Mazen Al-Jallad

Yomen Atassi
email: yomen.atassi@hiast.edu.sy

Eskandar Mounif

Matthieu Aressy

Abbas Tcharkhtchi

Oxidative solution polymerization of aniline hydrochloride onto electrospun nanofibers mats of polylactic acid: Preparation method and characterization

Keywords: composites, conducting polymers, electrospinning, nanostructured polymers, sensors and actuators

In this work, we present the preparation of polylactic acid (PLLA)/polyaniline (PANI) conductive composite nanofibers mats. They are prepared by bulk oxidative solution polymerization of PANI onto electrospun non-woven fibers mats of PLLA. The PANI ratio in the composite is about 70%w/w. Scanning electron microscopy (SEM) shows that PLLA nanofibers are randomly oriented, beads free with diameters of 186 6 85 nm, The PLLA/PANI composite nanofibers diameter values are 518 6 128 nm with a good adherence between PANI and PLLA nanofibers. DSC and XRD measurements reveal an amorphous structure of the electrospun PLLA fibers due to the rapid evaporization of the solvent. FTIR and UV-vis spectra reflect good mutual interactions between PANI and PLLA chains. The DC-conductivities (r50:0720:13 S:cm 21 ) far better than other published ones for similar composites prepared by bulk oxidative solution polymerization of PANI onto other electrospun nanofiber mats or with electrospun nanofibers from a solution mixture of PLLA and PANI.

INTRODUCTION

In recent years, conducting polymers have received important attention because of their potential applications in chemical and biological sensors, electronic devices, batteries, supercapacitors, and solar cells. . ., due to their remarkable physical and electrical properties such as low operating temperature, low cost, flexibility, and moderate processibility. [START_REF] Skotheim | Handbook of Conducting Polymers[END_REF][START_REF] Lange | [END_REF][3][4][5] Polyaniline (PANI) is one of the most studied electrically conductive polymers and it was an attractive choice for researchers to develop many techniques to produce PANI nanostructures especially nanofibers. [6][7][8][9] PANI is relatively more difficult to process compared to other polymers as it has a fairly rigid backbone due to the high aromaticity and as there are very few good solvents to dissolve it, so the elasticity of its solutions is generally insufficient to be electrospun directly into nanofibers. 10 To overcome this obstacle many approaches have been proposed to prepare PANI nanofibers, such as seeding polymerization, [11][12][13] interfacial polymerisation, [14][15][16] electrospinning PANI blends with more flexible, high molecular weight polymers that serve as processing aids, 6,10,17,18 and coating PANI onto a non-conducting nanofiber substrates using bulk oxidative solution polymerization process. [19][20][21][22] On the other hand, polylactic acid (PLLA) is biodegradable and biocompatible. It presents good thermoplastic processability. Because of its biocompatibility, it's used as scaffolds for tissue engineering and a substrate for implant devices. Recently, it has been used for the preparation of conducting nanofibers in combination with PANI for sensors and tissue engineering applications by electrospinning a mixture of the two polymers solutions. 23,[START_REF] Patra | IOP Conference Series[END_REF] In this study, we present the preparation of PLLA/PANI composite nanofibers mats by bulk oxidative solution polymerization of aniline hydrochloride onto electrospun PLLA nanofibers mats. To the best of our knowledge, this is the first preparation of PLLA/PANI composite nanofibers mats by this method. This work is a new approach to realize a good intercalation of PANI molecules with the PLLA nanofibers to form composite mats with promising electrical conductivities to be used in chemical sensors or as scaffolds for tissue engineering.

EXPERIMENTAL

Reagents and Chemicals

PLLA (M w 5 150,000 g/mol) from NatureWorks was kindly offered by ENSAM/PIMM laboratory (Paris-France). Anilinium chloride monomer, tetra n-butyl ammonium bromide (TBAB), ammonium peroxydisulfate [(NH 4 ) 2 S 2 O 8 , APS], dichloromethane, hydrochloric acid and acetone, all of analytical reagent grade, were purchased from Merck. Chemicals were used as received without further purifications.

Electrospining of PLLA

Electrospinning solution of PLLA with concentration of 6 wt % was prepared by dissolving PLLA granules in dichloromethane under magnetic stirring for 5 h, 1 wt % of TBAB was added as an electrolyte to enhance the conductivity of the electrospun solution. The electrical conductivity of spinable PLLA solution was 2 lS cm 21 without TBAB and 380 lS cm 21 with 1 wt % TBAB at 24 C. Polymer solution was added to 10 mL glass syringe with hypodermic needle used as nozzle. The inner and outer diameter of the needle is 0.6 and 0.8 mm, respectively. The flow of the polymer solution was controlled using a programmable syringe pump (TOP-5300, Japan). The high-voltage power supply was an ES813-D50.1 Dual output: 0 to 6 50 kV/1 mA Electrostatic/HV Generator (Rolla, USA). The collector was a sheet of aluminum (0.4 3 25 3 40 cm) covered with an aluminum foil.

The solution feed rate was kept at 1 mL h 21 and the distance between the collector and the needle tip was maintained at 13 cm.

As the electric field increased beyond 20 kV, the surface tension of the polymer solution was overcome by the electric force and the Taylor cone was initiated. A stable jet began to form a white nanofibers adhered smoothly to the aluminum foil collector. The voltage was kept in the range 20-22 kV during the experiments. The experimental temperature inside the electrospinning chamber was 22 6 2 C, and the relative humidity was maintained between 40 and 50% to have a good evaporation of the solvent. The duration of each electrospinning process was 1 h. The as-spun fibers were left on the aluminum foil inside the electrospinning chamber for at least 24 h at the room temperature and at about 45% relative humidity to complete the volatilization of dichloromethane. Then they were peeled off from the aluminum foil for further experiments.

Preparation of PLLA/PANI Composite Nanofiber Mats

The PLLA nanofibers mat had a circular shape with a diameter of about 15 cm and a thickness of approximately 0.1 mm. PLLA/ PANI composite nanofiber mat was produced using the oxidative solution polymerization process. Typically (1.295 g, 10 mmol) of aniline hydrochloride was dissolved in 25 mL of deionized water with ultrasonication aid. Ammonium peroxydisulfate (APS) (2.855 g, 12.5 mmol) was dissolved in 25 mL of deionized water using magnetic stirring. Both solutions were kept for 1 h at room temperature (20-24 C). PLLA nanofibers mat was then immersed into the aniline hydrochloride solution under the ultrasonic stirring for 30 min. When the PLLA nanofibers mat is saturated with aniline solution, the APS solution is then added dropwise to the above mixture always under ultrasonic stirring for another 30 min. The polymerization reaction begins as the first drop of APS solution is added, and the aniline monomer is oxidized with APS and doped with hydrochloride acid. The mixture was left for 5 h to insure that most of aniline monomers had been consumed and the polymerization reaction was almost finished. Next, the film was washed repeatedly with deionized water and acetone until the acetone washings were colorless, then washed three times with 50 mL of 0.2M HCl, and similarly with acetone. Finally, the nanofiber mats were dried in a desiccator at 40 C and stored in a closed vessel in the dark.

Characterization

PLLA and PLLA/PANI Composite Nanofiber Mats Morphology. The nanofibers morphology was analyzed using Tescan Vega-II XMU5136 variable pressure scanning electron microscopy (SEM).

The nanofiber mats thickness was measured using a digital micrometer (Mitutoyo CLM1).

X-ray Diffraction (XRD) Measurements. XRD patterns were performed with PHILIPS-PW3710X-RAY diffractometer operating at 60 kV using Cu-K a radiation (k5 0.154 nm). X-ray diffractograms were recorded in the 2h range: 5 -60 .

Differential Scanning Calorimetry (DSC). DSC analyses were carried out with a computerized SETARAM-INSTRUMENTATION TGA-DSC. Samples were heated to 200 C at a ramping rate of 10 C/min in nitrogen atmosphere. Crystallinity of the PLLA fiber films was investigated according to following equation: 25 Crystallinityð%Þ5

DH m 2DH cc DH 0 m 3C (1)
where DH m and DH 0 m are the endothermic enthalpy of the samples and that of 100% crystallized PLLA (DH 0 m 593 J=mol respectively. 25 DH cc is the enthalpy of cold crystallization. C is the PLLA mass percentage (m%) in the tested sample. FTIR Spectroscopy. FTIR spectra were recorded by BRUKER-VECTOR22 FTIR spectrophotometer. Samples of PLLA nanofiber mats and PLLA/PANI composite nanofiber mats were fixed on the support directly in the path of the optical beam. PANI powder was mixed with KBr and pressed in pellets. All spectra were corrected for the presence of moisture and carbon dioxide in the optical pathway.

UV-Vis Spectroscopy. UV-Vis spectra were recorded by JASCO V-350 UV-vis spectrophotometer in a wavelength range of 300-1100 nm. Samples of PLLA nanofiber mats and PLLA/PANI composite nanofiber mats were held perpendicularly to the path of the beam. PANI powder was dissolved in dimethylformamide (DMF) in a quartz cellule. All spectra were corrected for the presence of moisture and carbon dioxide.

