Anthony Boyer

Hugues Duffau
email: h-duffau@chu-montpellier.fr

Marion Vincent

Sofiane Ramdani
email: sofiane.ramdani@umontpellier.fr

Emmanuel Mandonnet
email: emmanuel.mandonnet@aphp.fr

David Guiraud
email: david.guiraud@inria.fr

François Bonnetblanc
email: francois.bonnetblanc@inria.fr

Electrophysiological Activity Evoked by Direct Electrical Stimulation of the Human Brain: Interest of the P0 Component

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

function execution. Its use lowers the probability of resecting essential functional areas, near or within the tumor. However, the electrophysiological effects of DES remain poorly understood, both locally and remotely, and thus require further investigations [START_REF] Vincent | The difference between electrical microstimulation and direct electrical stimulationtowards new opportunities for innovative functional brain mapping?[END_REF][START_REF] Vincent | Case report: Remote neuromodulation with direct electrical stimulation of the brain, as evidenced by intra-operative EEG recordings during wide-awake neurosurgery[END_REF]. In this perspective, the recording of Evoked Potentials (EPs) could be used to study the conductive and integrative properties of the neural ensembles being directly stimulated and/or indirectly affected by DES. Three different types of potentials evoked by DES should be distinguished: Cortical evoked-potential (called Direct Cortical Response, DCR), when recording the cortex activity at the stimulation site. Cortico-Cortical Evoked-Potential (CCEP), i.e. recording the cortex activity at a distant site from the stimulation site. CCEPs are elicited by a physiological propagation through white matter tracts from the locally stimulated area towards the distal area. Axono-Cortical Evoked-Potentials (ACEP), when a cortical response is recorded from a stimulation site located within the white matter.

The DCR is an EP recorded in the immediate vicinity (distance to the stimulation site < 10 mm) of a focal electrical stimulation applied on the cortical surface [START_REF] Adrian | The spread of activity in cerebral cortex[END_REF][START_REF] Goldring | Distinctive electrophysiological characteristics of functionally discrete brain areas: a tenable approach to functional localization[END_REF][START_REF] Vincent | A measure of cortico-cortical potentials evoked by 10 Hz direct electrical stimulation of the brain and by means of a differential recording mode of electrocorticographic signals[END_REF][START_REF] Vincent | Electrophysiological brain mapping: Basics of recording evoked potentials induced by electrical stimulation and its physiological spreading in the human brain[END_REF]. For the classical referenced mode, the signal is measured between each active electrode and a distant reference electrode or an average of electrodes' signals. In this context, the DCR appears to be negative. For a differential recording mode, the signal is measured between 2 nearby active electrodes to improve spatial resolution. In this case, the DCR can either be negative or positive depending on the location of the potential towards active and reference electrodes [START_REF] Vincent | A measure of cortico-cortical potentials evoked by 10 Hz direct electrical stimulation of the brain and by means of a differential recording mode of electrocorticographic signals[END_REF]. Its amplitude generally peaks between 15 and 25 ms after the stimulation onset. It has been suggested that the DCR mainly depends on postsynaptic events. A weak stimulus evokes a 20 ms negative deflection called the primary negative potential (N1) that represents excitatory post-synaptic potentials of apical dendrites [START_REF] Goldring | Distinctive electrophysiological characteristics of functionally discrete brain areas: a tenable approach to functional localization[END_REF]. A stronger stimulus intensity is supposed to elicit responses in which spikes of positive polarity and brief duration (approximately 5 ms) appear at the initial phase of the response, and are followed by N1. These brief positive spikes have been ascribed to serial "all or none" discharges in the soma of cortical pyramidal neurons and could be illustrative of the summation of synchronous action potentials [START_REF] Goldring | Distinctive electrophysiological characteristics of functionally discrete brain areas: a tenable approach to functional localization[END_REF]. The early positive deflection is called the P0 component.

For bipolar DES applied on the cortical surface at a given intensity, the depth of the electrical field is determined by the inter-electrode distance (IED). The longer the IED is, the deeper in the cortex the electrical field is. It has been

Electrophysiological Activity Evoked by Direct Electrical Stimulation of the Human Brain: Interest of the P0 Component*

Anthony Boyer, Hugues Duffau, Marion Vincent, Sofiane Ramdani, Emmanuel Mandonnet, David Guiraud, Member, IEEE EMBS and Francois Bonnetblanc demonstrated that large-diameter axons in the subcortex are the most excitable neural elements when electrical fields are generated and extend from the cortical surface to the subcortical white matter [START_REF] Landau | Site of excitation in stimulation of the motor cortex[END_REF]. In addition, when the delivered current intensity is increased, the electrical field penetrates deeper into the cortex. It has been demonstrated experimentally and theoretically through modeling, that the generation of action potentials in an axon is obtained with less charge injections when the Pulse Width (PW) is shorter than the chronaxy [START_REF] Mccreery | Charge density and charge per phase as cofactors in neural injury induced by electrical stimulation[END_REF][START_REF] Merrill | Electrical stimulation of excitable tissue: design of efficacious and safe protocols[END_REF]. The relationship between the charges injected to reach the threshold and the PW is not flat, but roughly an affine function with a positive slope (see figure 7 of [START_REF] Vincent | The difference between electrical microstimulation and direct electrical stimulationtowards new opportunities for innovative functional brain mapping?[END_REF]). The more the PW decreases the more the required charges to reach the threshold decrease.

Hypothetically, reducing the PW could facilitate the generation of action potentials in pyramidal neurons of deep cortical layers that project to remote cortical areas through subcortical white matter. In the literature reporting CCEPs triggered and measured with grids of 1 cm-spaced electrodes, PWs are inferior to those commonly used during intraoperative mapping with classical 5 mm-spaced bipolar Ojemann's stimulation [START_REF] Matsumoto | Functional connectivity in the human language system: a corticocortical evoked potential study[END_REF]. The effects of PW and interelectrodes spacing on EPs in the context of DES should be disambiguated. This work is a first attempt to clarify this issue as we manipulated these two parameters in order to determine whether the P0 increases when the inter-electrode distance is increased and the PW is decreased.

II. METHODS

A. Patient

This paper reports the case of a right-handed 50-years old woman who underwent a surgery for a low-grade glioma located within the left paralimbic region with frontal predominance and a beginning of contralateral extension. The present study protocol was approved by the Ethics Committee of the University Hospital Center of Montpellier (protocol: UF 965, n° 2014-A00056-43). The patient gave its signed written informed consent to participate in the study.

B. Electrophysiological recordings

Electro-corticographic (ECoG) data were recorded intraoperatively after the tumor resection, under general anesthesia. Two 4-contacts strips of ECoG electrodes (2.5 mm exposed surface platinium contacts, 10 mm spaced, DIXI, France) were positioned on the surface of the brain (Fig. 1B). The first strip was placed on the superior temporal gyrus and the second on the dorsolateral prefrontal cortex (electrode numbers range from 1 to 4 and from 5 to 8 respectively, as presented in Fig. 1B). ECoG signals were recorded using differential configurations for both strips, which means that the anode and cathode were two adjacent electrodes. A cup-electrode (Au) located on the left mastoid (ipsilateral to surgery) served as reference for the 4th electrode of each strip (i.e. electrodes 4 and 8, as seen in Fig. 1B, were recorded on common mode). Importantly, this method is not classically used but is less sensitive to noise by being independent from the positioning of a common reference electrode. ECoG signals were sampled at 10 kHz (PowerLab, ADInstrument) and band-pass filtered from 0.5

Hz to 1 kHz. The front-end amplifier (g.BSamp, G.tec, Austria) was grounded to a patch-electrode located on the left acromion and signals were recorded with a gain of 1,000 to avoid saturation.

Importantly, the 50 Hz notch filter integrated in the amplifier was turned off for the first strip ("ECoG 1" in Fig. 1B). This was used to avoid the prominent filter impulse response on recordings, which appears as a damped sine wave and requires additional post-processing. Removing the notch filter for the first strip allowed real-time observation of the early P0 component at the expense of significant and irregular signal contamination by the 50 Hz electrical noise. The notch filter was kept activated for the other strip ("ECoG 2" in Fig. 1B) allowing noise-free signal recordings and thus easier and more robust real-time observation of the late N1 component. Unused amplifier's channels were short-circuited to ground.

