V Vanpeene

J Villanova

J P Suuronen

A King

A Bonnin

J Adrien

E Maire

L Roué
email: roue@emt.inrs.ca

Monitoring the morphological changes of Si-based electrodes by X-ray computed tomography: A 4D-multiscale approach

Keywords: Li-ion batteries, silicon anode, morphological degradation, X-ray tomography

Visualization and quantification of the morphological changes of Si-based electrodes occurring upon cycling are essential for better understanding their degradation mechanism and for optimizing their formulation. In this context, in-situ and ex-situ Xray computed tomography (XRCT) analyses are here performed on Si-based electrodes for different cycling steps and at different scales (i.e. from the composite electrode level down to the Si particle one). Three different cell configurations and four different Xray sources (one laboratory and three synchrotrons) have been used and their impact on the image resolution/quality and the segmentation of the different solid, electrolyte and gas phases of the composite electrodes is highlighted. From these complementary XRCT analyses with a voxel size ranging from 0.8 to 0.05 m, key morphological features have been studied such as (i) the volume expansion/contraction of the electrode, (ii) the dynamics of the electrode macrocracking, (iii) the initial solid electrolyte interphase (SEI) layer growth and related formation of gas and consumption of electrolyte, which strongly depend on the presence of fluoroethylene carbonate in the electrolyte, (iv) the evolution of the electrode porosity and macrocrack volume fraction/connectivity/width after prolonged cycling.

Introduction

Li-ion battery electrodes have a complex porous 3D microstructure constituted of a network of active material particles and conductive additive connected together, and to the current collector, thanks to a binder. The porous network between the solid particles, allowing the electrolyte to access to the active material, also plays a key role in the electrode performance. Simulated analyses run in 3D and modelling have shown that the shape, the tortuosity, and the surface area of pores and active particles are all key parameters for the improvement of electrode performances [1-6]. Moreover, these complex 3D networks must be maintained upon cycling in order that all the active material particles remain electrochemically active and contribute to the electrode capacity. This is particularly challenging for high-capacity alloying anode materials such as silicon that undergoes a huge volume change upon its lithiation (up to ~280% focused ion beam/scanning electron microscopy (FIB/SEM) tomography [12,13], and X-ray computed tomography (XRCT) [14 -24]. The XRCT is the most versatile technique offering a large range of spatial resolution depending on the X-ray source and the setup used. Even if STEM provides a better resolution, XRCT allows the observation of electrode material in a more representative way thanks to the 3D quantitative information extracted on larger field of view and with less sample preparation. Compared to FIB/SEM tomography, XRCT is a non-destructive characterization technique. Thus, in-situ acquisition can be performed with an appropriate electrochemical cell in order to assess the morphological evolution of the electrode upon cycling. The XRCT spatial resolution is determined by different parameters such as pixel size of the detector, but also, for a conical beam configuration, by the X-ray spot size, which depends on the X-ray source and the source-sample working distance. Micrometric spatial resolution is usually obtained with a conventional laboratory X-ray source whereas tens of nm resolution can be reached using a synchrotron X-ray source. Moreover, the highly coherent and bright synchrotron X-ray beams are of special interest to perform phase contrast imaging in order to distinguish materials of low and/or similar X-ray attenuation, which are very common in the Li-ion battery field (e.g. carbon, silicon and electrolyte have similar attenuation coefficients) [START_REF] Pietsch | X-Ray Tomography for Lithium Ion Battery Research: A Practical Guide[END_REF].

In the present study, the morphological changes induced by cycling of Si-based electrodes are studied by in-situ and ex-situ post-mortem XRCT analyses performed at different scales (from the composite electrode scale to the Si particle one) and with different voxel sizes (ranging from 0.8 µm to 50 nm). For that purpose, different X-ray sources and electrochemical cell configurations are used and their impact on the XRCT image resolution is highlighted. The main morphological features of the Si-based electrodes observable at different length-scales and varying with cycling are presented and discussed.

Experimental

Electrode composition and preparation

Five Si-based electrodes were characterized by XRCT as listed in Table 1. In all cases, the composite electrodes were constituted of 80% wt of active material, 12% wt of conductive additive and 8% wt of binder. The active material was Si powder obtained by high-energy ball milling of commercial Si powder (99.999%, 20 mesh, Materion) for 20 h under argon atmosphere using a SPEX 8000 mixer with a ball-to-powder mass ratio of 5:1. The as-milled Si powder consists in micrometric agglomerates made of sub-micrometric particles more or less agglomerated together. More details on the characteristics of the as-milled Si powder are presented elsewhere [START_REF] Gauthier | A low-cost and high performance ball-milled Si-based negative electrode for high-energy Li-ion batteries[END_REF]. There is a deagglomeration of the as-milled Si powder during the slurry (ink) mixing and the size of the resulting Si powder in the electrode depends on the slurry mixing procedure (see below). The median diameter of the Si particles (Dv50) was 0.8 µm for electrodes #1, #3 and #5, and 2.4 µm for electrodes #2 and #4. Their respective particle size distribution (PSD) curves are shown in supplementary Fig. S1. The use of larger Si particles makes easier their identification (segmentation) by XRCT. For all electrodes, the binder was the carboxymethyl cellulose (CMC) (DS = 0.7, Mw = 90 000 g mol -1 , Sigma-Aldrich). For electrodes #3 and #4, the conductive additive was carbon black (CB) (Super P grade from Imerys Graphite & Carbon, particle size 40 nm, SBET = 62 m 2 g -1 according to the supplier's data). For electrodes #1, #2 and #5, the conductive additive was graphene nanoplatelets (GnP) (M grade from XGSciences, average diameter = 15 μm, average thickness = 6-8 nm, surface area = 120-150 m² g -1 according to the supplier's data). Our recent works have shown that GnP as conductive additive offers better cyclability for Si-based electrodes than usual CB [START_REF] Vanpeene | In situ characterization of Si-based anodes by coupling synchrotron X-ray tomography and diffraction[END_REF][START_REF] Karkar | Threshold-like dependence of silicon-based electrode performance on active mass loading and nature of carbon conductive additive[END_REF].

GnP or CB added in 0.5 mL pH3 buffer solution. The use of a buffered pH3 solution instead of neutral water as slurry medium increases the efficiency of the CMC binder by promoting the formation of covalent bonds between -OH groups present on the Si particles and -COOH groups of CMC, which improves the mechanical strength and cycling performance of the electrode 28,29. The slurry mixing was performed at 500 rpm for 1 h using a Fritsch Pulverisette 7 mixer with 3 silicon nitride balls (9.5 mm diameters) or by using a magnetic stirrer. With the former mixing procedure, the deagglomeration of the as-milled Si powder is more efficient, resulting in a Si median size of 0.8 µm compared to 2.4 µm by magnetic stirring as previously indicated.

Except for electrodes #4, a 3D carbon paper (AvCarb EP40, Fuel Cell Store) was used as substrate. The first reason of the choice of a carbon paper as substrate is that it enables proper X-ray tomographic imaging of the electrode without creating metal artefacts due to the hardly attenuating behavior of the conventional copper foil current collector. Additionally, the flexibility and 3D geometry of the carbon paper helps to maintain the electrical connections during cycling 22,24. The EP40 carbon paper consists in non-woven carbon fibers (~10 µm diam.) bound by a binder filled with micrometric carbon particles. According to its characterization by standard laboratory XRCT, its mean thickness is 144±15 µm and its mean porosity is ~82% with a median pore size of 36 µm (see ref. [START_REF] Vanpeene | In-situ X-ray tomographic study of the morphological changes of a Si/C paper anode for Li-ion batteries[END_REF] for more details). The carbon paper (3 or 1 mm diam. disc depending on the electrochemical cell used, see below) was loaded with the Si-based slurry as described in ref. 22. For electrodes #4, another approach was used for the electrode preparation, which is more suitable for local tomography at high resolution. In this case, the slurry was deposited on the tip (~100 µm diam.) of a conically machined copper wire. In all cases, the electrode was dried for 12 h at room temperature and then at 100°C under vacuum for 2 h. The areal Si mass loading of the electrodes was between 1.4 and 4.5 mgSi cm -2 (Table 1).