DC-Electrical Conductivity. DC-conductivity (r) was performed by four-probe technique using KEITHELY-220 programmable Current Source and KEITHELY-617 programmable electrometer. PLLA/PANI composite nanofiber mats were tested using four-probe homemade device consisting of four parallel platinum wires of 0.4-mm diameter positioned 2 mm away from each other. The contact length for each probe was 2.3 cm as shown in Figure 1. r was calculated using Van der Pauw relation r5 d t3w I V , where d is the distance between the electrodes (cm), t and w are the sample's thickness and width respectively (cm).

RESULTS AND DISCUSSION

Morphology of the Composite Nanofiber Mats

The peeled nanofiber mats of PLLA have a smooth and homogeneous surface as shown in Figure 2(a) with circular shape of about 15 cm diameter and about 0.1-mm thickness with good mechanical toughness and high flexibility.

SEM micrographs [Figure 3(a-d)] show that PLLA nanofibers are smooth and hollow, as they are very transparent with very thin nanofibers walls. PLLA fibers have a statistical distribution of diameters with values of 186 6 85 nm and they are beads free.

The surface of nanofiber mats becomes rough with less elasticity. The mat diameter shrunk to about 10 cm and the thickness increased to about 0.2 mm. The dark green color of the composite fiber mat indicated that PANI is in its emeraldine conductive form as shown in Figure 2(b).

SEM micrographs [Figure 3(e,f)] revealed that PANI polymer shields homogeneously the PLLA nanofiber with some aggregations of PANI adhered to the composite fiber surface. SEM micrographs [Figure 3(g,h)] of the cross section of PLLA/PANI composite nanofiber mat show that all the hollow PLLA nanofibers were shielded with PANI. This indicates that the anilinium chloride monomer was very well penetrated inside the mat before the beginning of the polymerization process by virtue of ultrasound stirring and indicate also the good distribution of the APS oxidant (dropwise added) under ultrasound stirring. So, this allowed to the polymerization process to proceed homogeneously in all parts of the mat. The diameter values of PLLA/PANI nanofibers are also statistical with values of 518 6 128 nm.

DSC Characterization

DSC was employed to characterize thermal properties of PLLA nanofiber mats and PLLA/PANI composite nanofiber mats. For all composite fiber mats prepared in this work, the PANI content was about 70%w/w.

From Figure 4(a), the glass transition ðT g Þ temperature was found at 53.8 C followed by a distinctive endothermic aging peak at about 62.4 C. A cold crystallization exothermic peak ðT cc Þ was observed at 90 C and a sharp melting peak ðT m Þ at 167 C. 6,26,27 Integrating the two peaks ðT cc Þ and ðT m Þ of PLLA nanofiber mat showed that they have the same absolute values (DH m DH cc 546 J=mol) which means that the melting phenomena that follows the cold crystallization concerned only the PLLA crystal phase developed during the heating scan. This indicates that the electrospun PLLA nanofibers were completely amorphous as it's predicted elsewhere by Gualandi et al. 28 As for PLLA/PANI composite nanofiber mat DSC curve, it showed [Figure 4(b)] a small shift in temperatures values mentioned above, where T g was found at 55.5 C followed by aging peak at 76.7 C. T cc was mounted up to 104 C and T m was shifted to 168.5 C. The aging peak of PANI was not observed in this spectrum because it is out of the heating range (250-260 C). 29 One can attribute these shifts in temperatures positions to the mutual interactions between PLLA and PANI chains which create intermolecular bonds like Van der Waals bonds and hydrogen bonds between these molecules.

FTIR Spectra

From Figure 5(a) it can be seen the eight main characteristic peaks of PLLA which were located at 3495, 2970, 2882, 1755, 1456, 1365, 1196, 1103 cm 21 . These peaks were assigned as follows: the weak peak at 3495 cm 21 is assigned to OAH stretching vibration. The bands located at 2970 cm 21 and 1456 cm 21 were assigned to CAH stretching vibration and ACH(CH3) bend vibration. The characteristic peak of ACH 3 bending was located at 1365 cm 21 . The weak shoulder at 2882 cm 21 was assigned to ACH 2 stretching vibration. The peak at 1755 cm 21 was assigned to C@O stretching vibration and the two peaks at 1196 and 1103 cm 21 were attributed to CAO stretching vibration. 25,30,31 For PANI powder FT-IR spectrum, there are seven characteristic peaks situated at 3230, 1566, 1478, 1300, 1240, 1135, 804 cm 21 [Figure 5(b)]. The weak and broad band at 3230 cm 21 is assigned to the free N-H stretching vibration of secondary amines.

The peak at 1566 cm 21 corresponds to the C@C stretching of quinonoid rings, while the peak at 1478 cm 21 is assigned to C@C stretching of benzenoid rings. The peaks at 1300 cm 21 and 1240 cm 21 are assigned to CAN and CAN 1 stretching vibration respectively. The strong peak centered at 1135 cm 21 is assigned to the vibration mode of N 1 @C. The peak at 804 cm 21 is characterized to the aromatic CAH out-of-plane bending vibration. [32][33][34][35] Figure 5(c) shows the FT-IR spectrum of PLLA/PANI composite nanofiber mat. It combines the main characteristic peaks of PLLA and PANI. There is a slight deviation in peaks positions with a red shift which reveals the mutual interaction between PLLA and PANI chains in the composite nanofiber and reflects the existence of intermolecular bonds between the PLLA and PANI chains.

XRD Measurements

Figure 6(a) shows no peaks for PLLA nanofibers over all the scanning range with an expressive amorphous halo around 10 , referring to their completely amorphous structure as most of PLLA electrospun nanofibers. 28,36,37 This XRD result is in accordance with the results obtained from DSC measurements which proves that there is no crystalline phase in these fibers. During the electrospinning process the solvent evaporizes quickly and since PLLA crystallizes slowly compared to other conventional thermoplastic polymers, 38 polymer chains don't have enough time to be arranged in a crystalline structure, so PLLA crystallization is inhibited.

Two broad peaks appear in PANI powder spectrum [Figure 6(b)], centered at 2h 5 20 and 25 ascribed respectively to periodicity parallel and periodicity perpendicular to the polymer chain, showing that the resulting PANI is amorphous. 21,[39][40][41] X-ray diffractogram of PLLA/PANI composite nanofiber [Figure 6(c)] is almost identical to PANI spectrum but with weak peaks intensities. One can deduce that the presence of PLLA nanofiber scaffold during the oxidative solution polymerization of PANI didn't affect the dominant tendency to form an amorphous structure for this polymer. From Figure 7(b), one can see three characteristic bands for PANI at 310, 458, and 618 nm, the first and the third bands can be attributed to the p-p* transition of the benzenoid ring and exciton absorption of the quinonoid rings, respectively. The band at 458 nm can be assigned to polarn transition. 40,[44][45][46] The UV-vis spectrum of PLLA/PANI composite nanofiber mat [Figure 7(c)] shows the three absorbance bands of PANI at 310, 420!465, 632 nm with a slight shift, and additional broad band at 900 nm indicating that PANI is in its conducting state. 8

UV-Vis Spectroscopy

DC-Conductivity

For DC conductivity (r), 30 measurements were carried out for each of the 12 PLLA/PANI composite nanofiber mats prepared as mentioned above with 15 measurements on each side. r values were in the range of 0:0720:13 S: cm 21 with good homogeneity in r values for each film. We can attribute the difference in r values between different composite films to the accumulation of small process deviations committed during the preparation of each composite film from solutions preparation until the final product.

Comparing r values of these composite films with those reported for compressed pellets of PANI powder prepared with the same polymerization conditions, we find bigger r values in the range 4-6 S cm 21 . 47 We can attribute this difference to the high porosity of the non-woven mats and to the random orientation of the fibers in the composite mat which implicates a random movement of the charge carrier between electrodes. The electrical conductivity could also be affected by the morphology of pconjugation polymers from respect of density of electrons and arrangement of PANI molecular chains in the composite mat. 48 Comparing our r values with that of other composite nanofiber films produced by oxidative solution polymerization like poly(vinylchloride-acrylonitrile)/PANI composite nanofibers mats where r52:2310 28 S cm 21 , 20 and PMMA/PANI composite nanofiber mats where r 10 26 S: cm 21 , 19 we find that our r values are many orders of magnitude bigger. We may attribute our high r values to the effectiveness of ultrasound stirring, used by us but not by the previous works, that allowed very good penetration of the monomer and the oxidant into the mat, so the PANI has completely shielded all the nanofibers of PLLA. In fact the SEM micrographs confirmed this assumption. To the best of our knowledge, the only bigger value than ours reported in the literature was for the composite nylon-6/PANI, 22 and it was r51:5 S cm 21 . It's one order of magnitude bigger than ours.

By comparing also our r values with the conductivity of electrospun nanofibers of PLLA blends with PANI where their conductivities are in the range 10 26 ! 10 29 S cm 21 , 17,30,49 we can deduce that mats produced by oxidative solution polymerization of PANI onto PLLA nanofibers have higher conductivity than mats resulting from electrospinning of PLLA and PANI blends.

