks seem to be Gaussian (figure 3). The nitrogen environment is probably also dominated by a single amorphous phase. A shift of the N(1s) peak to higher binding energy and a variation of the FWHM are also visible (table 5).

The larger FWHM obtained when the Ox ratio increases is probably caused by some more various chemical environments with the oxygen complex. The reason of the shift could be a consequence of the oxygen content increase. However, since N-O bonding is non-thermodynamically privileged, hydrogen atoms may also play a role due to their electronegativity. This hypothesis is strengthened by the behavior observed on the SiO sample: a strong shift of the N(1s) peak occurs to lower energy for this layer although oxygen was present in high concentration. But contrary to the oxygen, the hydrogen concentration fall steeply between the SiON (Ox = 0.87) and the SiO sample. Thus, the disappearance of the hydrogen could explain the shift of the N(1s) peak. Note that the FWHM reduction for the Ox = 1.00 sample suggests a more uniform bonding environment, but the signal of the nitrogen peak was too noisy to analyse the N(1s) peak unambiguously. The decomposition of the N(1s) peaks confirms that the evolution of the matrix is driven by a progressive replacement of the nitrogen atoms by the oxygen atoms.

Moreover, the hydrogen is probably localised preferentially near the nitrogen atoms, as suggested by the shift of the N(1s) peaks.

INFRARED SPECTROSCOPY MEASUREMENTS

In the photovoltaic field, the hydrogen content of the film is very important for the passivation point of view [26]. It is thus necessary to investigate in more details how the hydrogen is bonded within the films, and how it reacts when the layers are annealed during the metallic front contacts formation at the end of the standard solar cell fabrication process.

One set of the samples was annealed in a lamp furnace under pure air atmosphere at 800 °C during few seconds. The annealing profile is shown in the figure 5, and is equivalent to the standard annealing process for the contact formation. The Fourier-transform infrared (FTIR) spectra obtained with these samples are shown in the figure 6. We will describe the most important regions and confront them to the XPS results. A more detailed analysis of the FTIR spectra has been already published in [6].

The predominant band between 800 cm -1 and 1200 cm -1 is mainly caused by the Si-N and the Si-O groups in the stretching mode [START_REF] Alayo | [END_REF] [28]. The peaks localised at 1180 cm -1 and 3350 cm -1 correspond to N-H bending and stretching vibration respectively [29]. At 2200 cm -1 stands the Si-H stretching mode and lastly, the small peak at 3500 cm -1 can be identified as the H-O-H stretching vibration [17]. Note that the 2000-4000 cm -1 spectral region was magnified five times for appreciation.

Going from the SiN to the SiO films, the main peak moves from the Si-N stretching mode to the Si-O stretching and rocking modes as expected from the previous XPS analysis: the oxygen atoms take progressively the place of the nitrogen atoms and the oxygen reacts in priority with the silicon. This is confirmed by the decrease of the Si-N, N-H and Si-H related peaks. The presence of water is also detected through the H-O-H bond and the presence of absorption peaks in the 1400 -1800 cm -1 range, despite a complete atmosphere purge in the FTIR chamber. The presence of water in SiON films has also been reported by Yeh and Lee [30] for oxygen-rich samples deposited at 250 °C. The authors have suggested that the water presence was related to the decrease of the incoming rate of SiH n radicals towards the surface during the deposition. This would allow the hydrogen atoms in the plasma to remove the O-H bonded to silicon more easily, and to form water. Nevertheless, the quantity of water remains extremely weak in our layers. Note that no water-related peak is visible for the annealed films, which confirms its formation during the layer deposition.

The hydrogen is mainly bonded to the silicon and the nitrogen for the nitrogen-rich Si-ON, and to the nitrogen for the oxygen-rich SiON. Going from SiN to SiO, the Si-H and N-H bonds quantity decreases slowly, until the almost disappearance of both contributions in the spectra, probably due to the formation of preferential Si-O bonds.

No noticeable change are observed in the FTIR spectrum after annealing. The N-H stretching modes decrease in intensity (figure 7), and the Si-H stretching mode remains only slightly visible for the SiN and the nitrogen-rich SiON films. A shift of the Si-O stretching mode to a higher wavenumber is also visible (figure 8).

