Valentin Mazières

Romain Pascaud

Laurent Liard

Simon Dap

Richard Clergereaux

Olivier Pascal

Time reversal plasmas

Keywords: Time Reversal, Space time plasmas, Patterning deposition method

come

I. INTRODUCTION

In the context of thin film nanocomposite deposition, "fabricating functional structures […] with arbitrary patterns is central to the development of many technologies" [START_REF] Gates | Nanofabrication with molds & stamps[END_REF]. Thus, one of the challenges faced by these technologies is development of methods allowing an accurate control of the deposition pattern (shape, thickness…) over large areas. Various methods have been considered to attain this goal. They can be divided into two categories: "Mask-requiring methods" -lithography, molding, embossing and microcontact printing [START_REF] Gates | Nanofabrication with molds & stamps[END_REF] -which require fabrication of a new mask for each different design of patterns, thus making them not versatile and "Maskless methods" -dip-pen nanolithography, inkjet printing, laser printing and plasma spray [START_REF] Viswanathan | Challenges and Advances in Nanocomposite Processing Techniques[END_REF] -which consist in local deposition, providing flexibility in the control of the deposition pattern. In addition to the spatial control of the deposition pattern, a control of the process duration may also be of importance, for example for obtaining a better homogeneity of particle distribution in nanocomposites [START_REF] Makasheva | Dielectric Engineering of Nanostructured Layers to Control the Transport of Injected Charges in Thin Dielectrics[END_REF].

The aim of this communication is to discuss the possibility of using an innovative plasma source that we have developed recently [START_REF] Mazières | Plasma generation using time reversal of microwaves[END_REF][START_REF] Mazières | Transient Electric Field Shaping With the Linear Combination of Configuration Field Method for Enhanced Spatial Control of Microwave Plasmas[END_REF][START_REF] Mazières | Spatio-temporal dynamics of a nanosecond pulsed microwave plasma ignited by time reversal[END_REF] as an original versatile space-time patterning deposition method. This source, named "Space-Time Plasma Steering Source", has been introduced to address the challenge of controlling plasmas in large cavities (overmoded). Contrary to conventional microwave plasma technologies, for which the plasma occupies the entire volume of the plasma vessel, the idea is to rather ignite one or several localized plasmas whose locations in the vessel can be dynamically controlled. To that end, Time Reversal (TR) was used as it allows focusing of the electromagnetic waves [START_REF] Lerosey | Time Reversal of Electromagnetic Waves[END_REF]. It consists of two steps. First the impulse response between the desired location (at which we want to ignite a plasma) and an antenna is recorded. Then, this signal is time reversed and transmitted to the antenna, resulting in the back propagation of the waves toward the desired location. A spatio-temporal focusing then occurs at this location, of duration equal to that of the initial impulse and of dimension equal to half the wavelength. If the focusing electric field is high enough, a breakdown occurs at the focusing instant and location. Based on this principle, the locations of plasmas can be dynamically controlled by the shape of the transmitted waveform to the cavity through one emitting antenna [START_REF] Mazières | Plasma generation using time reversal of microwaves[END_REF][START_REF] Mazières | Transient Electric Field Shaping With the Linear Combination of Configuration Field Method for Enhanced Spatial Control of Microwave Plasmas[END_REF][START_REF] Mazières | Spatio-temporal dynamics of a nanosecond pulsed microwave plasma ignited by time reversal[END_REF].

In our pioneer paper demonstrating the experimental control of plasmas by TR [START_REF] Mazières | Plasma generation using time reversal of microwaves[END_REF], several applications for this innovative source have been mentioned, with among them, "surface treatments, etching, or thin film deposition" [START_REF] Mazières | Plasma generation using time reversal of microwaves[END_REF]. In the present paper, we focus on its possible application for thin film nanocomposite deposition. In section II, the space time capabilities of the Space-Time Plasma Steering Source based on time reversal are presented. Its principle is explained and the first experimental demonstration of this source [START_REF] Mazières | Plasma generation using time reversal of microwaves[END_REF] is briefly presented. Then, its ability to control simultaneous plasmas is experimentally demonstrated. In section III, a discussion is proposed on the possibility to use this original source as a versatile space time pattern deposition method.

II. SPACE-TIME PLASMA STEERING SOURCE BASED ON TIME REVERSAL

A. Principle

The principle of the innovative source we introduced recently is briefly explained in this subsection. It has been introduced to meet the challenge of controlling plasmas in overmoded cavities. Indeed, commonly used microwave plasma sources in cavities are based on the control of the spatial distribution of the field, and thus the plasma, by exciting a stationary resonant mode of the cavity [START_REF] Yu | Microwave discharges at low pressures and peculiarities of the processes in strongly nonuniform plasma[END_REF]. However, in overmoded cavities (large cavities), it becomes difficult, if not impossible, to control with this principle the spatial distribution of the field [START_REF] Sturm | Microwaves and microreactors: Design challenges and remedies[END_REF], and thus of the plasma. The idea of the present source is to dynamically control the plasmas location by changing the waveform of the transmitted signal 𝑠(𝑡) to an overmoded cavity. It is then the transient behavior of the waves inside the cavity that dynamically controls the plasmas location, hence the name of "Space-Time Plasma Steering Source".

The key element of this source is the shape of the waveform of the transmitted signal 𝑠(𝑡). Several techniques can be envisioned for determining this waveform, allowing the desired space-time behavior of plasmas in the cavity. This technique must allow a concentration of electromagnetic energy at the desired instant and location (at which we want the plasma) and a lower level of energy elsewhere in the cavity. The most obvious technique that meet these criteria is "Time Reversal", as it allows the focusing of waves inside overmoded cavities. We have shown that this technique allows an accurate control of plasmas on initiators in an overmoded cavity [START_REF] Mazières | Plasma generation using time reversal of microwaves[END_REF][START_REF] Mazières | Spatio-temporal dynamics of a nanosecond pulsed microwave plasma ignited by time reversal[END_REF]. Note that we have also shown that a more elaborate technique allows to enhance the spatial control of plasmas [START_REF] Mazières | Transient Electric Field Shaping With the Linear Combination of Configuration Field Method for Enhanced Spatial Control of Microwave Plasmas[END_REF], but for simplicity we focus in this paper on "Time Reversal" plasmas.

B. Experimental demonstration of Time Reversal plasmas

The principle of TR was first demonstrated by M. Fink, C. Prada et al. in the 1990's [START_REF] Fink | Self focusing in inhomogeneous media with time reversal acoustic mirrors[END_REF]. In practice, two steps are required. The first one consists in sending a short pulse from a source, and recording the signal that has propagated in a more or less complex medium using transducers located around this source. Then, the second step consists in reemitting by these transducers the information previously recorded, but time reversed. The waves thus back propagate toward the original location of the pulse. In the end, this method allows to focus efficiently microwave energy at given instant and location. The use of a reverberant and ergodic cavity has been shown to allow to reduce considerably the number of transducers needed, down to a single transducer [START_REF] Draeger | One-Channel Time Reversal of Elastic Waves in a Chaotic 2D-Silicon Cavity[END_REF]. The principle of the Space-Time Plasma Steering Source based on TR consists in obtaining a focusing field high enough so that a breakdown occurs at the desired instant and location. Following this idea, we have shown that an accurate space time control of plasma is possible on initiators [START_REF] Mazières | Plasma generation using time reversal of microwaves[END_REF]. The results presented in the following of this subsection are a brief synthesis these results.

Figure 1: Schematic of a plasma ignition experiment on initiator 1

The experimental setup in which we have shown that TR efficiently allows a space time control of plasmas in an overmoded cavity [START_REF] Mazières | Plasma generation using time reversal of microwaves[END_REF][START_REF] Mazières | Spatio-temporal dynamics of a nanosecond pulsed microwave plasma ignited by time reversal[END_REF] is represented on Figure 1. It consists in a reverberant cavity of 0.6 × 0.6 × 0.3 m 3 -that is to say 5𝜆 0 × 5𝜆 0 × 2.5𝜆 0 at our working microwave carrier frequency of about 𝑓 0 = 2.45 GHz -in which the microwave TR experiments are performed. This cavity includes four antennas: one located in an appendix, at atmospheric pressure (760 torr) in air, and three others located in the main cavity, at 1 torr in argon. The latter are 𝜆 0 /2 apart from each other, which is the spatial resolution of the TR process (meaning the spatial dimension of the focusing) [START_REF] Lerosey | Time Reversal of Electromagnetic Waves[END_REF]. These three antennas (which are metallic monopoles), act as emitting antennas during the first phase of the TR process. During the second step, they act as receiving antenna (allowing a measure of the field evolution at their locations) as well as initiators for plasma breakdown, as they produce a local enhancement of the electric field. Hence, they will be referred to as "initiator" in the following of this paper.

The first step of TR consists in recording the impulse responses (from a 8 ns impulse modulated at 𝑓 0 = 2.45 GHz) between initiators 1, 2, or 3 (then acting as emitting antennas) and the high pressure antenna (then acting as receiving antenna). These responses must then be time-reversed (𝑠 1 (-𝑡), 𝑠 2 (-𝑡), and 𝑠 3 (-𝑡), see Figure 1) and transmitted through the high-pressure transmitting antenna to achieve a focusing (of 8 ns) on initiators 1, 2, or 3. For example, a focusing experiment by TR on initiator 1 is shown in Figure 1. For plasma ignition by TR, during the second step, the signals are amplified before being transmitted to the antenna (see Figure 1). The high pressure in the appendix allows to avoid parasitic breakdown at the emitting antenna and allows to inject efficiently the microwave power into the low pressure part. Thus, under optimal breakdown conditions for a frequency of 2.45 GHz (argon at 1 torr), focusing by TR on one of the three initiators allows to ignite a local plasma on the corresponding initiator. The 2 kW amplifier used is a pulsed amplifier. Thus the TR focusing peaks are generated periodically, at a period 𝑇 𝑟𝑒𝑝 typically equal to 166 𝜇s [START_REF] Mazières | Plasma generation using time reversal of microwaves[END_REF].

