Thomas Hérisson De Beauvoir

Zakaria Ghomari

Geoffroy Chevallier

Andréas Flaureau

Alicia Weibel

Catherine Elissalde

Fabrice Mauvy

Rachman Chaim

Claude Estournès

Flash Spark Plasma Sintering of 3YSZ: Modified sintering pathway and impact on grain boundary formation

Yttria stabilized zirconia (3 mol% YSZ) ceramics were prepared by Flash-SPS, while allowing high heating rates up to 200°C/s, which led to the extremely fast densification within a few seconds. The high heating rates had strong impact on sintering mechanisms, in terms of densification and grain growth. While the specimens ended with 5 to 15 vol% porosity and limited grain growth (< 350 nm), their hardness is higher than fully dense counterpart SPSed ceramics. Using the sintering trajectories, microstructural observations, and impedance spectroscopy, we highlight altered sintering mechanism which resulted in very thin grain boundaries compared to SPS. It appears that densification is largely advanced at grain boundary interfaces, with no residual nano-pores at the grain junctions, where some pores with size comparable to grain size were present. This opens up opportunities for the fabrication of porous lightweight ceramics with good mechanical properties.

Introduction

Electric field assisted sintering techniques have attracted a huge interest in the last decade.

These allow the application of sintering to a very broad range of ceramics. Spark Plasma Sintering (SPS) technique is the most common field assisted sintering technique, due to its versatility in sintering of different materials, but also size and shape control [START_REF] Manière | Spark plasma sintering and complex shapes: The deformed interfaces approach[END_REF][START_REF] Hu | A review of multiphysical fields induced phenomena and effects in spark plasma sintering: Fundamentals and applications[END_REF][START_REF] Chaim | Densification and preservation of ceramic nanocrystalline character by spark plasma sintering[END_REF]. In addition, SPS technique relies on the application of a uniaxial pressure on the powder compact to enhance grain to grain contact, promote grain rearrangement in the first stage of sintering, and grain sliding during further steps [START_REF] Guillon | Field-assisted sintering technology/spark plasma sintering: Mechanisms, materials, and technology developments[END_REF]. While SPS relies on the application of high current density at low electric field, Flash Sintering (FS) consists the application of high electric fields at low current densities on the green powder compact. FS is mostly used for materials exhibiting semiconducting behavior and is a pressureless sintering technique [START_REF] Yu | Review of flash sintering: materials, mechanisms and modelling[END_REF]. Generally, high densification rates can be obtained thanks to the application of the electric field to a pre-heated specimen, leading to an electrical discharge hence extremely fast densification kinetics [START_REF] Ji | Ultra-fast firing: Effect of heating rate on sintering of 3YSZ, with and without an electric field[END_REF]. The main problems encountered during FS deals with the difficulty to control microstructural homogeneity over the sintered specimens [START_REF] Biesuz | Flash sintering of ceramics[END_REF]. In order to get benefit from both techniques while avoiding microstructural heterogeneity, the SPS setup was modified to reach heating rates in the same range as in FS [START_REF] Olevsky | Flash (Ultra-Rapid) Spark-Plasma Sintering of Silicon Carbide[END_REF][START_REF] Manière | All-Materials-Inclusive Flash Spark Plasma Sintering[END_REF]. Olevsky et al. [START_REF] Olevsky | Flash (Ultra-Rapid) Spark-Plasma Sintering of Silicon Carbide[END_REF] applied SPS using a modified die setup in which an empty Cu tube was used to avoid initial direct electric contact between the top electrode and the specimen. While the experiment was running, the current passed through the Cu tube resulted in its fast heating hence its plastic deformation. While Cu tube deformed, the top electrode came into contact with the punch, suddenly applying both pressure and electric current to the powder compact. This way, ultra-rapid sintering was imposed on SiC compact while controlling the thermal runaway by application of the uniaxial pressure. They further developed another setup, called net shape Flash SPS [START_REF] Manière | All-Materials-Inclusive Flash Spark Plasma Sintering[END_REF], to generate very high heating rates just by adding an isolating BN layer between the graphite foil and the die inner surface. This way, the electric current was forced to pass through the specimen or in the thin graphite foil which surrounded it, allowing high heating rate and efficient sintering. This technique was successfully applied to materials with negative temperature coefficient (NTC) behavior of their electric resistivity either ionic conductors (stabilized zirconia) or insulating oxide (Al2O3), and to metallic Ni. Similar heating rate effects directly through the specimen were achieved by Grasso and coworkers [START_REF] Grasso | Flash spark plasma sintering (FSPS) of pure ZrB2[END_REF][START_REF] Grasso | Flash Spark Plasma Sintering (FSPS) of α and β SiC[END_REF][START_REF] Mckinnon | Flash spark plasma sintering of cold-Pressed TiB2-hBN[END_REF] by powder consolidation into a cohesive pellet prior to SPS, after which the pressure and electric current were simultaneously applied to a sample wrapped in a graphite foil. They successfully densified non-oxide ceramics such as ZrB2, TiB2 and SiC. This technique, called Flash SPS (FSPS), has been recently applied for densification of binary (BaTiO3) and ternary (CaCu3Ti4O12) oxides [START_REF] Manière | Dielectric properties of flash spark plasma sintered BaTiO3 and CaCu3Ti4O12[END_REF]. The common feature of these setups is the application of a uniaxial pressure while the electric current (under a low voltage, typically < 10 V) is forced to pass across a porous specimen to promote its densification by thermal runaway. Another strategy is by using a classic SPS setup with thinner die, allowing the current to flow both through the die and the specimen, depending on their respective conductivity.

Using thinner die leads to an increased current density as compared to classic SPS, eventually leading to fast heating rates. Niu et al. [START_REF] Niu | Ultra-fast densification of boron carbide by flash spark plasma sintering[END_REF] applied this technique for fabrication of B4C. In their setup, the temperature was shown to increase from room temperature to ~ 1900°C in less than 20 seconds, with a 2 mm thick die.

FSPS was also applied to Yttria Stabilized Zirconia [START_REF] Vasylkiv | Flash spark plasma sintering of ultrafine yttria-stabilized zirconia ceramics[END_REF][START_REF] Biesuz | Flash spark plasma sintering of 3YSZ[END_REF], but evidences of sintering mechanisms and resulting microstructures are still missing. In the present work we applied SPS and FSPS to 3 mol.% yttria stabilized zirconia (3YSZ) to explore the influence of the FSPS process on the microstructural features, through the use of sintering trajectory, and to highlight their relations to the mechanical and electrical properties. In order to achieve very fast heating rates under the applied pressure, a 20 mm inner diameter graphite die was prepared with a die thickness of only 5 mm. Using this setup enables extremely high thermal ramps. The present study focuses on the microstructural evolution through sintering trajectories, and explore the effect of the observed microstructural changes on the mechanical properties. To further support our observations, electrical impedance spectroscopy was used to evaluate both grain and grain boundary contributions, comparing specimens sintered by SPS and Flash-SPS.

Experimental

Commercial 3YSZ (Tosoh) powder with nanometric average particle sizes (~ 40 nm) was used for all sintering experiments. SPS experiments were performed using a FUJI 632Lx and Flash-SPS (FSPS) experiments using a Dr. Sinter 2080 (SPS Syntex Inc, Japan) apparati (using pulsed DC sources), both located at the Plateforme Nationale CNRS de Frittage Flash at the University of Toulouse III -Paul Sabatier. Graphite dies (15 and 5 mm thickness for SPS and FSPS, respectively) were used while a 0.2 mm graphite paper was placed all around the specimen in all experiments under primary vacuum (~ 10 Pa). Typical specimen size prepared is 20 mm diameter, with a thickness of 3 mm. Using such setup allows the main current to flow through the die, generating heat. At elevated temperatures, 3YSZ becomes conductive, allowing the current to flow and generate heating from the thermal runaway [START_REF] Manière | All-Materials-Inclusive Flash Spark Plasma Sintering[END_REF]. In FSPS experiments, a lower pressure of 25 MPa was applied due to the lower die thickness. Temperature was first raised to 700°C and stabilized during 5 min. Following this, the current was manually and instantly increased to its maximum until a temperature of 1500°C was reached (within 5 to 7 seconds). Temperature was monitored with a pyrometer focused on the external surface of the die. Then the power was manually stopped, enabling natural cool down to room temperature.

Classic SPS experiments were performed under 100 MPa for dwell time of 3 min at temperatures ranging from 900°C to 1300°C every 50°C. After sintering, all specimens were annealed at 800°C to remove the graphite foil and enable re-oxidation of the 3YSZ (we assume that 3YSZ was exposed during SPS to low oxygen partial pressure hence possible formation of oxygen vacancies). Eight different specimens were prepared with a maximum sintering temperature ranging from 1515°C to 1710°C. X-ray diffraction (XRD) analyses were performed on specimens using a Bruker D4 Endeavor diffractometer with Cu-Kα wavelengths in a Bragg-Brentano geometry in the range 20° < 2θ < 70°. Pellets microstructures were examined at the fractured specimen surfaces with a field-emission-gun scanning electron microscope (FESEM, JEOL JEM 7800F) using 5 kV acceleration voltage at working distance of 6 mm. All images were recorded from secondary electrons on Pt sputtered specimens (≈ 2 nm thickness). SEM images were used to determine grain sizes of all specimens, measuring the minimum of 100 grains in different locations of the specimen, and applying the intercept method with a 1.56 correction factor [START_REF] Mendelson | Average Grain Size in Polycrystalline Ceramics[END_REF]. Densities for all specimens were determined by geometric measurements and weighing. Vickers hardness values on polished surfaces were determined using a Vickers Hardness Testing Machine (Mituyo HM200) applying 1 kg for a 10 s period. Ten measurements per specimen were performed to obtain an averaged value. High Resolution Transmission Electron Microscopy (HR-TEM) was performed on a FSPS specimen sintered at 1535°C using a JEOL JEM-2100F at 200 kV acceleration voltage available at the Centre de Microcaractérisation Raimond Castaing, University of Toulouse. The TEM specimen was prepared using an FEI Helios 600i focused ion beam (FIB) system.

The Electrical Impedance Spectroscopy measurements were performed in air using a Frequency Response Analyzer Autolab PGSTAT302 at 100 mV in the 10-10 6 Hz frequency range. ZView software was used for data fitting where equivalent circuit consists of two R-CPE (Resistor-Constant Phase Element) in series. The electric contacts were made using Pt grids as current collector and a Pt sputtered layer on specimen polished faces. The temperature, heating rate, electric power, and displacement profiles versus time during heating and at the FSPS temperature of 1565°C are shown in Figure 1. As depicted in Figure 1a, the temperature increases extremely fast, from 700°C to 1565°C in less than 5 seconds.