Despite its rapidity, the annealing step reached 800 °C and was efficient enough to break a significant amount of the weakest bonds in the SiON films. The FTIR spectra highlight clearly a loss in bonded hydrogen within the layers after the annealing. We would have expected a higher decrease of the Si-H bonds due to its relative weak energy compared to the others (3.3 eV against 4.0 and 3.7 eV for N-H and Si-N bonds [7][17]). In practice, some authors have observed a higher breaking rate for the N-H bonds than for the Si-H, caused by the so-called cross-linking effect [31]. It is a synergy effect between the Si-H and N-H bonds which leads to the reaction:

Si-H + N-H  Si-N + H 2
This effect is not always effective and depends on the layer formation conditions. In our case, the lost of N-H and Si-H bonds after annealing are both significant. The cross linking effect seems to play a major role for the nitrogen-rich SiON since more Si-N bonds are present after the annealing (figure 8). In the oxygen-rich films, this effect is not visible since the Si-O bonds formation is preferred and leads to a slight shift of the Si-O stretching mode after annealing. Note that the annealing seems to affect also the Si-N bonds in oxygen-rich SiON as the steep fall of the peak may suggest.

The bonded hydrogen seems to decrease evenly with the Ox ratio, although the ERDA analysis points out only a slight decrease for atomic hydrogen, followed by a strong drop for the SiO sample. This may indicate the existence of other forms of hydrogen bonds.

HYDROGEN CHARACTERISATION

To investigate more precisely the various form of hydrogen in our SiON films, ERDA, Raman and Temperature Programmed Desorption (TPD) measurements were used.

Both ERDA and Raman characterizations were performed on as-deposited and annealed samples.

The figure 9 displays the atomic hydrogen content for our SiON films determined by ERDA before and after annealing. The data before annealing is the same than the one presented on the figure 2. As assumed by the FTIR results, the annealing treatment decreases the hydrogen concentration, but not uniformly. Thus, another source of hydrogen should exist in the films. Trapped water could be a possible element but as shown in the FTIR section, the quantity seems to be too small to explain the whole change in the hydrogen content in the ERDA results. Moreover, this explanation could not work with nitrogen-rich SiON films since no water is detected. Another hypothesis is the presence of the dihydrogen molecules trapped in the SiON matrix.

Raman analysis

The Raman spectra on the figure 10 show the contribution of the H 2 molecule (near 4120 cm -1 ) [32] for the four nitrogen-richest films. We note that the spectra after annealing (not presented) show no evidence of dihydrogen molecules in any sample.

Although the Raman peak proves the presence of trapped dihydrogen molecules, the signal remains too weak to bring a significant contribution to the total content of hydrogen within the layer. This is confirmed by the weak variation of the hydrogen content for the SiN layer (figure 9) despite a clear loss of dihydrogen molecules with the annealing observed on Raman spectra.

The presence of trapped dihydrogen molecules in the nitrogen-rich SiON films could be possible within denser films than the oxygen-rich layers, which could probably not keep the H 2 molecules efficiently [30].

HYDROGEN DESORPTION

The temperature ramp used for TPD measurements is linear, with a rate of 20 °C per minute. This process is thus really different from the rapid thermal annealing profile used for solar cell contact firing.

The desorption profiles shown on figure 11 are quite different, depending on the type of SiON films. The strong signals observed at temperature higher than 750 °C are due to the destruction of the films. The SiN film begins to release hydrogen near 450 °C, whereas it starts at lower temperatures for the others samples. The desorption profile is also weaker for the SiO film according to its low hydrogen content.

The most important point is the desorption threshold temperature localized near 200 °C for most of the SiON films, whereas all the films depositions are performed at 370 °C (figure 1). This may be explained by the rapid cooling rate of the samples at the end of the deposition process: the samples are extracted from the PECVD reactor in the ambient air when they are still hot. Thus, a rapid cooling could occur and may freeze the SiON network suddenly. Consequently, a strong disorder might exist in the network, so that a moderate temperature increase would allow the release of a part of the hydrogen trapped in the films. For the SiN film, the higher density of the layer (2.6 versus 2.3 for the SiO layer) could refrain the hydrogen exodiffusion at low temperature. In all cases, a portion of the hydrogen is weakly linked to the SiON films. The FTIR spectra have shown the presence of covalent hydrogen bonds like N-H and Si-H, which are strong enough to be broken only above 400 °C, as suggested by the previous results for the SiN sample [7] [33]. The presence of dihydrogen and water in some SiON samples is thus demonstrated, but despite being good candidates to exodiffuse at low temperature, their quantities remain too small to be significant.