Photos of the initiators 1, 2 and 3 and the ignited plasmas by TR are shown in Figure 2-a). A plasma discharge can be observed on initiator 1, 2 and 3 for the emission of the signals 𝑠(𝑡) = 𝑠 1 (-𝑡) , 𝑠(𝑡) = 𝑠 2 (-𝑡) and 𝑠(𝑡) = 𝑠 3 (-𝑡) respectively [START_REF] Mazières | Plasma generation using time reversal of microwaves[END_REF]. Note that as discussed in [START_REF] Mazières | Spatio-temporal dynamics of a nanosecond pulsed microwave plasma ignited by time reversal[END_REF], the presence of the initiator has certainly a major influence on the plasmas dimension (centimetric) and shape. This is majorly due to the local enhancement of the electric field they produce.

C. Experimental demonstration of simultaneous Time Reversal plasmas

In order to develop a versatile patterning deposition method with high throughput by TR plasmas, it would be interesting to be able to control simultaneous plasmas. Space-Time Plasma Steering Source based on TR allows the simultaneous control of several plasmas in the cavity. In this case, several TR focusing peaks are obtained simultaneously at the corresponding locations. Based on the principle of superposition, this is achievable by sending the sum of the corresponding time reversed impulse responses to the transmitting antenna (high-pressure antenna of the appendix). For example, the top picture of Figure 2-b) is obtained by sending the signal 𝑠(𝑡) = 𝑠 1 (-𝑡) + 𝑠 2 (-𝑡)to the transmitting antenna. The two plasmas are ignited at the desired locations, meaning on initiators 1 and 2. The same method allows the ignition of simultaneous plasmas on initiators 2 and 3, and 1 and 3, as shown in Figure 2-b). Sending the sum of the three time reversed impulse responses 𝑠(𝑡) = 𝑠 1 (-𝑡) + 𝑠 2 (-𝑡) + 𝑠 3 (-𝑡) leads to the simultaneous ignition of the three corresponding plasmas, as shown is the bottom picture of Figure 2-b). These results shows that the position of the simultaneous plasmas is well controlled by the transmitted waveform. This is the first demonstration of simultaneous ignition of several plasmas by TR.

Thus, adequate shape of the signal 𝑠(𝑡) sent by an antenna, acquired during the learning phase, allows a spacetime control of one or several plasmas in overmoded cavities. This unique property makes this process a very promising candidate for certain applications requiring precise control of the plasma in time and space. A discussion on its use for deposition patterning is proposed in the following section.

It is important to notice that there is certainly a limit on the number of plasmas that can be controlled by TR. This limit depends on the plasma volume compared to the cavity volume and on the plasma frequency (that depends on the plasma density) compared to the wave frequency. Future work is planned on the determination of the limit number of simultaneous plasmas that can be controlled by TR for a given configuration.

III. DISCUSSION ON THE POSSIBILTY OF USING TIME REVERSAL PLASMA A VERSATILE SPACE TIME PATTERNING METHOD

In this section, we discuss the use of the "Space-Time Plasma Steering Source" based on Time Reversal as a possible versatile space time deposition method.

A. Principle

A deposition method based on TR plasmas, allowing the treatment of one or several substrates with complex 3D shapes, would require two steps.

During the first step, impulse responses between the desired locations and an antenna should be evaluated in locations spaced with 𝜆 0 /2 apart from each other, located all around the 3D complex shapes of the substrates. To that end, several solutions can be envisioned. We could for example think of modelling the cavity to obtain theses impulse responses in simulation. This has been done recently for timereversal experiments in 2D cavities [START_REF] Xiao | Focusing waves at arbitrary locations in a ray-chaotic enclosure using time-reversed synthetic sonas[END_REF], but would be for now difficult to implement for 3D cavities. Another and perhaps more promising solution consists in doing a spatial mapping by the means of non-intrusive probe, as follows. First, a non-intrusive probe could be placed at a desired location. The impulse response between this probe and the antenna should be recorded. Then, the non-intrusive probe should be placed at the next desired location and the corresponding impulse response recorded, and so on.

The interest of using a non-intrusive probe is the fact that moving the probe in the cavity does not change the behavior of the waves, so that when it is removed during the second step, sending a time-reserved impulse response by the antenna leads to a focusing at the desired location. This method of scanning the cavity in a non-intrusive manner has been proved to successfully work for microwave TR experiments using electro-optical probes (in a cavity of 6 × 3.5 × 2.5 m 3 ) [START_REF] Cozza | Steering Focusing Waves in a Reverberation Chamber With Generalized Time Reversal[END_REF].

Figure 3: Principle of TR plasmas used as a 3D patterning method

If the focusing field is high enough, breakdown of the gas could then occur at the desired locations without the use of any initiator. If not, pre-ionization of the cavity could be envisioned to reduce the level of this breakdown field [START_REF] Bandel | Effect of Preionization on Microwave Breakdown in Neon[END_REF], pre-ionization that could for example be obtained by an initial TR plasma ignited on an initiator.

During the second step, the transmitted signal 𝑠(𝑡) should then be constructed combining the time-reversed impulses responses, according to the desired space time evolution of the deposition process. A schematic representing TR plasmas used as a 3D patterning method of two complex 3D substrates is proposed on Figure 3. Using this method, the two dynamic plasmas could easily be controlled independently of one another, making possible the simultaneous treatments of different spatial 3D shapes.

B. Spatial resolution of the method

The features of this pattering deposition method based on TR plasmas would depend, among other things, on the spatial resolution of the TR process. In a classical case, this resolution is of one-half wavelength [START_REF] Lerosey | Time Reversal of Electromagnetic Waves[END_REF] and can thus be increased by increasing the wave frequency. Note that subwavelength resolution is also possible in some cases [START_REF] Lemoult | Time Reversal in Subwavelength-Scaled Resonant Media: Beating the Diffraction Limit[END_REF].

C. Influence of the substrate properties

The electromagnetic behavior of the substrate has an influence on the method to be followed. Two main behaviors may be distinguished: Dielectric behavior: in this case, the spatial scanning of the cavity (by means of a non-intrusive probe) should be done once and could be done indifferently before or after placing the substrates inside the cavity, as their presence do not change the behavior of the waves (as long as they are not too lossy).

Conductive behavior: in this case, the spatial scanning of the cavity has to be done for each configuration of the substrates, and has to be done after putting them inside the cavity, as their presence significantly change the behavior of the waves.

D. Influence of the material properties

The electromagnetic behavior of the material to be deposited may also have an influence on the method efficiency. Indeed, the deposition of conductive materials may not be possible, as their presence could have an influence on the behavior of the waves (but it would depend on how significant is this influence).

E. Influence of the cavity properties

To finish, it is important to notice that TR performances increase with the cavity volume. Indeed, the more the volume of the cavity is large the more the focusing by TR will be important1 [START_REF] Draeger | One-Channel Time Reversal of Elastic Waves in a Chaotic 2D-Silicon Cavity[END_REF]. Furthermore, TR performances also increase with the "chaoticity" of the cavity (in short, a chaotic cavity ensures, statistically, a uniform spatial distribution of the field, avoiding undesired energy concentrations that would compromise an efficient focusing at the desired location). Hence, a deposition method based on TR plasmas would easily deal with a large number of complex 3D substrates. This is a complete break with usual deposition methods, for which the control of the deposition pattern on large area with complex shapes remains major challenge [START_REF] Gates | Nanofabrication with molds & stamps[END_REF][START_REF] Samukawa | The 2012 Plasma Roadmap[END_REF][START_REF] Liu | Evolution of Dip-Pen Nanolithography (DPN): From Molecular Patterning to Materials Discovery[END_REF].

F. Note on this discussion

It should be noted that the discussion on the properties of the deposition method based on plasmas proposed in this section is a projection of what could be achieved in theory with TR plasmas, based on physical arguments. However, the issue of what materials can be deposited on what substrates of what maximal size has not been experimentally investigated yet. Answering this question requires a more precise and dedicated analysis.

IV. CONCLUSION

These unprecedented capabilities of space-time control of plasmas over large and complex 3D surfaces could offer new possibilities in the context of nanocomposite deposition. Indeed, this method, used in molecular gases, could also be adapted for the deposition of various thin films as well as nanocomposites, i.e. of nanostructured or nanofilled coatings. It could lead to the development of an innovative and versatile method allowing the patterning of complex 2D or 3D structures on large areas.

Figure 2 :

 2 Figure 2: a) Photo of the three initiators 1, 2 and 3 of Figure 1 (top photo) and photos of the plasmas ignited by TR (bottom photos) [4]. b) Photos of the simultaneous TR plasmas.

IEEE 16th Nanotechnology Materials and Devices Conference (NMDC)

Note that there is a saturation phenomenon, from which the TR performances become constant with the increase of the cavity volume[START_REF] Derode | Random multiple scattering of ultrasound. II. Is time reversal a self-averaging process?[END_REF]. However, an increase of the cavity volume certainly leads to a better control of plasmas by TR,

ACKNOWLEDGMENT

The authors would like to acknowledge the DGA/AID for their funding support and the CEA-Gramat for the material support. We are also grateful to K. Makasheva for her valuable comments.


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text:
Rida Farhan

M Rguiti

M Mazroui

M Meddad

C Courtois

Evaluation of performance of polyamide/lead zirconate titanate composite for energy harvesters and actuators

Keywords: Polyamide-6, lead zirconate titanate, piezoelectric properties, energy harvesting, actuator

By means of experimental tools, we have studied the effect of lead zirconate titanate volume fraction introduced in polyamide-6/lead zirconate titanate composites on dielectric, piezoelectric, mechanical, and structural properties. As the first result, we found that the insertion of lead zirconate titanate particles makes the dielectric permittivity of the polyamide-6 matrix increases from 10 to 95.8. The dielectric property studies reveal that under an electrical field of 1 kV the remnant polarization is also increased from 0.17 to 0.4, this behavior is related to both the increase of volume fraction of lead zirconate titanate from 20% to 40% and the piezoelectric coefficient changes proportionally with that of volume fraction of lead zirconate titanate. Furthermore, piezoelectric activity increases with lead zirconate titanate particle size at a range where there is a lower order of magnitude. Finally, the uniform dispersion of the ceramic lead zirconate titanate particles in polyamide matrix has been confirmed by scanning electron microscopy analysis. The performances reached by polyamide-6/lead zirconate titanate composites open new horizons for energy harvesting and actuators.