C. DES and anatomical sites of stimulation

Usual cortical and white matter mappings were completed on the awake patient. DES was delivered thanks to a bipolar probe (0.5 mm diameter electrode tips, 5 mm apart) (Nimbus, Innopsys, France). Biphasic constant-current square wave pulse of 1 ms duration was applied at a fixed frequency of 60 Hz. The current intensity was set to 2 mA. Brain mapping is presented in Fig. 1A. Functional sites were identified during the awake phase: cortical stimulations on tag 1 induced involuntary hemifacial movements and identified the primary motor area of the face. Stimulations on tags 2 and 3 led to complete anarthria and stopped movements of the contralateral upper limb respectively, identifying the ventral premotor cortex. Stimulation on tag 4, (precentral gyrus) also generated articulatory troubles. Stimulations on tag 5 (dorsolateral prefrontal cortex) and 50 (superior temporal region) led to complete anomia. At the bottom of the cavity, the insular surface was exposed and the inferior frontooccipital fasciculus identified: stimulations on tags 47 and 48 led to reproducible semantic paraphasia.

To study more precisely the electrophysiological effects of DES, we selected 3 functional sites, further studied under general anesthesia: (1) on tag 4 (near electrode 6); (2) on tag 50 (near electrode 1); (3) on tags 47-48 (subcortically). At each stimulation site, 4 stimulation conditions were tested as presented in Tab. 1. Each one was performed twice consecutively; after the tumor resection. The frequency of 9 Hz was chosen because it allowed long enough time-window (111ms) to record the N1 component, without requiring overly extended stimulation time for averaging purposes.

D. Evoked potentials

Mean EPs traces were obtained by averaging ECoG signals time-locked to the DES onset, upon a time window equals to the period of stimulation (111 ms at 9 Hz and 16 ms at 60 Hz). The number of stimuli available depends on the duration of the stimulation provided by the surgeon upon the tested area. In our case, stimulation durations ranged from 4 to 8 s.

III. RESULTS

DCRs were recorded on multiple sites and for various stimulation conditions on both electrodes. However, only recordings made between electrodes 2 and 3 of strip 1 ("EcoG 1" in Fig. 1B) are presented as they showed systematic DCR when DES was applied on tag 50 with good signal quality throughout the experiment. The number of stimuli available ranged from 52 to 65 for 9 Hz DES and we systematically used the first 50 stimuli for averaging. Similarly, for the 60 Hz DES, the number of stimuli ranged from 254 to 298 and only the first 250 stimuli were kept. Mean DCRs were thus obtained by averaging EPs for each stimulation condition. Mean EPs for the 3 conditions at 9 Hz contained N1 after DES artifact (N1 mean latency: 34±4 ms, N1 mean amplitude: -44±58 μV). As hypothesized, the P0 was magnified and peaked around 4 ms after stimulation when the IED was increased and the PW was decreased (Condition 3: P0 latency: 4 ms, P0 amplitude: 90μV; Condition 4: P0 mean latency: 3.6±0.2 ms, P0 mean amplitude: 470±14 μV ). A subset of the raw signal (Fig. 1C) revealed a repeated strong P0 component which seemed to diminish over time for the 9 Hz / I = 1.5 mA / IED = 10 mm / PW = 0.5 ms condition. Interestingly, for the 60 Hz condition (Fig. 1B), we did not observe the P0 component neither when averaging over the entire stimulation time (250 stimuli) nor when using smaller sliding time-windows. In other words, the 60 Hz DES is not associated with P0 and there is no evidence for possible attenuation of a P0 over stimulation repetitions. Figure 1. A: Mean DCR over 50 stimuli for the 3 conditions at 9 Hz (each condition was repeated twice), recorded between electrodes 2 and 3. The average P0 latency is 3.8 ms and N1 latencies range from 28 to 39 ms. DES was applied cortically on tag 50 (near the electrode 1 of the first ECoG strip). B: Mean DCR over 50 (9 Hz) and 250 (60 Hz) stimuli for the 9 and 60 Hz DES conditions using similar parameters (I = 1.5mA, PW=1ms, IED=5mm, each condition was repeated twice), recorded between electrodes 2 and 3. DES was applied cortically on tag 50 (near the electrode 1 of the first ECoG strip). C: Subset of the raw ECoG signal during 9 Hz DES on tag 50 with parameters: I = 1.5mA, PW=0.5ms, IED=10mm, recorded between electrodes 2 and 3. Both repetitions are presented as "Rep 1" and "Rep 2". The magnified P0 but also the N1 components can be observed after each stimulation artifact.

IV. DISCUSSION

It is assumed that the DCR has different profiles which are correlated to the local cytoarchitectonic organization of the stimulated area [START_REF] Goldring | Distinctive electrophysiological characteristics of functionally discrete brain areas: a tenable approach to functional localization[END_REF]. These profiles could be used to establish, in real-time and in vivo, the electrophysiological state of the stimulated cortical column in terms of excitability [START_REF] Vincent | A measure of cortico-cortical potentials evoked by 10 Hz direct electrical stimulation of the brain and by means of a differential recording mode of electrocorticographic signals[END_REF].

Decreasing the PW and increasing the IED should activate neural elements with less charge injections and allow the current field to reach pyramidal somas and/or axons in deeper cortical layers with a higher intensity and even subcortical white matter [START_REF] Vincent | Electrophysiological brain mapping: Basics of recording evoked potentials induced by electrical stimulation and its physiological spreading in the human brain[END_REF]. According to this hypothesis, we varied these two parameters and were clearly able to trigger a magnified P0, suggesting an initial summation of synchronous action potentials (not a summation of excitatory postsynaptic potentials as for the N1 component). Measuring P0 could be of great value in order to determine whether DES induces action potentials that propagate to other remote cortical areas.

A prediction would be that CCEP should be more frequently observed when a significant P0 is observed in DCR (assuming that the two cortical sites are anatomically connected). Logically, P0 should also be visible on ACEP since in this case, subcortical axons are stimulated and thus action potentials are triggered, propagating towards the cortical surface. This is the case in [START_REF] Vincent | Electrophysiological brain mapping: Basics of recording evoked potentials induced by electrical stimulation and its physiological spreading in the human brain[END_REF] (see Fig. 2, note that P0 was negative because of a differential recording mode) and [START_REF] Yamao | Intraoperative dorsal language network mapping by using single-pulse electrical stimulation[END_REF] (see Fig. 5 with different stimulation parameters) but could not be observed in [START_REF] Mandonnet | Axono-cortical evoked potentials: A proof-of-concept study[END_REF] because of durable stimulation artifacts (see Fig. 4, similar stimulation parameters as for [START_REF] Vincent | Electrophysiological brain mapping: Basics of recording evoked potentials induced by electrical stimulation and its physiological spreading in the human brain[END_REF]). However, the distant summation of action potentials (P0) in ACEP and CCEP could be limited due to the divergence of projection pathways from the stimulation site. Regarding DCR, the summation could be more important due to the activation of all the fibers in the vicinity of DES.

DES can be used to probe the spatiotemporal connectivity and dynamics of short-or long-range networks when combined with electrophysiological recordings. This approach has been used for pre-surgical planning of drugresistant epileptic patients, by using ECoG and a grid implanted at the surface of the grey matter [START_REF] Matsumoto | Functional connectivity in the human language system: a corticocortical evoked potential study[END_REF]. However, the effects of DES at higher frequencies remain unclear. It has been demonstrated that 20 Hz DES induces slow negativities in separated DCRs, which fuse to produce a progressive negative shift in the baseline of the ECoG signal. At the same time as this shift develops, the amplitude of sequential DCRs decreases [START_REF] Goldring | Direct response of human cerebral cortex[END_REF]. It was proposed that certain neural elements could not recover fast enough from DES and saturate because of the summation of DCRs. Hence, higher stimulation frequencies might induce local and progressive hyperpolarisation in the vicinity of the stimulated area, which may perturb its global functioning [START_REF] Vincent | Electrophysiological brain mapping: Basics of recording evoked potentials induced by electrical stimulation and its physiological spreading in the human brain[END_REF]. This might be an explanation for the use of higher frequencies (i.e. 50 -60 Hz) during cortical mapping as the stimulation period (i.e. 16 to 20 ms) is close to the DCR duration (about 15 to 20 ms). Similarly, we noticed a slight decrease in the amplitude of the P0 component over time during 9 Hz DES. However, physiological reasons remain unclear although membrane saturation could also be at the origin of weakened summation of action potentials.