Results and discussion

Sintering profile

Differential temperature profile (Figure 1b) shows a maximal heating rate of 200°C/s and an average heating rate of 144°C/s over the total heating stage (less than 5 s).

As recorded in Figure 1c, although simultaneously increased around 300 s, the current is not delivered immediately, as it takes 7 seconds to reach its maximum value of 2.7 kA, and is released during 10 seconds. This process is accompanied with a strong displacement (≈ 3 mm as shown in Figure 1d) which is ascribed to the densification of the specimen. After the die temperature of 1565°C is reached, natural cooling occurs to bring back the specimen below 700°C within tens of seconds (less than a minute). As in the case of B4C [START_REF] Niu | Ultra-fast densification of boron carbide by flash spark plasma sintering[END_REF], 3YSZ specimen is a NTC (negative temperature coefficient) ionic conductor in specific conditions, which is electrically insulating at room temperature and becomes more conductive as the temperature increases. This increase in conductivity enables current flow through the specimen [START_REF] Biesuz | Flash sintering of ceramics[END_REF], and in turn a thermal runaway hence accelerating thermal ramp as temperature increases. The overall FSPS experiment last less than 10 min, while the actual densification step lasts a few seconds only.

Some attention should be paid to the temperature measurement. Since in our FSPS device, the temperature is measured with a pyrometer focused on the outside wall of the die, some thermal gradients between the specimen's core and the external part of the die can be expected. Since the specimen becomes more conductive as the temperature increases, its temperature must be higher than the one measured on the die surface, where heat loss by radiation becomes important. This phenomenon, also valid for classical SPS experiments, is more important in FSPS due to the higher heating rates and higher current densities. Proper assessing of the temperature presents a technical challenge, also present in Flash Sintering experiments [START_REF] Lebrun | In-situ Measurements of Lattice Expansion Related to Defect Generation During Flash Sintering[END_REF],

and is beyond the scope of the present work. Thus, temperature measurement must be considered as valid for relative comparisons between different specimens but may not reflect the actual specimen temperatures. Sintered specimens from SPS and FSPS experiments were annealed at 800°C for 4 h and characterized by XRD to control the preservation of the tetragonal phase. As shown in Figure 2a, the as-received starting powder is composed of mixed tetragonal and monoclinic phases.

XRD phase analysis

After sintering and densification, pure tetragonal phase is obtained, with no significant difference between the two sintering processes. For all sintered specimens, no phase differences were observed.

Moreover, the specimen's structure homogeneity was evaluated using Raman spectroscopy.

Four different regions were probed at different locations at the specimen's cross-section (top, center, bottom and edge). The similar spectra presented on Figure 2b for the specimen sintered at 1620°C confirm the homogeneity over the whole cross section. The observed bands are characteristic of tetragonal zirconia phase [START_REF] Hemberger | Quantification of yttria in stabilized zirconia by Raman spectroscopy[END_REF], such as expected for 3YSZ and also observed in XRD, and confirm the absence of monoclinic phase (the bands at 180 and 192 cm -1 relative to the monoclinic phase are not observed). Moreover, the cubic phase is characterized by a shift of Zr-O stretching band from ~640 cm -1 in tetragonal phase down to ~600 cm -1 in cubic phase [START_REF] Hemberger | Quantification of yttria in stabilized zirconia by Raman spectroscopy[END_REF]. In the present case, no peak shifts appeared on the various Raman spectra, confirming the unique presence of the tetragonal phase.

Microstructure characterization SEM

SEM observations from the FSPS specimen's fracture surfaces are displayed in Figure 4. In all specimens faceted grains were observed together with neck formation and porosity between the grains. For the experiments performed at high temperatures, one may expect exaggerated grain growth. However, all specimens exhibited grain sizes below 400 nm in average, with a relatively narrow size distribution, which is most probably due to the very short sintering time of FSFS. In addition, the microstructure homogeneity was probed on the fractured specimens at different locations at the cross-section, as shown in Figure 4. Interestingly, the microstructure was very homogeneous over the specimen's fracture area, providing a great advantage compared to regular Flash Sintering technique that often leads to anisotropic microstructures and hot spots [START_REF] Biesuz | Flash sintering of ceramics[END_REF]. This may be assigned to the uniaxial pressure applied on the specimen that allows to maintain good electrical and mechanical contacts over the whole surface of the specimen. Electric current must then homogeneously flow through the specimen, resulting in a properly distributed heat and temperature increase.

Sintering trajectory

The grain sizes measured from the SEM image analyses were plotted versus specimen relative densities to evaluate their sintering trajectory in the sintering of 3YSZ as shown in Figure 5a. Our data on the SPSed specimens are in agreement to those obtained by Flaureau et al [START_REF] Flaureau | Study of the densification and grain growth mechanisms occurring during spark plasma sintering of different submicronic yttriastabilized zirconia powders[END_REF], as well as data from previous studies of Bernard-Granger et al. [START_REF] Bernard-Granger | Étude du frittage SPS d'une poudre de zircone ultrafine[END_REF] and Anselmi-Tamburini et al. [START_REF] Anselmi-Tamburini | Spark plasma sintering and characterization of bulk nanostructured fully stabilized zirconia: Part I. Densification studies[END_REF] on YSZ (all were added to Figure 5a for comparison). These trajectories follow the same pattern as shown by Bernard-Granger et al. evidencing two distinct domains.

A first domain concerns specimens below 97% relative density, for which densification occurs almost with no grain growth. In the second domain, between ~ 97 and 100% relative density, significant grain growth occurs along with the final densification of the specimens. Our data obtained from SPS experiments (red open circles in Figure 5) follow the same pattern as those from the literature [START_REF] Bernard-Granger | Étude du frittage SPS d'une poudre de zircone ultrafine[END_REF][START_REF] Anselmi-Tamburini | Spark plasma sintering and characterization of bulk nanostructured fully stabilized zirconia: Part I. Densification studies[END_REF]. It is noteworthy that the data from Anselmi-Tamburini et al. [START_REF] Anselmi-Tamburini | Spark plasma sintering and characterization of bulk nanostructured fully stabilized zirconia: Part I. Densification studies[END_REF] follow the same pattern as the one obtained by Bernard-Granger et al. [START_REF] Bernard-Granger | Étude du frittage SPS d'une poudre de zircone ultrafine[END_REF], while they deal with different Y2O3 compositions in YSZ (3% and 8% respectively). This tends to show that Y2O3 content, at least in this composition range, has small influence on the sintering trajectory, hence sintering/densification mechanism of YSZ in the nanometer particle size range subjected to classical SPS. On the contrary, FSPS results show significantly different behavior in the sintering trajectory as shown by the solid blue circles in Figure 5a. In this case, the results are not aligned with SPS data both from literature and from the present work (SPS data are obtained from the same starting powder). Grain growth is observed in all FSPS specimens even though they exhibit densities below 93%.

In order to describe the microstructure evolution (grain size vs. relative density), Bruch introduced a model that was applied to micron sized copper and submicronic alumina [START_REF] Bruch | Sintering kinetics for high density alumina process[END_REF][START_REF] Suzuki | Quantitative Analysis of Microstructure Development during Sintering of High Purity Alumina made by high-speed centrifugal compaction process[END_REF][START_REF] German | Sintering: from empirical observations to scientific principles[END_REF]:

𝐺 = 𝜃𝐺 0 √ 𝑝 (1)
were G and G0 are respectively the grain size (diameter) and the initial powder particle size, p is fractional porosity (ranging from 0 to 1) and θ is a constant, assumed to be related to a geometric parameters.

This model was successfully applied to the present data, but a much better fit could be obtained by modifying the previous equation due to the smaller particle size:

𝐺 = 𝜃𝐺 0 √ 𝑝 + 𝐾 (2)
Where K is a constant which is related to the initial particle size and green density. This was applied to the current dataset, along with data from Bernard-Granger et al. [START_REF] Bernard-Granger | Étude du frittage SPS d'une poudre de zircone ultrafine[END_REF], in the range 50 < RD < 99% (see Figure 5b). As expected, all SPS specimens showed similar trend, although the slope is slightly different (θG0 = 6.1 and 13.9 for data from [START_REF] Bernard-Granger | Étude du frittage SPS d'une poudre de zircone ultrafine[END_REF] and from our present work on SPS, with similar initial particle size of 60 and 40 nm, respectively). However, a significant difference is found for FSPS specimens which exhibit θG0 = 76.1. The resulting model obtained using equation ( 2) with fitted parameters are plotted in Figure 5a as dashed lines, showing a good agreement with the experimental data. To confirm the necessity to modify Burch's equation (1) to equation ( 2), the following information should be considered. i) the present FSPS and SPS experiments used the same 3YSZ powder, and therefore have a similar G0 value, ii) they exhibit a different slope in the G vs. 1/√p plot (Figure 5b), i.e. describing a different θ value. Thus, θ cannot be solely affected by a geometric constant. Considering our results, this difference may be ascribed to the sintering mechanism, as further discussed below.

The grain size (G) versus relative density (RD) plots are very common in the ceramic sintering science, where the trajectory of the curve reveals the competition between two major thermal processes, i.e. particle coarsening versus densification [START_REF] Barsoum | Fundamentals of ceramics[END_REF]. Sintering conditions that promote surface diffusion and evaporation-condensation mechanisms are favorable for particle while the overall SPS data (present data and those from ref. [START_REF] Bernard-Granger | Étude du frittage SPS d'une poudre de zircone ultrafine[END_REF] and [START_REF] Anselmi-Tamburini | Spark plasma sintering and characterization of bulk nanostructured fully stabilized zirconia: Part I. Densification studies[END_REF]) exhibit densification controlled by bulk diffusion [START_REF] Flaureau | Study of the densification and grain growth mechanisms occurring during spark plasma sintering of different submicronic yttriastabilized zirconia powders[END_REF], the FSPS data resemble sintering/densification mechanisms also assisted by diffusion at surfaces and interfaces.

Thus, according to equation (1), when RD → 0, i.e. p → 1, G should correspond to θG0.