Another possibility to explain the low-temperature exodiffusion of hydrogen may be the presence of hydrogen in the form of polar bond. This type of bond is essentially electrostatic, and is generally present in solution with high electronegative atoms; its energy is clearly inferior to a covalent bond [34]. The best example for these hydrogen bonds is the water where most of the individual molecules are linked to their neighbors, due to the polarity of the H 2 O molecule. The presence of a similar type of bond is possible in the SiON samples because the layers are rich in nitrogen and oxygen, both atoms with high electronegativity. During the annealing time shown on figure 5, the plateau at 450 °C during 25 seconds can lead to the release of this weak-bonded hydrogen for the SiON samples. But the SiN and SiO samples are only weakly affected by this plateau because most of the hydrogen is strongly bonded (SiN), or it is in small quantity (SiO).

The decrease in H content is thus more important for SiON samples (figure 9), and the release of hydrogen starts at lower temperature (figure 11). The TPD profiles differences between these three intermediate SiON samples could be attributed to their respective structural networks (see part 4.2) which might enhance the exodiffusion of the hydrogen. Finally, if a part of the hydrogen is effectively bonded to high electronegative atoms, the oxygen concentration can probably play a major role on the quantity of weak-linked hydrogen.

SURFACE PASSIVATION PROPERTIES

The investigation about the hydrogen gives information about its quantity and its chemical configuration within the layers. These parameters are known to be strongly related to the properties of the surface passivation layers. For example, in a silicon nitride study, Mäckel and Lüdemann [35] have considered the Si-H bonds concentration as a good indicator for the passivation quality of the layer. Surface passivation results obtained from previous work on our silicon nitride layers are detailed in [7,33].

The evolution of the minority carriers lifetime (MCL) is presented in the figure 12. For clarity, only the results for n-type silicon are plotted, but the trend for p-type is exactly similar, with slightly lower values due to the higher capture cross-section of electron in p-type silicon [36].

Before annealing the passivation effect decreases slowly from SiN to SiO. The MCL is one order of magnitude lower for the SiO than for the SiN sample. We have mentioned that the Si-H bond density might be considered as an indicator of the passivation quality [14]. In our case the hydrogen could be linked to the P b centers (Si 3 ≡Si•), which are reported to be the dominating defect in un-passivated SiO layer [START_REF]17 th NREL Workshop on Crystalline Silicon Technology[END_REF], and which can be well passivated by the hydrogen [START_REF] Stesmans | [END_REF]. In this point of view, the decrease of the MCL seems to be well correlated with the decrease of the Si-H stretching mode observed with the FTIR analysis. As we have already reported elsewhere [6], we can also expect a lower fixed charges density in SiON than in the SiN layer, due to the reduction of the K + centers concentration [1], i.e. the N 3 ≡Si + defect, which follows the decrease of the nitrogen content. This would also induce a reduction of the surface passivation when Ox increases. Nevertheless, additional charges might be brought by the P ox and similar centers (O 3 ≡Si•, O 2 N≡Si• and ON 2 ≡Si• defects) [1]. Although their charging states are not necessarily positives, it is known that the P ox centers bring mainly a positive contribution in the silicon thermal oxide fixed charge density.

After annealing, the results of the passivation change deeply: the nitrogen-rich samples exhibit poor MCL and the situation is opposite for the oxygen-rich SiON. The passivation effect does not change much for the SiN film and stays quite efficient (MCL near 100 µs). In our previous study, the strong MCL decrease for the nitrogen-rich Si-ON was suspected to be caused by a lower density of the layer [6]. The strong hydrogen desorption at low temperature (figure 11) partly confirms this point. Despite the formation of Si-N bonds with the annealing (figure 8), the passivation is affected by the loss of the weakly bonded hydrogen.

For the richer oxygen films, the passivation slowly increases and becomes even similar to that of the SiN layer with SiO. In these layers, the presence of a higher oxygen concentration seems to help in the creation of Si-O bonds as suggested by the figure 8.

Moreover, the exodiffusion of hydrogen from the SiO layer is clearly weaker than for the other layers. These two tendencies may explain the better passivation effect obtained with the oxygen-rich layers: the loss of hydrogen is counter-balanced by the formation of Si-O bonds, which passivate the surface. Besides, since the exodiffusion of hydrogen from the layer is slower in that case, it might also participate in the passivation improvement by decreasing the P b centers concentration and the other defects at the Si-ON/Si interface.

