Lilia Arapan
email: lilia.arapan@femto-st.fr

Guillaume Wong

Bernard Dulmet

Thomas Baron

Jean-Michel Friedt

Vincent Placet

Sébastien Alzuaga

Stress-Sensitivity of Wafer-Level Packaged SAW Delay Lines

This paper presents the investigation of the influence of wafer-level packaging (WLP) on the stress-sensitivity of 100 and 200 MHz delay lines aimed to wireless sensing of stresses. The devices were fabricated on YXl/128°cut of lithium niobate. The investigated WLP achieves the assembly of two wafers by a 50 µm-thick layer of SU-8 photoresist. The delay line is micro-machined on top of the first wafer while the second wafer realizes the function of protective cap in a way that should not be detrimental to the stress-sensitivity of the device. The paper gives a comparison between the theoretical and experimental phase sensitivity of both packaged and raw devices submitted to a three-points bending test.

I. INTRODUCTION

Controlling the shift of parameters induced by the packaging is a key issue for the actual production of MEMS and SAW sensors initially developped in the laboratory. Here-studied devices are 100 MHz and 200 MHz delay lines on YXl/128°L iNbO3. These devices are proof-of-concept samples close to higher-frequency sensors aimed to the wireless measurement of stresses in various kinds of structures. The actual wireless sensors are designed to operate in the 434 MHz and 2.45 GHz ISM bands. This circumstance puts significant constraints upon the microfabrication of the devices: wireless reading of SAW sensors is better achieved with high coupling piezoelectric substrate such as lithium niobate (LNO). The YXl-/128°orientation, suitable for this purpose, fixes the Rayleigh wave velocity around 3990 m/s on a free surface, yielding a wavelength about 9 µm at 434 MHz and 1.6 µm at 2.45 GHz. Then the devices are fragile and must be encapsulated to protect them from external agents. Wafer Level Packaging (WLP) is a more efficient approach than Die Level Packaging (DLP), especially in view of stress sensing because standard ceramic enclosures used to encapsulate RF devices are essentially designed from electrical viewpoint, are not aimed to transmit the strain of the analyzed external structure to the SAW device, and induce strong thermally-induced differential stresses in the sensor. This issue is solved by the WLP technique consisting of assembling two wafers from the same material and dicing the chips at the very end of the fabrication process. The most common wafer-bonding techniques used in RF MEMS are direct surface bonding, glass frit and metallic layer bonding, achieving a rigid contact between the wafers. In case of bending, this features minimizes the extensional stresses at the interface, close to the neutral fiber of the assembly. Since it coincides with the region of acoustic energy localization, such Wafer-Level Packaging (WLP) results into poor stress sensitivity of the sensors. Then, here-presented research was motivated by the need to reach a good compromise between the protection and the preservation of the stress sensitivity of the packaged delay lines.

II. DESIGN OF WAFER LEVEL PACKAGING

The most simple and generic WLP strategy relies on the assembly of 2 wafers of the same material and thickness. In such structure, traction-extension can be effectively transmitted along the entire cross-section of the assembly, but a flexural bending imposed by the monitored external structure has little chance to induce significant extensional strain and stress in the sensor if the surface acoustic wave propagates in the vicinity of the neutral fiber of the assembly. Conversely, by principle, the maximum longitudinal stress on the internal surface of a 2 wafers assembly is obtained when the sealing allows a perfect sliding between the wafers, as can be checked on Fig. 1 showing the FEA-computed distribution of the extensional strain ε xx in the entire structure. Fig. 1. Schematic distribution of extensional strain εxx for a three-points bending experiment applied to a typical two-wafers assembly with a sliding contact at the periphery. A 20 N net transverse force induces a value of εxx about 5.6 10 -4 at the upper surface of the base layer. Upon applying rigid contact conditions, the longitudinal strain drops to 1.8 10 -4 .