V. CONCLUSION P0 component, may be indicative of the spread of action potentials onto white matter tracts towards remote cortical areas. From a methodological perspective, P0 is of particular interest because it contrasts with N1 whose latency does not concord with the stimulation period when using usual cortical mapping frequencies. However, we did not observe the P0 component for 60 Hz DES condition, suggesting that there is no spread of electrophysiological activity in this particular case. Further manipulations are required in order to clarify whether and how classical uses of 60 Hz DES induce effects in remote cortical areas and decipher the electrophysiological implications of the clinical use of DES [START_REF] Vincent | Electrophysiological brain mapping: Basics of recording evoked potentials induced by electrical stimulation and its physiological spreading in the human brain[END_REF].

TABLE I

 I

		.	DES CONDITIONS
	Freq. Intensity Pulse width	Inter-Electrode Distance
	Condition 1 60 Hz 1.5 mA	1.0 ms	5 mm
	Condition 2 9 Hz	1.5 mA	1.0 ms	5 mm
	Condition 3 9 Hz	1.5 mA	0.5 ms	5 mm
	Condition 4 9 Hz	1.5 mA	0.5 ms	10 mm

*Research supported by the LabEx NUMEV project (n° ANR-10-LABX-20) funded by the French government's "Investissements d'Avenir" program managed by the French National Research Agency (ANR) and complementary grants from the Institut Universitaire de France and INSERM laboratory (U1093).


K Daffé

K Haddadi
email: kamel.haddadi@univ-lille.fr

C Gaquière

Keywords: MOS varactor, measurement accuracy, on-wafer calibration, vector network analyzer (VNA), two-port measurement, coplanar waveguide (CPW)

The objective of this letter oriented towards microwave measurement of high impedance devices using a conventional on-wafer probe station is multiple. First, we provided a quantification of the measurement uncertainty inherent to the set-up when measuring capacitors in the range 0.01-10 fF using both reflection and transmission methods up to 50 GHz. In particular, we demonstrate a clear improvement when using transmission method in series-through configuration. As a practical demonstration, on-wafer MOS voltage-tunable capacitors with capacitances ranging from 0.85 to 1.15 fF are extracted with uncertainties of 130 and 2 aF respectively for both reflection and transmission measurements at 10 GHz. Capacitance fluctuation related to the technological process in the order of 20 aF is then exemplary demonstrated using the series-through configuration.

I. INTRODUCTION

O foster the progress of miniaturization of electronic circuits, new metrological issues related to the electrical characterization of nanoelectronic devices must be addressed [START_REF]The International Technology Roadmap for Semiconductors[END_REF].The microwave characterization of extremely high impedance devices such as Attofarad (aF) capacitors [START_REF] Debroucke | Sub-femtoFarad MOS varactor characterization tools[END_REF]and 1D based devices [START_REF] Happy | Measurement techniques for RF nanoelectronic devices: new equipment to overcome the problems of impedance and scale mismatch[END_REF] is still challenging. In particular, the microwave calibrated measurement of RF voltage-tunable integrated capacitors, i.e. varactors with capacitance values ranging from few fF to sub-fF, is required to address RF tuning optimization within multi-bands wireless devices applications [START_REF] He | A 20-GHz VCO for PLL synthesizer in 0.13-µm BiCMOS[END_REF]- [START_REF] Lee | A 1.2V 37-38.5GHz 8-phase clock generator in 0.13um CMOS technology[END_REF]. Indeed, a slight discrepancy of the capacitance value can impact fatally the operating frequency stability of the targeted applications. Whereas available design kits are built up with HICUM models that consider process variability through material and topographic characterizations, there is an urgent need to assess the traceability and the variability of these models through actual electrical measurements. The critical issue is related to the measurement uncertainty, which degrades with device downscaling and the raise of operating frequency. Near-field microwave microscopy and nano-robotic micro-probing station [START_REF] Haddadi | Robotic on-wafer probe station for microwave characterization in a scanning electron microscope[END_REF]are interesting approaches but they are not suitable for industrial test in the general context of the silicon industry.

In this letter, a conventional device characterization set-up, i.e. a vector network analyzer (VNA) connected to a pair of GSG probes, is proposed in a CPW series-through measurement configuration to tackle the issue of extreme impedance microwave measurement. The Section II provides the theoretical background for capacitance uncertainty estimation using the proposed series-through configuration. In Section III, MOS RF voltage-tunable capacitors with capacitances ranging from 0.85 to 1.15 fF are determined through reflection and transmission coefficient measurements. In particular, measurement errors inherent to the microwave instrumentation, the probe repeatability and the manufacturing process are quantified.

II. CAPACITANCE UNCERTAINTY

The measurement uncertainty estimation starts from the commonly applied two-port error models corresponding to the series-through configurations in which an ideal capacitance C is considered as the device under test (DUT) (Fig. 1.). The quantities and (i = 1, 2) denotes the incoming and emerging traveling waves at the measurement planes respectively. The terms , , , and are the postcalibration residual calibration error terms, namely postcalibration residual directivity, reflection tracking, source match, transmission tracking and load match of the calibrated VNA that relate the difference between the scattering parameters obtained for two different calibrations. The crosstalk leakage term is neglected because of its very small contribution less than 10 $% . The complex values of the postcalibration residual error terms are extracted as the standard deviations in respect to the mean values related to 7 successive vector calibrations, i.e. line-reflect-reflect-match (LRRM). These non-systematic residual errors that include the random (noise, connector repeatability, probe contact

C DUT residual input error box residual output error box a 1 b 1 b 2 S11 S22 S21 1 1+ τ1 µ2 µ1 δ 1+ τ1 S12 a 1 b 1 b 2 DUT i a i b d 1 t 1 µ 2 t
repeatability), the drift and stability effects between measurements are quantified as follow. STEP 2: Flow graphs from Fig. 1 using post-calibration residual error terms are solved to determine the total system magnitude (│∆S11│ │∆S21│) and phase (∆Φ11 and ∆Φ21) uncertainties by the following forms [START_REF] Rytting | Network analyzer accuracy overview[END_REF].

(

(

STEP 3: The admittance terms of the Y-matrix of the DUT can be derived from S-parameters by where ω denotes the angular frequency.

Y '' = 1 2𝑍 + 1 -S '' S '' = 1 2𝑍 + cos𝜙 '' -|S '' | -𝑗sin𝜙 '' |S '' | (5)
The resulting capacitance uncertainties from both case studies are plotted in Fig. 3 at 1, 10 and 50 GHz. Fig. 3 highlights the performance of the two-port seriesthrough configuration in terms of capacitance uncertainty reduction. In the capacitances range considered, the uncertainty is reduced by a factor of nearly 20 when the capacitance is extracted from S21 in regards with the reflection coefficient measurement method. For example, the capacitance uncertainty value for a 1 fF calculated at 10 GHz is 5 aF for Δ𝐶 9' while it reaches the value of 101 aF for Δ𝐶 '' . It has to be mentioned that the degradation of the capacitance uncertainty is mainly caused by the residual directivity error term when considering Δ𝐶 '' . In other words, the two-port series-through configuration benefits from the excellent dynamic range performance of the VNA as the configuration is not offset by the directivity.