Electrochemical cells and cycling conditions

The three electrochemical cells used for the in-situ XRCT performed at different length scales are presented in Fig. 1a-c. These are all a cylindrical shape and in twoelectrode configuration with Si-based electrode as working electrode and a Li foil as counter and reference electrode. The first cell with polytetrafluoroethylene (PTFE) cell housing was used for laboratory XRCT on electrode #1 (Fig. 1a), where the cell cylinder (1.2 mm outer diam. cell, 1 mm diam. electrode) needs to be as thin as possible in order to reach sufficient resolution by pushing the cell closer to the X-ray source.

The second cell, with perfluoroalkoxy alkane (PFA) cell housing, is larger (8.2 mm outer diam. cell, 3 mm diam. electrode) (Fig. 1c). A slight compression was applied by a spring placed on the counter electrode side in order to keep better contact between the cell components. This compression leads to a gentle reduction of the C paper electrode thickness from 140 m before cell assembling down to 100 m after cell assembling.

It was used with electrodes #2 and #3 on the synchrotron radiation beamlines as the diameter of the cylinder is less critical for reaching high resolution. However, to reach a resolution as high as 0.05 µm, a smaller electrode cell (1.2 mm outer diam. cell) (Fig. 1b) was used for synchrotron XRCT on electrodes #4. Moreover, in this cell, the size of the electrode was reduced as low as possible by using a conically machined Cu wire as substrate (0. Additionally, ex-situ synchrotron XRCT (i.e. after cell disassembly) were performed on electrodes #5 after 30 and 50 cycles at a constant current of 400 mA gSi - 1 (C/9) in LP30 + 10% wt FEC with a conventional two-electrode Swagelok-type cell (1 cm diam.) and compared to their pristine state. The cycled electrodes were rinsed for 10 minutes in a dimethylcarbonate (DMC) solution to eliminate the remaining trace of electrolyte and then cut in 1 mm diam. samples. The samples were not exposed to air until the XRCT scanning, where they stayed ~3.5 h exposed to the room atmosphere conditions. The main specific features of each X-ray source are listed in

X-ray sources and image acquisition procedure

Table 2. Specific features of the X-ray sources

The laboratory XRCT experiments (performed on electrode #1) were achieved using an EasyTom (Rx Solutions) with a LaB6 cathode (E = 76 kV, I = 96 µA, spot size down to 0.25 µm) and a CCD Hamamatsu 4000 × 2624 pixels detector available at the MATEIS laboratory at INSA-Lyon, France. In this set up of conical X-ray beam, the sample-source distance (and the sample-detector distance) determine the reachable voxel size and it cannot be smaller than the physical size of the source because of the so-called "geometrical blur". Therefore, it is of particular importance to design the smallest reasonably possible electrochemical cell to decrease the sample/source distance and hence the voxel size. With our 1.2 mm diameter electrochemical cell (Fig. 1a), a voxel size of 0.8 µm was reached for a reconstructed electrode volume of 1358

× 1358 × 200 µm 3 . The images were taken continuously (on the fly) during the sample rotation without any averaging, thus the total acquisition time was reduced to 17 min per scan compared to 55 min for a standard triggered scanning procedure (see Fig. S2 and related comments in supplementary information for more details).

Higher resolution is mandatory for the observation of the phenomena occurring at a small length scale in the electrode and for the precise quantitative analysis of the electrode morphology. The image quality for reaching high resolution relies on the source brightness defined as:

𝐵 ∝ 𝛷 𝜎 𝑥 .𝜎 𝑦 .𝛿𝜃 𝑥 .𝛿𝜃 𝑦 (ph s -1 mm -² mrad -² 0.1%BW) ( 1
)
where Φ is the photon flux, x, y, x, y are the lateral source size and the angular spreads. BW is the bandwidth defined as the dispersion of the wavelength from the targeted value. A conventional X-ray source does actually not match the requirements for high brightness: the emitting area is large and the emission occurs in a broad range of directions. Synchrotrons are the brightest available sources. Soleil and SLS facilities can provide a brightness of 10 19 and ESRF 10 21 photons/s/mm²/mrad²/0.1%BW. In comparison, a laboratory tomograph like the EasyTom Nano has a brightness below 10 8 photons s -1 mm -² mrad -2 0.1%BW (Table 2).

The increase of required photons with decreasing pixel size is derived from the law [30]:

𝛷 ∝ 𝑆𝑁𝑅² ∆𝑥 4 .∆𝜇² (ph s -1 ) (2)
where SNR is the signal-to-noise ratio, x is the voxel size and µ is the mean variance of absorption coefficient of the constitutive elements of the analysed object. The relation implies that compromises should be done in terms of image quality or contrast (µ) in order to decrease the voxel size (x) and thus to increase the resolution. In fact, at a given flux and also brightness, the image quality and image contrast is restricted by the chosen voxel size. The ten times higher flux used on the Tomcat beamline (SLS facility) allowed the voxel size to be decreased from 0.65 m reachable on the Psiché beamline to 0.16 m without altering the image quality. The very important brightness of the ESRF allowed reaching higher resolution of 50 nm.

Additionally, for low attenuating materials such as carbon and silicon, phase retrieval can be mandatory in order to enhance the contrast between these materials.

The quality of the phase difference influences the phase retrieval process and depends mostly on the spatial coherence of the X-ray source and its monochromaticity. The more coherent and the more monochromatic the source, the better the quality of the phase retrieval. As a first approximation of the phase contrast mode, it is possible to use a Paganin-based algorithm [START_REF] Paganin | Oxford series on synchrotron radiation[END_REF] in order to reconstruct the first derivative of the phase and add some information about the interfaces in the bulk material on the image, while a higher brightness is required in order to perform a more complex phase retrieval calculation (second derivative of the phase), and then reconstruct a pure phase image in the Fresnel diffraction mode, like present at the ESRF end station ID16B [START_REF] Cloetens | Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation X rays[END_REF].

Synchrotron XRCT acquisitions were performed as follows: In all cases, image analyses were performed using the ImageJ software [START_REF] Schindelin | Fiji: an open-source platform for biological-image analysis[END_REF].

Details on the procedures for the image segmentation and for their quantitative analyses (dimensional change of the electrode, volume fraction, size distribution and intraconnectivity of the segmented phases, crack growth) are presented elsewhere (see supporting information in ref.

[39]).

Results and discussion

3.1. Impact of the X-ray source on the identifiable components in the electrode. Nonetheless, it is important to notice that the Si particles in electrode #2 (Fig. 2b) are larger with a median diameter of 2.4 µm three times higher than in electrode #1 (Fig. 2a). The fibers of the C paper are visible and overall, the electrolyte phase can be now clearly differentiated from the solid phase.

With a lower voxel size of 0.16 µm reached with the Tomcat beam line at SLS on electrode #3 (Fig. 2c), a three times reduced field of view of 293 × 293 m 2 (× 137 µm in thickness) is observable. This limited field of view does not allow covering the global electrode structure but it includes all of its interesting features, i.e. Si-rich areas, carbon fibers, pores filled with electrolyte and pores filled with gas, which can be clearly identified. The higher resolution and close-up view of the electrode allows a more precise segmentation between the electrode porosity, either filled with electrolyte or gas, and the solid material. However, the CMC binder and carbon black additive are still not discernible and single Si particles cannot be precisely segmented.

At the highest resolution reachable at the ESRF on beam line ID16B on electrode #5 (Fig. 2d), a really good close up view can be obtained on the carbon fibers and Si particles with a voxel size of 0.05 µm and a field of view of 128 × 128 m 2 (× 108 µm in thickness). This reveals here key information about the electrode structure at the submicrometric scale and especially about the morphology of the Si particles and of the porous network. Graphene nanoplatelets (GnP) used as conductive additive are also discernible. The composition of the electrodes and the main features of the X-ray sources are indicated in Table 1 and 2, respectively.

Impact of the X-ray source on the image quality (SNR and CNR).

Image quality of the 3D reconstructed renderings is evaluated thanks to the determination of the signal-to-noise ratio (SNR) and the contrast-to-noise ratio (CNR).