We investigated the possibility to improve the stresssensitivity of the packaged devicess by realizing a soft polymer seal between the two wafers of the assembly. The moderate stiffness of the polymer joined with a sufficient thickness is expected to significantly soften the mechanical link between the two LNO layers, thereby increasing the longitudinal strain and stress at the free surface of the delay line wafer, in order to improve the stress-sensitivity of the packaged device. In this purpose, a seal consisting of a 50 µm-thick layer of SU-8 photoresist was found worth investigating, while eliminating the need of any additional etching operation to permit the free propagation of the SAW on top of the base wafer. The delay line systems consisted of one IDT transducer with 10 finger pairs plus two short reflectors on the measurement path and another one on the opposite side of the IDT for calibration of the time delay. The period of the IDT is 40 µm for the test samples operating near 100 MHz, and 20 µm for the samples operating near 200 MHz. The fabrication process of the devices is illustrated on Fig. 2. Its main steps are the following: a) Processing of Wafer 1 (device):

• Patterning the delay lines (Au deposit).

• Sputtering a thicker layer for the contat pads aimed to receive antennas after processing the WLP.

• Patterning of crosses to guide the dicing operation to separate the packaged die at the final step.

• Deposit and patterning of the 50 µm-thick layer of SU-8 2075 polymer photoresist.

b) Processing of Wafer 2 (cap):

• Patterning dicing crosses (Au) to guide the dicing of the cap layer, aimed to provide access to the antennas contact pads.

• Spin-coat a thin layer of SU-8 2002 on the entire surface, in order to permit mutual adhesion by pressure and moderate heating.

c) Assembly and final operations:

• Wafers alignment and bonding.

• Dicing of wafer 2 to expose the contact pads.

• Dicing the entire thickness of the assembly in order to separate the chips.

III. PHASE-SHIFT MEASUREMENT UNDER 3-POINTS BENDING LOAD EXPERIMENT

Three-points bending tests were performed on both packaged and unpackaged chips with a traction machine of the The echoes correspond to the successive reflexions on the 3 reflectors present on the devices, including multiple reflexions along the acoustical path. The corresponding phase response is shown on Fig. 5. The phase behavior is altogether linear in the vicinity of the amplitude peaks. Then we selected the stress-induced phase change at 1.2 µs, 1.4 µs, 2.1 µs, and 2.7 µs to plot the force-sensitivity characteristics shown on Fig. 6.

IV. ANALYSIS OF RESULTS

The relative phase shift is related to the bias-induced velocity shift and the time delay by the following chain of relationships:

δϕ = ωδτ = ωδ L V = - ωL V 2 δV = -ωτ δV V (1)
where ϕ denotes the phase of the response at a fixed observation point, V denotes the phase velocity of the surface wave, τ is the time delay and L is the distance travelled by the wave. Since velocity is scalar and static strain and stress as well are second rank tensors, the velocity shift is related to strain and stress by second rank pseudo-tensors 1 , for instance:

δV V = α KL σ KL or δV V = β KL E KL (2)
where σ and E respectively denote the static stress and strain, whereas α and β merely define the stress-and strainsensitivity coefficients of the surface wave. These formulas hold only for uniform biases. The calculation of stresssensitivity coefficients coefficients can be found in [START_REF] Alzuaga | Stress-sensitivity mapping for surface acoustic waves on quartz[END_REF], [START_REF] Ballandras | Stress sensitivity coefficients: a general approach for bulk, rayleigh and surface transverse waves[END_REF] for the purely elastic problems but can also be derived for piezoelectric problems. Before proceeding further, we find enlightening and even necessary to consider the global context of the so-called acousto-elastic effect ruling the propagation of small-amplitudes elastic waves in a biased structure. Acoustoelastic effect and related problems were the subject of an 1 Although the value of the wave velocity is scalar, it is defined as the norm of the vector ∂ u/∂t where u is the particular displacement. Then V depends on the orientation of the propagation on the semi-infinite substrate and this must be taken into account when calculating the stress-sensitivity coefficients. Thus α is not a tensor. . . unless we consider it is defined for the unique problem of the YXl-/128°SAW propagation in lithium niobate.