Considering that θ also depends on the sintering mechanism (as shown by FSPS data), it is necessary to introduce an additional parameter K relating to the initial stage when no grain growth is expected (< 90 % RD). However, it appears that K can be neglected for larger particles/grains (probably above 100-200 nm) and equation ( 1) becomes a reasonable approximation. Although empirical, this model seems to be an interesting tool to predict a microstructural correlation between grain size and relative density for a given sintering mechanism. Therefore, the evolution of θ can be related to the nature of the sintering process rather than to the initial powder particle size, as was shown above for SPS and FSPS experiments made from the same starting powder. Consequently, it turns out that the fast heating rate and short sintering time have a strong impact on the competition between densification and grain growth regimes, so that the two may be concomitant. In classical SPS sintering experiments of 3YSZ, as shown on Figure 5a, densification occurs at lower densities, then growth is activated, as expected for slow rate diffusion mechanisms, i.e. diffusion with the bulk grains and along the grain boundaries within the particle. Because the heating rate in FSPS is extremely high, grain growth regime can be activated through surface diffusion before densification occurred, which may result in modified microstructure evolution, thus in different sintering trajectory. Nevertheless, high heating rate also leads to sintering conditions where high number density of particle surfaces are free for particle sliding under the externally applied pressure, to aid rapid densification. We assume that such free surfaces are either absent or partially sintered during the heating the classical SPS route. Therefore, the residual porosity during SPS is located at the grain boundaries, assisting densification by volume and grain boundary diffusion and as well inhibits grain growth. On the other hand, such porosities are absent at the grain boundaries during FSPS, most probably due to particle sliding and rapid surface and interfacial diffusions hence enhanced grain growth. To check the influence of such microstructural change (due to the high heating rates) on the properties, some hardness tests were performed on the specimens.

Hardness tests

The Vickers hardness (HV) of the FSPS sintered specimens were presented in Figure 6, and compared to the literature data from Muroi et al. [START_REF] Muroi | Preparation of nanograined zirconia ceramics by low-temperature, low-pressure spark plasma sintering[END_REF], Luo & Stevens [START_REF] Luo | Porosity-dependence of elastic moduli and hardness of 3Y-TZP ceramics[END_REF] and Fregeac et al. [START_REF] Fregeac | Relationship between mechanical properties and microstructure of yttria stabilized zirconia ceramics densified by spark plasma sintering[END_REF]. The Vickers hardness exhibited higher values for FSPS specimens relative to the reported literature data for 3YSZ with equivalent porosities. The same HV evolution with density was observed in zirconia with higher Y2O3 contents, i.e. 6 and 8 mol.% in YSZ [START_REF] Fregeac | Relationship between mechanical properties and microstructure of yttria stabilized zirconia ceramics densified by spark plasma sintering[END_REF][START_REF] Anselmi-Tamburini | Spark plasma sintering and characterization of bulk nanostructured fully stabilized zirconia: Part II. Characterization studies[END_REF]. In the present case, the FSPS specimen exhibited hardness values above the typical data obtained for a dense specimen, although FSPS specimens contain 5-15 vol.% porosity. The difference between our HV results for the FSPS specimens and the literature data for SPS specimens, is relatively high (almost doubled HV values) and may also be due to the load effects (i.e. 1 kg vs. 50 kg). It can be assumed that the improved hardness of FSPS specimens arises from an improved 'quality' of the grain boundaries after sintering compared to SPSed specimens. To get more insight about the 'quality' of these grain boundaries, TEM observations and electrical measurements were carried out on the FSPS specimens.

Local microstructure observation

To better understand the hardness results, local microstructure observations were performed.

HR-TEM images from the FSPS specimens revealed grains with faceted grain boundaries, as displayed in Figure 7.

Arrows indicate grain boundaries (GB) and dotted arrows highlight the atomic rows through GB interface on a.3).

As observed in the low magnification view in Figure 7a.1), a surprising feature of this specimen deals with the contrast between large inter-grain porosities and a triple junction showing no residual porosity. The magnified view in Figure 7a.2) confirms this observation with nicely uniform grain boundaries (GB) and the absence of small residual porosity at the triple junctions. The residual porosity (5 to 15 vol.%) is large and its average size is comparable to the grain size. This observation suggests that sintering went through its final stage in such junctions, while large open or closed pores observed between the grains (see SEM images in Figure 3), necessitate much longer process durations towards full densification. In Figure 7a.3), we focused the observations at the GB area. The magnified image shows (highlighted by dotted arrows) atomic rows coherently crossing the GB interface. This highlights the high crystalline quality of the grains at their GB, with extremely thin GB width, that may resemble epitaxial GB interface, or low angle grain boundaries. Observations of several other zones in the specimen, as shown in Figure 7b), c) and d), confirmed the low GB thickness. Such grain boundaries are characteristics of the hot-pressed or isostatically hot pressed 3YSZ with superior mechanical properties [START_REF] Wakai | Superplasticity of Yttria-Stabilized Tetragonal ZrO2 polycrystals[END_REF]. The present crystalline GBs are consistent with the high hardness of the porous FSPS specimens.

To confirm the GB 'quality', and step from local observation to macroscopic quantification, Electrical Impedance Spectroscopy measurements were performed on FSPS and SPS specimens.

Electrical impedance measurements

Electrical Impedance Spectroscopy (EIS) measurements were performed on SPS specimen sintered at 1250°C with RD of 99.5%, average grain size G = 220 nm and FSPS specimen sintered at 1620°C with RD of 90% and G = 225 nm. Therefore, albeit their different densities, their grain sizes are similar, hence enable comparison. Two main contributions were observed in the form of Debye-like relaxation, which are assigned to the grain (higher frequency) and the grain boundary (lower frequency) contributions (Figure 8). Both were modeled using equivalent circuit method. Each one of them are associated to an equivalent circuit made of a resistor, representing either bulk or grain boundary resistance (Rbulk and RGB) and a constant phase element (CPE) [START_REF] Barsoukov | Impedance Spectroscopy Theory, Experiment, and Applications[END_REF], connected in parallel as displayed in the inset of Figure 8. Typical impedance diagrams recorded at 300°C under air are reported in Figure 8. To better visualize the impedance ratio of bulk to GB for both SPS and FSPS specimens, the data was plotted as Z'/Rbulk and Z''/Rbulk. First, one can observe that GB contribution to the impedance is proportionally twice than the bulk (grain) contribution in the case of SPS as compared to the FSPS specimens at 300°C. This indicates that despite the lower specimen density, the GB's in the FSPS specimen exhibit higher conductivity than in the SPS specimen. The logarithm of frequencies are displayed for both plots.

Fitting the obtained values allowed to evaluate the conductivity (σi), capacitance (Ci), and relaxation frequency (f0i), with i denoting either bulk or grain boundary. The overall results are plotted in Figure 9 for temperatures ranging between 200 and 400°C in Arrhenius-like plots.

Temperature dependence of the conductivity is plotted in Figure 9a. In both bulk and GB, the difference between SPS and FSPS specimen is more visible at lower temperatures and tends to be reduced when temperature increases. However, FSPS conductivity is higher in both cases.

As a confirmation, the conductivity difference is larger in the case of GB. Capacitance and frequency are respectively temperature-free and geometric-free parameters and can be considered as identification parameters of the specimens. They can be used to qualify the nature of the observed contributions [START_REF] Irvine | Electroceramics: Characterization by Impedance Spectroscopy[END_REF]. Here it can be noticed that capacitance data are similar for SPS and FSPS specimens, both in the case of GB and bulk. The same observation can be made from relaxation frequencies. These data are close to those observed for sintered YSZ specimens [START_REF] M'peko | Impedance spectroscopy and dielectric properties of flash versus conventionally sintered yttria-doped zirconia electroceramics viewed at the microstructural level[END_REF][START_REF] Bernard-Granger | Spark plasma sintering of a commercially available granulated zirconia powder-II. Microstructure after sintering and ionic conductivity[END_REF] and confirm the chemical and structural nature of the electrical processes. Activation energies that depend on the line slope were calculated from the Arrhenius-like plots of frequency or conductivity for GB and bulk. The data obtained for SPS are consistent with that reported for 3YSZ after conventional sintering [START_REF] Steil | Densification of Yttria-Stabilized Zirconia : Impedance Spectroscopy Analysis[END_REF]. According to Figure 9c, we calculated the activation energy values of 0.86 eV and 1.03 eV for bulk and GB conductivity, respectively. The corresponding activation energies determined for the FSPS specimen are slightly lower with 0.82 eV and 0.98 eV, but remain in the same range of values found for ionic conductivity in YSZ densified by conventional sintering [START_REF] Steil | Densification of Yttria-Stabilized Zirconia : Impedance Spectroscopy Analysis[END_REF], as well as flash sintering [START_REF] M'peko | Impedance spectroscopy and dielectric properties of flash versus conventionally sintered yttria-doped zirconia electroceramics viewed at the microstructural level[END_REF][START_REF] Christian | Current-ramp assisted sintering of 3YSZ: Electrochemical and microstructural comparison to flash and thermal sintering[END_REF].

In the case of zirconia based ceramics, impedance data can be used to evaluate the grain boundary thickness [START_REF] M'peko | Impedance spectroscopy and dielectric properties of flash versus conventionally sintered yttria-doped zirconia electroceramics viewed at the microstructural level[END_REF][START_REF] Bernard-Granger | Spark plasma sintering of a commercially available granulated zirconia powder-II. Microstructure after sintering and ionic conductivity[END_REF]. To this end, the fact that the apparent dielectric properties may differ from intrinsic (specific) properties were considered. These depend on geometric parameters, and especially the GB thickness (δGB) to grain size (G) ratio. In the case of bulk contributions, it can be assumed that GB thickness is negligible compared to grain size. This induces that the values of specific dielectric properties for bulk contributions can be similar to the apparent values: σ bulk sp ≅σ bulk app , and ε bulk sp ≅ε bulk app (where σ bulk sp and ε bulk sp stand for specific bulk conductivity and specific bulk permittivity, and σ bulk app and ε bulk app stand for apparent bulk conductivity and permittivity, respectively). However, in the case of GB contributions, the δGB/G ratio must be considered. The following relations are commonly used in the literature [START_REF] M'peko | Impedance spectroscopy and dielectric properties of flash versus conventionally sintered yttria-doped zirconia electroceramics viewed at the microstructural level[END_REF][START_REF] Bernard-Granger | Spark plasma sintering of a commercially available granulated zirconia powder-II. Microstructure after sintering and ionic conductivity[END_REF][START_REF] Guo | Grain Boundary Blocking Effect in Zirconia: A Schottky Barrier Analysis[END_REF]:

σ GB sp = ( δ GB G ) σ GB (3) ε
GB sp = ( δ GB G ) ε GB (4)
And the capacitance is defined as:

C i =ε 0 ε i ( 5
)
Where ε0 is vacuum permittivity and εi the GB or bulk permittivity.