Introduction

With the growth of microelectronic and mechanical systems (MEMS) production in the last decade, the requisition of wearable electronics and cordless detectors is increasing. [START_REF] Amirtharajah | Self-powered low power signal processing[END_REF] Moreover, great advances in the domain of smart materials, because of their sensor and actuator capabilities, have given rise to research into the power harvesting capabilities of these materials. Recently, has been used for diverse applications like sensor 2 for improving performance. Assuring the mobility of various devices energetic autonomy on behalf of exploration and conversion of environmental energy sources such as solar, thermal, and vibrations, [START_REF] Krikke | Engine: Japan's Ubiquitous Computing Architecture is ready for prime time[END_REF][START_REF] Lallart | Synchronized switch harvesting applied to self-powered smart systems: Piezoactive microgenerators for autonomous wireless receivers[END_REF] became increasingly a challenging for scientific community. Investigations show that piezoelectric composites are reliable energy conversion purpose due to their flexibility, processability, and optical quality even at higher thicknesses. Piezoelectric composites are formed using particulate piezoelectric ceramic phase dispersed inside a polymer matrix. Composites prepared in such manner are also possible candidates for sensors devices. [START_REF] Wenger | Acoustic emission signal detection by ceramic/polymer composite piezoelectrics embedded in glass-epoxy laminates[END_REF][START_REF] Badcock | The use of 0-3 piezocomposite embedded Lamb wave sensors for detection of damage in advanced fibre composites[END_REF] Composite materials are an interesting technology as use of nano-seized fillers allows great structural improvements in comparison to micro-reinforcement polymer materials, which fits well to industrial aims to produce lighter, thinner, and stronger structures at reduced cost. [START_REF] Jagur-Grodzinski | Nanostructured polyolefins/clay composites: role of the molecular interaction at the interface[END_REF] The nano-sized fillers increase the area of contact between the matrix and the fillers, thus reduce the concentration of stress forces. Ferroelectric polymers such as polyvinylidene fluoride (PVDF), polyamide-6 (PA6), and polyamide-11 (PA11) display good electromechanical coupling coefficients and high ductility. [START_REF] Ibos | Annealing or storage influence on pyroelectricity of ferroelectric PVDF and P(VDF-TrFE) copolymer[END_REF][START_REF] Lacabanne | Study of the thermal and dielectric behavior of P(VDF-TrFE) copolymers in relation with their electroactive properties[END_REF] Though, one of the most exploited ferroelectric materials is the lead zirconate titanate (PZT) particles. Due to its excellent piezoelectric properties, it is often used in sensors. [START_REF] Sakamoto | Characterization and application of PZT/PU and graphite doped PZT/PU composite[END_REF][START_REF] Kim | Perovskite stabilization and electromechanical properties of polycrystalline lead zinc niobate-lead zirconate titanate[END_REF][START_REF] Sodano | Generation and storage of electricity from power harvesting devices[END_REF] However, vibratory harvesting application of PZT is hindered due to lack of flexibility. Yet, the piezoelectric responses of the polarization fields are higher 10 times than those used for polishing inorganic ceramics such as lead zirconate titanate (PZT). [START_REF] Kamel | Poling of soft piezoceramic PZT[END_REF][START_REF] Nayak | Dielectric studies of PZT-polymer composites[END_REF] Furthermore, has a high electromechanical property over a wide range of temperature. To take advantage of both, composites are prepared, where ferroelectric ceramic were introduced into a polymer matrix. [START_REF] Van Den Ende | Improving the d 33 and g33 properties of 0-3 piezoelectric composites by dielectrophoresis[END_REF][START_REF] Li | Polyamide-11/lead zirconate titanates-a novel composite material with high dielectric properties[END_REF][START_REF] Furukawa | Electromechanical properties in the composites of epoxy resin and PZT ceramics[END_REF] So as to keep the mechanical properties of the polymer for a higher volume fraction of inorganic particles, micronic fillers were substituted by submicronic ones. [START_REF] Sharma | PZT-PDMS composite for active damping of vibrations[END_REF][START_REF] David | Piezoelectric properties of polyamide 11/NaNbO3 nanowire composites[END_REF][START_REF] Carponcin | Electrical and piezoelectric behavior of polyamide/PZT/CNT multifunctional nanocomposites[END_REF][START_REF] Capsal | Electroactive influence of ferroelectric nanofillers on polyamide 11 matrix properties[END_REF] Depending on the final mechanical properties required, other solutions are proposed to provide a soft piezoelectric material by introducing a piezoelectric structural fiber into a polymeric matrix. [START_REF] Lin | Fabrication and electromechanical characterization of a piezoelectric structural fiber for multifunctional composites[END_REF][START_REF] Lin | Electrolytic deposition of PZT on carbon fibers for fabricating multifunctional composites[END_REF] There have been many studies into the behavior of piezoelectric materials and their application in the development of piezoelectric devices. Eddiai et al., [START_REF] Eddiai | Strain effects on an electrostrictive polymer composite for power harvesting: experiments and modeling[END_REF] Guyomar et al., [START_REF] Guyomar | The compressive electrical field electrostrictive coefficient M 33 of electroactive polymer composites and its saturation versus electrical field, polymer thickness, frequency, and fillers[END_REF] Shinde et al. [START_REF] Shinde | Novel ceramicpolyamide nanocomposites approach to make flexible film of PZT ceramics: structural and dielectric study[END_REF] have developed expressions to predict the dielectric, piezoelectric, elastic constants, and modulus for binary systems such as poly(vinylidene-fluoride)/PZT. Recently, this material is described as a highly dielectric compound, applicable in electrical energy harvesting. PA11, polyurethane, and PVDF are known to be semicrystalline polymers, with excellent dielectric, mechanical and piezoelectric properties. Therefore, we have developed new series of piezoelectric a 0-3 connectivity composites (PA6/PZT) by incorporating PZT into a matrix of PA6 that is able to realize composites with high dielectric permittivity and piezoelectric coefficient. The purpose of this work is to investigate the potential of piezoelectric composite for actuator and energy-harvesting applications. Polymeric composites gain increasing interest in materials research and practice applications due to their excellent properties of piezoelectric ceramic. A new composite with high dielectric constant has been developed by incorporating PA matrix through microparticles of ceramic PZT. A structural, electrical, and mechanical characterization of PA6/PZT composite has been performed in order to evaluate their potential for good application in sensing and actuator area. The obtained results show that the incorporation of the PZT particles increases significantly the intrinsic parameters of our composites. Finally, these augmentations make this composite as potential candidates for energy harvesting.

The paper is organized as follows. In the next section, we present the preparation method of polymer materials. The obtained experimental results and their discussion are given in the Results and discussion section. Finally, the last section briefly concludes the paper in which we mention the main findings of our experimental study.

Experimental procedure Materials

The PA6 was chosen as polymer matrix for its good mechanical properties particularly its high tensile strength. We notice that most of PA tend to be semicrystalline and overall is very rough material with good thermal and chemical resistance.

PZT is characterized by a very high constant dielectric, high charge coefficient, and high electromechanical coupling coefficient. The PZT particles were provided by Ferropem (Denmark) with an average diameter of 1 mm. Bulk ceramic exhibits a Curie temperature of 235 C and a piezoelectric coefficient d 33 of 600 pC/N (given by the manufacturer in the bulky state). The former X-ray diffraction measurement has shown the ferroelectric properties of these inorganic fillers in a way the can acquire piezoelectric after a poling step. [START_REF] Carponcin | Electrical and piezoelectric behavior of polyamide/PZT/CNT multifunctional nanocomposites[END_REF]

Composite processing

The composite PA6/PZT was prepared in laboratory by solutions casting. The PA6 granules were first dissolved in formic acid at 120 C. Particles were dissolved in solvent using an ultrasonic probe. Thereafter, the dispersed microscale PZT particles were mixed with the polymer solution; they were agitated at a rotational speed of 100 r/min for 15 min. The films were manually placed on a glass plate and dried in the oven at 40 C.

Results and discussion

Material properties

Figure 1 shows the permittivity versus frequency for a filled PA6/PZT. We have calculated the dielectric constants of the obtained samples from the capacitance at room temperature by using a Hewlett Packard 4274 A multi-frequency LCR meter. We observed a large decrease of the dielectric constant around 30 Hz for 20%, 30%, and 40% of PA6/PZT composites when the frequency increased. This behavior is due to the loss of one of the polarization contributions (interfacial polarization) of the dielectric constant. [START_REF] Mitchell | An introduction to materials engineering and science for chemical and materials engineers[END_REF] Considering the value of the frequency, this decrease could be actually attributed to the loss of the space charges inducing an interfacial polarization contribution. Furthermore, we could neglect the contribution of the space charge for frequencies higher than some tens of Hertz. For pure PA6, the dielectric permittivity remained constant in the considered frequency range.

With 40% of microscale PZT particles, the dielectric permittivity of PA6 pure increases up from above 10 to 95.8. PZT content in PA6 raises the dielectric constant and also dielectric loss value of PA6 as displays the dielectric study of the composite system. However, high content of ceramic in PA6 leads to agglomeration of ceramic particles in polymer matrix, which introduces void and pores in the composite film (as shown in SEM Figure 6) and thus deteriorate the dielectric behavior.

The frequency dependence of the loss tangent for the filled PA (20%, 30%, and 40% by volume) and pure PA is shown in Figure 2. At lower frequencies, an important increase is observed in the loss tangent. While for higher frequencies from 50 Hz to 100 Hz, the value of the tangent loss for the filled PA was practically constant over the considered frequency range.

Piezoelectric coefficient

A polarization step is required in order to make the composites piezoelectric. It is governed by three parameters: the value of applied electric field, the time, and the temperature of polarization. The coercive field in PA6 is 30 times higher than that of PZT, which has been polarized in this study. In order to keep away from breakdown situations under strong field, the composite materials are immersed in a castor oil bath with the dielectric permittivity greater than to that of the air. In order to optimize the polarisation parameter, it is necessary to study the piezoelectric coefficient d 33 of the PA6/PZT composite with a thickness of 60 mm and PZT contents of 20%, 30%, and 40% vol. Figure 3 describes the piezoelectric coefficient d 33 of filled PA as a function of electric field, during the poling process. It is obvious that the piezoelectric activity appears at 16.6 kV/mm and reaches a maximum of 45 kV/mm. The coefficient d 33 increases with the volume fraction of PZT: the composite loaded at 40% of PZT induces a maximum d 33 increase of 7 pC/N for a poling field of 45 kV mm À1 . While the composite loaded at 20% vol is characterized by a coefficient of 4 pC/N; at 30% by volume, the coefficient d 33 is equal to 5 pC/N for the same value of electric field.