CONCLUSION

Conductive PLLA/PANI composite nanofiber mats were successfully prepared by bulk oxidative solution polymerization method of PANI onto PLLA nanofibers produced by electro-spinning of 6% w/w PLLA in dichloromethane solution with the presence of 1% w/w TBAB as an electrolyte. PLLA nanofibers were beads free with good shielding of PLLA nanofibers by PANI and with a good electrical conductivity. The PANI produced in this less harmful method is the standard emeraldine, without the need to distillate the monomer and with no need to further doping of the resulting polymer as the starting monomer is the powder of aniline hydrochloride.

Figure 1 .Figure 2 .

 12 Figure 1. Photo of four-probe homemade device. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 3 .

 3 Figure 3. SEM micrographs of: PLLA nanofiber mat (a) without coating, (b-d) with graphite coating, (e, f) PLLA/PANI composite nanofiber mat and (g, h) cross section of PLLA/PANI composite nanofiber mat after immersing it in liquid nitrogen (SEM micrographs of composite are without coating).

Figure 7 (

 7 a) presents the UV-vis spectrum of PLLA. No characteristic bands appear in this spectrum with slight decrease in absorption intensity. PLLA fibers can be considered almost transparent in the wavelength region of 300-1000 nm.42,43

Figure 4 .Figure 5 .

 45 Figure 4. DSC analysis of (a) PLLA nanofiber mat and (b) PLLA/PANI composite nanofiber mat. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 6 .Figure 7 .

 67 Figure 6. X-ray diffractograms of (a) PLLA nanofiber mat, (b) PANI powder and (c) PLLA/PANI composite nanofiber mat. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]


Charles Kervrann

François Philippe Roudot

Francois Waharte

APPROXIMATE BAYESIAN COMPUTATION, STOCHASTIC ALGORITHMS AND NON-LOCAL MEANS FOR COMPLEX NOISE MODELS

Keywords: Denoising, Approximate Bayesian Computation, density learning, NL-means, fluorescence imaging

published or not. The documents may come     Approximate Bayesian Computation, stochastic algorithms and non-local means for complex noise models

INTRODUCTION

A digital imaging system consists of an optical system followed by a photodetector and associated electrical filters. The photodetector converts the incident optical intensity (i.e photons) to electrons. During the process, the true signals are damaged by many different sources of noise. For instance, in optical microscopy imaging, signals are known to be corrupted by intensity dependent Poisson noise but also by additional sources of electron noise [START_REF] Boulanger | Patch-based non-local functional for denoising fluorescence microscopy image sequences[END_REF][START_REF] Roudot | Noise modeling for intensified camera in fluorescence imaging: application to image denoising[END_REF]. More generally, we have to deal with images corrupted with heterogeneous mixed noises, which requires to adapt the usual denoising approaches including the non local(NL)-means algorithm [START_REF] Buades | A review of image denoising methods, with a new one[END_REF].

In the case of images damaged by additive white Gaussian noise, the NL-means [START_REF] Buades | A review of image denoising methods, with a new one[END_REF] has been shown to be efficient to reduce additive noise. This method exploits image redundancy captured by patches to restore information. In order to optimally perform in the case of Poisson noise, the NL-means has been combined with variance stabilizing transforms such as Anscombe [START_REF] Boulanger | Patch-based non-local functional for denoising fluorescence microscopy image sequences[END_REF] and Fisz transform [START_REF] Decker | Variance stabilizing transformations in patch-based bilateral filters for poisson noise image denoising[END_REF]. Other authors proposed to combine Principal Component Analysis [START_REF] Salmon | Poisson noise reduction with non-local PCA[END_REF] and dictionary [START_REF] Giryes | Sparsity based poisson denoising[END_REF] to patch-based representation to reduce Poisson noise. In [START_REF] Deledalle | Poisson NL-means: Unsupervised non local means for poisson noise[END_REF], the authors proposed an extension of the NLmeans based on probabilistic similarities to compare noisy patches and pre-estimated patches; this framework has been used to denoise SAR images [START_REF] Deledalle | Iterative weighted maximum likelihood denoising with probabilistic patch-based weights[END_REF] and is appropriate for general parametric noise models [START_REF] Deledalle | How to compare noisy patches? patch similarity beyond Gaussian noise[END_REF].

In this paper, a new Bayesian motivation for the NLmeans is given for generalized non-parametric noise models. Our approach inspired from the Approximate Bayesian Computation (ABC) framework [START_REF] Beaumont | Approximate Bayesian computation in population genetics[END_REF][START_REF] Marjoram | Markov chain Monte Carlo without likelihoods[END_REF], is especially adapted to complex situations where the posterior cannot be easily derived or computed. Furthermore, we exploit empirical noise statistics and propose a distance learning framework to adapt to different conditions. This is particularly relevant for images contaminated by heterogeneous sources of noise [START_REF] Boulanger | Patch-based non-local functional for denoising fluorescence microscopy image sequences[END_REF][START_REF] Roudot | Noise modeling for intensified camera in fluorescence imaging: application to image denoising[END_REF]. A major difference with previous methods [START_REF] Deledalle | Iterative weighted maximum likelihood denoising with probabilistic patch-based weights[END_REF][START_REF] Deledalle | Poisson NL-means: Unsupervised non local means for poisson noise[END_REF] is that we directly handle the structure of the noise, without precise parametric modeling of the noise.

The organization of the paper is as follows: in Section 2, we describe the NL-means in the Bayesian framework [START_REF] Louchet | Variational and Bayesian models for image denoising : from total variation towards non-local means[END_REF]. In Section 3 we describe the ABC method which serves to compute the data-driven posterior distribution. In Section 4 we demonstrate the flexibility of our stochastic Gamma NLmeans (SGNL-means) by showing how it can be adapted to tackle the noise in frequency domain fluorescence lifetime imaging microscopy (FD-FLIM) and cryo-electron tomography. We illustrate the potential of our approach on two examples of ultra-sound and SAR imaging.

BAYESIAN INTERPRETATION OF NL-MEANS

Consider a gray-scale image v = (v(x)) x∈Ω defined over a bounded domain Ω ⊂ R 2 and v(x) ∈ R + is the noisy observed intensity at pixel x ∈ Ω. Assume that the image v is a noisy version of an unknown image u,

that is v = u+noise. Define a √ n× √ n observed patch S v (x) at pixel x as: S v (x)(t) △ = v(x + t), ∀t ∈ [- √ n-1 2 , • • • , √ n-1 2 ] 2 .
The NL-means at pixel x is a weighted average of all gray values in the entire image. Formally, we have [START_REF] Buades | A review of image denoising methods, with a new one[END_REF]:

u NL (x) = 1 Z(x) y∈Ω exp - S v (x) -S v (y) 2 2 h 2 v(y) (1)
and Z(x) is a normalizing factor. The weights express the amount of similarity ( • 2 denotes the Euclidean distance)

between the n-dimensional image patches S v (x) and S v (y) of each pair of pixels x and y involved in the computation.

For the sake of simplicity, we omitted in (1) the choice of a weighted Euclidean norm over the patches as described in [START_REF] Buades | A review of image denoising methods, with a new one[END_REF]. The decay parameter h 2 ≈ 10σ 2 acts as a filtering parameter and σ 2 denotes the variance of the noise assumed to be Gaussian. The range of the search space can be as large as the whole image but, in practice, it is necessary to restrict the computation of weights to 21 × 21 pixel neighborhoods.

In the line of work of [START_REF] Buades | A review of image denoising methods, with a new one[END_REF][START_REF] Kervrann | Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal[END_REF], we describe a more recent interpretation of NL-means in the Bayesian setting [START_REF] Louchet | Variational and Bayesian models for image denoising : from total variation towards non-local means[END_REF]. Define a prior on patches z ∈ R n from the noisy image v. A simple histogram is given by p

(z) = 1 |Ω| y∈Ω 1[z = S v (y)]
where 1[•] denotes the indicator function. The Bayesian estimate S u (x) of a patch S u (x) with L 2 -risk and prior p on patches is given by the posterior expectation

S u (x) = E p [S U (x)|S v (x)], i.e. S u (x) = posterior p(z|S v (x)) z dz = prior p(z) likelihood p(S v (x)|z) z dz.
In the case of zero-mean white Gaussian noise (variance σ 2 ),

S u (x) = 1 Z(x) p(z)e -Sv (x)-z 2 2 2σ 2 z dz. (2)
Given p(z) as defined above and switching the sums, we get

S u (x) = 1 Z ′ (x) z∈R n 1[z = S v (y)] e -Sv (x)-z 2 2 2σ 2 z dz. (3)
For a given y, a patch z yielding a non-zero term can only be z = S v (y). Finally, by selecting the central pixel [START_REF] Salmon | Patch reprojections for Non-Local methods[END_REF], we get u NL (x) (see ( 1)). NL-means is therefore a posterior expectation and the prior model is based on the empirical histogram of patches taken in the input noisy image. In the next section, we consider more general likelihood models and priors.

APPROXIMATE BAYESIAN COMPUTATION NL-MEANS FILTERING

Principles of ABC rejection method

One of the basic problem in Bayesian statistics is the computation of the posterior for general forms of noise distributions.