Moreover, in zirconia based ceramics, it can be considered that ε GB sp ≅ε bulk sp [START_REF] Guo | Grain Boundary Blocking Effect in Zirconia: A Schottky Barrier Analysis[END_REF] (with ε GB sp and ε bulk sp being the specific permittivity of grain boundaries and bulk, respectively). According to equations ( 4) and ( 5): Resulting data of δGB at various temperatures were plotted in Figure 10a for SPS and FSPS specimens. In both cases, the GB thickness values are very stable with temperature evolution, and an average value of 13.1 nm and 5.3 nm were obtained for SPS and FSPS specimens, respectively. SPS specimen value is consistent with Bernard-Granger et al. data [START_REF] Bernard-Granger | Spark plasma sintering of a commercially available granulated zirconia powder-II. Microstructure after sintering and ionic conductivity[END_REF] for 3YSZ who reported an average value of 13 nm for δGB using similar calculation method, whatever the sintering temperature from 1050 to 1200°C (therefore independent on porosity, ranging from 0 to 24%). Thus, FSPS specimens exhibit a GB thickness 2.5 times thinner than those in the SPS specimens. This supports the previous observations made by HR-TEM. The resulting specific conductivity can then be calculated according to equation (3), and are plotted for both types of specimens in Figure 10b. Interestingly, GB specific conductivities of the two samples are almost the same (open circles and cubes in Figure 10b). Also, bulk specific conductivities of FSPS and SPS exhibit the same difference as the one observed for GBs. Thus, the two samples have the same intrinsic electrical behavior, confirming their similar GB and bulk nature (chemical and structural). The whole difference in their macroscopic (apparent) electrical behavior can be explained by their GB thickness (δGB) difference. This confirms that FSPS does not have different impact on chemical and structural nature of the initial powder, but rather strongly affect the GB thickness and most probably its mechanical strength. However, the microscopic observations confirm very high sintering efficiency at GB interfaces. This results in better ionic conductivity even for porous FSPS specimens than almost fully-dense SPS specimens. The lower GB thickness may also be associated to changes in the sintering mechanism; nevertheless this aspect needs further investigations.

δ GB = C bulk C GB G (6)
The present work highlights the impact of FSPS route on the 3YSZ microstructure and its macroscopic properties, associated with microscopic observations. This process also opens the possibility to rapidly densify materials regardless of their electric conductivity, along with a homogeneous microstructures, which is a great asset as compared to Flash Sintering. Further work will be needed to address the influence of processing parameters on the sintering mechanisms, so that various microstructures could be designed. In particular, working on pressure/time increase could be a relevant way to increase densities while preserving the submicron grain sizes.

Another focus should be paid to Yttrium segregation, which may result in phase transitions.

Segregation of Y2O3 to surfaces and grain boundaries of tetragonal zirconia during sintering and grain growth is well documented in the zirconia literature [START_REF] Guo | Grain Boundary Blocking Effect in Zirconia: A Schottky Barrier Analysis[END_REF]. It arises from decrease in solid solubility of Y +3 in YSZ with the temperature increase above 1000°C, and the two-phase cubic + monoclinic phase assemblage. Although our investigations by XRD and local Raman spectroscopy did not reveal the presence of other phases than tetragonal zirconia, a more refined local analysis are needed to confirm this aspect.

Conclusions

Using a conventional SPS setup with a modified die allowed to reach extremely high thermal ramp up to 200°C/s hence Flash-SPS (FSPS) which was applied to 3YSZ specimens. Within a few seconds, green nanoparticle compacts were densified by FSPS up to 93% of the theoretical density at measured temperature of 1710°C. Comparison of the sintering trajectory (densities, porosities, and grain sizes) with our conventional SPS reference specimens as well as to the 3YSZ literature data, point out different sintering mechanisms (both densification and grain growth) as compared to conventional SPS. This is further supported by the improved hardness compared to specimens sintered by SPS to equivalent porosity levels. HRTEM observations and electrical characterization further supported this aspect and revealed the role of the GB's in ceramic properties. The enhanced hardness was related to a specific sintering mechanism that promotes GB reinforcement despite the presence of porosity. Apparently, the rapid heating imposes sudden temperature increase at the nanoparticle surfaces that, in turn, undergo rapid sintering and densification facilitated by the applied pressure. This opens interesting opportunities for the preparation of porous lightweight structural ceramics with improved mechanical properties.

Figure 1 :

 1 Figure 1: Experimental parameters profile during FSPS: a) temperature, b) heating rate, c) electric current and d) displacement of 3YSZ specimen sintered by FSPS at 1565°C

Figure 2 :

 2 Figure 2: a) XRD patterns of as-received powder and sintered specimens (measured on specimen surfaces) and b) focused Raman spectra of FSPS sample sintered at 1620°C measured from various regions of the specimen cross section (dotted circles). m-ZrO2, t-ZrO2 and c-ZrO2 stand for monoclinic, tetragonal and cubic phases of zirconia.

Figure 3 :

 3 Figure 3: SEM images of 3YSZ specimens FSPS sintered at different temperatures: a) 1515°C, b) 1560°C, c) 1565°C, d) 1620°C, e) 1635°C and f) 1710°C, along with corresponding specimens relative densities.

Figure 4 :

 4 Figure 4: SEM images from the FSPS specimen sintered at 1620°C. a) low magnification, b) representation of specimen fracture prepared for observation, c) edge zone view, d) bottom, e) top and f) center. The homogeneous density and grain size at different loci are visible.

Figure 5 :

 5 Figure 5: Sintering trajectory of nanometric 3YSZ showing the average grain size versus a) relative density and b) 1/√p (where p is the fractional porosity). The FSPS and SPS results were obtained at different conditions (ramp, dwell time, applied pressures). Dashed lines represent fitting results from FSPS and SPS data using equation (2). Current work's data are compared to literature values from[START_REF] Bernard-Granger | Étude du frittage SPS d'une poudre de zircone ultrafine[END_REF][START_REF] Anselmi-Tamburini | Spark plasma sintering and characterization of bulk nanostructured fully stabilized zirconia: Part I. Densification studies[END_REF]. The arrow indicates changes in the sintering/densification mechanisms (see explanation within the text).

  coarsening, and yield almost linear G-RD dependence that ends at low RD values with extremely high values of θG0. Sintering conditions that promote grain boundary and bulk diffusions, are favorable for densification of the powder compact, and yield linear G-RD dependence that ends around 92% RD with extremely low values of θG0. Therefore, the large arrow in Figure 5a indicates the changes in the active diffusion mechanisms during sintering, starting from bulk diffusion at the bottom right, then interface/grain boundary diffusion at the diagram's center, and ending by surface diffusion at the top left of the diagram. In this respect,

Figure 6 :

 6 Figure 6: Vickers hardness of FSPS specimens compared to literature data, [27-29]. The error bars present the standard deviation of 10 measurements per specimen.

  Figure 7a.1) shows the typical microstructure of the grains, the inter-grain porosity and a triple junction. A magnified view is shown in Figure 7a.2), highlighting the triple junction with no porosity. Figure 7a.3) shows the lattice imaging of the grain boundary region assigned by rectangle in Figure 7a.2).

Figure 7 :

 7 Figure 7: HRTEM images from different locations of FSPS specimen sintered at 1535°C. a.1) to a.3) correspond to different magnifications of the same area, while b), c) and d) correspond to other regions in the specimen.

Figure 8 :

 8 Figure 8: Nyquist plot of electrical impedance of FSPS (1620°C) and SPS (1250°C) performed at 300°C and their respective fitting curves using the equivalent circuit. The axes were normalized to the fitted grain resistance (Rbulk).

Figure 9 :

 9 Figure 9: Data obtained from electrical impedance spectroscopy measurements fits. a) logarithm of conductivity, d) logarithm equivalent capacitance and e) logarithm of relaxation frequency. The activation energies are displayed on a) and c).

Figure 10 :

 10 Figure 10: a) Grain boundary thickness obtained from equation (6), and b) logarithm of specific conductivity.


Adrien Moll

Patrick Hermet

Jean-Louis Bantignies

Christophe Candolfi

Bertrand Lenoir

David Maurin

Michel Ramonda

Erwan Oliviero

Nicole Fréty

Influence of Nanostructuration on the Vibrational, Electronic and Optical Properties of CrSi 2 Thin Films

Keywords: chromium silicide, thin film, nanostructuration, amorphous semiconductor, electron scattering, vibrational properties, optical properties

We report a detailed experimental investigation of the influence of the formation of nanocrystallites on the vibrational, electronic and optical properties of CrSi 2 thin films. Both amorphous and nanostructured thin films were investigated by means of electrical resistivity, Hall effect measurements as well as Raman and infrared spectroscopies. We show that both types of films exhibit a semiconducting-like behavior, with the notable difference that the high defect concentrations in amorphous films act as hole donors, modifying the electronic band structure and optical constants. The effect of the film thickness on electrical properties is well captured by the Fuchs-Sondheimer model indicating a decrease in the charge carrier mean free path, likely due to the formation of amorphous/nano-crystallite interfaces that contribute to strongly scatter the charge carriers. Raman spectroscopy performed on nano-crystallized thin films evidences the presence of a Raman-active mode at 229 cm -1 and confirms DFT calculations predicting a mode at 248 cm -1 , the observation of which had remained elusive so far in polycrystalline CrSi 2 . Measurements of the refractive index and dielectric constants of amorphous thin films show a very high refractive index in the mid-IR range. Our results illustrate how the controlled growth of nano-crystallites can be used to tailor the electronic, vibrational and optical properties of amorphous thin films.

Introduction

Transition metal silicides have been considered over the last decades as important technological materials, particularly in microelectronics [START_REF] Murarka | Silicides for VLSI Applications[END_REF][START_REF] Reader | Transition Metal Silicides in Silicon Technology[END_REF][START_REF] Chen | Low Resistivity Metal Silicide Nanowires with Extraordinarily High Aspect Ratio for Future Nanoelectronic Devices[END_REF] . Among their numerous advantages, their high melting point, high thermal stability, and compatibility with silicon-based microelectronic devices explain the strong interest for these compounds. Moreover, the low cost and large abundance of silicon enables to consider large-scale development using its wellmastered processing technologies. While most of these compounds are metallic, some of them contain transition metals from group VI to VIII elements and exhibit a semiconducting or semimetallic behavior possibly accompanied by exotic magnetic or topological properties such as FeSi 2 , MnSi 1.7 , Ru 2 Si 3 and CoSi [START_REF] Lange | Electronic Properties of Semiconducting Silicides[END_REF][START_REF] Mühlbauer | Skyrmion Lattice in a Chiral Magnet[END_REF][START_REF] Takane | Observation of Chiral Fermions with a Large Topological Charge and Associated Fermi-Arc Surface States in CoSi[END_REF][START_REF] Pshenay-Severin | Band Structure and Unconventional Electronic Topology of CoSi[END_REF] .