abundant litterature in the second half of the 20-th century and constitute a particular application of the non linear theory of thermo-electro-elasticity in finite deformation. We illustrate below some of its aspects of interest for our purposes, while restricting here-presented formulas to the purely elastic case, for the sake of clarity and simplicity. Actually we performed all our numerical computations by taking into account the effect of the bias on the elastic part of the complete piezoelectric problem. In other words, we ignore bias-induced effects on the piezoelectric and dielectric behavior, although Rayleigh waves velocity is computed in the framework of piezoelectricity. Here we follow the well-established Lagrangian approach of small fields superimposed onto a bias [START_REF] Tiersten | On the nonlinear equations of thermo-electroelasticity[END_REF], [START_REF] Baumhauer | Non linear electroelastic equations for small fields superposed on a bias[END_REF]. Then the propagation equations of surface waves [START_REF] Sinha | On the influence of a flexural biasing state on the velocity of piezoelectric surface waves[END_REF] on a semi-infinite substrate of normal n 2 in a current frame, rotated w.r.t crystallographic axes, can be mapped onto the set of fixed and known material coordinates (X L ) of the structure defined prior exertion of any bias:

K 1γ,1 + K 2γ,2 = ρ 0 üγ , γ ∈ [1, 2, 3] K Lγ = G Lγ1ε u ε,1 + G Lγ2ε u ε,2 G LγM ε = c LγM ε + ĉLγMε (w P,Q ) ĉLγMε (w P,Q ) = T LM δ γε + c 3 LγM εP Q E P Q +c 2 LγM K w ε,K + c 2 LKM ε w γ,K T LM = c LM N P w N,P = c LM N P E N P (3)
where u (X L , t) is the dynamic displacement field, w (X L ) is the static displacement field (bias) and ρ 0 is the mass density of the undeformed body since the problem is mapped onto the fixed material coordinates. Also K Lγ denotes the first Piola-Kirchhoff stress tensor and G LγM ε indicates a component of the effective elastic coefficients in the so-called Lagrangian configuration. Then one should solve these equations together with the associated boundary conditions prescribed on the free surface of normal n 0 2 that we consider located at X 2 = 0:

K 2γ (X 1 , 0) = 0, γ ∈ [1, 2, 3] . (4)
Although Eq. ( 3) initially puts the bias-induced incremental elastic constant ĉLKMε as a function of the static displacement gradients w M,N it is possible to reformulate ĉ as a function of the static strain

ĉLγMε = T LM δ γε + c 3 LγM εAB E AB +c 2 LγM N E εN + c 2 LN M ε E γN . (5)
Because the static stress tensor is easily deduced from the static strain by inverting the tensor of second order elastic constants c 2 , it is easy to further rewrite the ĉ increment of elastic constants as a linear combination of the static stresses, which we find unnecessary to explicitly reproduce here. Because its linear expansion must be performed in terms of the displacement gradients which are non-symmetrical, instead of the classical strains which are symmetrical, the first Piola-Kirchhoff tensor K Lγ is asymmetric by nature. Then it must be stored in a matrix of dimension [9 × 9].

In case of stress-free bias such as free thermal expansion, it has been demonstrated that this matrix remains symmetric [START_REF] Dulmet | Lagrangian effective material constants for the modeling of thermal behavior of acoustic waves in piezoelectric crystlas. i. theory[END_REF] provided that the notations be properly chosen. Nevertheless, the expression of the bias-induced increments ĉLγMε clearly indicates that in case of a stress-generating or simply nonuniform bias, the resulting G matrix is no more symmetrical. Then, two approaches can be followed to compute the velocity of the surface acoustic waves from the incremental equations of motion:

• For uniform biases and some cases of non-uniform but rather simple biases, it is still possible to directly solve the equations following the same procedure as in linear elasticity problems, as long as the [9×9] size of the [G] matrix and its eventual asymmetry induce relatively small changes in the classical procedure.