If the posterior density cannot be computed explicitly or is time consuming, we usually resort to stochastic simulation to generate samples for the posterior. The commonly-used approach is the rejection method but, more recently, Beaumont et al. [START_REF] Beaumont | Approximate Bayesian computation in population genetics[END_REF] described a generalization of the usual rejection method in the domain of genetics. Formally, assume data D generated from a model determined by λ whose prior is denoted p(λ). The so-called ABC method is as follows [START_REF] Beaumont | Approximate Bayesian computation in population genetics[END_REF][START_REF] Marjoram | Markov chain Monte Carlo without likelihoods[END_REF] As δ → ∞, accepted observations come from the prior. When δ → 0, this rejection algorithm is exact and accepted observations are independent and identically distributed from the posterior distribution p(λ|D). Nevertheless, most samples are rejected if we set δ = 0. Then, this approach requires the setting of δ and the selection of a metric ρ(•, •) (e.g. L 2 distance). The next step is to calculate expectations of the form E(λ|D) = p(λ|D) λ dλ where the expectation is taken with respect to the posterior distribution of λ. The simplest way to approach this is to draw samples {λ i } i=1,••• ,N , from p(λ|D) using the previous algorithm and then approximate using the sum N -1 λ i . However, a more stable estimate can be obtained by weighting the λ values with the posterior. Consequently, all values of λ are included in the the sum and there is no rejection step. This is a direct extension of the estimate given in Beaumont et al. [START_REF] Marjoram | Markov chain Monte Carlo without likelihoods[END_REF] which used Epanechnikov kernels to weight each value of λ.

Patch-based ABC method

The interpretation of ABC given above allows us to revisit previous analyzes of the NL-means in the Bayesian setting. The objective is to restore the pixel x given an observed patch S v (x). Denote λ the unknown scalar intensity value at a given pixel whose prior p(λ) is assumed to be uniform in the range [0, • • • , λ M ] where λ M is the maximum intensity value. Consider the ABC procedure following the previous guidelines in the case of zero-mean white Gaussian noise:

1. Generate λ ∼ U [0, • • • , λ M ];
2. Find a pixel y in the entire image such that y = arg min y ′ ∈Ω |v(y ′ ) -λ| (not unique) and select the patch S v (y) whose center is y; 3. Calculate the error ǫ(x, y) = Sv(y)-Sv(x) 2 2 2σ 2 between the "simulated" patch S v (y) and the "observed" patch S v (x) at pixel x, compute π(ǫ(x, y)) and return to 1. Here π(•) denotes the unknown probability density function of the error term. Instead of uniformly drawing independent samples in the n-dimensional space, Step 2 is expected to generate more plausible "artificial data" in the sense of ABC, "closer" to the observed data. Note that Step 2 amounts to uniformly drawing a patch in the entire image domain.

Data-driven density learning

In the Gaussian case and non-overlapping patches, the errors are not centered at 0 but are expected to follow a chi-square distribution χ 2 n with n degrees of freedom. Yet, for overlapping patches, it is established that the error is the sum of three independent χ 2 n variables: ǫ(x, y) = z 1 + 2z In the case of variable and multiple overlappings in 2D, a general form for the distribution of the error cannot be easily obtained (e.g. see [START_REF] Wu | Probabilistic non-local means[END_REF]). Nevertheless, it is established in [START_REF] Feiveson | The distribution and properties of a weighted sum of chi squares[END_REF] that the sum of weighted chi-squares variables can be approximated by a Gamma distribution controlled essentially by two parameters k and β. Consequently, we have experimentally investigated this idea of approximating the empirical density π(•) of errors by fitting Gamma distributions using the moment method, yielding the following algorithm.

Stochastic Gamma NL-means (SGNL-means)

The proposed ABC-based Gamma NL-means is based on the following stochastic two-step procedure (one iteration):

Step 1: Data-driven density learning 1. Draw uniformly with replacement |B r ||Ω| pairs of patches (S v (x), S v (y)) in the noisy image v such as xy 2 ≤ r and B r is a ball of radius r > 0. Compute the empirical density π(•) of errors ǫ(x, y) = S v (y) -S v (x) 2 2 /(2σ 2 ); 2. Estimate the Gamma distribution parameters k and β by fitting the empirical mode = (k -1)β and variance = kβ 2 of the density.

Step 2: ABC-based denoising

u SGNL (x; k, β) = 1 C(x) y∼Ur (x) (ǫ(x, y)) k-1 e - ǫ(x,y) β v(y) (4)
where the set of N variables y ∼ U r (x) in the sum are uniformly drawn from a ball B r of radius r (same value as in Step 1) centered at pixel x and C(x) is normalization constant.

In the implementation, we adopted a blockwise approach with patch overlapping [START_REF] Buades | A review of image denoising methods, with a new one[END_REF][START_REF] Kervrann | Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal[END_REF][START_REF] Coupé | Nonlocal means-based speckle filtering for ultrasound images[END_REF]. Due to the overlap of patches, the restored value at a pixel x is finally obtained by uniform averaging the different estimators available at that position. Finally, we denote u SGNL = D SGNL v the "filtered" image using the proposed SGNL-means.

Bias reduction and noise adaptation

Instead of repeating applications of the SGNL-means to reduce noise progressively, it is possible to get better denoising results by exploiting the residual image vu SGNL , as first suggested in [START_REF] Tukey | Exploratory Data Analysis[END_REF]. The so-called "twicing" approach has been recently described in [START_REF] Milanfar | A tour of modern image filtering: New insights and methods, both practical and theoretical[END_REF][START_REF] Cornillon | Iterative bias reduction: a comparative study[END_REF] and is known to improve the estimator bias. Formally, define the bias of the estimator as:

Bias[u SGNL ] = E[u SGNL ] -u = -E[v -u SGNL ] (5) ≈ -D SGNL (v -u SGNL ).
Given this approximation of the bias, we correct u SGNL (using the same estimated parameters k and β) as [START_REF] Milanfar | A tour of modern image filtering: New insights and methods, both practical and theoretical[END_REF][START_REF] Cornillon | Iterative bias reduction: a comparative study[END_REF]:

ũSGNL = u SGNL + D SGNL (v -u SGNL ) (6)
Reducing the bias is done at the cost of increasing the variance but the second iteration better preserves structural details. Additional iterations do not improve the results.

In the statistical framework, we have assumed that images are corrupted by white Gaussian noise. An approach to potentially adapt the SGNL-means is to substitute a dedicated noise variance model to σ 2 in (4), for instance as explained in [START_REF] Roudot | Noise modeling for intensified camera in fluorescence imaging: application to image denoising[END_REF] in FD-FLIM imaging. Such a noise variance model can be derived in closed-form for other image modalities [START_REF] Kervrann | Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal[END_REF][START_REF] Coupé | Nonlocal means-based speckle filtering for ultrasound images[END_REF]. . Middle: ultra-sound 2D image (liver) from a 3D volume (see [START_REF] Coupé | Nonlocal means-based speckle filtering for ultrasound images[END_REF] for details). Right: SAR Lelystadt image (Netherlands) c ESA (see [START_REF] Deledalle | Iterative weighted maximum likelihood denoising with probabilistic patch-based weights[END_REF]).

EXPERIMENTAL RESULTS

All our results use the two following control parameters: n = 7 × 7 and r = 7. We considered N = |B r | draws to compute ( 4) and the SGNL-means provided better results with 2 iterations (twicing). As illustrated in Figs. 1-2 for several image modalities, the parameters k and β are robustly estimated given a large set of distances computed from pairs of noisy patches. We automatically discard too large distances and we select the most homogeneous patches in the input image by using global and local noise variances estimated as in [START_REF] Kervrann | An adaptive window approach for image smoothing and structures preserving[END_REF]. The computational time of the SGNL-means (including twicing) is of about 80s on a 512 × 512 image and C++ implementation on an Intel Core i7 64-bit CPU 2.4GHz. First, on images corrupted artificially by white Gaussian noise, SGNL-means produced better results1 than NL-means (IPOL / www.ipol.im). Performances of SGNL-means are especially demonstrated on real images in confocal imaging combined with frequency domain fluorescence lifetime imaging (FD-FLIM) (see Fig. 1). In [START_REF] Boddeke | Quantitative fluorescence microscopy[END_REF], it is established that the ICCD response v(x) is of the following form: v(x) = g INT (x)g CCD ℵ(x)+ξ(x) where ℵ(x) is the incident photon number assumed to follow a Poisson distribution, ξ is the CCD read-out Gaussian noise such as ξ ∼ N (m ξ , σ 2 ξ ), g CCD is the constant gain of the CCD sensor and g INT (x) is the spatially varying gain of the intensifier assumed to be random. Noise variance σ 2 (x) is spatially varying [START_REF] Roudot | Noise modeling for intensified camera in fluorescence imaging: application to image denoising[END_REF] but the likelihood function cannot be explicitly derived. Consequently, we have resort to stochastic simulation to generate samples from the posterior distribution. The denoising results on four subsequent images with temporally varying signal-to-noise ratios are de-picted in Fig. 1 (left bottom). Assuming a mixed Poisson-Gaussian noise, we compared the performance of the ND-SAFIR algorithm [START_REF] Boulanger | Patch-based non-local functional for denoising fluorescence microscopy image sequences[END_REF] and BM3D [START_REF] Dabov | Image denoising by sparse 3-D transform-domain collaborative filtering[END_REF] combined with variance stabilization [START_REF] Makitalo | Optimal inversion of the generalized Anscombe transformation for Poisson-Gaussian noise[END_REF] to adaptive variance SGNL-means. BM3D has not a significant impact on the resulting image and ND-SAFIR tends to create piecewise constant areas contrary to SGNL-means combined to adaptive noise variance [START_REF] Roudot | Noise modeling for intensified camera in fluorescence imaging: application to image denoising[END_REF].