Among these semiconducting silicides, chromium disilicide, CrSi 2 , is a p-type narrow-bandgap material that remains chemically and thermally stable up to at least 1000 K under air [START_REF] Ma | Synthesis and Thermal Stability of Nanocrystalline Chromium Disilicide[END_REF][START_REF] Stathokostopoulos | Formation of the Thermoelectric Candidate Chromium Silicide by Use of a Pack-Cementation Process[END_REF] . Due to its indirect bandgap measured to be about 0.35 eV [START_REF] Bost | An Investigation of the Optical Constants and Band Gap of Chromium Disilicide[END_REF][START_REF] Lange | Growth and Optical Characterization of CrSi 2 Thin Films[END_REF] , low temperature coefficient of resistance [START_REF] Trofimov | Effect of Deposition Conditions on the Structure, Phase Composition and Electrical Properties of the Chromium Silicide Films[END_REF][START_REF] Hieber | Structural and Electrical Properties of CrSi 2 Thin Film Resistors[END_REF][START_REF] Waits | Sputtered Silicon-Chromium Resistive Films[END_REF] and promising thermoelectric power factor ( ) resulting from low electrical resistivity, , and high Seebeck coefficient, , [START_REF] Fedorov | Thermoelectrics Handbook -Macro to Nano[END_REF][START_REF] Nishida | The Crystal Growth and Thermoelectric Properties of Chromium Disilicide[END_REF] , this compound has been considered for various applications ranging from IR detection [START_REF] Bost | An Investigation of the Optical Constants and Band Gap of Chromium Disilicide[END_REF][START_REF] Goroshko | Enhancement of Near IR Sensitivity of Silicon-Silicide Based Photodetectors[END_REF][START_REF] Migas | Semiconducting Silicides as Potential Candidates for Light Detectors: Ab Initio Predictions[END_REF] , thin-film resistor in integrated circuits [START_REF] Trofimov | Effect of Deposition Conditions on the Structure, Phase Composition and Electrical Properties of the Chromium Silicide Films[END_REF][START_REF] Hieber | Structural and Electrical Properties of CrSi 2 Thin Film Resistors[END_REF][START_REF] Waits | Sputtered Silicon-Chromium Resistive Films[END_REF] , contact material in nanosystems [START_REF] Chang | Core-Shell Chromium Silicide-Silicon Nanopillars: A Contact Material for Future Nanosystems[END_REF] , Schottky junctions [START_REF] Aniltürk | Electrical Transport at a Non-Ideal CrSi 2 -Si Junction[END_REF][START_REF] Barus | Analysis if I-V Measurements on CrSi 2 -Si Schottky Structures in a Wide Temperature Range[END_REF] or for thermoelectric power generation at high temperatures [START_REF] Fedorov | Thermoelectrics Handbook -Macro to Nano[END_REF][START_REF] Nishida | The Crystal Growth and Thermoelectric Properties of Chromium Disilicide[END_REF] .

Due to the high number of potential applications, a wealth of studies of the electrical properties of CrSi 2 in bulk polycrystalline and single-crystalline forms and in thin films have been reported.

However, widely differing results were obtained, with values ranging from 0.21 mΩ.cm [START_REF] Luches | Laser-Assisted Synthesis of Semiconductor Chromium Disilicide Films[END_REF] to 18.5 mΩ.cm [START_REF] Galkin | Semiconducting and Structural Properties of CrSi 2 A-Type Epitaxial Films on Si( 111 )[END_REF] at room temperature. This wide range of values can be explained by differences in deposition methods, heat treatments, film thickness and Cr:Si stoichiometry. Studies of thin films obtained by co-sputtering of Cr and Si [START_REF] Burkov | Energy Filtering Enhancement of Thermoelectric Performance of Nanocrystalline Cr 1-x Si x Composites[END_REF][START_REF] El Qader | Electrical, and Thermoelectric Properties of CrSi 2 Thin Films[END_REF][START_REF] Gong | Electrical and Structural Properties of Thin Film of Sputtered CrSi 2[END_REF][START_REF] Koudelka | Raman Scattering of Ni and Cr Amorphous Disilicides[END_REF] , evaporation [START_REF] Hieber | Structural and Electrical Properties of CrSi 2 Thin Film Resistors[END_REF][START_REF] Novikov | Enhancement of Thermoelectric Properties in Nanocrystalline M-Si Thin Film Composites (M=Cr, Mn)[END_REF][START_REF] Nava | Temperature Dependence of Semiconducting and Structural Properties of Cr-Si Thin Films[END_REF] or pulsed laser deposition 22, 30 at room temperature, have all reported the formation of an amorphous material. Partial or full crystallization of thin films were observed by annealing between 420 and 870 K, resulting in an increase in the values 24-26, 28, 29, 31-33 . One possibility would be that high annealing temperature and duration may induce the formation of cracks due to thermal expansion and crystallographic orientation mismatches between the thin film and the substrate [START_REF] El Qader | Electrical, and Thermoelectric Properties of CrSi 2 Thin Films[END_REF][START_REF] Gong | Electrical and Structural Properties of Thin Film of Sputtered CrSi 2[END_REF] .

Nevertheless, the increase in the electrical resistivity with crystallization is mostly explained by charge carrier scattering at the amorphous phasenanocrystallites interfaces [START_REF] Burkov | Energy Filtering Enhancement of Thermoelectric Performance of Nanocrystalline Cr 1-x Si x Composites[END_REF][START_REF] Novikov | Enhancement of Thermoelectric Properties in Nanocrystalline M-Si Thin Film Composites (M=Cr, Mn)[END_REF][START_REF] Nava | Temperature Dependence of Semiconducting and Structural Properties of Cr-Si Thin Films[END_REF] and by the presence of acceptor-like extended or localized states near the valence band in the amorphous material disappearing by crystallization [START_REF] Novikov | Crystallization and Transport Properties of Amorphous Cr-Si Thin Film Thermoelectrics[END_REF][START_REF] Lenzlinger | Effect in Silicon-Chromium Films[END_REF] . Thus, the electrical properties of thin films are highly sensitive to the process route, heat treatments applied and to the nature of the substrate.

Gong et al [START_REF] Gong | Electrical and Structural Properties of Thin Film of Sputtered CrSi 2[END_REF] studied the influence of annealing on the electrical properties of sputtered CrSi 2 thin films deposited on Si(100) wafer with SiO 2 sublayer with thicknesses spanning the 40 -90 nm range. An increase in was observed after annealing 1 h at 573 K under nitrogen atmosphere, a behavior attributed to the full crystallization of the thin film with the formation of wide boundaries surrounding columnar grains. Recently, Burkov et al [START_REF] Burkov | Energy Filtering Enhancement of Thermoelectric Performance of Nanocrystalline Cr 1-x Si x Composites[END_REF] reported the study of CrSi 2 thin films with a thickness of 100 nm deposited by sputtering on oxidized Si wafer. Partial crystallization from 500 to about 900 K was shown to lead to the formation of non-percolating nano-crystallites within the amorphous matrix that behave as scattering centers. Concomitantly, enhanced values were observed in this heterogeneous material, tentatively ascribed to an energy-filtering mechanism of holes.

Despite the abundant literature data available for CrSi 2 , the physical properties of the amorphous phase have been only scarcely investigated [START_REF] Luches | Laser-Assisted Synthesis of Semiconductor Chromium Disilicide Films[END_REF][START_REF] El Qader | Electrical, and Thermoelectric Properties of CrSi 2 Thin Films[END_REF][START_REF] Gong | Electrical and Structural Properties of Thin Film of Sputtered CrSi 2[END_REF][START_REF] Nava | Temperature Dependence of Semiconducting and Structural Properties of Cr-Si Thin Films[END_REF][START_REF] Novikov | Crystallization and Transport Properties of Amorphous Cr-Si Thin Film Thermoelectrics[END_REF][START_REF] Kim | Electrical Properties of CrSi x , Cr/CrSi x /Cr/CrSi x , and CrSi x /Si/CrSi x /Si Sputtered on Alumina Plates[END_REF] . To the best of our knowledge, the vibrational properties were only measured by Koudelka et al [START_REF] Koudelka | Raman Scattering of Ni and Cr Amorphous Disilicides[END_REF] , while optical properties have not been reported yet. Amorphous materials are characterized by the absence of long-range atomic order with a high number of dangling bonds acting as dopants. Moreover, disorder drastically alters the phonon properties, strongly scatters charge carriers, thereby reducing their mobility, and triggers the formation of long tails of localized states in the band gap of amorphous semiconductors. These effects can significantly impact the vibrational, optical and electrical properties of the materials. The control of interface charge carriers and phonons scattering mechanisms by structural defects or further nanostructuration is of great importance for some applications such as thermoelectricity [START_REF] Kim | Precision Interface Engineering of an Atomic Layer in Bulk Bi 2 Te 3 Alloys for High Thermoelectric Performance[END_REF][START_REF] Vineis | Nanostructured Thermoelectrics: Big Efficiency Gains From Small Features[END_REF] and the substrate was about 5 cm. The base pressure in the chamber was 210 -6 mbar before deposition. Argon gas (99.999 % purity) was used to create the plasma with a controlled pressure of 5.1 Pa. The sputtering power was set to 120 W. The target and the substrate were water cooled during sputtering. The film thickness was controlled by measuring the height of a step made by lift-off process using atomic force microscopy (AFM). Thermal treatments of thin films were performed during 1 h at 723 K in dynamic vacuum (10 -4 mbar) with a heating rate of 100 K h -1 and natural cooling. The temperature was controlled with a K-type thermocouple next to the sample. in a Van der Pauw configuration with an Ecopia HMS 5000 equipment under air. Good electrical contacts were achieved using indium. A magnetic field of 0.5 T was used for Hall effect measurements. At high temperatures (300 -700 K), in-plane electrical resistivity of thin films deposited on glass substrate was measured with a ZEM-3 (Ulvac-Riko) apparatus under a low helium pressure using a conventional four-probe method. Electrical contacts were ensured by deposited thin gold tracks on the thin films. The thin films were maintained in a vertical position using a dedicated sample holder (Ulvac-Riko).