III. EXPERIMENTAL VALIDATION

As a demonstration, sub-fF MOS RF voltage-tunable capacitors from STMicroelectronics TM were considered (Fig. 4). The devices were biased from -2.5 to 2.5V to achieve capacitance values ranging from 0.85fF to 1.15fF. The measured S-parameters were mathematically corrected using a LRRM calibration algorithm [Fig. 5(a)]. An open/short deembedding procedure is also used to remove RF pad (YPAD), the access line (ZLINE) and the metal vias (ZVIA) contributions [Fig. 4(c)] [START_REF] Carbonero | On-wafer highfrequency measurement improvements[END_REF]. S11 data show high impedance mismatch (│S11│), i.e. the effective capacitance C11 is mainly related to the phase-shift [equation [START_REF] Rytting | Network analyzer accuracy overview[END_REF]]. S21 data together with relation [START_REF] Daffé | RF wafer probing with improved contact repeatability using nanometer positioning[END_REF] show that measured transmission coefficient │S21│vary with the voltage whereas the phase-shift Φ21 remains nearly constant. At the first order, by neglecting the denominator term of ( 8), the effective capacitance can be determined directly by 𝐶 9' ≈ 𝐼𝑚(𝑆 9' ) 2𝑍 + 𝜔 ⁄ . Indeed, Fig. 5(b) shows the effective capacitances determined using ( 7) and ( 8) together with the approximate capacitance discussed above for V = 2.5V. C11 clearly shows a non-constant frequency behavior. In contrast, C21 indicates a flat response up to 25 GHz. Above 25 GHz, the model using a single capacitance C is no more available (slope of the curve) and the VNA becomes more sensitive to stochastic measurement errors (fluctuations of the signal [START_REF] Daffé | RF wafer probing with improved contact repeatability using nanometer positioning[END_REF]). The measurement uncertainty imputable to the probe contact repeatability ( , ) was highlighted by performing six capacitance-voltage measurements of the same device. The time duration for the six measurements was less than 15 mn [Fig. 6(a)]. For a bias voltage of 2.5V, the corresponding values are = 130 aF and = 2aF. Finally, measurement uncertainty relating to the process variability is investigated through die-to-die measurements on six different wafers location [Fig. 6(b)]. The corresponding errors ( , ) for a biased voltage of 2.5V are respectively 430 and 20aF. From these two experiments, considering C21, the capacitance fluctuation due to the process variability (20aF) is 10 times bigger than the capacitance uncertainty (2aF). Therefore, the measurement can be used to assess the capacitance fluctuation accurately related to the process variability. On the other hand, considering C11, the capacitance uncertainty of 130aF is bigger that the capacitance fluctuation due to the process variability. Therefore, process variability cannot be studied by the reflection method.

IV. CONCLUSION

We have estimated theoretically the measurement accuracy of fF capacitance extracted from reflection and transmission coefficient measurement considering an ideal capacitance connected in series-through configuration. The capacitance measurement error less than 1% is experimentally confirmed in the case of a 1fF varactor embedded in two-port seriesthrough configuration dealing with the transmission coefficient measurement. In contrast, the measurement error is about 8% when the capacitance is extracted from reflection coefficient measurement.

Fig. 1 .

 1 VNA two-port series-through capacitance measurement configuration (a) and associated flow graph (b).

STEP 1 :

 1 An N5225A PNA VNA from ®Keysight is used with frequency step set to 100 MHz (491 points) in the frequency range spanning from 50 MHz to 50 GHz. The RF signal power is set to 0 dBm and an intermediate frequency bandwidth (IFBW) of 100 Hz is used. The positioner is equipped with a 100 µm pitch GSG ®Infinity probe. A microwave cable (2.4mm) from ®Gore with high phase and amplitude stability with flexure is used to connect the probe to the VNA. The Impedance Standard Substrate (ISS) reference is #101-190 from ®Cascade Microtech. The mechanical onwafer station is a MPS150 from ®Cascade. The experimental post-calibration residual error terms are shown in Fig. 2.

Fig. 2 .

 2 Fig. 2.Standard deviations (2σ) of measurement error terms versus frequency.

  |𝑐𝑜𝑠𝜙 9' -1 + j|S 9' |𝑠𝑖𝑛𝜙 9' 1 -2|S 9' |𝑐𝑜𝑠𝜙 9' + |S 9' | 9 (6)

  Fig.3. (a) and (b) Calculated capacitance uncertainties as a function of the capacitance. (c) Impact of the individual residual error terms on the capacitance uncertainty -f = 10 GHz (─ full ; ─ Source match ; ─ Load match ; ─ Transmission tracking).

Fig. 4 .

 4 STMicroelectronics BEOL of the 55 nm SiGe BiCMOS Technology. (b) Micrograph of the varactor. (c) Equivalent electrical circuit model. (a) (b) Fig. 5. (a) Measured S-parameters versus varactor voltage -f = 10GHz. (b) Effective capacitance versus frequency for V = 2.5V.

Fig. 6 .

 6 (a) Measured effective capacitance for (a) six successive measurements and (b) for six successive locations -f = 10 GHz.

5 │S

 5 11 │(dB) │S 21 │(dB) Φ 11 (deg) Φ 21 (deg)

µ On-Wafer Series-Through Broadband Measurement of Sub-fF55nm MOS RF Voltage-Tunable Capacitors K. Daffé, G. Dambrine, Fellow, IEEE, C. Durand, C. Gaquière and K. Haddadi, Member, IEEE T

funded by the National Research Agency (ANR).


Padmajan Suchithra

Wilfrid Sasikala

Philippe Neri

Cyril Poulin

Aymonier

Sasikala

Wilfrid Neri

Philippe Poulin

Cyril Aymonier

An effective in situ reduction strategy assisted by supercritical fluids for the preparation of graphene -polymer composites

    An effective in situ reduction strategy assisted by supercritical fluids for the preparation of graphenepolymer composites

Introduction

Graphene in particular in monolayer state has remarkable properties such as high mechanical strength, elasticity, optical transparency, electrical and thermal conductivity, gas impermeability, and environmental stability [ [START_REF] Bonaccorso | Graphene photonics and optoelectronics[END_REF], [START_REF] Ambrosi | Electrochemistry of graphene and related materials[END_REF], [START_REF] Allen | Honeycomb carbon: a review of graphene[END_REF], [START_REF] Roy-Mayhew | Graphene materials and their use in dye-sensitized solar cells[END_REF], [START_REF] Lee | Graphene-based transparent conductive films[END_REF], [START_REF] Schwierz | Graphene transistors[END_REF]]. Incorporation of graphene into a polymer matrix should allow the utilization of these appealing properties for a wide range of applications such as conductive nanocomposites for organic electronics, flexible electronics, actuators, energy harvesting, sensors, safety systems and micro-electro mechanical systems [ [START_REF] Potts | Graphene-based polymer nanocomposites[END_REF], [START_REF] Sun | Graphene/polymer composites for energy applications[END_REF], [START_REF] Du | The fabrication, properties, and uses of graphene/polymer composites[END_REF], [START_REF] Kuilla | Recent advances in graphene based polymer composites[END_REF]]. In order to achieve these applications, graphene should be homogeneously dispersed throughout the polymer matrix so that an effective interfacial load transfer exists between the polymer and the graphene sheets. However, graphene is difficult to disperse in classical solvents and polymers without the use of surfactants/chemical functionalization. This characteristic of graphene in fact limits its direct use in synthesizing graphene-polymer composites.