The piezoelectric coefficient values are directly related to the amount of the piezoelectric phase introduced in the composite. The SEM images showed a wide particle size distribution. At room temperature, the better piezoelectric coefficient is obtained with the PA6/PZT as shown in Table 1. Compared to the PA11/PZT 20 composite, the d 33 coefficient is increased by a factor of 2.6. This result indicates that the polarization of ceramic particles is enhanced at high dielectric permittivity of the polymer matrix. This result brings the conclusion that the polarization of ceramic particles is more efficient in case of an intrinsically high dielectric permittivity of the polymer matrix. Another phenomenon is susceptible to play a role in these results, a homogeneous distribution of electrical dipoles from the PA6/ PZT compared to the one induced by the PA11/PZT.

Hysteresis loop analysis

In order to measure the electrical properties, gold electrodes were deposited on the samples and then the poling process was performed in silicone oil at 166.6 kV/cm for the DC electric field. The hysteresis loops were getting by Radiant Precision Workstation ferroelectric testing system. Figure 4 shows the filled PA6/PZT hysteresis loops for various volume fractions. For comparison, the hysteresis loop of the pure polymer was also plotted. The results obtained show that below a low electric field, the PA6 has to make a hysteresis loop. PA6/PZT 20 vol%, PA6/PZT 30 vol%, and PA6/PZT 40% have the polarization saturation higher than the pure PA6.

Under an electrical field of 1 kV, the lower remnant polarization of filled PA film (0.17 mC/cm 2 )m a yb e affected by the random distribution of PZT (Figure 5). The higher remnant polarization (0.4 mC/cm 2 ) in our composites (20%, 30%, and 40% of PZT) can be attributed to the enhanced polarization from the dipole-dipole interaction of directly filled powders as well as fracture free and defect free composite formation in the polymer film.

Scanning electron microscopy

The microstructure and the morphology of the samples were characterized using scanning electron microscopy (SEM, Hitachi S-3500N). The samples were sputtered with a thin layer of carbon prior to SEM analysis at magnifications from 5Â and imaging was conducted at a voltage of 0 kV. SEM was used to study PZT dispersion in the PA matrix. To have elaboration conditions similar to that of various composites, the dispersion of the microscale particles of ceramics PZT in the PA6 was carried out for duration and a rotation speed of the screws of 15 min and 7 r/min, respectively. The compounds that have loaded at 20%, 30%, and 40% by volume, were prepared by solutions casting, are shown in Figure 6.

The surface microstructure of 20%, 30%, and 40% composites show that the PZT particles are distributed throughout PA6 matrix. For 20% and 30% PA6/PZT films, dispersion of PZT is found identical with very few pores as compare to other composition (40% PA6/ PZT). It could be seen that the ceramic incorporation dispersed homogeneously over the polymer matrix and there are no large agglomerations of ceramic powder. Nevertheless, higher volume of PZT in composition shows agglomeration with important number of void; it causes reduction in dielectric constant and hence increases in dielectric loss.

Mechanical testing

Principle and experimental setup. Rectangular test samples (20 Â 36 mm 2 ) were cut from our composites. Then, longitudinal traction was performed at 25 C using testometric traction machine at the max capacity 3 kN.

We have made our tests by placing the sample between two self-locked jaws where the superior one is movable.

For recording stress-strain measurements, an extensional rate of 2, 5, and 10 mm min À1 was used. When the specimens are geometrically similar, the comparative survey between different produced composites would be possible. The important information that can be got from this kind of study is that the stress result is equal to our measured force over the surface of the section. Another point, which must be taken in consideration is the awareness of the initial length of the sample as well as the elongation applied; allow the strain of the sample. The hook's law is an accurate approximation to describe the perfectly flexible solids.

In this law, the stress and the deformation are proportional and related by Young's modulus. The polymer retrieves its main extension when the value of the imposed deformation is reduced to zero. Beyond the elastic domain, the strain of the polymer becomes viscoelastic then plastic. [START_REF] Gendre | Mechanical properties of three-phase polyamide 6 nanocomposites[END_REF][START_REF] Regrain | Experimental and numerical study of creep and creep rupture behavior of PA6[END_REF] Experimental setup of traction.

Longitudinal traction. In this work, tensile properties of PA6/PZT composites were investigated. Stressstrain curves of PA6/PZT composites are reported in Figure 7 with different velocity. Equal diameters, the composites loaded at 20%, 30%, and 40% by volume are compared with PA6. The tests of these various composites were done with the same experimental tools used for the pure PA6 tests. On the other hand, we have used three different velocities for the traction test such as 2, 5, and 10 mm min À1 to exhibit the impact of the velocity along the tests.

In general, tensile modulus increases with PZT volume fraction: the composites are reinforced. For different filled composites and for a speed traction 2, 5, and 10 mm min À1 the maximum stress is close to the PA6 one for volume fraction at 20% and 30% (between 9 MPa and 16 MPa) and the rupture arrives above 1.5% of strain. At 40% of the volume, the tensile stress is at 8.8 MPa for the deformations less than 0.4%. We clearly see that the choice of the filler integrated to the PA6, is an important factor and have a great effect on the mechanical properties of the composites concerning the strain at break, two behaviors arise. The composites loaded at 20%, 30%, and neat PA6 present a ductile behavior since a plastic deformation remains above 0.5% strain. The composites loaded at 40% are characterized by a fragile behavior. We clearly observe in these figures, that the performance of tensile stress versus tensile strain is linear up to 3 MPa, and there is no major effect of the extensional rate on stress levels of PA6/PZT composites charged at 20%, 30%, and 40% by volume under 5 MPa. Results of the tensile tests for different composites are presented in Table 2. For different speeds, the obtained results clearly show that the addition of the particles in the starting matrices has an important influence on Young's modulus and on the surface, which describes the mechanical losses. This slight increase makes it possible to keep the flexibility of the elastomers for a good performance on actuation and to take advantage of the elevation of the relative permittivity by the incorporation of the particles for energy recovery.

Conclusion

By putting submicronic ferroelectric particles (PZT) into a semicrystalline thermoplastic matrix (PA6), a new composite has been elaborated by solution casting. In parallel, the dielectric and mechanical properties of the composites with different volumes were evaluated, where the dielectric ones are modified by the presence of PZT. The ferroelectric properties of the composite depend on the dielectric permittivity of the organic phase. Due to the insertion of PZT particles, the dielectric permittivity and the loss indices of the PA6 matrix have been increased. Furthermore, the piezoelectric coefficient increases with the content of the ceramic particles.

According to the SEM images, PZT particles are perfectly dispersed in the polymer matrix at a micronic scale and that the PA6/PZT composites have aggregates only up to 40% by volumes. On the other hand, the hysteresis loops of these composites exhibit a dependence on the ceramic volume fraction. In addition, a larger remnant polarization and coercive field have been obtained when the volume fraction increases from 20 vol% to 40 vol% of PZT. Finally, this work opens opportunities to improve thermoplastic-based composite with an excellent enhancement of the polymer dielectric permittivity.

Future works will concern the effect of the size of the particles PZT to increase the permittivity of the composite and its capabilities to harvest electrical energy on mechanical vibrations.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Figure 3 .

 3 Figure 3. Piezoelectric coefficient d 33 of 20% PA6/PZT, 30% PA6/PZT, and 40% PA6/PZT composites as a function of electric field.

Figure 1 .

 1 Figure 1. Dielectric permittivity of composites with different volume fractions as a function of frequency.

Figure 2 .

 2 Figure 2. Losses as a function of the frequency for the filled PA6.

Figure 5 .

 5 Figure 5. Remanent polarization (Pr) as a function of the PZT volume fraction.

Figure 4 .

 4 Figure 4. Hysteresis loops of the composites with different PZT volume fractions at 80 Hz.

Figure 7 .

 7 Figure 7. Stress-strain curves of the composites at different volume fractions with different velocities (a) 2 mm min À1 , (b) 5 mm min À1 , and (c) 10 mm min À1 .

Figure 6 .

 6 Figure 6. SEM image of (a) 20% PA6/PZT, (b) 30% PA6/PZT, (c) 40% PA6/PZT, (d) neat PA6 film, (e) SEM micrograph of PZT powder, and (f) layer thickness of composite 30% PA6/PZT.

Table 1 .

 1 Comparison of piezoelectric coefficients d 33 of 30% PA6/PZT and 30% PA11/PZT composites at 26 C.

	Composite	PA6/PZT	PA11/PZT 20
	d 33 (pC/N)	7	2.7

PA6: polyamide-6; PZT: lead zirconate titanate.

Table 2 .

 2 Tensile properties of the different composites at room temperature with velocity 2 mm min À1 .

		Maximal		Stress
	Composite	force (N)	Strain (%)	(MPa)	Y (MPa)
	PA6 pure	21.5	8.6	20.5	675.2
	PA6 20% PZT	16.1	1.8	13.4	990.3
	PA6 30% PZT	11.8	1.01	9.7	1356.2
	PA6 40% PZT	19.4	0.9	14.6	2091.4
	PA6: polyamide-6; PZT: lead zirconate titanate.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.


J Brandelero
email: j.brandelero@fr.merce.mee.com

P Pichon

M Legros

Impact of Heat Treatment on the Lifetime of Wire-Bonded Power Modules

Wire bondings in power modules are one of the weakest links in the packaging, often leading the entire power module to failure. Thermo-mechanical stresses in the wire bonds related to CTE mismatch induce cracks that propagates in a region close to the bonding interface. In this paper, Scanning Electron Microscope (SEM) analysis after a bonding process clearly shows small grains and a different texture close to the interface of the wire and the die metallization. In order to improve the reliability of the wire bonds, a heat treatment after power module manufacturing is proposed. The heat treatment affects positively the bonding region by increasing the grain size, reducing the dislocation density and merging the grains of the wire and the metallization. Furthermore, power cycling has been performed showing an increase of the lifetime on the heat-treated power modules compared to a reference composed by the same non-treated (as-delivered) power IGBT's modules.