Microstructural characterization. High Resolution Transmission

IR and Raman measurements. Reflectance and transmittance infrared (IR) measurements

were carried out with a 161 nm thick film deposited on a transparent CaF 2 substrate. The measurements were performed on the same film before and after annealing. IR spectra were recorded using a Bruker IFS 66 V Fourier transform spectrometer covering the 800-7500 cm -1 spectral range. A black body source, a KBr beam splitter, and a Mercury-Cadmium-Telluride (MCT) detector were used. Room-temperature transmittance and reflectance measurements were performed using the reflection of a Transmittance Bruker accessory (A510 Q/T) with an angle of incidence (θ) of 11° placed in the sample compartment of the FTIR spectrometer. Micro-Raman spectroscopy experiments were conducted at room temperature on a 480 nm thick CrSi 2 film grown on Si(100) substrate after annealing at 873 K for 20 min under Ar. A LabRam Aramis spectrometer from Horiba Jobin-Yvon was implemented using a He-Ne laser ( = 633 nm). The beam power was set to 7.3 mW to avoid sample thermal heating.

Results and discussion

3.1.Thin film microstructure and effect of thermal treatment

The TEM cross-section images of a 45 nm thin film (deposited on Si(100) wafer) before and after annealing performed at 723 K for 1 h are shown in Figure 1. A typical columnar structure is observed for the as-deposited thin film with the presence of the native silicon oxide sublayer ( 5 nm) at the substrate/film interface (Figure 1a). The electron diffraction pattern mainly consists in a large halo characteristic of the amorphous nature of the thin film (Figure 1b). The halo is located between inter-reticular distances of 1.80 and 2.37 . The intense and regular spots observed are characteristic of the single-crystalline Si(100) substrate.

The annealing step does not alter the columnar structure which is maintained (Figure 1c). A modification of the microstructure of Si is observed at the Si/CrSi 2 interface by TEM. This is due to Cr diffusion into the Si substrate up to about 10 nm as estimated by Electron Dispersive X-ray Spectroscopy (EDXS) analysis. Nevertheless, the diffraction pattern shows additional spots, evidencing the crystallization of the hexagonal CrSi 2 phase (Figure 1d). Their low intensity is attributed to the nanometer size of the crystallites, ranging from 3 to 10 nm. A weak diffuse halo is still observed. The annealed thin film is therefore made of CrSi 2 nano-crystallites embedded in an amorphous matrix.

Vibrational properties of CrSi 2 thin films

At the Brillouin zone center, the optical phonon modes of crystalline CrSi 2 can be classified according to the irreducible representations of the D 6 point group = A 1 + 2A Raman spectra of as-deposited and annealed thin films of 480 nm thickness grown on Si(100) are shown in Figure 3 and are compared with that obtained for powders [START_REF] Hermet | Revisited Phonon Assignment and Electro-Mechanical Properties of Chromium Disilicide[END_REF] . For the as-deposited thin film, no lines are observed in agreement with its amorphous state, as previously reported by Koudelka et al [START_REF] Koudelka | Raman Scattering of Ni and Cr Amorphous Disilicides[END_REF] . After annealing, the spectrum is composed of 6 Raman lines centered at 229, 300, 350, 394, 408 and 453 cm -1 . The contributions between 300 and 410 cm -1 have been reported in the literature on CrSi 2 thin films [START_REF] Lange | Growth and Optical Characterization of CrSi 2 Thin Films[END_REF][START_REF] Borghesi | Far-Infrared Vibrational Spectroscopy in CrSi 2[END_REF] , powders [START_REF] Hermet | Revisited Phonon Assignment and Electro-Mechanical Properties of Chromium Disilicide[END_REF] and single crystal [START_REF] Chaix-Pluchery | Vibrational Study of Transition Metal Disilicides[END_REF] and their frequency positions are clearly identified (see Ref. [START_REF] Hermet | Revisited Phonon Assignment and Electro-Mechanical Properties of Chromium Disilicide[END_REF] for the assignment of these Raman lines).

The Raman line at 229 cm -1 is unambiguously identified for the first time on a CrSi 2 film to be the E 1 mode predicted by DFT calculations [START_REF] Hermet | Revisited Phonon Assignment and Electro-Mechanical Properties of Chromium Disilicide[END_REF] . Although this line has already been observed in single crystal [START_REF] Chaix-Pluchery | Vibrational Study of Transition Metal Disilicides[END_REF] and powders [START_REF] Hermet | Revisited Phonon Assignment and Electro-Mechanical Properties of Chromium Disilicide[END_REF] , its significantly weaker intensity prevented any definitive conclusion to be drawn about its frequency position. Interestingly, an additional tiny Raman line can also be identified at 248 cm -1 in Fig. 3. This line had been previously observed only in powders [START_REF] Hermet | Revisited Phonon Assignment and Electro-Mechanical Properties of Chromium Disilicide[END_REF] , but with a very low intensity. The fact that this line is experimentally observed on different samples and confirmed by first-principles calculations makes its assignment and position firmly established. The broad line observed at 453 cm -1 has never been reported in literature, should it be on thin films, powders or single-crystalline CrSi 2 . DFT calculations assign the 440 -450 cm -1 range as either E 2 modes or longitudinal optical (LO) E 1 modes [START_REF] Hermet | Revisited Phonon Assignment and Electro-Mechanical Properties of Chromium Disilicide[END_REF] . At this stage, these two possible modes cannot be distinguished, which will require additional polarization-like experiments.

Electronic properties of CrSi 2 thin films

Evolution of the electrical resistivity with temperature

The electrical resistivity, , was measured from 300 to 685 K for a CrSi 2 thin film grown on glass substrate with a thickness of 480 nm. As shown in Figure 4, does not significantly vary from room temperature up to 520 K, with a mean value of 0.46 mΩ.cm. This behavior, characterized by a low temperature coefficient of resistance (TCR ), is consistent with an amorphous material [START_REF] Rao | Amorphous Metallic Alloys[END_REF] . It should be noted that contrary to crystalline materials, a positive or negative TCR is not related to either a metallic or semiconducting state [START_REF] Rao | Amorphous Metallic Alloys[END_REF] . Above 520 K, significantly increases up to 0.94 mΩ.cm at 685 K. This behavior, similar to that reported previously for amorphous CrSi 2 thin films with a transition at temperatures ranging from 450 to 600 K 24-26, 28, 29 , was attributed to the partial crystallization of the material. Upon cooling, remains practically temperature-independent with a mean value of 0.94 mΩ.cm.

The electrical resistivity of bulk polycrystalline CrSi 2 , reported by Dasgupta et al. [START_REF] Dasgupta | Thermal, and Electrical Properties of CrSi 2[END_REF] , increases from 0.9 mΩ.cm at 300 K to a maximum value of 1.8 mΩ.cm at 550 K, before decreasing at higher temperatures. These two distinct regimes correspond to the degenerate and intrinsic regime, respectively, of a semiconductor [START_REF] Nishida | Semiconducting Properties of Pure and Mn-Doped Chromium Disilicide[END_REF] . Our results also show a positive TCR for CrSi 2 nanostructured films, about K -1 around 300 K, in contrast to as-deposited amorphous films, but with values significantly lower than those reported in bulk CrSi 2 ( K -1 at 300 K) [START_REF] Dasgupta | Thermal, and Electrical Properties of CrSi 2[END_REF] . These results suggest that the nanostructured films are already above the percolation threshold after annealing at 700 K. This is in agreement with the work of Gladun et al. [START_REF] Gladun | Transport Properties of Nanodisperse Cr x Si 1-x Thin Films[END_REF] , where a positive TCR for Cr x Si 1-x films ( to ) was measured after annealing at a temperature that was varying with (at 573 K for with K -1 ). They notably showed that this effect was related to the percolation of CrSi 2 crystallites formed within the amorphous matrix during annealing for x > 0.11. To better understand the origin of the increase in after partial crystallization, the effective charge carrier density, , and mobility, , were measured by Hall effect between 80 and 230 K. For the amorphous films, both cm -3 and cm 2 V -1 s -1 are thickness-and temperature-independent. This value is in good agreement with that reported by Lenzlinger et al [START_REF] Lenzlinger | Effect in Silicon-Chromium Films[END_REF] for sputtered amorphous films on oxidized silicon wafer and is significantly higher than the values reported for bulk CrSi 2 ( 4 to 610 20 cm - 3 16, 44, 45 ). Meanwhile, decreases by two orders of magnitude compared to bulk CrSi 2 for which 12 cm 2 V -1 s -1 [START_REF] Shinoda | Semiconducting Properties of Chromium Silicides[END_REF] . This low mobility can be attributed to the structural disorder inherent to amorphous compounds that strongly scatters the charge carriers. After partial crystallization, decreases to cm -3 , regardless of the thickness, and remains constant in the temperature range covered. This effect originates from the decrease in the defect concentration induced by crystallization and atomic rearrangement. In contrast, the observed increase in is no longer thickness-independent. The mobility values increase from cm 2 V -1 s -1 to cm 2 V -1 s -1 for 12 and 164 nm thick films, respectively. These values remain substantially lower than those measured in the bulk counterpart. It should be noted that values in CrSi 2 are highly related to the defect concentration as shown by Zhu et al [START_REF] Zhu | Formation of n-Type CrSi 2 Semiconductor Layers on Si by High-Current Cr Ion Implantation[END_REF] who obtained 1085 cm 2 V -1 s -1 for epitaxial films due to a lower defect concentration compared to the present sputtered amorphous and nanostructured films.

Influence of film thickness on the electrical resistivity

Figure 5 shows the evolution of the electrical resistivity as a function of temperature for amorphous and nanostructured thin films deposited on Si(100) wafers with SiO 2 sublayer with a thickness varying from 12 to 164 nm. For amorphous films, increases with decreasing the thickness over the entire temperature range. This behavior is characteristic of charge carrier scattering at the film surface, as previously observed for example for Cu [START_REF] Zhou | Resistivity Scaling Due to Electron Surface Scattering in Thin Metal Layers[END_REF] , W [START_REF] Choi | On the Potential of Tungsten as Next-Generation Semiconductor Interconnects[END_REF] , Mo [START_REF] Schmid | Effect of Substrate Properties and Thermal Annealing on the Resistivity of Molybdenum Thin Films[END_REF] or CrSi 2 amorphous thin films [START_REF] Trofimov | Effect of Deposition Conditions on the Structure, Phase Composition and Electrical Properties of the Chromium Silicide Films[END_REF] . In contrast, the thickness effect is less significant for nanostructured thin films. This different behavior cannot be explained by the surface roughness as similar values were measured for both films (see Figure 2). For this reason, we believe that charge carrier scattering mechanisms at the film surface are equivalent in both films. Nevertheless, the formation of nano-crystallites in the annealed thin film likely leads to an additional scattering mechanism at the amorphous matrix / nano-crystallite interface. To explain this behavior, we considered the well-known Fuchs-Sondheimer (F-S) model, which is based on the Boltzmann transport equation [START_REF] Fuchs | The Conductivity of Thin Metallic Films According to the Electron Theory of Metals[END_REF] . This model is generally used to describe surface scattering of electrons in metallic thin films, and can be extended to semiconducting thin films by neglecting surface states within the flat-band approximation [START_REF] Anderson | Conduction in Thin Semiconductor Films[END_REF] . The F-S model, which assumes a single parabolic conduction band, a thickness-independent structural disorder, plane parallel surfaces and isotropic scattering processes [START_REF] Wißmann | Surface Physics-Springer Tracts in Modern Physics[END_REF] , yields the following equation:

where is the electrical resistivity of an infinitely thick film with the same microstructure (including contributions from phonons, grain boundaries, impurities or point-defect scattering mechanisms), where is the film thickness and is the charge carrier mean free path in a bulk material with the same defect and impurity concentrations, and ( is the specularity coefficient describing the fraction of electrons that are specularly scattered from the surface. These scattered electrons have a conserved momentum and hence, do not contribute to the electrical resistivity. In contrast, in the case of totally diffused scattering ), all the electrons are scattered with a random direction resulting in increased electrical resistivity.