The higher the SNR and CNR, the better the reconstructed images. The SNR can be estimated in a reconstructed image as the ratio of the mean grey level value of the voxels of interest to the standard deviation of the grey level value of the voxels in the background:

𝑆𝑁𝑅 ≅ 𝑚𝑒𝑎𝑛(𝑣𝑜𝑥𝑒𝑙𝑠𝑜𝑓𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡) 𝜎 𝑑𝑒𝑣 (𝑣𝑜𝑥𝑒𝑙𝑠𝑜𝑓𝑏𝑎𝑐𝑘𝑔𝑟𝑜𝑢𝑛𝑑) (3)
The CNR is the difference of the mean grey level value of the voxels of interest and the background voxels over the standard deviation of the grey level value of the voxel of interests, as described by the equation: SNR and CNR are calculated for each sample following equation ( 3) and ( 4) respectively. SNR is higher for the synchrotron images compared to laboratory images (SNR ~20 vs. ~10 respectively). This difference is due to the higher flux, coherence and monochromaticity of the synchrotron sources (Table 2). In fact, monochromaticity (E/E) is improved by a factor of ten and more using a synchrotron source and the flux can be 10 4 to 10 6 times higher. By comparing Fig. 3a and3b, having approximately the same voxel size, but SNR very different (more than a factor of two), we can conclude that twice the information from the signal is recovered for synchrotron imaging compared to laboratory measurements. Surprisingly, by comparing Fig. 3b and3c, the SNR are almost equivalent with Soleil and SLS facilities despite a ten times higher flux at SLS (~10 14 for SLS compared to ~10 13 for Soleil). A CNR increase is however noticeable thanks to a lower energy (20 keV for SLS compared to 25 keV for Soleil) which increases contrast between low attenuating materials. Obviously, best resolution is obtained with the smallest voxel size obtained at the ESRF synchrotron (Fig. 3d)

𝐶𝑁𝑅 ≅ 𝑚𝑒𝑎𝑛(𝑣𝑜𝑥𝑒𝑙𝑠𝑜𝑓𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡)-𝑚𝑒𝑎𝑛(𝑣𝑜𝑥𝑒𝑙𝑜𝑓𝑏𝑎𝑐𝑘𝑔𝑟𝑜𝑢𝑛𝑑) 𝜎 𝑑𝑒𝑣 (𝑣𝑜𝑥𝑒𝑙𝑠𝑜𝑓𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡) (4)
even if the SNR of this image is slightly inferior compared to those obtained for other synchrotron sources; the higher CNR insures satisfying image reliability and higher distinction between low attenuating elements. (in green). It appears that the measured mean value 𝑚 varies with the domain size but stays equal to the exact 𝑚° value at ±5%. However, the lower the domain size, the larger the mean value oscillations, and the more important the measured dispersion. As seen in Fig. 4b, a similar tendency is observed by considering a higher spatial resolution with pristine electrode #3 (SLS synchrotron with a voxel size of 0.16 µm) and a lower whole reconstructed volume of 293 ×293 × 90 µm 3 . This suggests that the voxel size has no major impact on the determined value for the minimum representative volume.

The criteria that we suggest to choose for representativeness is that the average value measured should be in the ±5% interval and 95% of the measured values should equal to the exact 𝑚° value at ±15%. Following these criteria the parameters estimated from a sub-domain randomly selected in the volume should be representative of the total electrode volume. From Fig. 4a-b, the minimum lateral domain size found is ~200 × 200 µm 2 over the all thickness of the electrode. Smaller reconstructed volumes are likely to be non-representative and in this latter case, several measurements must be repeated and their average could be representative of the studied electrode. In the first stage of lithiation, the formation of gas can be detected by laboratory and synchrotron XRCT, as evidenced by the low absorbing zones pointed out by the yellow arrows in Fig. 5b-c at a depth-of-discharge (DOD) of 5%. Moreover, the high strains endured by the electrode contraction during delithiation lead to its cracking.

Expansion/contraction of the electrode

Nevertheless, no crack is visible on the electrode #1 imaged by laboratory XRCT with a voxel size of 0.8 m. By reaching a better spatial and contrast resolution thanks to synchrotron (SLS) XRCT with a voxel size of 0.16 m (electrode #3), it is possible to discretize clearly the macro-cracks formed in the bulk of the electrode as shown in Fig. 5c at a state-of-charge (SOC) of 100%. These cracks are filled with electrolyte or gas.

More detailed analyses on gas release and electrode cracking are presented below.

Figure 5. Relative variation of the electrode thickness measured during the 1 st cycle by laboratory XRCT on electrode #1 (black curve) and by synchrotron (SLS) XRCT on electrode #3 (blue curve) (a). Transversal (x,z) and lateral (x,y) XRCT images for different steps of the 1 st cycle on electrode #1 (b) and on electrode #3 (c). The red dashed line on the transversal (x,z

) images sets the electrode/separator interface.

Impact of the FEC electrolyte additive on gas release and related SEI formation

As previously shown in Fig. 5b-c, some electrolyte-filled pores become much less absorbing for the X-ray beam during the initial stage of the discharge (5% DOD).

We believe this is the result of gas release (e.g., H2, C2H4, CO2) originating from the electrolyte decomposition during the initial SEI formation [START_REF] Ellis | Quantifying, Understanding and Evaluating the Effects of Gas Consumption in Lithium-Ion Cells[END_REF]. It is actually reasonable to assume that the capacity recovered during this period (~200 mAh g -1 Si) is mostly related to the SEI formation as the electrode potential (1-0.2V) is higher than the expected Si lithiation potential and no significant electrode thickness expansion is observed during this period (Fig. 5a andS3). The formation of gas channels was also highlighted from in-situ synchrotron XRCT on a Si-based electrode by Sun et al. As seen in Fig. 6a, gas formation related to the SEI formation during the initial discharge step (5% DOD) results in a rapid increase in the volume of gas-filled pores to ~140 L cm -3 of electrode with the LP30 electrolyte compared to ~20 L cm -3 of electrode in LP30+FEC. This in accordance with the study of Petibon et al. indicating that FEC reduction does not lead to the generation of gaseous products and prevents the formation of methane, ethane and ethylene gas associated with the initial reduction of EC 44. This is correlated to the lower electrolyte consumption highlighted by the electrolyte volume drop observed at 5% of DOD, which is 10 times lower in presence of FEC, i.e. 21 L cm -3 versus 210 L cm -3 in the FEC-free LP30 electrolyte (Fig. 6b).

Subsequently, because of the electrode expansion, the gas is likely to move more freely in the electrode, which can explain the decrease of the gas volume fraction in the smallest imaged volume of electrode #2 (Fig. 6a). The electrode volume expansion also draws electrolyte from the separator to the electrode, which is estimated at about 8010 L cm -3 for both electrodes (Fig. 6b) for a pristine electrode porosity of ~45% and a maximal thickness expansion of 60% in both cases. Thus, one can estimate the excess of electrolyte required for accommodating both of these effects (i.e. SEI formation and electrode swelling) at about 280 L cm -3 for the electrode #3 cycled in LP30 and 110

L cm -3 for the electrode #2 cycled in LP30 + FEC. When cycled in the FEC-free electrolyte, the major part (75%) of this electrolyte volume excess is resulting from the electrolyte consumption due to the SEI formation. In order to study in more detail the impact of the FEC additive on the initial SEI layer formation on the Si particles, in-situ synchrotron (ESRF) nano-tomography has been performed on two similar Si-based electrodes (labeled #4 in Table 1), one in LP30

electrolyte and the other one in LP30+ 10% wt FEC, using the capillary electrochemical cell presented in Fig. 1b. These two electrodes were imaged at their initial state and after reaching a discharge capacity of ~250 mAh g -1 of Si for a total reconstructed volume of 128×128×108 µm 3 with a voxel size of 50 nm. As previously discussed, such an electrode discharge capacity extracted at a potential higher than 0.2 V vs Li/Li + is assumed to mainly originate from the SEI formation. Their respective dQ/dV curves recorded during the nano-XRCT experiments are shown in supplemental Fig. S4, highlighting the lower intensity of the EC reduction peaks in presence of FEC. Four Si particles have been selected in each electrode and their morphological evolution from 0 to 250 mAh g -1 of Si has been analysed as described below. with a mean diameter of a few m, in accordance with the fact that their synthesis by high-energy ball milling results in the formation of micrometric agglomerates made of cold-welded submicrometric particles, which are partially deagglomerated during the subsequent ink mixing by magnetic stirring as previously discussed in the Experimental section. At 250 mAh g -1 , a slight increase (typically around 10%) of the Si particle volume is observed, whereas no particle cracking is detected. The darker regions in the grey-level 3D images correspond to the morphological difference between 0 and 250 mAh g -1 . For more clarity, the local thickness distribution of this expanded area is displayed in 3D color scale images. A 2D cross-section located at the middle of the Si particle is also added. First it appears that the layer growth on the Si particle cycled in LP30 (Fig. 7a) is more heterogeneous in thickness than in LP30+FEC (Fig. 7b). This lower SEI layer uniformity in LP30 seems to be rather reproducible among the different Si particles analysed (see Fig. S5 vs. S6). It is also confirmed by the non-spherical ratio of the mean particle volume expansion over the mean thickness growth of the different XRCT analyzed Si particles, which is close to 4 only for the LP30+FEC formulation.