In the second experiment, we addressed the problem of denoising in cryo-electron microscopy as already investigated in [START_REF] Darbon | Fast nonlocal filtering applied to electron cryomicroscopy[END_REF][START_REF] Wei | An optimized locally adaptive non-local means denoising filter for cryo-electron microscopy data[END_REF]. Specimen are known to be very sensitive to electron radiation involving the spreading out of the electron dose on the whole tilt series, causing noise in the background. A closed-form for the likelihood function cannot be easily derived, and we have applied SGNL-means to improve signalto-noise ratio on 2D images from a 3D stack (see Fig. 2 left). Finally we tested the algorithm on images damaged by multiplicative noise in ultra-sound (Fig. 2 middle) and SAR (Fig. 2 right) imaging. The procedure preserves sharp discontinuities and details while reducing noise with fewer processing artifact. In these experiments, we considered the noise variance to be constant. Results can be improved by considering more dedicated signal-dependent noise variance models [START_REF] Coupé | Nonlocal means-based speckle filtering for ultrasound images[END_REF][START_REF] Deledalle | Iterative weighted maximum likelihood denoising with probabilistic patch-based weights[END_REF].

CONCLUSION

An extension of the NL means has been proposed for images damaged by different sources of noises. It is based on similarity metric learning to compare noisy patches. A Bayesian estimator for NL means, based on the idea of ABC, has been proposed. With the ABC framework, it is also possible to capture information using a number of marginal statistics [START_REF] Kervrann | Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal[END_REF][START_REF] Coupé | Nonlocal means-based speckle filtering for ultrasound images[END_REF].Finally, visual results support the efficiency of the proposed method. More satisfying results will be obtained if a noise variance model is specialized in each study case.

: 1 .

 1 Generate λ from p(•); 2. Simulate D ′ from the model with parameter λ; 3. Calculate a distance ρ(D, D ′ ) between D ′ and D, accept λ if ρ(D, D ′ ) ≤ δ, and return to 1.

Fig. 1 .

 1 Fig. 1. Experiments in FD-FLIM microscopy. Left: FNAR1 tagged with Green Fluoresence Protein (GFP) observed in a epithelial cell with mCHerry-tagged Tyk2 (confocal microscopy with spinning disk set-up, UMR 144 CNRS Institut Curie, Paris, France); Gamma distribution fitting and SGNL-means denoising on four subsequent images with temporally varying signal-to-noise ratios. Right: views of denoised images with state-of-the-art methods and comparisons.

Fig. 2 .

 2 Fig.2. Gamma distribution fitting, denoising of images with SGNL-means and residual images (v -ũSGNL ). Left: Xenopus Microtubule Associated proteins and taxoal stablized microtubule interaction in cryo-electron tomography (Technai 200KV LaB 6 , Ultrascan 1000 Gatan CCD Camera, IGDR UMR6290, Rennes, France). Middle: ultra-sound 2D image (liver) from a 3D volume (see[START_REF] Coupé | Nonlocal means-based speckle filtering for ultrasound images[END_REF] for details). Right: SAR Lelystadt image (Netherlands) c ESA (see[START_REF] Deledalle | Iterative weighted maximum likelihood denoising with probabilistic patch-based weights[END_REF]).

e.g. Lena image (σ noise =

20): 32.56 (SGNL) vs 31.52 (NL-means); Barbara image (σ noise = 20): 31.05 (SGNL) vs 30.21 (NL-means)


Olaf Wolkenhauer
email: olaf.wolkenhauer@uni-rostock.de

Charles Auffray

Olivier Brass

Jean Clairambault

Andreas Deutsch

Dirk Drasdo

Francesco Gervasio

Luigi Preziosi

Philip Maini

Anna Marciniak-Czochra

Enabling multiscale modeling in systems medicine: From reactions in cells to organ physiology

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

COMMENT

Enabling multiscale modeling in systems medicine

Olaf Wolkenhauer 1,2* , Charles Auffray 3 , Olivier Brass 4 , Jean Clairambault 5,6,7 , Andreas Deutsch 8 , Dirk Drasdo 6,7,9 , Francesco Gervasio 10 , Luigi Preziosi 11 , Philip Maini 12 , Anna Marciniak-Czochra 13 , Christina Kossow 1 , Lars Kuepfer 14,15 , Katja Rateitschak 1 , Ignacio Ramis-Conde 16 , Benjamin Ribba 17 , Andreas Schuppert 18,19 , Rod Smallwood 20 , Georgios Stamatakos 21 , Felix Winter [START_REF]Coordinating Action Systems Medicine[END_REF]22 and Helen Byrne 23 From reactions in cells to organ physiology Systems medicine is an interdisciplinary approach that integrates data from basic research and clinical practice to improve our understanding and treatment of diseases. Systems medicine can be seen as a further development of systems biology and bioinformatics towards applications of clinical relevance. The term 'systems' refers to systems approaches, emphasizing a close integration of data generation with mathematical modeling [1-3]. The (mal)functioning of the human body is a complex process, characterized by multiple interactions between systems that act across multiple levels of structural and functional organization -from molecular reactions to cell-cell interactions in tissues to the physiology of organs and organ systems. Over the past decade, we have gained detailed insights into the structure and function of molecular, cellular and organ-level systems, with technologies playing an important role in the generation of data at these different scales.

Under the umbrella of systems biology, workflows of data-driven modeling and model-driven experimentation have led to the development of computational models that describe processes at all levels, including gene regulatory networks, signal transduction pathways and metabolic networks, cell populations, structured tissues, pharmacokinetic and pharmacodynamic models that analyze drug or vaccine action at the whole organism level, and pharmacogenomic models of disease risk and drug and vaccine exposure at the patient-population level.

Major challenges exist for the development of quantitative and predictive models that span the gap between cell-level biochemical models and organism-level pharmacokinetic and pharmacodynamic models. One hurdle is the technical difficulty associated with generating sufficiently comprehensive quantitative datasets for large numbers of system variables, across different levels of organization. Another major challenge is the development of efficient tools that can handle the wide variety of available data and identify relevant data subsets from existing repositories. Overcoming these hurdles will lead to the development of models that can be used in clinical practice while accounting for the uncertainty in the data.

Another important challenge for systems medicine is the integration of this knowledge across the relevant levels of organization. Large, long-term research initiatives, like the Virtual Physiological Human, the Virtual Liver or the Human Brain Project, are aiming to develop comprehensive, computational representations of organs and organ systems. Here, we focus on opportunities for comparatively small interdisciplinary collaborations between clinicians and modelers who are targeting specific questions of clinical relevance. In the projects that we envisage, modeling is not the final goal; rather, it is a tool that can be used to advance understanding of the system, to develop more directed experiments in the laboratory and, ultimately, to generate testable predictions to enable improved therapies and prophylaxes.

Multiscale modeling

The fields of theoretical and mathematical biology have pioneered the development of mathematical and computational models of biological systems. Systems biology has contributed workflows for data-driven modeling and model-driven experimentation to the life sciences. Taken together, these provide a considerable body of experience for modeling at different levels (Box 1). This list is necessarily incomplete and serves here to indicate the progression of modeling efforts, with an increasing diversity of approaches available, a tendency to combine approaches in modeling workflows, and clear indications of an increasing number of successful case studies.

Multiscale modeling serves as a 'macroscope' that integrates the evidence available at different levels of a particular system's structural and functional organization while enabling us to zoom in on the details where necessary. For experimental models, it is almost certain that not all parameters influencing a disease will be known and, often, known parameters cannot be influenced and/ or measured. This makes it difficult to unambiguously identify the mechanisms at work in diseases. Modeling therefore makes an epistemic contribution by allowing in silico (simulation) experiments under defined conditions, aiding the exploration of hypotheses by explicitly accounting for the uncertainty that arises from biological complexity.

Central to these efforts are data of high quality that are quantitative, derived from reproducible studies and that cover multiple levels of functional and structural organization, generated from a range of experimental systems. A particularly important challenge is to enable clinical validation of models and simulations.

Actions required for multiscale modeling

Our discussions have identified a number of recommendations.