Suchithra Padmajan Sasikala, Wilfrid Neri, Philippe Poulin, Cyril Aymonier. An effective in situ reduction strategy assisted by supercritical fluids for the preparation of graphene -polymer composites. Carbon, Elsevier, 2018, 139, pp.572-580. 〈10.1016/j.carbon.2018.06.076〉. 〈hal-01865407〉

A variety of techniques such as in situ polymerization, melt mixing and solution casting with ultrasonication mixing has been reported for the synthesis of graphene-polymer composites, which are however limited by nonuniform and low graphene loading (<1 wt%) [START_REF] Layek | Enhancement of physical, mechanical, and gas barrier properties in noncovalently functionalized graphene oxide/poly(vinylidene fluoride) composites[END_REF]. Another straight forward approach is to use graphene oxide (GO) instead of graphene to synthesize graphene-polymer composites. The abundant oxygenated functional groups in GO provide excellent dispersion and processing ability with polar solvents and hydrophilic polymers. Therefore, it is very easy to make homogenous GO-polymer composites in desired forms such as powder/film/fiber with hydrophilic polymers. The GO should be reduced either ex situ or in situ in the polymer composite to be able to make use of the superior electrical properties of graphene, without which GO is limited to a mechanically stabilizing passive component for the polymers [ [START_REF] Cui | Liquid-phase exfoliation, functionalization and applications of graphene[END_REF], [START_REF] Stankovich | Graphene-based composite materials[END_REF], [START_REF] Stankovich | Synthesis of graphene-based nanosheets via chemical reduction of exfoliated graphite oxide[END_REF]]. Similar to graphene, rGO also is poorly processable to form homogenous polymer composites and hence ex situ reduction of GO to rGO, followed by composite formation with polymer is not efficient. In this scenario, in situ reduction of GO in GOpolymer composite would be much more convenient and practical. Nevertheless in this case, the maximal reduction temperature is generally limited to the temperature that the polymer matrix can sustain without being degraded [START_REF] Elsagh | Enhanced electrical conductivity properties of Graphene Oxide nanocomposites functionalized with Polyvinyl Alcohol[END_REF]. This is again a strong limitation because a significant level of reduction of GO can be achieved only at high temperatures. As a consequence, the electronic properties of low temperature reduced composite films are not satisfactory. Another method is to utilize chemical reducing agents in a GO-polymer latex solution to reduce GO and swell the structure [START_REF] Yang | Highly electrically conductive rGO/PVA composites with a network dispersive nanostructure[END_REF]. Composite formation and in situ chemical reduction of GO can be also achieved through coagulation process [START_REF] Liu | High mechanical performance of layered graphene oxide/poly (vinyl alcohol) nanocomposite films[END_REF]. In all existing chemical approaches that are found to be effective in reducing GO, the systems have to be washed to remove reducing components and reaction byproducts, making chemical approaches more tedious and time consuming.

Here, we demonstrate a facile and efficient strategy that overcomes all the above limitations in the synthesis of rGO-polymer composite films. We developed an in situ reduction method for GO in polymer nanocomposite film using supercritical CO2+ethanol binary system (Fig. 1). This method provides an efficient reduction way while keeping the temperature well below the degradation temperature of the polymer and thus avoiding to affect the structure of the composite film. The method is scalable and environmentally friendly and the as obtained freestanding rGO-polymer film/fiber show excellent electronic conductivity and mechanical stability.

Experimental Section

Preparation of GO-Polymer film

Graphene Oxide (GO) was purchased from Graphenea (Spain) as a suspension with a concentration of 4 mg/ml in water. Polyvinyl alcohol (PVA) with molecular weight of 195 K (98%) and Polyethylene glycol (PEG) with molecular weight of 20K were purchased from Sigma Aldrich. We have prepared and used aqueous PVA/PEG solutions of concentration 40 mg/ml during overall process. A series of GO-polymer composites with desired weight percentages (ranging from 0.5 to 20 wt% of GO) were prepared by mixing definite weights of GO and PVA/PEG aqueous suspensions. The mixture was subjected to mild ultrasonication for 30 min and then slowly but consistently stirred for at least 5 h to get a homogenous dispersion. The as prepared GO-PVA composite suspension was then poured into a teflon petri dish and allowed to dry at 50 °C for 48 h. The dried composite was then peeled off from the petri dish to get GO-polymer film.

Preparation of GO-PVA fiber

A syringe pump was used to inject (at a constant rate set at 6 mL/h) the desired concentration of GO-PVA solution into a coagulation bath (320 g/L sodium sulfate saturated solution) maintained at 40 °C. At the outlet of the syringe needle, the GO-PVA solution coagulated instantly to form a solid filament. The fibers were then allowed to flow through a washing bath for removing the salt residues present in the fiber after the coagulation process. As PVA is soluble in water, the washing bath cannot be composed only by water; otherwise, the wet fiber will stretch too much and end up by breaking. The addition of sodium tetraborate at 1 wt% in the washing bath allowed overcoming this problem. The fiber was then dried with the help of two infrared lamps, at a temperature of 75 °C, and finally collected on a winder rotating disk.

In situ reduction of GO-polymer film/fiber

The in situ reduction experiments were carried out in high temperature and high pressure reactors; a schematic of the reduction set-up is shown in Fig. S1. The reactor was purged with N2 for 1 h to remove the air trapped in the system, before all experiments unless otherwise stated. For the nearcritical ethanol reduction experiment, the dried GO-PVA films were transferred to the reactor containing 30 ml of ethanol. The reactor was tightly closed and heated to a temperature of 150 °C and a pressure of 200 bar for desired time. In the case of in situ reduction experiments with scCO2+ethanol binary system, the GO-polymer film/fiber were firstly immersed in ethanol for 10-20 min, and the wet samples with a maximum of 1 ml ethanol were transferred to the high temperature and high-pressure reactor of 50 ml capacity. Then CO2 was filled in the reactor up to a pressure of 40-60 bar and heated up to the desired temperature from 100-150 °C. The pressure of the reactor is increased with the temperature. At this point, the pressure in the reactor was maintained at 200-250 bar by adjusting a side valve.

The reaction was allowed to progress for 1-3 h. After a given time, reaction was terminated by removing the heating zone and gradually submerging the hot reactor into the ice-cold water bath. The outlet valve of the reactor was opened to flush out the gas when the reactor temperature reached below 50 °C. For comparison GO-polymer films were reduced as described earlier with only scCO2 and also thermally reduced in a conventional tube furnace in both inert and ambient conditions.