In addition, the SEI layer formed on the Si particles is two times thicker in LP30 than in LP30+FEC (mean thickness of 1.4±0. However, in this latter case, the SEI layer was thinner (<0.2 m) than observed here, which can be partially explained by the low surface roughness and nanowire morphology of their Si material likely to be favorable to the formation of a more compact surface film than on the present irregularly shaped and rough Si particles.

The formation of a gas bubble was also formed on top of the electrodes #4 (not shown). The size of this gas bubble was significantly smaller in presence of FEC additive, but this difference can only be qualitatively appreciated. This observation however agrees with the previous XRCT analyses performed at lower resolution and indicating a lower formation of gas in presence of FEC (Fig. 6a). Note that the formation of a gas bubble at the surface of the electrode in the present capillary cell results in the undesired interruption of the cycling, preventing XRCT analyses for prolonged cycling. Consequently, it was not possible to study the morphological evolution of the Si particles (e.g. their cracking) associated with their lithiation from our in-situ synchrotron (ESRF) nano-tomography experiments.

Electrode macro-cracking

As previously shown in Fig. 5c, the macro-cracks formed during the deflation (delithiation) of the Si-based electrode can be clearly identified with a coherent and bright X-ray source, and a voxel size of 0.16 m as performed at the Tomcat beamline of SLS facility. Such a spatial resolution is however insufficient to observe the microcracks likely to occur within the Si particles.

The formation of macro-cracks during the 1 st charge (delithiation) and their closing during the subsequent 2 nd discharge (lithiation) of the electrode #3 are described in Fig. 8a-c. This is completed by XRCT movies, highlighting the dynamics of the electrode cracking process (see Video 1 and 2, Supporting Information). The crack formation at different steps of the 1 st delithiation, labelled 1 to 6 on the potential curve,

and their closing at different steps of the 2 nd lithiation, labelled 7 to 9 on the potential curve, are expressed in volume fractions in Fig. 8a. The red scale bar corresponds to gas-filled cracks and the blue ones to electrolyte-filled cracks. Fig. 8c presents the 3D renderings of cracks observed at each step (gas-filled in red and electrolyte-filled in blue). In order to appreciate more clearly the preferential direction of the cracks, Fig. 8b presents the maximum length of the largest intra-connected crack volume projected along the three Cartesian directions.

The first initiated crack, accounting for ~0.6% v , is formed after reaching 40% SOC and a potential of 350 mV vs Li + /Li. This crack initiation may correspond to the breaking point of the CMC binder network, associated with a contraction of the electrode thickness of about 20% (equivalent to 30 m) as seen in Fig. 5a. This crack is entirely gas filled and is mainly oriented toward the lateral y direction with a 145 m maximum length. For comparison, its maximum length projected along the transversal z direction is around ~50 m, which is close to the maximum value of ~65m reached at the end of the 1 st delithiation (Fig. 8b). At 50% SOC, this crack is enlarging and another one (filled with electrolyte) is appearing nearby in the bulk electrode (Fig. 8c2)

for a total volume fraction of ~0.9% v . These two cracks are connecting while 60% SOC is reached (Fig. 8c3). The total crack volume fraction is then doubled (~1.8% v ) and a steep increase of its (x,y) lateral length is observed (Fig. 8b), with a maximum length of propagation path of approximately ~290 m, whereas only ~10 m are added along the z direction. It must be kept in mind that the lateral size of the imaged region (293×293 m) does not allow the observation of cracks longer than ~290 m in the lateral directions, meaning that the cracks may in reality be longer in these directions.

The fact that the electrode cracking preferentially occurs in the lateral directions although the electrode contraction is higher along the transversal direction (Fig. S3b), fact that previously formed cracks have allowed the electrode to expand more freely along the lateral directions compared to the 1 st lithiation. Nonetheless, this cracking process appears reversible since the electrode recovers nearly the same morphology after the 1 st and 2 nd lithiation. Note also that the cracking mechanism discussed in detail here in the early cycling state of the electrode can be drastically limited by replacing carbon black conductive additive by graphene nano-platelets as reported in our previous work [START_REF] Vanpeene | In situ characterization of Si-based anodes by coupling synchrotron X-ray tomography and diffraction[END_REF][START_REF] Karkar | Threshold-like dependence of silicon-based electrode performance on active mass loading and nature of carbon conductive additive[END_REF]. Despite this, the capacity fade observed for this formulation after prolonged cycling needs to be assessed, and is thus discussed in more details in the subsequent part.

Electrode degradation after prolonged cycling

The amount of allocated synchrotron X-ray beam time (typically, a few days) is too short to perform in-situ XRCT experiments during prolonged cycling. Therefore, with the objective to evaluate the morphological degradation of the electrode after prolonged cycling, ex-situ nano-XRCT analyses were performed at ESRF (voxel size of 50 nm) on Si-based electrodes (labelled #5 in Table 1) at the pristine state and after At the pristine state (Fig. 9a), the thickness of the electrode #5 is ~76 m and its porosity is 47%. The solid material part (i.e. including the Si particles, the GnP conductive additive, the CMC binder and the C fibers of the C paper) is well intraconnected (~99.9%). In the zoomed image (Fig. 10a), the Si particles with various shapes and sizes can be discerned in grey as well as the stringy GnP conductive additive and one C fiber of the C paper in black.

After 30 cycles, resulting in a discharge capacity decay of ~30% (see supplementary Fig. S7), the electrode morphology has drastically changed (Fig. 9b).

The electrode thickness has increased to ~96 m (+26% compared to the pristine state).

Moreover, its porosity has shrunk down to 28% (-40% compared to the pristine state) in accordance with the swelling of the solid material part as noticeable on the (x,z) and (x,y) slices. This can be attributed to the accumulation of SEI products (LiF, Li2CO3, CH3OLi…) in the electrode [START_REF] Etiemble | Evolution of the 3D microstructure of a Si-based electrode for Li-ion batteries investigated by FIB/SEM tomography[END_REF][START_REF] Mazouzi | New insights into the silicon-based electrode's irreversibility along cycle life through simple gravimetric method[END_REF][START_REF] Oumellal | The failure mechanism of nano-sized Si-based negative electrodes for lithium ion batteries[END_REF] and also to the irreversible expansion of some SiLix particles due to their electrical disconnection. The accumulation of SEI products in the cycled electrodes is confirmed from the cross-section SEM images and corresponding EDX mapping images (Si, C, O and F elements) shown in supplemental Fig. S8. Additionally, the electrode appears cracked, with a crack volume fraction of ~10% v . The cracking pattern is mostly constituted of elongated cracks of up to ~100 m length with a median width of ~1 m, separating the solid material in 25-30 m wide "islands" with a mean thickness of ~45 m, which is comparable to the cracked morphology observed at the end of the 1 st cycle (Fig. 8). Despite its important volume change and cracking, the solid material in the electrode still seems to be held on together, as its intra-connectivity is still 92.9% (Table 3). The close-up image (Fig. 10b) confirms that the connection to the C paper is maintained. However, the Si particles are no longer discernible. This is attributed to the important SEI layer formed on their surface and in the electrode micro-porosity, presumably helping thus holding on together the electrode solid materials. However, this mechanical connection does not preclude their electrical disconnection, as the SEI layer is not electrically conductive.

At the 50 th cycle, the electrode discharge capacity decay reaches ~40% (see supplementary Fig. S7) and its morphological degradations keep intensifying (Fig. 9c).