Short-term recommended actions

With respect to data collection and modeling, in the short-term (that is, the next one to two years), the following actions should be given priority:

1. Exploitation of existing data as a starting point for multiscale modeling. This will lead to the identification of gaps in data and, therefore, in understanding of underlying mechanisms, and will improve the targeted generation of new data that can be exploited for quantitative models. 2. Development of standard operating procedures and quality standards for the systematic collection of quantitative data and information. This will enable models to be built and validated for specific applications. 3. Definition of test scenarios and proof-of-concept studies. 4. Identification of required standards and ontologies (for example, a markup language and ontology for individual-based models) for models and data repositories in systems medicine.

Development of concepts for dedicated modeling

workflows for the integration of data and models.

These research actions would benefit from initiatives that coordinate training and encourage collaborations between clinicians and multiscale modelers; support coordinated clinical projects to bring clinicians, modelers and biologists together; and run sandpits for modelers and clinicians to develop proposals to address clinical questions, to improve mutual understanding and provide realistic expectations for such collaborations.

Medium-term recommended actions

In the medium-term of two to three years, attention should focus on the provision of suitable information technology infrastructure and the development of standards, such as: Box 1. Different levels at which modeling of biological systems has been carried out 1. The development of computational tools and algorithms for efficient multiscale simulations.

The development of mathematical formalism to

analyze and compare multiscale models such as parameter estimation, sensitivity analysis, identifiability analysis and image analysis. 3. Support for the development of workflows for modeling, including computational tools that support data management, model construction and analysis. 4. Methods to integrate different physical phenomena, including those of mechanotransduction, electrical, mechanical and chemical origin. 5. Methods to investigate the interplay between the environment, cell behavior and cell fate.

In the medium term, the goal is to develop multiscale models of normal physiology and disease. The development of these models should be driven by clinical questions to provide the basis for clinical validation in the longer term. This will require technologies that promote and facilitate the collaboration of multidisciplinary teams.

Longer-term recommended actions

On a timescale beyond four years, the focus should be on the application and validation of multiscale models in the clinic. To this end, it is desirable to:

1. Enhance the formation of small-scale networks focused on specific clinical needs, possibly clustered in a larger integrated project (longer timescale). 2. Have a funding model in place for small groups of two to three partners (one to two modeling postdocs, one to two experimental postdocs plus consumables and travel between laboratories). Such a funding model has been applied in systems biology to good effect, with smaller groups being integrated through networks.

The main priority for systems medicine is the development of computational models that integrate data and knowledge from the clinics and basic science (in vitro and animal model experiments) and are applicable to individual patients. The aim is to derive a mechanistic understanding of pathologies, prophylaxy and support of therapy optimization. This requires the development of concepts, methods and tools that support the integration of organizational levels to develop interfaces between the computational and mathematical frameworks used in systems medicine.

  Molecular modeling, for example •Drug/vaccine target interactions •Prediction of pathogenic mutations •Protein-protein interactions Modeling of subcellular processes, for example: •Signaling pathways, gene regulatory networks, metabolic networks •Drug target prediction by sensitivity analysis •Linking signaling pathways to phenotypic changes (for example, regression models) Individual-cell or cell-based models,fore xample: •Behavior of individual cells in their microenvironment •Cell-cell interactions •Control of cell material properties and shape by molecular mechanisms, and the effect of physical properties of cells and their environment on cell decisions Tissue/organ level models,f o re xa mp l e : •Population dynamics, the formation and maintenance of tissue architecture •Cell-stroma interactions, for example epithelial-mesenchymal transition •Mechanobiology/biomechanical models Body systems level models,f o re xa mp l e : •Pharmacokinetic/pharmacodynamic modeling •Physiologically based pharmacokinetic modeling for applications in systems pharmacology •Modeling environmental influences and long-term clinical events (for example, overall survival).

http://genomemedicine.com/content/6/3/21

Acknowledgements

The workshop that launched the collaborative writing of this paper was funded through CASyM, a Coordinating Action for the Implementation of Systems Medicine across Europe (www.casym.eu). CASyM is an initiative of the European Commission, Health Directorate DG Research & Innovation, under grant agreement #305033.

Competing interests

The authors declare that they have no competing interests.


Alexandre Sarafianos
email: alexandre.sarafianos@st.com

Olivier Gagliano

Valérie Serradeil

Mathieu Lisart

Jean-Max Dutertre

Assia Tria

Building the electrical model of the pulsed photoelectric laser stimulation of an NMOS transistor in 90nm technology

Keywords: component, NMOS transistor, pulsed PLS, 1064nm wavelength, parasitic bipolar transistor. I

This paper presents measurements of pulsed photoelectrical laser stimulation of an NMOS transistor in 90nm technology. The laser power was able to trig the NPN parasitic bipolar Drain/Psubstrate/Source. An electrical model is proposed in order to simulate effects induced by the laser. Results extracted from the electrical simulator are compared to measurements.

INTRODUCTION

A laser beam passing through silicon creates electron-hole pairs along its path as a result of energy absorption: the socalled photoelectric effect. Failure analysis (FA) methodologies make an extensive use of laser stimulation techniques. In this paper, we present an electrical model of the backside Photoelectric Laser Stimulation (PLS) of an NMOS transistor in 90nm technology. We used a pulsed laser at 1064nm wavelength to conduct the PLS experiments. The obtained measurements were used to validate and tune the model. This electrical model makes it possible to simulate the response of an NMOS transistor to laser pulses in a very small amount of calculation time by comparison with real experiments on laser equipment, or TCAD simulations. Thus, a new model has to be built for any technology improvement. Such models are intended to reduce the time passed on laser equipments. This work presents the electrical model (thanks to ELDO, the SPICE simulator from Mentor Graphics [START_REF]ELDO user's Manual -Software Version 6.6_1 Release[END_REF]), of the effect of a laser pulse applied to the backside of an NMOS transistor in 90nm CMOS technology. This model is valid for laser power ranging from 0 to ~2W. In order to validate and correlate the model, measurements on NMOS transistors under laser illumination at a wavelength of 1064nm were performed with a laser equipment.

Moreover TCAD analyses are needed, in order to well understand the phenomenon involved when an NMOS transistor is under PLS. TCAD takes into account the complex flow of semiconductor fabrication steps leading to detailed information on geometric shape and doping profile distribution of a semiconductor device in scope (like a MOS transistor) [START_REF] Minixhofer | TCAD as an integral part of the semiconductor manufacturing environment[END_REF] to model its behavior. Three-dimensional simulation is computationally intensive and requires very long simulation times. Thus, only two dimensional (2D) TCAD simulations have been considered in this paper. We assume that the third space dimension does not significantly affect the behavior of the fundamental mechanisms involved in the following results, as the third dimension of the device (width of the transistor) is taken as long enough to neglect edge effects (W=10µm). The laser waves used in all TCAD simulations were in every case, a plane wave which illuminates the whole backside of the studied devices.

Moreover, comparisons between measures and simulations will rather be qualitative than quantitative because TCAD simulations are first used as an analysis tool of physical laws effects inside a structure, and should be accurately calibrated before any quantitative analysis. Electrical measurements associated with Finite Element Modeling software are the tools necessary to understand and model PLS impact on NMOS transistors.

Former electrical models of NMOS transistors u n d e r pulsed-laser stimulation were generally m a d e o f a simple current source which represents the photocurrent induce by the laser [START_REF] Glowacki | laser stimulation techniques for functional analysis and reliability of semiconductor devices by in-depth investigation of the optical interaction with the devices[END_REF]. We have already introduced electrical models for continuous illumination at small laser power (below ~100mW), which only consider photoelectrical effects [START_REF] Liddo | Characterization and TCAD simulation of a 90nm technology NMOS transistors under continuous photoelectric laser stimulation for failure analysis[END_REF], [START_REF] Liddo | Characterization and TCAD simulation of a 90nm technology PMOS transistors under continuous photoelectric laser stimulation for failure analysis[END_REF], [START_REF] Sarafianos | Building the electrical model of the Photoelectric Laser Stimulation of an NMOS transistor in 90nm technology[END_REF], [START_REF] Tria | Building the electrical model of the Photoelectric Laser Stimulation of an PMOS transistor in 90nm technology[END_REF]. The novelty of the model presented in this paper is that it takes into accounts the laser's parameters (i.e. spot size, power, pulse duration, etc.), spatial parameters (i.e. the spot location, NMOS' geometry, wafer thickness, focus of the laser beam, etc.), the NMOS' bias, in addition to the possible activation of the NMOS' bipolar parasitic transistor at higher laser power. Besides, the model was calibrated for each laser settings (power, spot size, location, etc.). This article is organized as follows. Section 2 reports both measurements made on silicon and TCAD simulations. It permits to draw the electrical model of a PN junction under PLS. This model is used in turn to build a complete electrical model of an NMOS transistor under PLS, thanks to measurements made for different laser and NMOS parameters. This model offers the ability to draw 3D cartographies of an NMOS under pulsed laser for FA purposes as reported in section 3. These electrical cartographies are compared to measurement. Finally, our findings are summarized in t h e concluding section 4 with some perspectives.