Introduction

In wire bonded power modules, one of the most dominant failure mode is wire bond lift off. It is known that the ultra-sonic bonding process creates small/micro-cracks at the bond tail, which precipitates the formation of the cyclic strain driven crack, leading to the eventual wire bond lift off [START_REF] Agyakwa | Damage Evolution in Al Wire Bonds Subjected to a Junction Temperature Fluctuation of 30 K[END_REF]. The bonding process induces significant microstructural changes and grain refinement above and in the metallization area due to strain hardening and dynamic recrystallization during the bonding process (e.g. [START_REF] Dornic | Élaboration et comparaison de deux modèles de durée de vie des fils d'interconnexion des modules de puissance, l'un basé sur les déformations et l'autre sur les dégradations[END_REF] [3] [START_REF] Ruffilli | In-depth investigation of metallization aging in power MOSFETs[END_REF], [START_REF] Ruffilli | Aluminum metallization and wire bonding aging in power MOSFET modules[END_REF]).

At the same time, several reports have shown a significant effect of the presence of oxides layer on the bond quality [START_REF] Ciappa | Selected failure mechanisms of modern power modules[END_REF], [START_REF] Ruffilli | Fatigue mechanisms in Al-based metallizations in power MOSFETs[END_REF], [START_REF] Arjmand | Predicting Lifetime of Thick Al Wire Bonds Using Signals Obtained From Ultrasonic Generator[END_REF], [START_REF] Loh | Wire Bond Reliability for Power Electronic Modules -Effect of Bonding Temperature[END_REF]. One of the roles of the ultrasonic energy is to smear the native oxide layer at the metallization and wire and expose high energy surfaces for boding. Previous works demonstrated significant positive effect of oxide plasma cleaning [START_REF] Nowful | Effects of plasma cleaning on the reliability of wire bonding[END_REF] and/or reduced time of storage prior to bonding on bond strength and degradation rate.

A positive effect of a higher average temperature during thermal cycling on bond shear strength degradation rate was demonstrated in [3], [START_REF] Matsunaga | Thermal Fatigue Life Evaluation of Aluminum Wire Bonds[END_REF]. This was attributed to two thermally activated processes:

1. Wire-metalization interface stabilization: interdiffusion between metallization and wire material, ripening of oxide precipitates, 2.Material damage reduction: grain growth, softening of the material and dissipation of residual, or cycling-induced damage (dislocation structures).

Futhermore, a post-wirebond heat treatmen in the Al wires bonding on the rage of 280°C to 400°C demonstrated an increase in reliability in [START_REF] Wu | Reliability Improvement of Aluminum Wirebonds in High-Power IGBT Modules[END_REF], and an increase of the adhesion strength between Cu wirebonding to the Al bond pad in [START_REF] Yun | Cu wire bond reliability improvement through focused heat treatment after bonding[END_REF].

In this paper, a heat treatement after wire bonding is proposed to increase the lifetime with temperatures on the safe operating area of the power modules (150°C-175°C). The aim of this heat treatment is to induce recrystallization between the wires and the metallization and increase the grain size in the bond. Consequently, tougher material properties are achieved with a softer material that can endure higher plastic deformations and a reduced crack growth rate.

In the fist section of this paper the experimental heat treatement and power cycling tests are presented. The last section details a microstructure analysis and comparison of wire bonds between as delivered and thermal treated power modules.

Experimental tests and results

Sample preparation

Thermal treatment preparation procedures were developed to apply the heat treatment on IGBT power modules. The power module samples are state-of-art IGBT devices (150A rated current) with 23 bonds of Aluminium wires per die having a diameter of 400µm. Two batches of thermal treatements were conduced without deteriorating the thermal interfaces, as the maximum specified junction temperature (175°C) was respected:

1. The first batch was heat treated by applying a DC current of 150A for 96 hours through the collectoremitter of IGBT dies, inducing a temperature of approximately 160°C by Joule heating. The temperature of each die was controlled using optical fiber infrared sensors (OpSens OTG-F-10-62LCA-2.5PTFE) with the associated RadSen-2 system. Accurate and identical positionning of the optical fibers on each IGBT die surfaces was ensured using a 3D printed holder (Figure 1a).

2. A second batch was prepared to generate two samples from a same power module for microstructural analysis in a SEM (Scanning Electron Microscopy): one heat treated sample and one asdelivered sample. As a result, the wirebond microstructure comparison will be based on IGBT dies and bonds produced with the same process conditions and bonding parameters. For this sample, the baseplate of the power module was cut to thermally decouple both IGBT dies. To force a large thermal gradient, one side of the power module was attached to a cold plate (at 15°C) and the other side, to be thermally treated, was kept in air, as shown in Fig. 1b. A low current of 7A was then injected in a desaturated IGBT at 5.6V of Vge. The voltage across the IGBT was then around 17.8V, generating 124W of power dissipation and a junction temperature of 165°C, as measured with the optical fiber-based infrared sensor. The non-treated power device junction temperature was measured at 35°C. The treatment was applied for 91 hours. No significant modification was observed visually on the power module after treatment. Overall, 4 power modules were prepared. The first 3 were thermally treated with the first method at 165°C/96hours and then power cycled. The 4 th power module was prepared following the second method (heat treated die: 165°C/91hours, non-treated die: 35°C/91hours). 3 other non-treated (as-delivered) power IGBT were taken for reference and power cycled with the first 3 heat-treated power IGBTs.

Power cycling tests

The Tj(Vce) dependency of the power modules was calibrated and the power modules were power cycled with a cyclic direct current test bench under the following conditions: Δ𝑇𝑗 ≈ 90𝐾, 𝑡𝑜𝑛 = 3𝑠, and Tj𝑚𝑖𝑛 = 45°𝐶. The individual Δ𝑇 𝑗 was ranged from 88K to 102K while conducting a maximum of 150A.

The power cycling tests were stopped given the wire lift-off causing a Vce increase of more than 5%. In general, the modules without the heat treatment had a smaller Δ𝑇 𝑗 , but regardless, there was a significant improvement (more than 20%) in lifetime for the set of 3 IGBTs that underwent heat treatment, see Figure 2. The solid lines in Figure 2 represents a damage-law (𝑁𝑓 = 𝐴 • ∆𝑇 𝛼 ) with the coefficient α determined with other power cycling tests at various ∆𝑇 using the same non-treated power module but not shown in the figure and the coefficient A is determined to reduce the error from the power cycling data. While all the devices from the test failed in the same way, an interesting behavior is observed from the evolution of the on-state voltage during the lifetime of the untreated power dies against the treated power dies. As shown in Figure 3 with approximately the same Δ𝑇𝑗 value the first wire bond lift-off occurs later for the treated dies, and at a higher on-state voltage evolution (101.8% against 103.6%).

Micro-structure analysis

A typical procedure to determine the quality of the wire bond interconnection is to measure the strength of the interface between the bond wire and the metallization, usually through shear and pull tests [START_REF] Goehre | Interface degradation of Al heavy wire bonds on power semiconductors during active power cycling measured by the shear test[END_REF]. Here, motivated by the lifetime increase induced by the thermal treatement, we focused on the microstructure of the wire bonding in order to understand the impact of the ultrasonic bonding process and the heat treatment.

Effect of bonding process on Al bonds microstructure

The Aluminum wire bond microstructure of an asdelivered module was analysed by Electron Back Scattering Diffraction (EBSD). At low magnification (figure 4a), three zones could be distinguished:

An 'unaffected' zone, where the microstructure of the wire is largely unchanged from wiredrawing. Grains are preferentially oriented with their x-axis aligned with the wire direction as a result of the wiredrawing process ('red grains').

A process-affected zone (below the black line), where grains show sub-structures/ sub-grain boundaries (dark lines within the grains under band contrast map). These sub-structures are dislocation networks which are formed because of the strong deformation during the bonding process. The material is likely hardened in this area.

A second region with refined grains, close to the metallization (below the white line). Previous works have shown that during power cycling the fatigue crack propagated preferentially at large angle grain boundaries in this zone.

Significant microstructure transformations occur during wire bonding process. High density of local misorientation is often correlated to the presence of high concentration of geometrically necessary dislocations. Figure 4b shows the local misorientation of the as-delivered power module where each pixel orientation is compared to its neighbor. The dislocations formed during the wire bonding process merged to form sub-grain boundaries. Thus, the local mechanical properties are likely affected by this work hardening effect. The dislocations are defects that store energy in the material that can drive recrystallization and recovery phenomena. The mean grain size is larger for the treated power die in comparison to the 'as-delivered', as shown in Figure 6. The analysis was conducted on the interface region (below the white line of Fig. 4a) and on the central position (below the black line of Fig. 4a). The mean equivalent diameter is respectively 3.82µm and 8.54µm for the non-treated and treated power module at the interface and 4.32µm and 5.9µm at the central wire position. Fig. 6 Evolution of the grain size at the interface regions and at the center of the bond.

Bond interface before cycling

At higher magnification a continuous string of Aluminium oxides particles is observed at the position of the original metallization surface on the not treated chip. Comparatively the string of Aluminum oxide particles is more dispersed on the thermally treated chip, see Figure 7. EBSD maps were acquired at high magnification at the wire-metallization interface to identify whether the grain structure of the metallization and the wire material merged, see 8. A zone dynamically recrystallized during bonding can still be identified on the heat treated sample showing as 'green grains' on x-axis projection. Only at one point over the total analyzed interface length of 785μm could be observed a merging of the grains of the wire and the metallization (at the red arrow). This indicates that the process of thermal treatment can be improuved more in the future. After thermal treatment some grains seem to have 'merged' between the wire material and the metallization showing that interdiffusion was more pronounced. Measured by the intercept method, the mean grain size is slightly larger for the treated chip in the metallization (4.6μm versus 3.6μm). In the wire material, 10μm away from the interface, the same method leads to an average 9.0μm grain size in the treated cheap versus 6.2μm in the non-treated one. EBSD measurements shown in Figure 6 show the same trend for grains in the wire, both in the plastic-affected region and away from it. Fig. 8 High magnification EBSD analysis at the bond interface after thermal treatment. projection on the x axis (green)

Metallization-wire interface after cycling

At the end of life of the power modules, the fracture surfaces are similar for the as-delivered module and the heat-treated module. FIB cross-section through the remaining material shows that in both the treated and non-treated chips, the oxide particles are more dispersed than on the as-delivered chip, Figure 9. Fracture occurred at variable distance from the chip surface in both cases, sometimes below and above that aluminium oxide string.