The electrode decohesion is visible: an upper part of the electrode has detached from the rest during the electrode rinsing step, as indicated by the delaminated red area in Fig. 9c. The electrode thickness is then reduced down to ~40-70 m and its porosity is increased up to ~61%. Moreover, the solid material areas are highly pulverized owing to the increased crack density, resulting in a decrease of the material phase intraconnectivity down to 80.3% (Table 3). The crack volume fraction after 50 cycles is increased up to ~39%, and their median width size is also four times larger (~3.6 m).

Besides, its intra-connectivity has increased between the 30 th and the 50 th cycle, from 68.3 to 95.6%, traducing the higher crack density as qualitatively observed in Fig. 9c.

The material phase is thus segregated into smaller "islands" of 5-10 m width and an average thickness of ~10 m. This can be appreciated more clearly on the close-up image in Fig. 10c. At this step of cycling, the electrode is much more disposed to lose active material by electrode delamination as previously reported [START_REF] Hernandez | A Facile and Very Effective Method to Enhance the Mechanical Strength and the Cyclability of Si-Based Electrodes for Li-Ion Batteries[END_REF]. Nonetheless, the electrode compression by a spring in the electrochemical cell is likely to keep its mechanical integrity in some extent and allow different segregated material parts to reconnect upon cycling, as suggested by the capacity jump events observed at different periods of cycling (especially from 25 cycles) in supplementary Fig. S7 and also reported by Nguyen et al. [46]. Finally, the X-ray contrast appears darker after 50 cycles (Fig. 9c) than after 30 cycles (Fig. 9b), meaning that it attenuates the beam harder and that, its constituting solid material gets presumably denser as cycling progresses. This can be explained by the fact that prolonged cycling causes the submicrometric porosity (i.e. interstices between the Si particles) to be filled with accumulated SEI products. This is also supported by the structural changes observed by SEM at the silicon particle level on these electrodes (see supplementary Fig. S9). Their morphology becomes more fractal after prolonged cycling and their SEI covering appears denser, especially after 50 th cycle. This implies that the major challenge facing prolonged Si-based electrode cycling lies in minimizing the SEI growth, especially through the development of more efficient electrolyte additives than FEC.

Conclusion

This study has shown that XRCT is a powerful in-situ characterization method for visualizing and quantifying the morphological degradations of Si-based electrodes from the microscale (i.e. at the composite electrode level) to the nanoscale (i.e. at the Si particle level). It was highlighted that the XRCT resolution limit strongly depends on the X-ray source and the electrochemical cell configuration. A spatial resolution as low as 50 nm can only be reached by using a very bright X-ray source such as available at the European Synchrotron Radiation Facility. It was also shown that a minimum lateral domain size of ~200 × 200 µm 2 over the all electrode thickness must be imaged to be well representative of the total electrode volume. With a synchrotron X-ray source, the porous network of the electrode (filled or free of electrolyte) can be clearly differentiated from the solid components of the electrode (Si particles, binder and conductive additive). Differentiation (segmentation) of the solid components is more challenging due to their small size and low X-ray contrast. However, micrometric Si particles are discernible. After appropriate image processing, segmentation and analysis procedures, valuable qualitative and quantitative information on the 3D morphological evolution of the electrode can be obtained:

(i) The expansion/contraction of the electrode associated with its lithiation/delithiation mainly occurs in the transversal direction (electrode thickness)

and is partially reversible. The electrode volume expansion upon discharge also draws electrolyte from the separator to the electrode.

(ii) During the initial stage of discharge, the formation of gas and the consumption of electrolyte attributed to the SEI formation can be quantified. They are both significantly decreased in presence of FEC electrolyte additive. Moreover, the initial SEI layer formed on the Si particles seems to be thinner and more uniform in the presence of FEC.

(iii) The dynamics of the formation of macro-cracks in the electrode during its charge and their closing during the subsequent discharge has been studied. It appears that the macrocracks grow preferentially in the lateral plan of the electrode and they are mainly gas-filled.

(iv) The electrode cracking and decohesion as well as the SEI thickening are exacerbated upon prolonged cycling as confirmed from post-mortem XRCT and SEM analyses of the Si-based electrodes after 30 and 50 cycles. This suggests that the excessive SEI growth despite the presence of FEC electrolyte additive plays a key role in the morphological degradation of the electrode.

[ 7 ]

 7 compared to only 10% for a conventional graphite anode). This leads to the disintegration of the electrode architecture (cracking, collapse, and/or peeling-off), which results in a poor electrode cycle life [7]. Another key aspect affecting the cycle life of silicon based electrodes is the instability of the solid electrolyte interphase (SEI) [8,9]. Hence, new challenges lay in the manner of measuring Li-ion electrode morphological changes occurring upon cycling, especially at a very small length scale and in 3D. Recently, different imaging techniques have been used to study various Sibased electrodes, like scanning transmission electron microscopy (STEM) [10,11],

  2 mm diam. electrode including the Si-based coating). The cells were assembled in an argon filled glove box. At the exception of the conical electrode cell, a borosilicate glass-fiber (Whatman GF/D) was used as a separator and was soaked with the electrolyte.

Figure 1 .

 1 Figure 1. Schematic representation of the electrochemical cells used for in-situ laboratory (a) and synchrotron (b,c) XRCT.

Four

  different X-ray sources were used for the XRCT measurements: one lab source and three synchrotron sources, namely (i) the Psiché beamline of the SOLEIL facility in Gif-sur-Yvette (France), (ii) the Tomcat beamline of the Swiss Light Source (SLS) facility at the Paul Scherrer Institut (Villigen, Switzerland) and (iii) the ID16B beamline of the European Synchrotron Radiation Facility (ESRF) in Grenoble (France).

( i )

 i For acquisitions performed on electrode #2 at the Soleil beamline Psiché, 1500 projections were acquired over 180°, with a 45 ms exposure time each, and 21 reference and dark were taken regularly along the scan. The total acquisition time was around 1 minute per scan. The image reconstruction was done on site using the PyHST2 implementation of the Paganin phase retrieval calculation (delta/beta ~25) [31] resulting in 3D tomographic volumes of 943 × 943 × 208 µm 3 (after reframing) with an isotropic voxel size of 0.65 µm reconstructed in 32 bit floating-point from 2D projections [33]. (ii) For acquisitions performed on electrode #3 at the SLS beamline Tomcat, 1001 2D projections were acquired over 180° with 700 ms of exposure time, and 21 and 11 reference and dark were taken regularly during the scan. The total acquisition time was 17 minutes per scan. Image reconstruction was achieved on site using optimized software based on Fourier methods and an ImageJ plug-in user interface and Paganin phase retrieval calculation [34] (delta/beta ~35) resulting in 3D tomographic volumes of 293 × 293 × 137 µm 3 (after reframing) with an isotropic voxel size of 0.163 µm reconstructed in a 32 bit floating-point from 2D projections [35-36]. (iii) For acquisitions performed in-situ on electrodes #4 and ex-situ on electrodes #5 at the ESRF beamline ID16B [37] using holotomography [32], phase contrast imaging was acquired for four different distances between the detector and the sample along the beam propagation way. 2003 projections, as well as 20 and 21reference and dark images, were recorded on a PCO edge camera (2560×2160 pixels) along a 360° rotation with an exposure time of 300 ms per step. The total acquisition time was around 97 minutes per scan. 3D reconstructions were achieved in two steps: (i) phase retrieval calculation using an in-house developed octave script based on a Paganin-like approach using a delta/beta ~50 and (ii) filtered backprojection reconstruction using ESRF software PyHST2[START_REF] Hintermüller | Image processing pipeline for synchrotron-radiation-based tomographic microscopy[END_REF]. Final volumes of 128×128×108 µm 3 (after reforming) with a voxel size of 50 nm in a 32 bit floating point were obtained.

Fig. 2a -

 2a Fig. 2a-d compares lateral XRCT images acquired at different length scales

Figure 2 .

 2 Figure 2. Lateral XRCT images of pristine Si-based electrodes at different scales and resolution obtained with a laboratory X-ray source on electrode #1 (a) and with synchrotron X-ray sources at Soleil beamline Psiché on electrode #2 (b), SLS beamline Tomcat on electrode #3 (c) and ESRF beamline ID16B on electrode #5 (d). The composition of the electrodes and the main features of the X-ray sources are indicated inTable 1 and 2, respectively.

Fig. 3

 3 Fig. 3 compares lateral images of Si-electrodes for an equivalent domain size

Figure 3 . 3 . 3 .