II. SILICON MEASUREMENT UNDER PLS AND ASSOCIATED ELECTRICAL MODEL

In an NMOS transistor there are mainly two PN junctions which may give rise to a photoelectric effect if exposed to a laser beam: the Drain/Psubstrate and Source/Psubstrate junctions. Therefore a first step toward building the electrical model of NMOS transistors under pulsed PLS is the study and the modeling of the PN junctions under pulsed laser. In order to reach this goal, the Device Under Test (DUT) used is the N+ diffusion on Psubstrate of an NMOS transistor (W=L=10µm) embedded in a test structure designed in STMicroelectronics 90nm technology.

A. N+/Psubstrat junction

The study of the N+/Psubstrate PN junction under PLS is a necessary step i n t h e c o m p r e h e n s i o n o f the phenomena involved when a pulsed laser stimulates the backside of an NMOS transistor.

1) Beam centered on the component

In order to well model the effect of PLS on a PN junction the laser spot must firstly be centred in the middle of the junction.

a) Measurements and TCAD simulation

The test experiments were performed with a 20X lens (which delivers a spot size of diameter equal to 3.25µm). The laser spot was located in the middle of the Drain/Psubstrate junction (See Figure 1). The focus was made on the active zone. The laser power at the output of the chosen 20X lens was adjustable between 0 and 1.25W. Moreover, the pulse width used for the measurements was equal to 20µs. This value was used in order to analyze the PLS effect during a stationary regime. The main characteristics of the experiment are presented on figure 1. The red spot represents the location of the laser beam on the Drain/Bulk PN junction. The bias applied to the structure was the following: the drain potential was adjustable between 0V and 1.2V, and the Psubstrate was grounded. Gate and source are left floating, in order to focus the study only on the n+/Psubstrate junction (Drain/Bulk junction) of the NMOS transistor. The I(V) characteristics depicted on figure 2 were obtained for various laser power according to the aforementioned settings. For each point the photocurrent was measured during the laser pulse. For a given laser power, more the PN junction is reverse biased and more the electrical field between the two electrodes increases, which induces a higher photoelectric current. This effect is amplified when t h e l a s e r p o w e r i s increased. Moreover, for validation purposes, TCAD simulations were ran on a N+/Psubstrate junction. The aim of this simulation was to reproduce the photocurrent induced in the Space Charge Region (SCR) o f t h e d e v i c e . I n t h i s w o r k , Synopsys simulation tools are used and especially Sentaurus Device Editor (SDE) for grid generation and SDevice for device simulation. The simulated device is a Drain/Psubstrate (or Source/Psubstrate) junction of an NMOS transistor from a STMicroelectronics 90nm CMOS technology (See fig. 3). Advantages to proceed this way are that a single structure is generated and information about phenomena taking place in the PN junctions present in an NMOS transistor is obtained. Current versus voltage characteristics of the junction were simulated as a function of the laser power. Due to calculus convergence problem, the level of the laser power simulated in TCAD is very low in comparison with measurement. At these laser power, the increase of the photocurrent versus the reverse bias is negligeable. However, it is possible to notice the increase of the photocurrent with the laser power. Therefore it is possible to approximate coefficients a and b by two functions which depend of the laser power P laser expressed in W:

(2)

(3) Coefficients p, q, r and s are expressed in Table I.

Coefficient Value

p 4E -9 q -5E -7 r 9E -6 s 4E -6
The first step in order to simulate an NMOS transistor under pulsed laser stimulation is to well model its effects on the N+/Psubstrate junction.

According to the previous paragraph, it is possible to approximate the photocurrent generated in a P N j u n c t i o n during a l a s e r p u l s e v e r s u s t h e bias applied to its two electrodes with equation ( 1), ( 2) and (3).

In order to simulate this effect, a sub circuit (called Subckt Iph_nplus_psub) which contains a voltage controlled current source was created. (See figure 6). The laser_trig signal is used to set the start and duration of the laser pulse. The value of the current source Iph is set by the same equation than expressed in (1) with equations ( 2) and ( 3) which coefficients are expressed in table I.

Figure 7 reports both simulation and experimental results. It highlights the very good correlation obtained.

2) Study of the spatial dependence a) Measurement

The distance between the laser spot and the PN junction has a strong impact on the value of the generated photocurrent. In the following, this effect is studied for a N+/Psubstrate junction.

When the laser beam is centered on the PN junction (Drain/Psubstrate junction of an NMOS transistor), the induced photocurrent is maximum; as the laser beam is moved outside the junction the value of the photocurrent decreases. In order to model the spatial dependence effect on a Drain/Psubstrate junction (N+/Psubstrate junction), an NMOS transistor with long channel (W=L=10µm) was used. The measurements were made with the drain at 1.2V, the Psubstrate bias grounded, and the two other electrodes left floating. The laser spot was moved on a line from the center of the junction to a distance of 300µm. (See Fig. 8). For each step, the photocurrent was measured. This experiment was conducted for the three lenses of our laser equipment (5X, 20X, and 100X). The obtained photocurrent versus distance curves are depicted on figure 9 after normalization according the maximum photocurrent. Their shapes exhibit a Gaussianlike behavior. For each lens, the coefficients β, γ, c 1 and c 2 were found different (see Table II).

b) Electrical modeling of the Spatial dependency

A more complete electrical model, that takes into account the spatial dependency between the induced photocurrent and Increased laser power the laser beam location, is obtained by multiplying equations ( 1) and ( 4):

(5)

3) Wafer thickness effect

The substrate thickness has a significant effect on the photocurrent generation of PN junctions under PLS [START_REF] Pouget | Simulation expérimentale par impulsions laser ultra-courtes des effets des radiations ionisantes sur les circuits intégrés[END_REF]. The light intensity exponentially decreases throughout the material and so does the photocurrent effect. Indeed more the wafer thickness is thin and more the photocurrent generated on PN junction under PLS was found important.

In order to validate this effect, the photocurrent of a PN (Drain/Psubstrate) under PLS on wafers with different thickness was measured. These measures are reported on figure 10. During these experiments, the Drain was biased at 1.2V, the bulk was grounded and the other electrodes were left floating. The laser beam was centered on the drain junction. The laser power was equal to 1.25W. The pulse width of the laser impulsion was set at 20µs. Therefore it is possible to model the effect of the wafer thickness thanks to equation ( 6): [START_REF] Sarafianos | Building the electrical model of the Photoelectric Laser Stimulation of an NMOS transistor in 90nm technology[END_REF] where Wafer thickness is the thickness of the wafer expressed in µm. Hence, equation [START_REF] Tria | Building the electrical model of the Photoelectric Laser Stimulation of an PMOS transistor in 90nm technology[END_REF], that incorporates the wafer thickness dependency, is obtained by multiplying equations ( 5) and ( 6):

(7)

4) Focus effect

Moving the z axis of the laser lens has an influence on the photocurrent generated by a PN junction. In order to highlight the effect of the vertical moving of the z stage of the lens, a Drain/Psubstrate junction of an NMOS transistor (W=10µm / L=10µm) was used and biased as following: the drain voltage was set to 1.2V, the Psubstrate was grounding and the others electrodes were left floating. By convention, when z was equal to 0, the focus was done on the active area of the PN junction. Figure 11 represents the normalized photocurrent induced in the PN junction versus the z axis. The model of the Iph_z curve is given by equation 8:

where coefficients c, d, e, f, g, h, i, and j are expressed in table III. Coefficient Iph_z, which takes into account the energy absorption through silicon depending of the wafer thickness, is used to derive the model of equation ( 9) from equation ( 8) by multiplication: [START_REF] Douin | Contribution à la modélisation et au développement de techniques de test et d'analyse dynamique de circuits intégrés par faisceau laser pulsé[END_REF] Therefore our model of the PN junction under PLS takes into account the position of the laser beam versus the topology of the junction, the wafer thickness, and the focus of the laser beam.

B. NMOS transistor under PLS 1) Study at low laser power

Once the behavior of single PN junctions under PLS is understood and modelled, the phenomena involved when an NMOS transistor is stimulated by a pulsed laser m a y b e studied. In this section an NMOS transistor (W=L=10µm) was used in its OFF state (the drain was at 1.2V and the gate, source and Psubstrate electrodes were grounded). The 20X lens was chosen for this experiment. The pulse duration was set to 20µs, and two different laser powers (25mW and 420mW) were used. At these laser power, we have only observed photoelectrical effects on the NMOS transistor (this was confirmed by TCAD simulations: see figure 12). For validation purpose of the measurement results, TCAD simulations without laser stimulation were made. It was also aimed at well characterizing the parasitical bipolar transistor NPN (Drain/Source/Psubstate).

As seen in TCAD simulation, when the Psubstrate voltage is greater than 0.6V, the Psubstrate/Source junction starts conducting. The Psubstrate/Drain junction stays in reverse bias conditions. Therefore an increase of the Psubstrate potential trigs the parasitic bipolar Drain/Psubstrate/Source. The current gain of this bipolar transistor is small (~10 -3 ) since almost the amount of current flows from Psubstrate to source.

b) Electrical model

A specific sub circuit called Subckt SD was created in order to simulate the effect of the NPN parasitic bipolar transistor (Drain/Psubstrate/Source). It was built with t w o voltage controlled current sources (one between Drain and Psubstrate and the other between Psubstrate and source) (See fig. 14). These current sources were calibrated thanks to the measurements reported in figure 13.