Conclusions

The thermal treatment promoted interdiffusion between the metallization and wire and slight grain growth. The EBSD results so far are consistent with literature description of grain growth and recrystallization. However, it is not yet clear whether in our case the lifetime improvement is dominated by the effect of 1) wire-metalization interface stabilization or that of 2) ultrasonic bonding defect healing, relaxation in the material.

If 1) dominates: we should expect a significant effect of the initial thermal treatment on the crack path, the nont thermal treated dies should fracture more at the interface. The improvement is also expected to saturate. To test this hypothesis the effect of the thermal treatment on the propagation path should be studied in more details.

If 2) dominates: heat treatment by applying a temperature step should have a cumulative effect. Initial annealing should remove the damage in the ultrasonic process affected zone ('one-time' effect). This was visible by comparing large area EBSD analysis before and after initial annealing.

Periodic heat treatment during PC cycling may also relax the damages induced by cyclic plasticity and creep and suggest a new domain of repairable wire bonded power modules. The thermal control techniques [START_REF] Murdock | Active Thermal Control of Power Electronic Modules[END_REF] are good candidates for heat treatment for on-line applications.

Finally, the heat treatment conditions were not optimized, as shown by the remaining dynamically recrystallized grains that still visible after treatment) and merit to be optimized to further extend the lifetime of a power module. Furthermore, investigations on different power cycling conditions are necessary to validate the approach for a product application.

Acknowledgement

Thank you ELEMCA, Toulouse-FR, that conducted the low magnification SEM-EBSD analysis.

Fig. 1 .

 1 Fig. 1. Heat treatment for power modules a) with high current b) with desaturated IGBT

Fig 2 .

 2 Fig 2. Lifetime comparison between reference power die and heat-treated power die.

Fig. 3 .

 3 Fig. 3. Vce evolution during power cycling with the indication of the first wire bond lift-off

Fig. 4 .Fig. 5

 45 Fig. 4. As-processed wire bonding a) EBSD orientation map: projection on the x axis (red) b) local misorientation >0.5° colored in green. (scalebar: 500µm)

Fig. 7

 7 Fig. 7 High Magnification SEM analysis at the bond interface a) as-delivered b) heat treated

Fig. 9

 9 Fig. 9 SEM analysis of the wire-metallization interface after power cycling a) as-proceeded b) thermally treated

  20μm


César Debeunne

Alex Torres

Damien Vivet

Design of a bi-monocular Visual Odometry System for Lava Tubes exploration

With the discovery of potential extra terrestrial Lava Tubes, their exploration has become a hot topic for space agencies. Autonomous robots are needed to answer many questions that are raised by their discovery. We propose in this paper to discuss the design of a feasible and performing Visual Odometry (VO) solution to enable a safe navigation for spatial rovers in such environment. For this, we propose a modular bimonocular indirect approach adapted to every camera model while keeping the processing load as low as possible. This paper presents an experimental study in a self illuminated cave environment. We focus on keypoint / descriptor pairs, feature association modalities and camera models. We show results on both real and simulated scenario to enhance the comprehension of methods widely used in the robotic community and their adaptation to such environment. Results from these experiments will be used to design a visual based navigation adapted for extra terrestrial Lava Tubes exploration.

I. INTRODUCTION

Spatial exploration is a exciting and challenging application of robotics that demands an advanced level of autonomy while using low embedded power and processing capabilities. Planetary robots are mostly Unmaned Ground Vehicles (UGV) that rely on several sensors to execute autonomous tasks. To navigate in an unknown environment, a robot needs to perform state estimation and mapping in order to plan and follow trajectories. On the second successful rover mission on Mars in 2004, the Mars Exploration Rovers (MER) [START_REF] Goldberg | Stereo vision and rover navigation software for planetary exploration[END_REF], a pair of stereo cameras is used for VO and point cloud generation to navigate safely in hazardous terrain. However, spatial context imposes computational limitations: the motion of the rover was only estimated with two stereo pairs thanks to a Maximum-Likelihood estimator. On Mars Science Laboratory (MSL) mission in 2012, a similar but faster and more robust algorithm was implemented [START_REF] Johnson | Robust and efficient stereo feature tracking for visual odometry[END_REF]. The observations from the MER mission were determinant to highlight the main improvements necessary for a better solution [START_REF] Maimone | Two years of visual odometry on the mars exploration rovers[END_REF]. Important wheel slippage was noticed during this mission. As a result, odometers measurements are not incorporated into the navigation solution.

Recently, satellite images from Lunar and Martian volcanic areas show features that may be interpreted as lava tubes [START_REF] Sauro | Lava tubes on earth, moon and mars: A review on their size and morphology revealed by comparative planetology[END_REF]. These hypothetical caves seem similar to their terrestrial analog, but subsurface exploration is needed to determine their precise morphology. Moreover, as a consequence of the small gravity, they could be large enough to firstname.lastname@isae-supaero.fr 2 Alex Torres is with the CNES, France alex.torres@cnes.fr host artificial bases shielded from radiation. Thus, robotic exploration in a lava tube context may be the goal of a future extra terrestrial mission and an appropriate navigation software needs to be developed. Such missions require to push further the navigation capabilities of the rovers while keeping in mind the intrinsic limitations and constraints of spatial technologies.

Cave mapping has gained a lot of interest during the Subterranean Challenge that saw many solutions reaching outstanding performances [START_REF] Reinke | LOCUS 2.0: Robust and computationally efficient lidar odometry for real-time 3d mapping[END_REF]. Most of them use rotating LiDARs and redundancy in the system to reach high levels of robustness. However, rotating devices like LiDARs are not ready to be send in space yet because of their power consumption, bigger mass and reliability concerns regarding their fast spinning motors. Moreover, redundancy in the system requires too much power and processing cost for spatial applications. The only mature LiDAR solution for space is the solid state LiDAR but, such device provides a very narrow Field of View (FoV) and is more dedicated to traversability analysis. In the context of cave mapping an important FoV is required in order to optimize both the mapping and the localisation capabilities of the rover. It has been shown that a Stereo Fisheye setup, which has a wider FoV, may offer larger navigability maps for rover navigation [START_REF] Torres | Omnidirectional stereoscopic vision systems for planetary exploration rovers[END_REF].

Consequently, visual navigation is the solution that needs to be studied in this context. On Earth, the robotic community has reached a very good knowledge of the Visual SLAM problem. Versatile and robust systems have emerged in the past few years in both direct [START_REF] Engel | Direct sparse odometry[END_REF] and indirect [START_REF] Mur-Artal | ORB-SLAM2: An open-source SLAM system for monocular, stereo, and RGB-d cameras[END_REF] fashions. However, these systems have also reached a great degree of complexity. Many design choices in the SLAM pipeline deserve to be discussed to improve our knowledge of these powerful tools and for a potential use of VSLAM in space application.

A major issue in the use of visual sensor in such environments is that it requires artificial light to operate. Thus, we propose to investigate a design solution for a bi-monocular VO system for lava tube navigation with onboard illumination. This paper sheds light on three design choices and is the support of a preliminary work toward a pertinent visual navigation solution for extra terrestrial lava tube exploration:

• Keypoint and Descriptor choice for feature extraction and association, • Method for associating features frame to frame, • Comparison between standard and wide angle camera setup.

II. NOTATION

In this paper, we note the pose of a camera at timestamp i in the world frame as w T c i ∈ SE(3). We parameterize landmark j with its 3D position in the world frame l w j ∈ R 3 . We can compute the coordinates of j-th landmark in the i-th camera frame with l c i j = w T -1 c i l w j = c i T w l w j . We denote the projection function of a camera π : R 3 -→ R 2 that maps a 3D point in the camera frame in the 2D image x i, j = π( c i T w l w j ). We note abusively π -1 : R 2 -→ R 3 the function that computes the bearing vector of a given pixel u i, j = π -1 (x i, j ). We work with a set of keyframes in a sliding window W and each keyframe K i has a set of map point L i . We concatenate all landmarks and keyframe poses in a state vector X.

III. SYSTEM OVERVIEW

In order to evaluate the performances of a bi-monocular VO design in an underground cave exploration context, we first need to get a simple modular baseline odometry framework. This section aims to present the proposed baseline with some specificities (Figure 2).

A. Feature detection 1) Image pre-processing: A first mandatory step while navigating in dark environment with artificial illumination is to enhance the contrast of the image. Indeed, due to the lighting conditions, the appearance of the environment is changing as the robot moves. The image pair taken by the robot at each step is first pre-processed with CLAHE [START_REF] Yadav | Contrast limited adaptive histogram equalization based enhancement for real time video system[END_REF].

2) Feature extraction and association: Then the features have to be detected and associated between the different acquired images. As in classical bi-camera approaches there is two association steps: between cameras from the same frame and between successive frames on one of the two cameras. We compared and evaluated two techniques to proceed such association: tracking and matching (see Section IV-B). Finally, the map is updated with the matched features and a landmark recovery phase is performed to recover lost features due to illumination change or occlusion.

B. Estimation step and match rejection

From the matches between the currently detected features and the map landmarks, a first pose estimation is produced using P3P algorithm [START_REF] Kneip | A novel parametrization of the perspective-three-point problem for a direct computation of absolute camera position and orientation[END_REF] in a RANSAC fashion to remove false feature-to-landmark associations.

A second outlier rejection phase is performed by checking the epipolar constraint due to the newly estimated camera motion. Instead of checking the classical distance to the epipolar line (or curve in the case of fisheye camera), we propose to check the angle to the epipolar plane (Figure 1). This rejection method makes use of bearing vectors and can be generalized to any camera model with less computational time. The residual δ e can be computed as follow: with t = t ||t|| being the direction of the translation vector between the two views and u 1 , u 2 the bearing vectors of the same observation in both views.