Results and Discussion

Because of the numerous hydrophilic functional groups on its surface, GO is very compatible with hydrophilic polymers like PVA. Thermogravimetric analysis (TGA) were conducted for GO, PVA, and GO-PVA in order to investigate the decomposition temperature of polymer (Fig. 2a). GO due to the abundant oxygen functionalities and trapped water molecules showed significant weight loss of 40.0% between 100 and 250 °C. PVA showed a weight loss of 8.0% between 100 and 240 °C, attributed to the loss of absorbed water and a drastic weight loss >240 °C indicating the decomposition of the polymer. This is in accordance with the previous reports of chemical degradation of PVA resulting from carbon-carbon bond scission in the polymeric backbone above 250 °C [START_REF] Guirguis | Thermal and structural studies of poly (vinyl alcohol) and hydroxypropyl cellulose blends[END_REF][START_REF] Taghizadeh | The investigation of thermal decomposition pathway and products of poly (vinyl alcohol) by TG-FTIR[END_REF]. Further, we performed an isothermal TGA of the samples at 180 °C for a maximum time of 6 h. As shown in Fig. 2b, while GO and GO-PVA showed a weight loss of 17.4 and 9.1%, respectively, PVA showed a small weight loss of 4.0% when the reaction progressed up to 6 h. Thus, we fixed the reduction Supercritical ethanol is validated earlier for its proton donating and subsequent dehydration reaction with GO [START_REF] Seo | Supercritical alcohols as solvents and reducing agents for the synthesis of reduced graphene oxide[END_REF][START_REF] Sasikala | High yield synthesis of aspect ratio controlled graphenic materials from anthracite coal in supercritical fluids[END_REF]. However since the critical temperature of ethanol (Tc: 241 °C and Pc: 62.7 bar) is above the temperature limit of decomposition of PVA, we have employed the nearcritical conditions for ethanol (T: 150 °C and P: 200 bar). The nearcritical ethanol reduction of GO-PVA solution have resulted in reduction of GO. Nevertheless, concurrent agglomeration and separating out of reduced GO (rGO) from the PVA matrix also occurred. In order to tackle this problem, we employed an alternative strategy in which GO-PVA films are made by simple solution casting of GO-polymer composite solutions as a first stage followed by the in situ reduction of GO in the dried composite films. Information about size and homogeneity of the films can be acquired from the scanning electron microscopy (SEM) images. The average thickness of films ranged from 30 to 50 μm. A morphology comparison of PVA film and GO-PVA film is given in Fig. 2c-f. As expected, GO-PVA films are found to be electrically insulating due to the oxidized defects of GO and the intrinsic insulating nature of the polymers. In order to restore graphene -polymer composites. Carbon, Elsevier, 2018, 139, pp.572-580. 〈10.1016/j.carbon.2018.06.076〉. 〈hal-01865407〉 the electrical conductivity of GO in the polymer composite films, we immersed the films in ethanol in a closed high-pressure reactor and increased the temperature and pressure of the reactor to 150 °C and 200 bar, respectively. The analysis of the film after this nearcritical ethanol (ncEtOH) treatment for 2 h, showed favorable reduction of GO, but the homogeneity of the films had been lost considerably due to swelling in the ethanol (Fig. 2g andh). Thus we modified our experimental protocol such that the films are only allowed to wet in ethanol for a short span of time which is then subjected to supercritical CO2 (scCO2, Tc: 31 °C Pc: 73.8 bar) treatment in the high pressure reactor at 150 °C and 200 bar (Please see the details in Experimental Section). Since the ethanol is soluble in scCO2, and also the diffusive power of scCO2 is very high, we can anticipate that scCO2 helps ethanol on the surface to diffuse into the entire volume of film and reduce GO to restore the graphene crystal lattice without decomposing the polymer [START_REF] Sasikala | Prospects of supercritical fluids in realizing graphene-based functional materials[END_REF][START_REF] Sasikala | Advances in subcritical hydro-/solvothermal processing of graphene materials[END_REF]. Gong et al. have validated the reduction mechanism of ethanol for GO under thermal conditions, with the help of in situ infrared absorption spectroscopy, ab initio molecular dynamics calculations and density functional theory [START_REF] Gong | Graphitization of graphene oxide with ethanol during thermal reduction[END_REF]. According to authors, thermal annealing (as low as 100 °C) causes the formation of bare etch holes in the GO crystal lattice. Ethanol in the interlayers of GO integrates into these etch holes and reacts with neighboring oxygenated groups such as carbonyls or ethers to reopen the hexagonal carbon ring for further carbon incorporation. Thus, ethanol not only removes the oxygenated groups but also fosters the graphitization. This kind of observation of scavenging of holes in GO crystal lattice by ethanol is also seen under laser irradiation [START_REF] Moussa | Laser assisted photocatalytic reduction of metal ions by graphene oxide[END_REF]. As shown in Fig. 2i andj, the homogeneity of GO-PVA films were well maintained after the supercritical reduction. Fig. 3a shows the XRD patterns of GO, rGO, PVA and GO/PVA nanocomposite films before and after supercritical reduction (rGO-PVA). A diffraction peak in the XRD spectrum at 10.4° (0.85 nm) is typical in the case of GO which represents oxygen containing functional groups in the interlayers of stacked GO sheets in the GO film. After reduction treatment, many oxygen containing groups will be removed from GO and as a result the interlayer distance decreases significantly as observed in the spectrum of rGO that the diffraction peak is shifted to 23.6°(0.37 nm) [START_REF] Gu | The electrocapacitive properties of hierarchical porous reduced graphene oxide templated by hydrophobic CaCO3 spheres[END_REF]. However this typical diffraction peak of GO/rGO is absent in the polymer composite (GO-PVA) film which showed the diffraction peak of pure PVA at 19.4°.This can be regarded as a sign of an individual and homogenous integration of monolayer GO sheets into the polymer matrix, so that the periodic structure of stacked graphene oxide is lost [ [START_REF] Ghavaminejad | Network formation in graphene oxide composites with surface grafted PNIPAM chains in aqueous solution characterized by rheological experiments[END_REF], [START_REF] Shi | In situ reduction of graphene oxide nanosheets in poly(vinyl alcohol) hydrogel by γ-ray irradiation and its influence on mechanical and tribological properties[END_REF], [START_REF] Kim | Transparent and high gas barrier films based on poly (vinyl alcohol)/graphene oxide composites[END_REF], [START_REF] Li | Interfacial stress transfer in graphene oxide nanocomposites[END_REF]]. After the supercritical reduction of composite film, the characteristic PVA diffraction peak broadened. Fig. S2 shows the XRD spectra of neat PVA films before and after supercritical reduction. The characteristic diffraction peak at 19.4° is sharper after the supercritical treatment.

This peak sharpening can be regarded as an increased crystallization [START_REF] Zhao | Enhanced mechanical properties of graphene-based poly (vinyl alcohol) composites[END_REF]. The absence of such increased crystallinity in presence of rGO suggests that the rGO impart steric barrier for PVA crystal growth [START_REF] Yang | Highly electrically conductive rGO/PVA composites with a network dispersive nanostructure[END_REF][START_REF] Assender | WindleCrystallinity in poly (vinyl alcohol). 1. An X-ray diffraction study of atactic PVOH[END_REF]. In the IR spectrum of GO (Fig. 3b), the broad peak centered around 3364 cm -1 and broadened up to 3600 cm -1 indicates the simultaneous presence of free hydroxyl groups and hydrogen bonded -O-H stretch. On the contrary, this peak is sharpened in the IR spectra of PVA indicative of strong hydrogen bonding interaction between PVA molecules. The intensity of sharp peak around 3300 cm -1 is found to decrease in GO-PVA compared to that of PVA. This can be attributed to the dissociation of hydrogen bonding in hydroxyl group of PVA and hydrogen bond formation between hydroxyl groups of GO and PVA chain [START_REF] Shi | In situ reduction of graphene oxide nanosheets in poly(vinyl alcohol) hydrogel by γ-ray irradiation and its influence on mechanical and tribological properties[END_REF]. After supercritical reduction of GO-PVA film (rGO-PVA), we can observe a reduction of the intensity in this peak, indicative of removal of hydroxyl functionalities from the composite. In addition, the band around 1100 cm -1 which can be assigned to the -C-OH stretching displayed a similar behavior, indicating that even though the hydroxyl functionalities are reduced in the GO-PVA composite, still an extent of hydrogen bonded hydroxyl group exists in the film.

The extent of reduction of GO in the composite is further evaluated by Raman spectroscopy. For comparison purposes, the Raman spectra of PVA and GO are also shown in Fig. 3c a characteristic band at 2909 cm -1 , which can also be found in GO-PVA and rGO-PVA composite films. In GO and GO-PVA characteristic D band (1337 cm -1 ) and G band (1588 cm -1 ) can be shown (Fig. 3c). The ratio of intensity of the D to G band (ID/IG) is used to measure the degree of disorder, and number and average size of the sp 2 domains in graphene materials. The ID/IG ratios for GO and GO-PVA were found to be 1.2 ± 1.0. It is to be noted that the basal plane of GO is heavily defected with epoxide groups and hydroxyl groups. Many carboxyl groups are also present in the edge sites [START_REF] Dikin | Preparation and characterization of graphene oxide paper[END_REF]. After the reduction treatment many epoxide/hydroxyl/carboxyl groups were removed leading to the recovery of distorted six-fold aromatic ring, and carbon lattice returns to graphitic state resulting in the activation of D peak. Depending on the extent of defect sites, number and size of recovered sp 2 domains the ID/IG ratio can increase or decrease [START_REF] Stankovich | Synthesis of graphene-based nanosheets via chemical reduction of exfoliated graphite oxide[END_REF]. After the supercritical reduction, ID/IG value decreased to 0.95 ± 0.1 which can be accounted as the formation of new graphitic sp 2 domains. Notably, in the spectrum of rGO-PVA, the D, G and 2D peaks shifted to lower wave numbers of 1321, 1581 and 2626 cm -1 , respectively (Fig. 3c andd). This indicates the recovered hexagonal network of carbon atoms and confirms the successful reduction of GO to rGO.

We have also conducted XPS analysis of GO films without polymer after supercritical reduction maintaining the same experimental conditions as in the case of GO-PVA films in order to have an insight on the extent of deoxygenation by the supercritical reduction (Fig. S3). As shown, after supercritical reduction C/O ratio increased from 1.89 (GO) to 5.94 (rGO) indicating significant deoxygenation of GO by the reduction conditions employed.