CONCLUSION

We have contributed in the chemical and structural description of the silicon oxynitride layers deposited by plasma enhanced CVD. This films have numerous advantages for photovoltaic applications. Their adjustable refractive index makes them suitable for multi-layers antireflection coating, in combination with a silicon nitride layer.

The ERDA and XPS characterizations have underlined the strong influence of the oxygen on the SiON network: the favourable formation of the Si-O bonds disturbs strongly the SiON matrix and a part of the hydrogen becomes weakly bonded to the layer. Thus, a rapid thermal annealing has a strong impact on the hydrogen content of the layer and may degrade the passivation properties of the films.

The differences between FTIR and ERDA measurements for the bonded hydrogen and the total hydrogen content suggest the presence of other forms of hydrogen within the SiON layers. Although dihydrogen and water have been detected in the samples, their quantities are not significant to explain the differences between the ERDA and FTIR results. Thus, it is possible that the hydrogen is linked within the layer by another type of weak chemical bonds, such as polar bonds.

Although the hydrogen does not contribute to the passivation as much as in the SiN layer due to its strong exodiffusion, the formation of Si-O bonds for the oxygen-rich films leads to a similar surface passivation. Consequently, in addition to antireflection coatings, the PECVD SiO layer becomes a good candidate for the surface passivation of solar cells. It is already widely studied in combination with SiN on the rear side of thin solar cells.

ACKNOWLEDGMENTS

The authors want to thanks the Nanolyon platform staff for its technical contribution, and the National Research Agency (ANR) with the French Agency for Environment and Energy Management (ADEME) for their financial contributions through the national projects PHARE, REDUCOP and INFIME.

LIST OF TABLES :

Table 1: Gas precursors flow for the five samples used in this study. cies to the experimental peak with their relative FWHM. The energy position of the chemical species came from [7], [21] and [22].

  bution of the Si-O 4 species related to SiO 2 right from the nitrogen-rich SiON (Ox = 0.20) : nearly 40 % of the peak decomposition is associated with Si-O 4 although the layer contains only 20% of oxygen (figure 2). Besides, as suggested by the high FWHM, the bonding environment is more varied and four contributions are needed to decompose correctly the richer nitrogen SiON films (Ox = 0.20 and 0.58) as shown in the figure 4. The contribution of the Si-O 4 species does not vary for the three intermediate SiON: the decrease of the Si-N 4 is counter-balanced by the increase of the O x -Si-N y species.

Table 5 :

 5 Nitrogen 1s peaks position and FWHM results for a Gaussian fit of the five samples studied.

Figure 1 :

 1 Figure 1: Diagram of the LF-PECVD reactor. The table on the right summarizes the

Figure 2 :

 2 Figure 2: Atomic composition of the five studied SiON samples. Lines are guide for the

Figure 3 :

 3 Figure 3: Normalized XPS peaks of the silicon (for the 2p electron configuration) and

Figure 4 :

 4 Figure 4: XPS silicon 2p peak of four SiN films.

Figure 5 :

 5 Figure 5: Temperature profile of the rapid thermal annealing step.

Figure 6 :

 6 Figure 6: Thickness normalized FTIR spectra of the as-deposited SiON layers in func-

Figure 7 :

 7 Figure 7: Zoom on the normalized FTIR N-H stretching bond spectrum. The solid and

Figure 8 :

 8 Figure 8: Subtraction of the annealed samples FTIR spectra with the un-anneal ones.

Figure 9 :

 9 Figure 9: Evolution of the hydrogen atomic composition with the Ox ration determined

Figure 10 :

 10 Figure 10: Raman H 2 peak before annealing the SiON films.

Figure 11 :

 11 Figure 11: Hydrogen desorption profiles of the SiON films.

Figure 12 :

 12 Figure 12: Evolution of minority carrier lifetime for different SiN and SiON layers according to the Ox ratio and for an excess carrier concentration of 7.10 14 cm -3 . The incer-

Table 2 :

 2 Summary of the refractive indexes and thicknesses of the five samples studied.

Table 3 :

 3 Silicon 2p peaks position and FWHM results for a Gaussian fit of the five samples studied.

Table 4 :

 4 XPS Si2p peaks decomposition. The table gives the contribution of each spe-