C. Model proposed of NMOS transistor under PLS 1) Measurement

Therefore when the laser power is at 1.25W, the local increase of the Psubstrate potential trig the NPN parasitic bipolar (Drain/Psubstrate/Source).

It is also possible to highlight the inversion of the source current during the laser pulse represented by the red arrow. (See fig. 15).

III. CURRENT CARTOGRAPHIES

A. Principle

The electrical model we have obtained makes it possible to draw current cartographies. It is based on the creation of a mesh on the layout of the transistor. The step of the meshing is a parameter called stepXY defined in the ELDO netlist. It is necessary to calculate in every point of the mesh two distances: the distance between the centre of the laser spot and the center of (a) the drain junction, and (b) the source junction.

To illustrate the principle of drawing current cartographies, we have chosen the example of a NMOS transistor (W=L=10µm). The laser power was set near 0W for two main reasons. The first one is that this laser power did not trig the NPN parasitic bipolar t r a n s i s t o r Drain/Psubstrate/Source i n order to compare the effects of the location of the laser beam on the photocurrent generated on the source and the drain. The second one is that at low laser power the photocurrent generated at the source and the drain is approximately the same whatever the voltage value. Three cases were studied by locating successively the laser spot on the centre of the drain junction, on the centre of the source junction, and in the middle of the NMOS transistor. For each case, drain, source and Psubstrate currents were extracted from the electrical simulation (See Fig. 18). In this case stepXY is equal to 5µm, with m being a parameter evolving between 0 and 2 by step of 1. L is the gate length of the NMOS transistor expressed in micrometer.

When the laser beam is centered in the middle of the drain, the photocurrent generated by the drain is more important than the source's photocurrent. The electrical charge conservation of currents is respected. If the beam is centered on the source junction, it is the photocurrent generated by the source that is more important than the drain photocurrent. In the last case, when the laser beam is centered in the middle of the NMOS, the photocurrents generated by the source and the drain are identical (12).

(12) On the same principle, it is possible to create more complex cartographies, by creating a denser mesh. The same method is always used. In every point of the mesh, two values of distances are associated. The first value is the distance between the centre of the laser spot and the closest edge of the drain. And the second value is the distance between the centre of the laser spot and the closest edge of the source.

B. Results: Comparison between measurement and simulation

In this section, it is proposed to draw 3D current cartographies (extracted from the ELDO simulator) of photocurrents generated on an NMOS transistor W=L=10µm and to compare it with measurements. The laser power was maximal ( 1 . 2 5 W ) . It is also possible to extract 3D cartographies of photocurrents generated by the two PN junctions of an NMOS [START_REF] Glowacki | Systematic characterization of integrated circuit standard components as stimulated by scanning laser beam[END_REF].

Figures 19a and19b highlight the good correlation between electrical simulation and measurements. It is also possible to extract cartographies of the source current (electrical simulation and measurements are respectively reported in fig. 20 Source cartographies highlight the triggering of the NPN parasitic bipolar transistor (Drain/Psubstrate/Source). This phenomenon appears when the laser beam is centered on the transistor (The current value is positive).

The same process than for source and drain current cartographies was made for the Psubstrate. (See fig. 21a and21b).

IV. CONCLUSION

The process of building an accurate electrical model of an NMOS transistor in 90nm technology under pulsed laser was reported in this paper. The phenomena revealed by measurement were included in our model (i.e. the triggering of the parasitic bipolar transistor beyond a laser power of ~1W). The validity of the approach was assessed by the very good correlation obtained between electrical simulations (based on SPICE language) and measurements. TCAD physical simulations were also ran to explore the underlying physical phenomena. In failure analysis it could have a great utility in order to compare the simulated response of a golden circuit under pulsed laser with actual measurements. This work will be extended to PMOS transistors which contains an additional Nwell/Psubstrate junction. Due to this fact, the model will be more complex, with three PNP parasitic bipolar transistors (One Source/Nwell/Drain, anothers Drain/Nwell/Psubstrate and Source/Nwell/Psubstrate). Therefore, as a perspective, it will permit us to simulate the behavior under pulsed laser of complex logic gates made of NMOS and PMOS transistors.

Figure 1 .

 1 Figure 1. Study of the N+/Psubstrate diode of an NMOS transistor.

Figure 2 .

 2 Figure 2. I(V) characteristics of the PN junction under pulsed laser for different laser powers.

Figure 3 .

 3 Figure 3. Structure used for TCAD simulation of the PN junction.

Figure 4 . 1 )Figure 5

 415 Figure 4. I(V) characteristics of the PN junction under pulsed laser for different laser power extracted from TCAD simulations. b) Electrical model In first approximation, it is possible to highlight the fact that the photocurrent induced in a reverse biased PN junction by a l a s e r pulse c o u l d b e a p p r o x i m a t e d b y a f i r s t order polynomial function (1):

Figure 5 .

 5 Figure 5. Coefficients a and b from equation (1) versus the laser power.

Figure 6 .

 6 Figure 6. Electrical modeling of a PN junction under pulsed laser embedded in a sub circuit called Subckt_Iph_nplus_psub.

Figure 7 .

 7 Figure 7. Comparison between measurement and electrical model of a PN junction under PLS for different laser power -I(V) characteristics.

Figure 8 .

 8 Figure 8. Schematic presentation of the experiment in order to know the spatial effect of the laser on a PN junction.

Figure 9 .

 9 Figure 9. Spatial dependance of the induced photocurrent for the three different lenses of our laser equipement.

Figure 10 .

 10 Figure 10. Normalized photocurrent generated in a PN junction versus the wafer thickness.

Figure 11 .

 11 Figure 11. Normalized photocurrent generateg by a PN junction versus the displacement of the axis z of the laser lens which modify the focus.

Figure 12 .

 12 Figure 12. Slide of an NMOS transistor extracted from TCAD simulation which represents the photoelectrical effect induced by PLS.The photocurrent generated in the two junctions of the transistor has for consequence to increase the local Psubstrate

Figure 13 .

 13 Figure 13. Measured currents of the parasitical bipolar transistor NPN (Drain/Bulk/Source) versus the Psubstrate voltage.

Figure 14 .

 14 Figure 14. Electrical model of the parasitic bipolar effect under pulsed laser embedded in a sub circuit called Subckt_SD.

Figure 15 .

 15 Figure 15. Current measurement of an NMOS transistor under PLS at 1.25W.

2 )

 2 Electrical model A proper modeling of the effects of pulsed PLS on an NMOS transistor involved two sub circuits Subckt_Iph_nplus_psub (one for the Source/Bulk junction and another for the Drain/Psubstrate junction). It must also involve the effect of a local increase of the Psubstrate's voltage which may trig the parasitic bipolar transistor: subckt_SD in figure 16. Resistance Rb and capacitante Cb are used to set the time constant of that phenomenon. This constant describe the time of dielectric relaxation [9].

Figure 16 .

 16 Figure 16. Electrical model of an NMOS transistor under pulsed PLS.

Figure 17

 17 Figure17displays the currents simulated for a laser pulse duration of 20µs and a laser power of 1.25W. Note the good correlation obtained between measures (fig.15) and simulation (fig.17).

Figure 17 .

 17 Figure 17. Simulation currents obtained from the electrical model of an NMOS transistor under pulsed PLS.

Figure 18 .

 18 Figure 18. Electrical simulation thanks to ELDO for different localisation of the laser spot.In a simple case as this one where the meshing is established by only three aligned points, it is possible to define the parameters d d (distance of the centre of the laser spot to the closest edge of the drain) and d s (distance of the centre of the laser spot to the closest edge of the source).[START_REF] Glowacki | Systematic characterization of integrated circuit standard components as stimulated by scanning laser beam[END_REF]

  Figure 19. 3D current cartographies of the photoelectrical contribution of the drain under PLS extracted from ELDO (a) and measurement (b).

  (a) and (b) ).

Figure 20 .

 20 Figure 20. 3D current cartographies of the photoelectrical contribution of the source under PLS extracted from ELDO (a) and measurement (b).

  Figure 21. 3D current cartographies of the photoelectrical contribution of the bulk under PLS extracted from ELDO (a) and measurement (b).

TABLE I .

 I

VALUES OF COEFFICIENTS P, Q, R AND S.

TABLE II .

 II COEFFICIENTS OF THE GAUSSIAN FUNCTION (4) FOR THE DIFFERENT LENSES OF OUR LASER EQUIPEMENT FOR THE DRAIN/PSUBSTRATESTUDY.

	Coefficient		Lens used
		5X	20X	100X
	β	0.4	0.6	0.7
	γ	0.6	0.4	0.3
	c 1	2.5	23.8	1000
	c 2	55	654	15000

TABLE III .

 III

	Coefficient	Values
	c	-3.E-19
	d	-9E-17
	e	-8E-13
	f	2E-10
	g	-8E-7
	h	-1E-4
	i	0.49
	j	0.5

COEFFICIENTS OF FUNCTION (8) WHICH PERMIT TO APPROXIMATE THE FOCUS EFFECT.