Mechanical Test of rGO-PVA films

H-bonding helps in the interfacial adhesion between GO and polymers and offers effective load transfer which in turn enhances the mechanical properties of the composite [START_REF] Liang | Molecular-level dispersion of graphene into poly(vinyl alcohol) and effective reinforcement of their nanocomposites[END_REF]. The mechanical performance of composite films is assessed and compared with pure PVA film in order to analyze the mechanical stability (Table S1). Fig. 4a represents the stress-strain relationship for nanocomposite films for a range of GO/rGO weight fractions. The mechanical strength of the GO-PVA and rGO-PVA films is found to be significantly increased as that of PVA film. Both tensile stress and elongation at break had increased for GO-PVA and rGO-PVA compared to PVA. In the case of GO-PVA films, there has been a maximum of 34% increase in the tensile strength as compared to pure PVA film with only 1 wt% GO in the composite film. The tensile strength has been found to increase further Suchithra Padmajan Sasikala, Wilfrid Neri, Philippe Poulin, Cyril Aymonier. An effective in situ reduction strategy assisted by supercritical fluids for the preparation of graphene -polymer composites. Carbon, Elsevier, 2018, 139, pp.572-580. 〈10.1016/j.carbon.2018.06.076〉. 〈hal-01865407〉 up to a maximum of 48.4% when the loading of GO increased to 3 wt%. The corresponding elongation at break has increased to 38.9% compared to pure PVA. However further increase of GO up to 5 wt% found to decrease the elongation at break compared to GO-PVA containing 3 wt% GO. The increase in strain % was limited to 7.7% for GO (5 wt%)-PVA compared to PVA. Nevertheless, the tensile strength of GO (5 wt%)-PVA has increased by 53.3% compared to PVA. Notably, when the concentration of GO has increased up to 10 wt%, the mechanical performance of the composite significantly decreased with respect to pure PVA film. The elongation at break has decreased from 5.6% of PVA to 1.7% for GO (10 wt%)-PVA. The reinforcement at low concentration is presumably due to strong adhesion of the GO particles with polymer through H-bonding. However, when the concentration of GO is increased, neighboring sheets interact and may effectively act as aggregates which may lead to inhomogeneous stress distribution in the composite. This inhomogeneity makes the composite more brittle.

Notably, the tensile strength of neat PVA film range from 17 MPa to 100 MPa in the literature [ [START_REF] Liang | Molecular-level dispersion of graphene into poly(vinyl alcohol) and effective reinforcement of their nanocomposites[END_REF], [START_REF] Zhao | Enhanced mechanical properties of graphene-based poly (vinyl alcohol) composites[END_REF], [START_REF] Xu | Strong and ductile poly (vinyl alcohol)/graphene oxide composite films with a layered structure[END_REF], [START_REF] Bao | Poly(vinyl alcohol) nanocomposites based on graphene and graphite oxide: a comparative investigation of property and mechanism[END_REF], [START_REF] Cheng | Poly (vinyl alcohol) nanocomposites filled with poly (vinyl alcohol)-grafted graphene oxide[END_REF], [START_REF] Yang | Synthesis and characterization of layer-aligned poly (vinyl alcohol)/graphene nanocomposites[END_REF], [START_REF] Morimune | Uniaxial drawing of poly (vinyl alcohol)/graphene oxide nanocomposites[END_REF]] and the measured mechanical properties of our GO-PVA composites are somewhat lower than better values reported in the literature. Nevertheless, the degree of improvement of mechanical properties of PVA films after incorporation of GO is comparable to other reports [ [START_REF] Xu | Strong and ductile poly (vinyl alcohol)/graphene oxide composite films with a layered structure[END_REF], [START_REF] Bao | Poly(vinyl alcohol) nanocomposites based on graphene and graphite oxide: a comparative investigation of property and mechanism[END_REF], [START_REF] Cheng | Poly (vinyl alcohol) nanocomposites filled with poly (vinyl alcohol)-grafted graphene oxide[END_REF], [START_REF] Yang | Synthesis and characterization of layer-aligned poly (vinyl alcohol)/graphene nanocomposites[END_REF], [START_REF] Morimune | Uniaxial drawing of poly (vinyl alcohol)/graphene oxide nanocomposites[END_REF]]. These variations can be understood considering that mechanical properties depend on many variables such as processing conditions, type (molecular weight in the case of polymer, aspect ratio in the case of graphene oxide), concentration (of polymer and graphene oxide) and source of materials (purity, manufacture).

Interestingly, the tensile strength of the composite film was enhanced after supercritical reduction treatment by 59.7 and 82.2% for 1 and 3 wt% rGO, respectively, compared to the corresponding GO-PVA. This can be related to the increased PVA crystallinity after the reduction process which may increase the reinforcement effect of rGO with the PVA matrix. It can also be due to the increase of Young's modulus of the sheets after reduction. However, it can be noticed that at higher GO concentration (10 wt%) the tensile strength of rGO-PVA film is very poor.

The materials become brittle again because of the large concentration of reinforcing particles. Fig. 4(b) represents the relative enhancement of Young's modulus of the composites. The modulus has increased linearly with increase in GO/rGO wt% in the composite. The tensile modulus of the pure PVA is 0.9 GPa which has increased by 78% and 244% for the composite containing 10 wt% GO and rGO, respectively. It is normal that a comparatively stronger inorganic material such as GO and rGO, when added to a soft organic polymer like PVA will enhance the Young's modulus value of the resulting composites. It is also expected that rGO display a better reinforcement because of its greater stiffness compared to GO.

Electrical Conductivity Test

Suchithra Padmajan Sasikala, Wilfrid Neri, Philippe Poulin, Cyril Aymonier. An effective in situ reduction strategy assisted by supercritical fluids for the preparation of graphene -polymer composites. Carbon, Elsevier, 2018, 139, pp.572-580. 〈10.1016/j.carbon.2018.06.076〉. 〈hal-01865407〉

While graphene is a good conductor of electricity (10 8 S/m), GO is electrically insulating. Since PVA is also electrically insulating (5.3 × 10 -12 S/m), the GO-PVA composite is electrically insulating as well. Thorough reduction of GO in the composite to rGO should make the resulting composite electrically conductive. In this study, we tested different reduction methods such as thermal reduction under N2, nearcritical ethanol (ncEtOH), supercritical CO2 (scCO2), and scCO2 + ethanol binary system reduction treatments to regain the electrical conductivity of GO-PVA film and their respective electrical conductivity values are shown in Fig. 4c. Notably, all above listed reduction methods have changed the colour of the film from brown to black, which can be accounted as partial restoration of the π-conjugation network within the rGO sheets by removing many hydroxyl/carboxyl functionalities originally present in GO. However, in order to achieve significant improvement of electrical conductivity, π-conjugation should be restored by removing most of the epoxide groups as well. As shown, the scCO2+ ethanol binary system reduction method gives the best electrical conductivity values among the tested methods. It has been found that the GO-PVA films became well-conductive after being reduced (rGO-PVA) for a minimum time of 30 min, and the electrical conductivity value has increased with increasing reduction time (Fig. 4d). Nevertheless, increasing the reduction time beyond 2 h is found to demerit the mechanical stability of the rGO-PVA film. The films became brittle presumably due to the increased crystallinity. The electrical conductivity of the rGO-PVA film was found to increase with increasing initial GO weight% in the composite also (Fig. 4e). A photographic illustration is provided in Fig. 4f to demonstrate the recovered electrical conductivity of rGO-PVA film after supercritical reduction, which used as a conductive element in the circuit with 9V battery to light a green light emitting diode (LED). The conductivity of the rGO-PVA film increased from 0.01 to 51.7 S/m as the rGO content increases from 0.5 wt% to 10 wt%. The sharp rise of electrical conductivity as a function of GO weight% indicates a percolation type behavior with a percolation threshold between 1 and 2 wt%, corresponding to a volume fraction typically between 0.5 and 1 vol%, assuming a density of 1.8 g/cm 3 [START_REF] Dikin | Preparation and characterization of graphene oxide paper[END_REF][START_REF] Zamora-Ledezma | Liquid crystallinity and dimensions of surfactant-stabilized sheets of reduced graphene oxide[END_REF]. We note that this percolation threshold is much higher than the threshold expected for randomly oriented platelets of large aspect ratio. The percolation threshold should be of the order of t/D where "t" and "D" are the thickness and diameter of the GO flakes, respectively. Here, this threshold would be theoretically less than 0.1 vol% considering the giant anisotropy of GO materials. The greater value of percolation threshold presently observed suggests that the flakes are oriented, as a result of the tendency of GO particles to form liquid crystal phases [START_REF] Yuan | Graphene liquid crystal retarded percolation for new high-k materials[END_REF][START_REF] Mathew | Connectivity percolation in suspensions of hard platelets[END_REF].