δ e = π 2 -arccos t × u 1 .u 2 , (1)
If δ e is superior to a threshold, the new matched feature can be classified as an outlier. Finally, a pose refinement is performed with a classical single frame bundle adjustement.

C. Keyframe selection

As we have limited power and memory on embedded devices, the number of frames to keep in memory has to be reduced while retaining the maximum information. We use the parallax information as a keyframe indicator as we initially proposed in [START_REF] Vivet | Pavo: a parallax based bimonocular vo approach for autonomous navigation in various environments[END_REF]. Parallax can be seen as an increase of information over each landmark: a bigger parallax value enables a more precise landmark triangulation. If the average parallax increase of all the landmarks in the map since the last keyframe goes over a certain threshold, the new frame has to be kept in memory. This metric does not take into account landmark loss due to illmination change for instance, so we also select a keyframe if the number of tracked landmark since the last keyframe goes below a certain threshold.

D. Landmark initialization

In order to reduce computation, we choose to initialize landmarks only when a keyframe is voted. At this time, all the landmarks linked with a feature that was associated with the previous keyframe are initialized. We prioritized features that were associated on both left and right cameras, then features that were associated on left cameras only and finally, if the number of features is still too low, landmark are initialized from left / right associations of the current frame.

In most cases, landmarks are initialized from more than two views. Thus, we implemented a generalization of the mid-point algorithm to n-points for triangulation of landmarks. However, the 3D triangulation doesn't return the optimal landmark position in term of reprojection error as the residual is in the 3D space and not in the 2D observation space. This rough initialization is then followed by the minimization of the reprojection error To mitigate the influence of outliers, we apply the robust Huber norm ρ to our reprojection error in the first iterations. Based on the mean reprojection error, an outlier rejection is finally performed to filter out wrong landmarks.

L * i = arg min L i ∑ l w j ∈L i ||x i, j -π( c i T w l w j )|| ρ . (2)

E. Local Map optimisation

Finally, a Bundle Adjustement (BA) step is performed on a sliding window of keyframes by minimizing the reprojection error of every landmark l w j observed in our window

W X * = arg min X   ∑ K i ∈W ∑ l w j ∈L i ||x i, j -π( c i T w l w j )|| 2   . (3)
We solve this problem with the Levenberg-Marquardt algorithm from the library Ceres. To reduce the processing time and because of the multiple outlier rejection mechanism, the Euclidean norm is now used in the global BA step.

IV. DESIGN CHOICE AND VALIDATIONS

From the previously introduced modular VO framework, we investigate the impact of different designs on both the performances and processing time. We focus on three main points :

• the feature choices,

• the association step,

• the camera model. The impacts of such design choices have been analysed on both simulated and real data. Real data were provided by the OIVIO dataset [START_REF] Kasper | A Benchmark for Visual-Inertial Odometry Systems Employing Onboard Illumination[END_REF], that provides video sequences in dark scenes with self illumination. Simulated data were made on Gazebo, in a cave world inspired by the Subterranean challenge [START_REF] Koval | A subterranean virtual cave world for gazebo based on the darpa subt challenge[END_REF]. The software has been developed in C++, and all experiments has been performed by a desktop station equipped with an Intel Core i7, 3.2 GHz clock rate. Even for SuperPoint extraction, we have not used a GPU.

A. Keypoints and Descriptors 1) Comparison of keypoints in artificial illumination conditions: In any indirect SLAM methods, sparse representation of the observations are composed of keypoints. Such features must be stable over time, robust to changes in pointof-view and illumination conditions so they can be matched over frame. Moreover, we aim to have low computational cost for both keypoints extraction and descriptor calculation. We propose to follow Ferrera et al [START_REF] Ferrera | Real-time monocular visual odometry for turbid and dynamic underwater environments[END_REF] work on submarine navigation, by implementing additional solutions and adapting their approach to subterranean images using onboard illumination.

We select and compare the most used features from the robotic community namely: SIFT [START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF], KAZE [START_REF] Fernández Alcantarilla | Kaze features[END_REF], ORB [START_REF] Rublee | Orb: An efficient alternative to sift or surf[END_REF], BRISK [START_REF] Leutenegger | Brisk: Binary robust invariant scalable keypoints[END_REF], FAST+ORB and SuperPoint [START_REF] Detone | Superpoint: Selfsupervised interest point detection and description[END_REF]. Super-Point is a learned detector based on a Convolutionnal Neural Network architecture. We used the pre-trained model from the original publication. KAZE, SIFT and SuperPoint are obviously too computationally expensive for our application, nevertheless we think that studying their robustness in challenging lighting conditions is of interest for the community.

2) Experimental comparison: To study the performance of each detector / descriptor pair, we have run our VO on a trajectory of the OIVIO dataset (MN 050 GV1). The configuration was the same for every experiment: 500 keypoints were extracted in each frame, with a bucketing strategy for a better spatial dispersion of keypoints. The feature association is done by matching.

We have computed several indicators:

• The full extraction process time, including the nonmaximum-suppression and the bucketing. • The percentage of outlier per matching: it describes the ability to match reliable features. It has to be compared to the total number of match to have an idea of the global quality of the feature association. The outlier detection was done via essential matrix computation in a RANSAC scheme. Descriptor matching is done by computing the distance between the descriptors of keypoints. In our system, when we match points in two consecutive frames, we compare a keypoint from the first frame with all the keypoints in a rectangle centered on the same position in the second frame. The size of this rectangle is a hyperparameter that can be tricky to tune as it depends on the frame rate and the dynamics of the robot. A trade off between computation load and the level of motion allowed between frames has to be found.

Tracking is performed using Kanade-Lucas-Tomasi (KLT) algorithm. It is based on optical flow computation on different scale pyramids of the images [START_REF] Bouguet | Pyramidal implementation of the lucas kanade feature tracker[END_REF]. To avoid wrong tracks, we implemented it in a "forward backward" fashion. The tracking is performed from the first frame to the second one and the tracked features are tracked back from the second frame to the first one. If the initial point is not recovered, the track is considered wrong. This method is based on the optical flow equation that is valid under the constant intensity hypothesis. Only small motions, in a short timeline can produce valid tracks. A good point is that features do not need to be detected on each frames while this is needed for matching. In our pipeline, frames are repopulated with features only for keyframes. The difference between our VO matching based and our VO tracking based can be observed on figure 2.

2) Association performances: We compared the performance of both feature association strategies on the OIVIO dataset which provides six sequences in a mine on a UGV with groundtruth. Three levels of onboard light intensity (1500, 5000 and 10000 lumens) are tested on two different trajectories. The Absolute Trajectory Error (ATE), Relative Pose Error (RTE) and the average duration of an iteration are the metrics evaluated. The couple FAST+ORB was chosen for all these experiments and the results are presented on table II. For these experiments, 1000 keypoints were detected on each frame with Matching while 250 keypoints were detected on each Keyframes with KLT.

In most cases, Matching based VO seems to be more accurate than KLT based method, especially on the RTE metric. When keypoints are tracked, as the point is not redetected at each frame, there can be a small drift over time which can explain the loss of accuracy. But for every sequence, KLT design is faster. The necessity to detect keypoints on each frame in the Matching case increases the average running time. Also, we noticed that more Keyframes were voted due to a lack of features tracked with the Matching design and Keyframes require more computations than frames. KLT enables to track features on more frames (Figure 3) so that Keyframes are more spaced in time.

In both systems, there seems to be no influence of the light intensity on the global performances. The image processing step permits to handle well low enlighten scenes. This is a good point as it shows that heavy power lights are not mandatory to perform VO in such conditions. The performances of ORBSLAM2 [START_REF] Mur-Artal | ORB-SLAM2: An open-source SLAM system for monocular, stereo, and RGB-d cameras[END_REF] on these sequences are also provided on table II. Its accuracy is better but it comes at a higher computational cost, mainly due to its restrictive landmark selection and complex map management.

C. Classical vs Fisheye optics 1) Camera model choice:

Capturing an image flow is a fundamental piece of a VO system. Choosing the device with the most suitable Fov depends mainly on the application. For earth based applications like autonomous vehicles, high frame rate and classical optics are the standard as the FoV is mainly focused on the front of the vehicle and the positioning relies mainly on Global navigation Satellite System (GNSS). Intuitively, a wide FoV may help to maintain features in sight for a longer time to make the navigation more robust. This is why, when going in GNSS denied environment, the FoV is increased using multiple sensors or rotating LiDAR to improve the localisation and mapping capabilities. In the case of spatial applications, none of these solutions is possible. The increase of the FoV is directly linked to the number of sensors, the optics of the camera or the use of a rotating head on a mast. In this section, we aim at investigating the improvement of using fisheye over standard camera. A classical lens can be modeled by the well known "pinhole" model. Given a 3D point in the camera frame x ∈ R 3 , the projection function of a pinhole camera is defined with four parameters { f x , f y , c x , c y } as

π(x) = f x x z f y y z + c x c y . (4)
However this function cannot represent wide FoV cameras, as it goes to infinity for points with an angle of view close to 180°. To address this problem, we propose to model fisheye lens with the normalized spherical model

π(x) = f x g(θ )x r f y g(θ )y r + c x c y , r = x 2 + y 2 , θ = arctan 2(r, z), (5)
with g(θ ) a function that gives the distance of the projected point from the optical center given the angle of view. This mapping function depends on the type of lens used, a summary of the different mapping functions is given on Table III. We provide bellow the comparison between these two models considering both processing time and accuracy.

2) Influence of the Camera model: On our simulated dataset, both fisheye (with an equidistant mapping function) and classical camera pairs were simultaneously mounted on the robot, at the same position and with the same orientation. The respective camera resolution are 848×848 and 1280×720 for the fisheye and pinhole cameras. For this experiment, the tracking design with FAST keypoints was implemented as it was retained as a good compromise from the two previous sections. The sequence lasts 200 seconds and is 70m long. Onboard illumination is simulated and the images were provided at 10 Hz. This cave environment is poorly textured and offers challenging conditions for VO (Figure 5). According to table IV, the fisheye setup outperforms the standard setup in term of accuracy, number of feature tracked and length of tracks. On figure 4, we note that with the classical camera setup, drift can be accumulated at some points of the trajectory. It is especially the case at moments when the robot is facing poorly textured surfaces, many landmark are then lost and the pose estimation is corrupted. In such cases, the wide angle camera enables to keep more landmarks in sight to keep a consistent estimate.