 333 Figure 3. Lateral images of Si-electrodes for an equivalent domain size of 90 × 90 µm² obtained with the different X-ray sources. To each image corresponds a graph (on right) that represents the normalized grey value along the red dotted line on the XRCT image.

Figure 4 .

 4 Figure 4. Evolution of the mean volume fraction of pores and its dispersion as a function of the lateral length of the analyzed volume for the pristine electrode #2 (Soleil synchrotron, voxel size of 0.65 µm) (a) and pristine electrode #3 (SLS synchrotron, voxel size of 0.16 µm) (b).

Fig. 5a shows

  Fig.5ashows the relative variation of the electrode thickness measured during the 1 st cycle by laboratory XRCT on electrode #1 (black curve) and by synchrotron

  It is known that the presence of FEC additive in the electrolyte has a positive impact on the SEI formation and cycle life of Si-based electrodes 41-44. It appears thus relevant to perform comparative in-situ XRCT analyses on Si-based electrodes cycled in presence or not of FEC electrolyte additive. In this context, Fig.6acompares the evolution of the volume of formed gas during the 1 st discharge in the electrode #3 cycled in LP30 (black curve) and in the electrode #2 cycled in LP30 + 10% wt FEC (red curve). As complementarily data, Fig.6bpresents the corresponding electrolyte volume variation in L per cm 3 of electrode. The difference in the spatial resolution of the electrodes #2 and #3 (respectively 0.65 and 0.16 m) questions nonetheless the reliability of this comparative quantitative analysis. However, this spatial resolution gap does not affect the image segmentation procedure as it depends mostly on the phase contrast resolution, which is very similar for both synchrotron X-ray sources.Additionally, the analysed volume of 0.185 mm 3 for electrode #2 and 0.012 mm 3 for electrode #3 can be considered as representative of their whole volume for both electrodes on the basis of Fig.4.

Figure 6 .

 6 Figure 6. Evolution during the 1 st discharge of the gas volume change (a) and electrolyte volume change (b) in electrode #3 cycled in LP30 (black curves) and in electrode #2 cycled in LP30 + 10% wt FEC (red curves).

Fig. 7a -

 7a Fig. 7a-b shows the 3D rendering for one Si particle in each electrode at the pristine state and at 250 mAh g -1 of Si. The other analysed particles for in LP30

4

 4 m and 0.65±0.3 m, respectively). The formation of a thinner and more uniform SEI layer in the presence of FEC electrolyte additive was also observed by Etacheri et al. from ex-situ SEM analysis of Si nanowire electrodes and was attributed to the formation of a flexible surface film due to the presence of polycarbonates in the film resulting from the FEC decomposition [41].

Figure 7 .

 7 Figure 7. 3D XRCT views of a Si particle at the pristine state and at discharge capacity of 250 mAh g -1 in LP30 (a) and LP30 + 10%wt FEC (b) electrolyte. The darker regions in the grey-level 3D images correspond to the morphological difference between the 0 and 250 mAh g -1 discharge states. The local thickness distribution of the expanded area is displayed in the 3D color-scale images and 2D color-scale images located at the middle of the Si particle.

Figure 8 .

 8 Figure 8. Evolution during the 1 st charge (delithiation) and subsequent 2 nd discharge (lithiation) of the 3 electrode potential and volume fraction of macrocracks (a) and of the maximum length of the largest intra-connected crack volume projected along the x, y and z directions (b). 3D rendering of the cracks at different steps of the 1 st charge and 2 nd discharge (gas-filled cracks are in red and electrolyte-filled cracks in blue) (c).

  30 and 50 cycles in LP30 + 10%wt FEC using a conventional two-electrode Swageloktype cell. Two adjacent areas were imaged for each electrode by moving the sample horizontally on the acquisition platform in order to increase the analysed volume. The total imaged volume is ~213 × 128 × 108 µm 3 , which can be considered as representative of the whole electrode volume. Fig. 9a-c show transversal and lateral XRCT images of the electrode at the pristine state (a), after 30 cycles (b) and after 50 cycles (c). The images are here in inverted grey-scale level for more clarity, i.e. the more attenuating parts appears darker (i.e. electrode solid materials) and reciprocally the less attenuating material appears brighter (i.e. electrode pores). The z position of the lateral (x,y) image is indicated by the yellow dashed line on the transversal (z,x) image, located in the electrode bulk. For a more detailed analysis, Fig. 10a-c present close-up lateral images obtained from Fig. 9a-c. The main morphological features extracted from the quantitative analyses of the XRCT images are presented in

Figure 9 .Figure 10 .

 910 Figure 9. Transversal and lateral ex-situ XRCT images of the electrode 5 at the pristine state (a), after 30 cycles (b) and after 50 cycles (c). Rendering are in inverted greyscale look up table

Table 1 .

 1 Experimental details on the Si-based electrodes analysed by XRCT

	Electrode	Electrode	Median Si	Substrate Electrode	Cycling	X-ray	Imaged	Voxel
	composition	loading	particle size		diameter	conditions	source	volume	size
	(% wt )	(mgSi cm -2 )	(µm)		(mm)			(µm 3 )	(µm)
	#1 Si/GnP/CMC	1.8	0.8	C paper	1	1 cycle at C/9 in	Lab.	1358 ×1358	0.80
	(80/12/8)					LP30+FEC	source	× 200
	#2 Si/GnP/CMC	2.6	2.4	C paper	3	1 cycle at C/9 in	Soleil	943 × 943	0.65
	(80/12/8)					LP30+FEC	Psiché	× 208
	#3 Si/CB/CMC	1.4	0.8	C paper	3	1.5 cycle at C/9 in	SLS	293 ×293	0.16
	(80/12/8)					LP30	Tomcat	× 137
	#4 Si/CB/CMC	4.5	2.4	Cu tip	0.2	1.5 h of discharge	ESRF	128 ×128	0.05
	(80/12/8)					at C/20 in LP30	ID16B	× 108
						and LP30+FEC
	#5 Si/GnP/CMC	1.8	0.8	C paper	1	Ex-situ XRCT after	ESRF	128 ×128	0.05
	(80/12/8)					0, 30 and 50 cycles	ID16B	× 108
						at C/9 in LP30+FEC

Table 2 .

 2

	X-ray source	E	ΔE/E Flux Φ	Brightness
		(keV)		(ph s -1 )	(ph s -1 mm -² mrad -²
					0.1%BW)
	Lab. source	10	10 -1	~10 8	<10 8
	Soleil Psiché	25	10 -2	~10 13	~10 19
	SLS Tomcat	20	10 -2	~10 14	~10 19
	ESRF ID16B	17.5 10 -2	~10 12	~10 21

Table 3 .

 3

	Pristine	30 th cycle 50 th cycle
	Electrode thickness (m)	~76	~96	~40-70
	Electrode porosity (%)	47	28	61
	Material intra-connectivity (%)	99.9	92.9	80.3
	Crack volume fraction (%)	-	10	39
	Crack intra-connectivity (%)	-	68.3	95.6
	Median crack width (m)	-	0.8	3.6

Table 3 .

 3 Main morphological features extracted from the ex-situ nano-XRCT analyses of the electrode #5 at the pristine state, after 30 cycles and after 50 cycles.

Acknowledgments

The authors thank the Natural Sciences and Engineering Research Council (NSERC) of Canada for its financial support (Grant No. RGPIN-2016-04524). The authors also thank M. Mokhtari at SLS, G. Meyruey and Q. Lemarie at Soleil, and S. Labouré at ESRF for their help for the XRCT measurements.

may be due to the higher constraint imposed by the current collector in the x and y directions as the C paper is more flexible in the z direction. As the delithiation keeps forward, the cracking of the electrode intensifies and new cracks are formed in the electrode bulk leading to an important crack intra-connection of 85% and a maximal crack volume fraction of 8.4% v at 100% SOC (Fig. 8c6). At this moment, the cracks are spread along the entire electrode length with a mean crack size around ~8 m, forming small polygonal "islands" of ~50 m edge. These so-called "islands" of active material are still connected to each other as the intra-connectivity of the material phase remains high (99.8% vs 99.9% initially), sustaining the fact that the use of a 3D structuring matrix helps reducing the electrode decohesion. Moreover, the maximum volume fraction of cracks measured at the end of 1 st lithiation in this case is 40% lower than obtained for a conventional electrode deposited on a Cu current collector [START_REF] Vanpeene | Dynamics of the morphological degradation of Si-based anodes for Li-ion batteries characterized by in-situ synchrotron X-ray tomography[END_REF].