Further we successfully tested the supercritical fluid assisted reduction method to produce rGO-PEG films, which, similarly to rGO-PVA films, showed increased electrical conductivity values with increase in rGO content in the composite (Fig. 5a-c). The rGO-PEG films which contain 10 wt% of GO showed an electrical conductivity value of 15.1 S/m, which has increased to 24.9 S/m when GO loading increased to 20 wt%. Raman spectrum of rGO- PEG film is compared with GO-PEG film in Fig. S4, which showed considerable decrease in ID/IG value after supercritical reduction similar to rGO-PVA film. In addition, this method is found to effectively reduce in-situ GO in rGO-PVA fibers also (Fig. 5d-f). Note that, a direct comparison of effectiveness of a particular reduction method is difficult in graphene-polymer nanocomposites since various factors were found to influence the percolation threshold and electrical conductivity of resulting composite such as graphene loading, aspect ratio of graphene sheets, functionalization and aggregation of graphene, type of polymer, processing methods, wrinkles (in the case of film/fiber morphology) and homogeneity of the composite. Nevertheless, we compare in Table 1, the electrical conductivity and mechanical property of GO-PVA composites prepared by supercritical fluid assisted reduction method with other reported reduction methods in order to establish the effectiveness of this method for preparing conductive graphene-polymer composite with favorable mechanical properties. The reason for such enhanced properties can be accounted for the supercritical fluid assisted reduction method that we employed. Due to intrinsically high diffusive nature, scCO2 can impregnate ethanol into the whole volume of the composite film which result in much effective reduction of the GO and at the same time the homogeneity of the composite film is also preserved. Consequently, high electrical conductivity can be achieved without sacrificing mechanical properties of the composites. This work

Conclusion

The graphene-polymer composite fiber/films can be fabricated using an environmentally friendly supercritical fluids assisted reduction method. The GO-PVA/PEG films/fiber are easily processable due to the hydrophilic nature of GO. The challenging task of reduction of GO in the composite film without degrading polymer can be achieved using a combination of CO2 and ethanol at 150 °C and 200 bar. Significant enhancement of the mechanical properties and electrical conductivity was obtained at very low loading of GO. While the electrically conducting graphene network in the polymer matrix is the key reason for the increased electrical conductivity after supercritical reduction, high loading of graphene was found to decrease the mechanical property of composite film. The demonstrated in situ supercritical fluid reduction strategy is very effective in low temperature reduction of GO in the polymer matrix without the cost of mechanical properties and yet industrially scalable and for this reason expected to find potential applications in graphene-polymer nanocomposite field.

Figure 1 .

 1 Figure 1. Schematic representation of synthesis of rGO-polymer composite via supercritical fluid assisted reduction of graphene oxide-polymer film/fiber.

Figure 2

 2 Figure 2 (a) TGA of GO, PVA and GO-PVA composite with different loading of GO. (b) Isothermal TGA at 180 °C of GO, PVA and GO-PVA.SEM surface and cross-sectional image of (c,d) PVA, (e,f) GO-PVA, and rGO-PVA composite films obtained by (g,h)nearcritical ethanol and (i,j) scCO2 + ethanol binary system treatment.

Figure 3 (

 3 Figure 3(a). XRD of GO, PVA, GO-PVA, rGO-PVA and rGO (b) IR spectra of GO, PVA, GO-PVA and rGO-PVA (c) Raman spectra of GO, PVA, GO-PVA and rGO-PVA films, (d) Magnified 2D peak of GO, GO-PVA and rGO-PVA.

Figure 4

 4 Figure 4 (a) Representative stress-strain curves as a function of GO/rGO loading and (b) Increase in Young's modulus of the composites with GO weight%. Inset of (b) is a photograph of rGO (3wt%)-PVA film demonstrating the mechanical flexibility of the film. (c) Electrical conductivity of rGO-PVA film containing 10 wt% rGO after different reduction methods at 150 °C for 1h, (d,e) Increase of electrical conductivity of rGO-PVA film containing 10 wt% rGO after supercritical reduction using scCO2+ethanol binary system at 150 °C with increasing (d) reduction time and (e) rGO loading, (f) Photograph of rGO-PVA film used as a conductive element in the circuit to light a green LED.

Figure 5 .

 5 Figure 5. (a) Surface and (b) lateral SEM image of rGO-PEG film, (c) Increase of electrical conductivity of rGO-PEG film after supercritical reduction using scCO2 and ncEtOH at 150 °C with increasing rGO loading, (d,e) Cross sectional SEM image of rGO-PVA fiber (f) photograph of rGO-PVA fiber used as a conductive wire in an electrical circuit to light an LED.

Suchithra

  Padmajan Sasikala, Wilfrid Neri, Philippe Poulin, Cyril Aymonier. An effective in situ reduction strategy assisted by supercritical fluids for the preparation of graphene -polymer composites. Carbon, Elsevier, 2018, 139, pp.572-580. 〈10.1016/j.carbon.2018.06.076〉. 〈hal-01865407〉

  Suchithra Padmajan Sasikala, Wilfrid Neri, Philippe Poulin, Cyril Aymonier. An effective in situ reduction strategy assisted by supercritical fluids for the preparation of graphene -polymer composites. Carbon, Elsevier, 2018, 139, pp.572-580. 〈10.1016/j.carbon.2018.06.076〉. 〈hal-01865407〉

  . The Raman spectrum of PVA displayed

Suchithra Padmajan Sasikala, Wilfrid Neri, Philippe Poulin, Cyril Aymonier. An effective in situ reduction strategy assisted by supercritical fluids for the preparation of graphene -polymer composites. Carbon, Elsevier, 2018, 139, pp.572-580. 〈10.1016/j.carbon.2018.06.076〉. 〈hal-01865407〉

  Suchithra Padmajan Sasikala, Wilfrid Neri, Philippe Poulin, Cyril Aymonier. An effective in situ reduction strategy assisted by supercritical fluids for the preparation of graphene -polymer composites. Carbon, Elsevier, 2018, 139, pp.572-580. 〈10.1016/j.carbon.2018.06.076〉. 〈hal-01865407〉

Table 1 .

 1 Comparison of electrical conductivity of rGO-PVA films prepared through different reduction methods

	Type of	Synthesis method	Weight% of	Reduction method	Electrical	Ref
	Composite		GO (wt%)		conductivity
					(S/m)
	GO/PVA	Solution mixing	4	Thermal reduction,	0.063	[15]
		followed by vaccum		60 •C, over night
		filtration
	Graphene/copo	Solution casting	5	------------------	10 -4	[39]
	lymer/PVA	followed by hot
		pressing at 200 •C
	GO/PVA	Solution casting	14	Na2S2O4/NaOH,	5.92	[16]
				60•C, 2h
	GO/PVA	Solution casting	1.6	hydrazine	10 -7	[32]
				hydrate

Suchithra Padmajan Sasikala, Wilfrid Neri, Philippe Poulin, Cyril Aymonier. An effective in situ reduction strategy assisted by supercritical fluids for the preparation of graphene -polymer composites. Carbon, Elsevier, 2018, 139, pp.572-580. 〈10.1016/j.carbon.2018.06.076〉. 〈hal-01865407〉

Acknowledgments

SPS is thankful to University of Bordeaux and the IdEx postdoctoral fellowship programme. This work has received financial support from the French State in the frame of the "Investments for the future" Programme IdEx Bordeaux, reference ANR-10-IDEX-03-02". The authors declare no competing financial interest.