V. DISCUSSION

Due to space rover constraints, current state of the art visual navigation solutions are not directly applicable as they are too complex and computational power consuming. This preliminary work discussed some specific points for a simple VO design and dig into existing works to get some insight for the development of a VO dedicated to lava tube exploration. However, some points are left for future research:

• Considering illumination changes, we applied CLAHE as an image enhancement technique, but other methods exist. For instance, a simple histogram equalization or an adaptative gamma correction should be tested [START_REF] Veluchamy | Image contrast and color enhancement using adaptive gamma correction and histogram equalization[END_REF]. • In this first design, we simply discard measurements when a frame is removed from the sliding window. This procedure leads to an information loss that can be compensated with marginalization [START_REF] Sibley | Sliding window filter with application to planetary landing[END_REF]. Such an operation enables to have a prior on our problem for a better accuracy. But this comes at a certain computational cost that may be too demanding for spatial application. A solution for this can be to explore sparsification methods [START_REF] Hsiung | Information sparsification in visual-inertial odometry[END_REF] to make it suitable for our requirements. • Moreover, as the proposed solution is bi-monocular, the method is highly dependent on the assumption of a good rigidity of the transform between the cameras. Under the constraints of launch, cruise and planetary operation, the extrinsic cameras calibration may change. Works to include the calibration as a parameter or using constraint in the estimation [START_REF] Vivet | Robust filterbased visual navigation solution with miscalibrated bi-monocular or stereo cameras[END_REF] have to be investigated to improve the global robustness of the system. • Our conclusions on the choice of the camera lens will be useful to build an experimental setup for real data acquisition. With real fisheye images, the question of which camera model we should choose will be raised. The presented model is not the only one available [START_REF] Usenko | The double sphere camera model[END_REF], an investigation for an accurate and low computational model will be needed. • Finally, the proposed analysis of features, descriptors and association strategies from this paper will be extended for real fisheye images to validate our conclusions.

VI. CONCLUSION

This paper presents a modular VO system, able to handle both pinhole and fisheye cameras, and an experimental study of some of its essential components. We proposed a simple design for extra terrestrial lava tube exploration and justified our choices with comparison experiments on both real and simulated data with onboard light and in unstructured environments. The proposed fisheye based VO solution shows good performances in simulated data and limits drift in comparison with a standard setup. Our future work will focus on image processing, VO back-end and camera modelling to reduce the estimation step complexity and the global power consumption.

Fig. 1 :

 1 Fig. 1: Illustration of the epipolar angular error. ∏ is the epipolar plane, {C 1 ,C 2 } are the optical centers of the two views and {u 1 , u 2 } are the two bearing vectors of landmark l observation.

Fig. 2 :

 2 Fig. 2: Pipeline of both matching based and tracking based Visual Odometry. Steps relative to tracking design are in red, whereas boxes referring to matching design are in blue.

Fig. 3 :

 3 Fig. 3: Histogram that represents the lengths of tracks i.e. the number of keyframes on which a landmark is detected for a matching based VO and a tracking based VO.

Fig. 4 :

 4 Fig. 4: Trajectories returned by our VO in a stereo fisheye setup and a standard stereo camera setup on the simulated dataset.

Fig. 5 :

 5 Fig. 5: On the left, a Fisheye image from the simulated sequence and on the right a standard image from the same frame.

•

  The average number of matches per frame pair before filtering.• The track length i.e. the number of matched features per landmarks.The results are presented in table I. KAZE and SIFT offer obviously superior performances in terms of confident point selections but KAZE is disappointing on track length. Its robustness to light changes is limited. BRISK and ORB have similar performances in frame to frame matching, but BRISK has less repeatability. ORB descriptor is quite robust

TABLE I :

 I Performance comparison between the selected detector / descriptor pair. In order to get multiple views of a given keypoint, two main techniques have emerged in the literature: descriptor matching or feature tracking.

		dt (ms) % outliers matches / frame track length
	SIFT	71	1.0	180	9
	KAZE	66	1.5	220	6
	ORB	15	6.9	175	6.8
	FAST/ORB	5	3.4	95	10
	BRISK	25	5.9	200	4.5
	SuperPoint	350	8	280	9.0
	to lighting changes and the combination FAST + ORB is
	the most effective for associating features on the long run:
	less points are matched, but they are matched longer. BRISK,
	ORB and KAZE produce binary descriptors that are matched
	efficiently with the Hamming distance, SIFT produces patch
	descriptors that are matched with L2 norm that is more
	computationally expensive. SuperPoint seems also effective
	in our context as it can match a lot of points and track them
	for a great number of keyframes. However, such a solution
	is not suitable for real time applications on a power limited
	hardware.
	B. Feature Association Strategies
	1) Matching vs Tracking:

TABLE II :

 II Performances on OIVIO Dataset

					KLT			Matching			ORBSLAM2
	Scenario	Distance(m) Duration(s) ATE(m) RTE(m) dt(ms) ATE(m) RTE(m) dt(ms) ATE(m) RTE(m) dt(ms)
	MN 015 GV1			0.19	0.07	33	0.38	0.04	35	0.11	0.04	43
	MN 050 GV1	80	218	0.26	0.08	25	0.43	0.05	39	0.12	0.04	47
	MN 100 GV1			0.35	0.09	24	0.25	0.06	39	0.14	0.05	46
	MN 015 GV2			0.13	0.04	25	0.14	0.04	38	0.11	0.03	40
	MN 050 GV2	82	150	0.15	0.04	30	0.10	0.03	30	0.10	0.03	47
	MN 100 GV2			0.14	0.04	26	0.10	0.04	31	0.10	0.03	40

TABLE III :

 III Mapping functions for the normalized spherical camera model

		Mapping function	Note
	Equidistant	g(θ ) = θ	Maintains angular distance.
	Equisolid Angle Orthographic	g(θ ) = 2 sin θ 2 g(θ ) = sin(θ )	Maintains area relations. Maintains planar illuminance.
	Stereographic Rectilinear	g(θ ) = 2 tan θ 2 g(θ ) = tan(θ )	Maintains angles. Equivalent to the pinhole model.

TABLE IV :

 IV Experimental comparison between a VO system with a standard camera and a VO system with a fisheye camera.

		dt(ms) n matches track length ATE(m) RTE(m)
	Fisheye	48	235	10.1	0.18	0.04
	Classical	55	220	9.1	1.4	0.05


Bernard Chevalier

Gérard Demazeau

Jean Etourneau

published or not. The documents may come     Pressure dependence of the resistivity of the rare earth oxide nitrides Eu1-x2+Lnx3+NxO1-x (Ln = Nd, Eu)


Pierre-Emmanuel Poulet
email: pierre-emmanuel.poulet@inria.fr

Bruno Jedynak

Stanley Durrleman

Aramis

Learning treatment effect in neurodegenerative diseases with a Bayesian mixed-effect model

Ø Introduction

Ø Method

Ø Results

Ø Conclusions

Disease progression models have successfully been used with longitudinal data in the field of neurodegenerative diseases. In particular mixed-effect models recover the natural history of the disease at a population level but are also able to uncover individual heterogeneity. However these models usually have a hard time coping with the addition of a treatment. A treatment can be purely symptomatic or disease-modifying. We propose a method to learn the first kind of treatment effect and apply it to dopaminergic treatment in Parkinson, which is known to be symptomatic. The goal is to be able to predict how a patient is likely to answer to treatment at a certain point in time. Our method uses a Bayesian mixed-effect model as baseline and learns the treatment effect as an additive effect to the model output. 2) A mixed-effect model learning 𝒚 !" #$ and 𝒚 !" #%% jointly (DCM)

3) A kernel regression using radial basis functions with dose and disease state as 𝑿 !"

1) A linear model (LME) with dose and disease state as 𝑿 !"

Our results show that treatment effect in the case of Parkinson can be partially explained by the disease stage and the dose. We proposed a generic method to model symptomatic treatment. The potential applications of our model include determining the optimal dose when a new patient starts the treatment and testing which covariates influence treatment effect.

-12

Estimated MDS-UPDRS 3 Estimated MDS-UPDRS 3

•

  Observations : 𝒚 !" #$ ∈ [0, 1] % of patient i at time 𝒕 !" after taking drug (ON state), 𝒚 !" #&& when treatment effect wears off (OFF state) • Disease course mapping (DCM) model : a Bayesian mixed-effect model predicts natural progression of the disease • 𝒚 !" #&& = 𝜸 𝒕 !" ; 𝜽, 𝒛 ! + 𝜀 !" • Population parameters 𝜽 and individual parameters 𝒛 ! are estimated with a MCMC SAEM. • Treatment effect is the difference between OFF state and ON state: 𝒚 !" #&& -𝒚 !" #$ ≈ 𝜸 𝒕 !" ; 𝜽, 𝒛 ! -𝒚 !" #$ = ∆ !" • Treatment model: ∆ !" = 𝑓 𝑿 !" ; 𝜓 with time-dependent variables 𝑿 !" • We compare several models for 𝑓 with different variables 𝑿 !" : Performance (R 2 ): • LME: 0.13 • Joint DCM model: 0.11 • Kernel regression: 0.47Results:• Values are low due to inherent noise in the data • Kernel regression performs better, suggesting that the relationship between treatment effect and the selected variables is non-linearAnalysis of variables:• Selection of variables was made by fitting several models and selecting the best BIC • There is no clear relation between age and treatment effect, thus age was not selected • Other covariates were not selected either (imaging and biologic fluid biomarkers, other cognitive scores) • For the remaining selected variables : there seems to be a linear link between treatment effect and current disease state (measured by MDS-UPDRS 3) • For the dose we have a sweet spot to maximize the effect; taking too much or too few dopaminergic drug is less efficient (note that there is a bias due to the doctors adjusting the dose for the patient at each visit) • Interaction of dose and current disease state was captured by the kernel regression (cf plot on the left) Disorder Society -Unified Parkinson's Disease Rating Scale (MDS-UPDRS) part 3 (motor examination). Treatment dose is computed as Levodopa (dopaminergic drug) equivalent daily dose (LEDD).Patient samples∆ !"