However, this high intra-connectivity of the solid phase does not preclude the electronic disconnection of some Si particles due to their displacement or cracking at the submicrometric scale, which is not detectable here due to resolution limitation. It appears also that these cracks are predominantly gas filled, as their volume fraction is three times higher than the electrolyte filled cracks. The latter are moreover mostly located at the separator/electrode interface, where the electrolyte supply is sufficient to ensure the cracks filling.

During the subsequent lithiation (steps 7 to 9), the electrode expansion is resulting in crack closing, and after reaching nearly 20% of DOD the crack volume fraction is already reduced by a half. At 45% DOD, nearly 95% of the previously formed cracks have disappeared (Fig. 8a). Strikingly, the decrease of the crack volume fraction is initiated in the x and y directions, while nearly no change is observed along the z direction before reaching 35% of DOD (Fig. 8b). This can be explained by the


Kévin Hérissé

Benoit Larras

Antoine Frappé

Andreas Kaiser

Keyword Spotting System using Low-complexity Feature Extraction and Quantized LSTM

Keywords: Spotting System using Low-complexity Feature Extraction and Quantized LSTM Spotting, Machine Learning, Long Short-Term Memory, MFCC

come

I. INTRODUCTION

The latest developments in consumer electronics made voice-activated devices used every day. The need to embed Keyword Spotting (KWS) solutions at the edge led to the development of always-on low-power preprocessing units to avoid the computation of the audio signal by power-hungry elements. Figure 1 shows a typical architecture, in which a preprocessing unit triggers the main processor only if the analyzed audio signal is a relevant keyword. The unit is composed of a feature extractor that will divide the audio signal into multiple frequency bands to compute the per band energy. A classification neural network uses these features as inputs to detect if the audio signal corresponds to one of the predefined classes learned by the classifier. Long Short-Term Memory (LSTM) [START_REF] Kaiser | Long Short-Term Memory[END_REF] neural networks are well-suited classifiers to manage sequential data. However, LSTMs require lots of data and computational power and therefore need to be optimized for integration at the edge. This is achieved, for example, by training the network with a small number of hidden units (56 in [START_REF] Giraldo | Laika: A 5uW Programmable LSTM Accelerator for Always-on Keyword Spotting in 65nm CMOS[END_REF]) or by quantizing weights (5-bit in [START_REF] Schaefer | LSTMs for Keyword Spotting with ReRAM-based Compute-In-Memory Architectures[END_REF]). These optimizations are made possible thanks to the use of input features such as Mel Frequency Cepstral Coefficients (MFCC). However, MFCC extraction requires Fast Fourier Transforms (FFT) and Discrete Cosine Transforms (DCT). For this reason, the feature extraction (FE) block usually consumes most of the energy of the system. To tackle this challenge, this paper presents the following contributions:

-A low-complexity feature extraction technique with a 16 channels filter bank with a quality factor of 1.3 was used to compute the power spectral density.

-An associated optimized LSTM model with 64 hidden units post-quantized on 8 bits for inputs and 9 bits for weight/activation achieving 89.45% accuracy on recognition of 12 classes of the Google Speech Command Dataset (GSCD) [START_REF] Warden | Speech Commands: A Dataset for Limited-Vocabulary Speech Recognition[END_REF].

The remainder of this article is structured as follows. Section II reviews different feature extraction methods and introduces the proposed filter bank together with simulations using Matlab ® . Section III presents the LSTM neural network and the method to quantize it. Section IV explores the results in comparison with the state-of-the-art circuits before section V concludes this paper.

II. FEATURE EXTRACTION

The GSCD is used as a reference for keyword spotting applications. It is composed of 60,000 audio files of approximately 1-second length with recordings of 31 different keywords. A common test case for comparison is to train networks using 12 classes (10 selected keywords + unknown words + silence).

A. Impact of feature extraction on the global consumption

To extract features from this dataset, state-of-the-art solutions [START_REF] Giraldo | Laika: A 5uW Programmable LSTM Accelerator for Always-on Keyword Spotting in 65nm CMOS[END_REF], [START_REF] Schaefer | LSTMs for Keyword Spotting with ReRAM-based Compute-In-Memory Architectures[END_REF], [START_REF] Giraldo | Vocell: A 65-nm Speech-Triggered Wake-Up SoC for 10-$\mu$ W Keyword Spotting and Speaker Verification[END_REF], [START_REF] Shan | A 510-nW Wake-Up Keyword-Spotting Chip Using Serial-FFT-Based MFCC and Binarized Depthwise Separable CNN in 28-nm CMOS[END_REF] use MFCC features. The MFCC is computed in this order: (i) FFT of an audio sample window, This work was supported in part by the French National Research Agency under Grant ANR-18-CE24-0006-01 LEOPAR. (ii) Mel filtering using a digital high-order filter bank, (iii) computation of the log of the power for each filter output, and (iv) DCT of each computed value. The MFCCs are extracted as the amplitudes of the output spectrum. We can analyze from the literature (Table I) that the contribution of the feature extraction is more than half of the global consumption of the classification system. In [START_REF] Giraldo | Vocell: A 65-nm Speech-Triggered Wake-Up SoC for 10-$\mu$ W Keyword Spotting and Speaker Verification[END_REF], the authors report that the computational power is dominated by the FFT, which accounts for 72% of the total number of sums and multiplications of the FE block. To reduce the computationally expensive MFCC extraction, [START_REF] Villamizar | An 800 nW Switched-Capacitor Feature Extraction Filterbank for Sound Classification[END_REF] presents a 32-channel analog filter bank employing a passive N-path filter topology consuming 800nW, while [START_REF] Mourrane | Event-Driven Continuous-Time Feature Extraction for Ultra Low-Power Audio Keyword Spotting[END_REF] introduces an event-driven approach, in which the system simulations show up to a 4000x lower consumption compared to a conventional discrete-time system.

B. Proposed feature extraction architecture

The proposed FE architecture is composed of a 16channel filter bank, with center frequencies spread from 50 Hz to 5 kHz. The quality factor Q is only 1.3, making this solution easily realizable in analog or mixed-signal domains. Table II presents the configuration of our filter bank and Figure 2 presents the frequency response of the filter bank according to Mel, Bark, and Logarithmic scales. Mel and Bark scales are perceptual scales and are created from how humans hear. Classification results using these scales are compared in section V.

When the spectral signal is divided into 16 bands, the energy in each band is calculated as:

𝐸𝐸 = � |𝑦𝑦(𝑡𝑡)²| 𝑡𝑡 0 +𝑑𝑑𝑡𝑡 𝑡𝑡=𝑡𝑡 0 (1)
with 𝑦𝑦(𝑡𝑡) the filtered audio signal and dt the frame duration (set to 25 ms with an overlap of 12.5 ms). The filter bank is simulated in Matlab using Butterworth filters. There is no logarithmic scaling on the output data, meaning that when the energy is extracted from each band, it can directly be converted using an ADC and sent to the classifier.

III. CLASSIFICATION NEURAL NETWORK

A. Long Short-Term Memory

LSTM networks are a type of recurrent neural network composed of 4 intermediate sets of neurons called gates (input 𝑖𝑖 𝑡𝑡 , forget 𝑓𝑓 𝑡𝑡 , output 𝑜𝑜 𝑡𝑡 , candidate gate 𝑔𝑔 𝑡𝑡 ) (2)-( 5) that will compute a state vector 𝑐𝑐 𝑡𝑡 (6) that in turn is used to compute the hidden vector ℎ 𝑡𝑡 [START_REF] Villamizar | An 800 nW Switched-Capacitor Feature Extraction Filterbank for Sound Classification[END_REF]. This vector will be used in the next inference together with the next input vector 𝑥𝑥 𝑡𝑡 .