In the present study, we tried to apply this approach to model the low-temperature experimental data measured on amorphous and nanostructured thin films. These data were fitted by a least-squares method using the Gauss-Newton algorithm to evaluate the values of . Within this model, however, the value of is usually unknown and strongly depends on the deposition method and substrate [START_REF] Kasap | Springer Handbook of Electronic and Photonic Materials[END_REF] . In the case of copper thin films, for instance, Marom et al. [START_REF] Marom | The Effect of Surface Roughness on the Resistivity Increase in Nanometric Dimensions[END_REF] have shown that the scattering of electrons on smooth surfaces (that is, below the de Broglie wavelength) is mostly specular, synonymous with values close to 1. In the present case, the values of the CrSi 2 thin films are low, varying from 0.5 to 0.8 nm and from 0.7 to 1.2 nm for amorphous and nanostructured thin films, respectively, that is, below the de Broglie wavelength of CrSi 2 estimated to be 5 nm [START_REF] Novikov | Grain Boundary Scattering Contribution to the Thermopower in Cr-Si Nanocrystalline Films[END_REF] . Based on this empirical criterion, we may therefore expect a mostly specular diffusion scattering in both cases, giving rise to high values. Both , and parameters cannot be independently determined by the F-S model [START_REF] Choi | Electron Mean Free Path of Tungsten and the Electrical Resistivity of Epitaxial (110) Tungsten Films[END_REF][START_REF] Milosevic | Resistivity Size Effect in Epitaxial Ru(0001) Layers[END_REF] . Due to the lack of direct experimental probes to easily determine , a totally diffused scattering with is usually assumed in the literature [START_REF] Trofimov | Effect of Deposition Conditions on the Structure, Phase Composition and Electrical Properties of the Chromium Silicide Films[END_REF][START_REF] Milosevic | Resistivity Size Effect in Epitaxial Ru(0001) Layers[END_REF][START_REF] Jagielinski | Magnetic and Galvanomagnetic Properties of Amorphous CoZr Thin Films[END_REF][START_REF] Dranenko | Dimensional Dependence of Electric Resistance of Thin TiB 2 Films[END_REF] . For these reasons, we have implemented this model with several values of varying from 0 to 1. As illustrative examples of the quality of the fits obtained, similar across the entire temperature range and for each value, Figures 6a and6b show the results obtained at 80 and 205 K assuming .

In the case of amorphous thin films, surface scattering occurs for thicknesses below about 45 nm (Figure 6a and 6b), thereby increasing the electrical resistivity of thinner films. This value is in good agreement with the thickness limit of 40 nm reported by Novikov et al. [START_REF] Novikov | Crystallization and Transport Properties of Amorphous Cr-Si Thin Film Thermoelectrics[END_REF] . The estimated values of at each temperature are reported in Figure 6c and are similar for value ranging from 0 to 1 (Figure S2). The value of = 0.56 mΩ.cm does not depend on temperature, which is consistent with the amorphous nature of the film, as previously discussed. In contrast, strongly depends on , as shown in Figure 6d, resulting in charge carrier mean free paths that increase with increasing , from nm for up to nm for . These values are similar across the entire temperature range covered. A wide range of electron mean free paths in amorphous metallic films were reported in literature, ranging from nm in Co 94 Zr 6

films [START_REF] Jagielinski | Magnetic and Galvanomagnetic Properties of Amorphous CoZr Thin Films[END_REF] (at 300 K, with ) to 18 -30 nm 60 in Y films (at 4.2 K, determined using another model) through 10 -13 nm 61 in Pt films (at 300 K, with varying from 0.13 to 0.15). Based on these reported values, the large mean free paths obtained herein for higher values, up to 240 nm for , are unrealistic. For this reason, we have restricted our analysis to values of near 0. These considerations thus suggest that diffused scattering of charge carriers prevails in amorphous films despite their low roughness, with 15 nm.

For nanostructured thin films, the values of are higher compared to amorphous thin films and slightly increase with increasing temperature (Figure 6c) from 0.78 mΩ.cm at 80 K to 0.89 mΩ.cm at 255 K (without any dependence on ). Figure 6d shows that the charge carrier mean free path is reduced for each value of , compared to the amorphous thin films, with, for instance, decreasing from 15 nm to 3 nm if . We note that these values are in good agreement with the value of 2 nm inferred by Trofimov et al. assuming 0 [START_REF] Trofimov | Effect of Deposition Conditions on the Structure, Phase Composition and Electrical Properties of the Chromium Silicide Films[END_REF] for nanocrystallized CrSi 2 thin films with thicknesses of up to 20 nm and crystallite sizes varying from 25 to 100 nm. The reduction in the charge carrier mean free path can be explained by the formation of nano-crystallites with sizes comparable to that induce additional charge carrier scattering at the nano-crystallites / amorphous phase interfaces.

, and that the charge carriers mean free path is significantly reduced by scattering at the nanocrystallites / amorphous phase interfaces, explains why is less influenced by the film thickness.

Electronic structure

The optical electronic bandgaps, , of the thin films have been determined by IR reflectance and transmittance measurements for thin film with a thickness of 161 nm deposited on a CaF 2 substrate. The direct and indirect optical bandgap values have been determined using Tauc plots, a representation particularly well adapted for amorphous and nano-crystalline materials [START_REF] Tauc | Optical Properties of Solids[END_REF] :

where is the absorption coefficient, is the band tailing parameter, is the incoming photon energy, and is a constant related to the transition process ( and for indirect and direct transitions, respectively). Numerous models are used for the determination of from experimental reflectance and transmittance measurements depending on the experimental conditions. After comparison of some models, we used the method of Galkin et al. [START_REF] Galkin | Optical and Photospectral Properties of CrSi 2 A-Type Epitaxial Films on Si(111)[END_REF] , the details of which are given in the Supporting Information Part 3. This model is adapted in the case of an absorbing thin film and considering multiple reflections in the thickness of the film and the substrate. The inferred values of with the corresponding Tauc plots are shown in Figures 7a and7b. A steep increase in can be observed for photon energies above 0.23 and 0.43 eV for amorphous and nanostructured CrSi 2 thin films, respectively (Figure 7a). It clearly indicates a semiconducting nature of both materials, while a metallic behavior of amorphous CrSi 2 films was suggested based solely on electrical resistivity measurements [START_REF] Luches | Laser-Assisted Synthesis of Semiconductor Chromium Disilicide Films[END_REF][START_REF] Nava | Temperature Dependence of Semiconducting and Structural Properties of Cr-Si Thin Films[END_REF][START_REF] Kim | Electrical Properties of CrSi x , Cr/CrSi x /Cr/CrSi x , and CrSi x /Si/CrSi x /Si Sputtered on Alumina Plates[END_REF][START_REF] Dvorina | Special Features of the Crystallization of Thin Films of Silicides of Some Transition Metals[END_REF] . The non-zero absorption at low energies can be attributed to extrinsic absorption from free carriers. Tauc plots (Figure 7b) show that amorphous and nanostructured CrSi 2 thin films have indirect band gaps of eV and eV, respectively, and direct band gaps of eV and eV. The errors have been estimated from the linear regression dependence on the selected data range. Thus, amorphous CrSi 2 thin films show a very low band gap value explaining the low electrical resistivity and nearly-metallic behavior.

An increase in the band gap can be observed upon partial crystallization, although the value is not equivalent to that of crystallized CrSi 2 ( 0.35 eV 10 ). This modified electronic structure is in agreement with the increase in the electrical resistivity and decrease in the charge carrier concentration measured experimentally, which can be attributed to the reduction of defect level and nano-crystallization during the annealing process. Such changes of the electronic structure of CrSi 2 thin films due to nano-crystallization are consistent with previous optical conductivity measurements [START_REF] Luches | Laser-Assisted Synthesis of Semiconductor Chromium Disilicide Films[END_REF] .

In contrast to crystalline materials that exhibit well-defined band gap edges, amorphous materials can be characterized by band tails due to structural defects [START_REF] Baranovski | Charge Transport in Disordered Solids with Applications in Electronic[END_REF]

Optical properties of amorphous and nanostructured CrSi 2 thin films

The refractive index, , and extinction coefficient, , shown in Figure 8a, were determined from the IR absorbance coefficients (see Figure 7a). The observed variations are in line with the electronic structure modifications induced by the nano-crystallization.

The behavior of agrees with those reported for well-crystallized or epitaxial films and single crystals [START_REF] Bost | An Investigation of the Optical Constants and Band Gap of Chromium Disilicide[END_REF][START_REF] Galkin | Optical and Photospectral Properties of CrSi 2 A-Type Epitaxial Films on Si(111)[END_REF][START_REF] Bellani | Theory and Experiment on the Optical Properties of CrSi 2[END_REF] . A broad maximum is observed around 0.16 -0.25 eV and 0.43 -0.53 eV for asdeposited and annealed films, respectively. These energy windows are consistent with those reported in the literature for well-crystallized CrSi 2 thin films, extending from 0.3 -0 .55 eV [START_REF] Bost | An Investigation of the Optical Constants and Band Gap of Chromium Disilicide[END_REF] to 0.47 -0.56 eV [START_REF] Galkin | Optical and Photospectral Properties of CrSi 2 A-Type Epitaxial Films on Si(111)[END_REF] . The energy shift of the maximum in upon annealing is directly related to electronic structure modifications due to the change of inter-band transition as the band gap increases. Moreover, a large reduction of values is observed after nano-crystallization, as expected from an increase in the band gap. Nevertheless, the values of annealed CrSi 2 thin films are still higher than those reported previously [START_REF] Bost | An Investigation of the Optical Constants and Band Gap of Chromium Disilicide[END_REF][START_REF] Galkin | Optical and Photospectral Properties of CrSi 2 A-Type Epitaxial Films on Si(111)[END_REF][START_REF] Bellani | Theory and Experiment on the Optical Properties of CrSi 2[END_REF] because of the partial crystallization of the material after the thermal treatment. As for , both amorphous and nanostructured samples show a similar behavior with a shift of about 0.25 eV. A large increase in with decreasing the energy is observed, due to the absorption by free charge carriers [START_REF] Bost | An Investigation of the Optical Constants and Band Gap of Chromium Disilicide[END_REF] . The slope of this part is higher for the amorphous thin film due to the high defect concentration. A minimum value of 0.8 is observed around 0.3 eV and 0.5 eV for amorphous and nanostructured thin films, respectively.