𝑓𝑓 𝑡𝑡 = 𝜎𝜎 𝑠𝑠 (𝑊𝑊 𝑓𝑓 𝑥𝑥 𝑡𝑡 + 𝑅𝑅 𝑓𝑓 ℎ 𝑡𝑡-1 + 𝑏𝑏 𝑓𝑓 ) (2)
𝑖𝑖 𝑡𝑡 = 𝜎𝜎 𝑠𝑠 (𝑊𝑊 𝑖𝑖 𝑥𝑥 𝑡𝑡 + 𝑅𝑅 𝑖𝑖 ℎ 𝑡𝑡-1 + 𝑏𝑏 𝑖𝑖 ) (3)
𝑜𝑜 𝑡𝑡 = 𝜎𝜎 𝑠𝑠 (𝑊𝑊 𝑜𝑜 𝑥𝑥 𝑡𝑡 + 𝑅𝑅 𝑜𝑜 ℎ 𝑡𝑡-1 + 𝑏𝑏 𝑓𝑓 ) (4)
𝑔𝑔 𝑡𝑡 = 𝜎𝜎 ℎ (𝑊𝑊 𝑔𝑔 𝑥𝑥 𝑡𝑡 + 𝑅𝑅 𝑔𝑔 ℎ 𝑡𝑡-1 + 𝑏𝑏 𝑓𝑓 ) (5)
𝑐𝑐 𝑡𝑡 = 𝑓𝑓 𝑡𝑡 ∘ 𝑐𝑐 𝑡𝑡-1 + 𝑖𝑖 𝑡𝑡 ∘ 𝑔𝑔 𝑡𝑡 ( 6
)
ℎ 𝑡𝑡 = 𝑜𝑜 𝑡𝑡 ∘ 𝜎𝜎 ℎ (𝑐𝑐 𝑡𝑡 ) (7)
where 𝑊𝑊 * and 𝑅𝑅 * are weight matrices for each gate and 𝑏𝑏 * biasing values that are obtained by training the neural networks. Figure 3 shows a schematic of the LSTM architecture. The length of the states and hidden unit vectors allows storing information in time at each loop, meaning that the LSTM has the faculty to remember what just happened and therefore modify its outputs knowing this information, making this type of network a good choice for sequential tasks. LSTM models can be stacked and are followed by one or more fully connected layers:

𝑧𝑧 𝑡𝑡 = 𝑊𝑊 𝑓𝑓𝑓𝑓 ℎ 𝑡𝑡 (8)
where 𝑊𝑊 𝑓𝑓𝑓𝑓 is a weight matrix for the fully connected layer. A softmax layer is added at the end to perform the prediction as can be seen in Figure 4. This network is trained using Stochastic Gradient Descent algorithms.

B. Post-Quantization

Post-quantization techniques are introduced to perform an nbit quantization of the LSTM model. The custom LSTM layers are described in Matlab ® and are initialized with the weights obtained from the full-precision training, to accelerate the convergence. At each forward propagation, the results of equations ( 2)-( 7) are quantized using equation [START_REF] Choi | PACT: Parameterized Clipping Activation for Quantized Neural Networks[END_REF].

𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑡𝑡(𝑥𝑥) = 𝑟𝑟𝑜𝑜𝑞𝑞𝑞𝑞𝑟𝑟( 𝑥𝑥 max(𝑥𝑥) × 2 𝑛𝑛-1 -1) × max (𝑥𝑥) 2 𝑛𝑛-1 -1 ( 9
)
where 𝑞𝑞 is the number of quantization bits. Figure 5 shows that the weights and activation vectors follow a normal distribution. Therefore, to improve the internal representation of the system, clipping can be introduced with little impact. The introduced method consists of performing iterations with decreasing clipping values until the accuracy drops by a given amount. The clipping value associated with the maximum accuracy is eventually selected. This simple and effective method is suited to a low-complexity network that allows exploring several parameters over multiple iterations. However, for larger and computationally-intensive networks, more efficient in-training quantization methods such as PACT [START_REF] Choi | PACT: Parameterized Clipping Activation for Quantized Neural Networks[END_REF] have been developed.

IV. SIMULATION RESULTS To compose the dataset, 10 keywords are chosen from the GSCD: {"zero", "one", "two", "three", "four", "five", "six", "seven", "eight", "nine"} (around 1800 samples of each word) plus 20% of other keywords from the dataset labeled "unknown" and 4,000 samples of background noise. The selected dataset is shared between training, validation, and testing datasets following this repartition: 70%, 15%, and 15%. The simulations are made with an LSTM composed of 64 hidden units. Using the computed spectrograms from the FE block as described in section II, multiple simulations are run to observe the impact of the number of bands and the input bit width on the accuracy. The per-band energy values are quantized on n bits and are then trained with the basic LstmLayer model from Matlab ® with weights and activation coded on 32 bits. Figure 6 recapitulates those simulations and shows that there is no particular scale that stands out and would give better results than others. However, filter banks with more than 12 frequency bands offer better results than the 8 band case. An input bit width below 8 bits significantly decreases the accuracy. The best accuracy obtained for the test dataset is 90.02% for a 16-channel filter bank using a logarithmic scale with input data quantized on 8 bits. This setup is taken as a reference point for the development of the quantized LSTM model. 1 https://github.com/kevinherisse/leo_lstm b. Texas Instrument Massachusetts Institute of Technology dataset [START_REF]TIMIT: acoustic-phonetic continuous speech corpus[END_REF] A custom LSTM model has been developed to explore the impact of quantization. Simulating our custom LSTM model with the previous setup gives a similar reference accuracy value. The code of our model and the simulation methods are available on GitHub 1 . The model allows quantizing the network to n bits using the proposed post-quantization method. The simulated accuracy is shown in Figure 7. The quantization only implies an accuracy drop of 0.55% for 8-bit input and 9-bit activation/weight.

Table III shows a comparison with state-of-the-art approaches. Similar accuracy is obtained while the feature extraction method is much less complex than the MFCC computation. The presented method uses a 16-channel filter bank, with third-order filters and a quality factor of 1.3 that could be implemented with low-consumption techniques such as [START_REF] Villamizar | An 800 nW Switched-Capacitor Feature Extraction Filterbank for Sound Classification[END_REF] or [START_REF] Mourrane | Event-Driven Continuous-Time Feature Extraction for Ultra Low-Power Audio Keyword Spotting[END_REF].

V. CONCLUSION This paper shows that it is possible to extract relevant audio features with a simple FE block composed of a 16-channel third order filter bank. Using a quantized 64-hidden unit LSTM model, an accuracy of 89.45% on 12 classes of the GSCD is demonstrated. These results open significant perspectives on reducing the hardware complexity of the FE function. Future work will concern the implementation of the complete processing chain and measurement of the impact on energy consumption.

Fig. 1 .

 1 Fig. 1. Typical architecture of a preprocessing unit

Frequency range 50 Hz to 5 kHz Q 1 . 3 Fig. 3 .

 133 Fig. 3. Schematics of a Long Short-Term Memory neural network

Fig. 5 .

 5 Fig. 5. Histograms showing the weights and activation functions distributions.

Fig. 4 .

 4 Fig. 4. Schematics of the neural network used in this paper.

Fig. 7 .Fig. 6 .

 76 Fig. 7. Accuracy versus quantization weight bit width for multiple activation quantization

TABLE I

 I

	.	CONTRIBUTION OF FE IN STATE-OF-THE-ART CIRCUITS
	Reference		[2]	[3]	[5]	[6]
	Embedded FE	FE on software	FE on software	Real FFT -MFCC	Serial FFT -MFCC
	Global Consumption (µW)	5	0.5 a	16.1	0.51
	Percentage of global consumption due to FE	-(Soft.)	-(Soft.)	50%	66%

a. Estimation from available metrics

TABLE III .

 III COMPARISON WITH SOA

	Reference	[2]	[3]	[5]	Our Work
	Feature Extraction	MFCC	MFCC	MFCC	Power Spectrum
	FFT	Yes (soft.)	Yes (soft.)	DFT	No FFT
	DCT	Yes (soft.)	Yes (soft.)	Yes	No DCT
	Number of channels	39	40	13	16
	Quantization Method	Post Quantization	In-training	Post Quantization	Post Quantization
	Hidden Units	56	128	64	64
	Inputs Bit width	8	5	8	8
	Weights Bit width	8	5	8	9
	Activation Bit width	32	8	8	9
	Number of classes	4	12	12	12
			GSCD:	GSCD:	GSCD:
	Dataset	TIMIT b : 4 KW	10KW + unknown	10KW + unknown	10KW + unknown
			+ silence	+ silence	+ silence
	Accuracy	91.7%	90%	90.87%	89,45%