The real ( ) and imaginary ( parts of the dielectric function, were calculated from the and values using the following relations [START_REF] Jensen | Handbook of Optical Constants of Solids[END_REF] :

The and values, reported in Figure 8b, are analogous with and . Broad maxima of are observed at 0.16 -0.25 eV and 0.43 -0.53 eV for amorphous and nanostructured thin films, respectively, due to inter-band transitions. The values are nevertheless larger in the case of the amorphous thin films. As for , a large increase is observed at low energies, as previously described in the case of .

Similarly to our results on nanostructured film, a maximum in at about 0.5 eV is reported for epitaxial and polycrystalline CrSi 2 films [START_REF] Galkin | Optical and Photospectral Properties of CrSi 2 A-Type Epitaxial Films on Si(111)[END_REF][START_REF] Bellani | Theory and Experiment on the Optical Properties of CrSi 2[END_REF] , but with a smaller value (near 50) due to the residual amorphous phase in our sample.

Conclusion

Contrasting the electrical, vibrational and optical properties of as-deposited, amorphous and annealed, nanostructured CrSi 2 thin films have revealed interesting insights into the influence of nano-crystallites, successfully grown in the amorphous matrix through annealing for 1 h at 723 K under vacuum. Raman spectroscopy has evidenced a line at 229 cm -1 , predicted to be a E 1 mode by DFT calculations, that had remained elusive so far in experiments on thin films. In agreement with first-principles calculations, these measurements further enabled the identification of a weak Raman line at 248 cm -1 , which had been previously observed solely on polycrystalline CrSi 2 , but with a significantly lower intensity. The presence of high defect concentrations in amorphous films, acting as acceptor dopants, significantly increases the hole concentration to values usually encountered in metals. The amorphous nature of these films explains the strong lowering of the band gap width evidenced by optical spectra ( due to band tails that cover nearly entirely the band gap ( 0.13 eV). Upon annealing, the nano-crystallization induces a decrease in the defect concentration, leading to a concomitant increase in the band gap and reduction in the band tail width, in agreement with the measured lower carrier concentration.

Thus, the increase in the electrical resistivity in partially-crystallized thin films can be explained by both the reduction of defect concentration by annealing, which modifies the electronic structure, and the formation of nano-crystallites that promotes an additional interface scattering mechanism reducing the charge carrier mean free path. Using the Fuchs-Sondheimer model, we showed that a charge carrier mean free path of 15 nm in amorphous films is responsible for the variations in electrical properties as a function of the thickness by surface scattering that dominates for thicknesses below 45 nm. The variations in the electronic structure also manifest in the optical and dielectric constants. The decrease in the band gap in amorphous thin films produces a shift of the and constants towards low energy and a modification of their intensities. A large index of refraction in the mid-IR range was obtained for amorphous CrSi 2 thin films, which can be of practical relevance to form waveguides for instance. Our study provides a robust basis to understand the vibrational, electronic and optical properties of both amorphous and nanostructured CrSi 2 thin films. In particular, our results demonstrate the possibility to tailor the electrical, optical and vibrational properties by controlling the crystallization rate during annealing and the thickness of the thin films for a given application.

ASSOCIATED CONTENT

Supporting Information

Atomic Force Microscopy (AFM) observations, details of the Fuchs-Sondheimer model, absorption coefficient calculation and Urbach energy determination.

Figure 1 .

 1 Figure 1. TEM cross-sectional images of a 45 nm thin film deposited on a Si substrate: a) and b)

Figure 2 .

 2 Figure 2. Roughness of amorphous (as-deposited) and nanostructured (annealed) CrSi 2 thin

Figure 3 .

 3 Figure 3. Raman spectra of amorphous and nanostructured CrSi 2 thin films compared with that obtained on powders 37 .

Figure 4 .

 4 Figure 4. Electrical resistivity as a function of temperature for a CrSi 2 thin film with a

Figure 5 .

 5 Figure 5. Evolution of the electrical resistivity with the thickness of the CrSi 2 film for a)

Figure 6 .

 6 Figure 6. Experimental data (points) and fitted model (lines) of the electrical resistivity as a

  . They are quantified by the Urbach energy, , inferred from the exponential part of the absorption coefficient near the gap using the relation . The value of corresponds to the width of the tails of localized states near the band edge and are obtained from the plot of the variations in with near the bandgap (see Supporting Information Part 4). Herein, a dramatic decrease of by nano-crystallization is observed with values of of 0.13 eV and 0.06 eV for as-deposited and annealed films, respectively, due to a decrease in the defect level. Thus, these band tails, nearly identical to the band gap values, can explain the quasi-metallic behavior of the amorphous thin films.

Figure 7 .

 7 Figure 7. Optical properties of amorphous (as-deposited) and nanostructured (annealed) CrSi 2

Figure 8 .

 8 Figure 8. a) Refractive index and extinction coefficient as a function of the photon

  2 + 4E 2 + 4E 1 + 3B 2 + 2B 1 . The E 1 representation is both infrared and Raman active. The A 1 and E 2 representations are Raman active while the A 2 representation is only infrared active. The B 1 and B 2 representations are silent. The frequencies of the silent modes have never been measured so far but they have been predicted by DFT calculations[START_REF] Hermet | Revisited Phonon Assignment and Electro-Mechanical Properties of Chromium Disilicide[END_REF] at 204 and 300 cm -1 (B 1 modes), and at 238, 284 and 393 cm -1 (B 2 modes). The two infrared A 2 modes have been reported in the literature to be around 295 and 375 cm -1 , in agreement with calculations.

Caractérisation Chimie Balard, Montpellier, France. Infrared Reflectance experiments were performed at the IR-Raman technological platform of the Université de Montpellier, France.

AUTHOR INFORMATION

Corresponding Author

Adrien Moll -Institut Charles Gerhardt Montpellier, UMR5253, CNRS, Université de Montpellier, Montpellier 34095, France ; Email : moll@icmpe.cnrs.fr Nicole Fréty -Institut Charles Gerhardt Montpellier, UMR5253, CNRS, Université de Montpellier, Montpellier 34095, France ; Email : nicole.frety@umontpellier.fr

Present Addresses

Adrien Moll -now at Univ. Paris Est Creteil, CNRS, ICMPE, UMR 7182, Thiais 94320, France

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. The authors contributed equally.

ACKNOWLEDGMENT

The authors would like to greatly acknowledge Dr R. Viennois for fruitful discussions. Thin films were prepared at the Centrale de Technologie en Micro et nanoélectronique (CTM), Université de Montpellier, France. The authors would like to particularly thank F. Pichot for his precious help. They also thank D. Troadec (IENM, Lille, France) for the FIB sample preparation. This work was partly supported by the French RENATECH network. The authors also thank L.

Daenes for Raman spectroscopy measurements performed at the Plateforme d'Analyse et de


MD Florence Renaldo
email: florence.renaldo@aphp.fr

MD François Chalard

MD, PhD Stephanie Valence

MD, PhD Lydie Burglen

MD, PhD Diana Rodriguez

Area Postrema Syndrome as the Initial Presentation of Alexander Disease

Keywords:

Disclosures: All the authors report no disclosures relevant to the manuscript: F Renaldo reports no disclosures relevant to the manuscript.F Chalard reports no disclosures relevant to the manuscript. S Valence reports no disclosures relevant to the manuscript.L Burglen reports no disclosures relevant to the manuscript. D Rodriguez reports no disclosures relevant to the manuscript.

A 16-year-old boy presented with six years evolution of anorexia, failure to thrive, nocturnal vomiting, and dysphagia. He was exhaustively explored. Neurologic examination was normal except hoarse voice. MRI revealed a hyperintensity of the area postrema (figure).

Faced with this chronic and isolated area postrema syndrome we looked for Alexander disease rather than neuromyelitis optica spectrum disorder. GFAP gene sequencing identified a reported, de novo, heterozygous variant c.1290C>A;p.Arg430Arg 1 .

Several patients with juvenile onset or type II Alexander disease have been reported with episodic vomiting, anorexia, and MRI lesions which can retrospectively be recognized as an impairment of the area postrema.

2

 2

  de Neuropédiatrie & Centre de Référence Neurogénétique, APHP.SU, Hôpital Trousseau, Paris, France designed the study, collected and analyzed the data, drafted the manuscript François Chalard, MD Department of Pediatric Imaging, APHP.SU, Hôpital Trousseau, Paris, France analyzed and interpreted the radiologic data Stephanie Valence, MD, PhD Service de Neuropédiatrie & Centre de Référence Neurogénétique, APHP.SU, Hôpital Trousseau, Paris, France analyzed the data, critically reviewed and revised the manuscript de Référence Neurogénétique, APHP.SU, Hôpital Trousseau; Inserm U1141-FHU I2-D2 ; Paris, France analyzed the data, critically reviewed and revised the manuscript DOI 10.1212/WNL.0000000000012462 published online July 7, 2021 Neurology Florence Renaldo, François Chalard, Stephanie Valence, et al. Area Postrema Syndrome as the Initial Presentation of Alexander Disease This information is current as of July 7, 2021 Services Updated Information & citation.full http://n.neurology.org/content/early/2021/07/07/WNL.0000000000012462. including high resolution figures, can be found at: Subspecialty Collections http://n.neurology.org/cgi/collection/mri MRI http://n.neurology.org/cgi/collection/all_pediatric All Pediatric collection(s): This article, along with others on similar topics, appears in the following Permissions & Licensing http://www.neurology.org/about/about_the_journal#permissions entirety can be found online at: Information about reproducing this article in parts (figures,tables) or in its Reprints http://n.neurology.org/subscribers/advertise Information about ordering reprints can be found online: Print ISSN: 0028-3878. Online ISSN: 1526-632X. reserved. is now a weekly with 48 issues per year. Copyright © 2021 American Academy of Neurology. All rights ® is the official journal of the American Academy of Neurology. Published continuously since 1951, it Neurology

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The authors report no targeted funding