• A first order perturbation procedure [START_REF] Tiersten | Perturbation theory for linear electroelastic equations for small fields superposed on a bias[END_REF] involving the computation of integrals relying on the knowledge of the partial derivatives of the unperturbed (unbiased) displacement field and of the static (biasing) displacement field.

The problem of SAW propagation in rectangular plates submitted to pure extensional or pure bending biases can be solved with either one approach. Ref. [START_REF] Sinha | On the influence of a flexural biasing state on the velocity of piezoelectric surface waves[END_REF] provides with a detailed comparison of the direct and perturbation approaches to compute the velocity shift of Rayleigh waves in a purely bended structure. For here-presented work, we designed a computer program able to numerically determine the velocity of the SAW for the Y Xl/128°orientation of a LiNbO 3 plate submitted to a uniform bias, and in particular in the case of a pure longitudinal stress. Despite of the bias, the structure of the Rayleigh waves could still be assumed to comply with the classical combination obtained in case of propagation on a unbiased substrate:

u i = 4 n=1 C n β (n) i e jωs (n) 2 x2
e jω(s1x1-t) ,

where C n represents the weight of a given partial wave in the combination, β

is a component of the normalized amplitude vector of the n-th partial wave, s 1 is the slowness of the guided propagation and s 2 (n) is the slowness of the partial wave in the vertical direction. We intend to provide more details about the direct approach in a further paper. The obtained value of the velocity-shift was found about 80% of the value provided by an earlier program elaborated at LPMO laboratory at the end of the nineties [START_REF] Alzuaga | Stress-sensitivity mapping for surface acoustic waves on quartz[END_REF], [START_REF] Ballandras | Stress sensitivity coefficients: a general approach for bulk, rayleigh and surface transverse waves[END_REF]. The latter program is based on simplifications occuring in Tiersten's perturbation integral for the computation of Rayleigh velocity [START_REF] Tiersten | A perturbation analysis of the attenuation and dispersion of surface waves[END_REF] in the case of uniform elastic bias. The perturbation formula for the twodimensionnal problem of the proagation of Rayleigh waves of quasi-infinite aperture is the following:

δV V 0 ≈ S0 ĉLγMε (w M,N ) R u 0 ε,M u 0 * γ,L dS 0 2ρ 0 ω 2 S0 R u 0 α u 0 * α dS 0 , (7)
where R denotes the real part, the superscript * denotes the complex conjugate, S 0 being the sagittal plane. In case of a uniform bias, the integrals can be reduced to simpler integrals over the depth of the semi-infinite substrate:

δV V 0 = ĉLγMε 0 -∞ u 0 ε,M u 0 * γ,L dx 2 2ρ 0 ω 2 0 -∞ u 0 α u 0 * α dx 2 . ( 8
)
Because of the exponential character and the convergence in the depth of the substrate of the partial waves [START_REF] Dulmet | Lagrangian effective material constants for the modeling of thermal behavior of acoustic waves in piezoelectric crystlas. i. theory[END_REF] entering the structure of Rayleigh waves, the integrals are easily calculated, leading to the final result:

δV V0 = 2 L=1 3 γ=1 2 M =1 3 ε=1 ĉLγMε 4 n=1 4 m=1 CnC * m β (n) ε β (m) * γ s (n) M s (m) * L s (n) 2 -s (m) * 2 2ρ0 3 α=1 4 n=1 4 m=1 CnC * m β (n) α β (m) * α s (n) 2 -s (m) * 2 (9)
The stress-sensitivity coefficients α LM introduced at Eq. ( 2) are easily computed from both this expression and [START_REF] Sinha | On the influence of a flexural biasing state on the velocity of piezoelectric surface waves[END_REF]. Using the set of elastic constants provided by Ref. [START_REF] Warner | Determination of elastic and piezoelectric constants for crystals in class (3m)[END_REF] gives the following value of σ xx stress-sensitivity coefficient of Rayleigh wave velocity for the considered problem:

α 11 ≈ -4.257 10 -11 /P a (10)
The FEA-computed stress for the 3 points bending test on top of the packaged delay line wafer was found close to -3.2 10 7 P a when the net transverse force reached 20 N and assuming a rigid contact of the polymer with the 2 layers of niobate. Substituting this value together with (10) into (2) and the obtained result back into (1) yielded a phase-shift of 20°for the fourth echo (τ ≈ 2.7µs) of the phase-response. The corresponding measurement of δϕ observed on Fig. 6 for this point was 23°. Then the agreement between theory and experiment was found good. Assuming that the polymerniobate contact allows a free sliding, which corresponds to the "ideal" case of Fig. 1 yielded a FEA-computed value σ xx ≈ 1.47 10 8 P a at the surface of the chip. Then the corresponding predicted sensitivity becomes nearly 5 times larger than the one that we actually observed. Nevertheless a further experiment was required, given the variablity of results between direct and perturbation approach, the even larger variability induced by the values of elastic constants (nearly a factor 2 between the results calculated from [START_REF] Cho | Non linear, elastic, piezoelectric, electrostrictive, and dielectric constants of lithium niobate[END_REF] and [START_REF] Warner | Determination of elastic and piezoelectric constants for crystals in class (3m)[END_REF]) and the expectable unaccuracy arising from the simplifying assumption of the essential contribution of the stresses near the surface. Then another three-points bending test was performed with a raw (unpackaged) chip. In that case the chip was flipflopped in the traction apparatus in order to permit the free propagation of the SAW. The force had to be reduced since the chip broke at a much smaller transverse load (near 25 N ), as expected. We performed the calculation for the same echo at 2.7µs as previousy and for a transverse force equal to 9 N , giving a FEA-computed longitudinal stress σ xx ≈ 2.4 10 8 P a.

Then, using the same computation procedure as previously, we obtained a theoretical phase-shift close to -180°, whereas the measured value was found close to -195°. The similar agreement between theory and experiment for the cases of the packaged and the raw chips confirms to a large extent the validity of the approach and the conclusion drawn about the rather adhesive link between the polymer layer and the lithium niobate wafers.

V. CONCLUSION

Here-presented study indicated a satisfactory agreement between calculated and measured values of the phase-shift of the response of packaged and raw delay lines under a transverse load, assuming that the polymer used to perform the WLP assembly achieves a rigid link with the two wafers of lithium niobate. The loss of sensitivity between a firm contact and a sliding contact at the interfaces is about 5, and the sliding contact case would still represent a loss of a factor 2 with respect to the raw chip, which seems unavoidable if the two wafers have the same thickness, since two identical plates in parallel double the stiffness with respect to a single plate. Then a further optimization of the packaging is still needed to improve the stress-sensitivity of the device in case of bending imposed by the supporting structure. Nevertheless, this WLP design is promising since the stress-sensitivity is still largely measurable in case of pure bending of the chip. In addition, one must point out that the actual biasing states imposed to the SAW sensor by the monitored structures are combinations of bending and extension-compression rather than pure flexure.

Fig. 2 .

 2 Fig. 2. Principle of soft polymer assembly for here-studied WLP design.

Fig. 3 .Fig. 4 .

 34 Fig. 3. Three-points bending experiment of a packaged chip (inside the ellipse mark).

Fig. 5 .

 5 Fig. 5. Phase response of a 200 MHz packaged delay line.

ACKNOWLEDGMENT

The authors would like to thank the LAbeX ACTION for the postdoctoral support of L. Arapan throug the ECCO project and the DGA for the support of the PhD of G. Wong through the ALCASAR/LANCASTER project.


Emeline Sadoulet-Reboul

Gaël Chevallier

Pierre-Henri Cornuault

Théo Citerne

Guilhem Michon

Vibroimpact induced damping in an architected sandwich composite

Keywords: Damping, vibroimpact, functionalization

Sandwich composites are widely used in design especially in transport because they combine bending rigidity and lightness. On the other hand, their attenuation properties are not always as good as expected, and it is necessary to overcome this limitation in order to improve the vibratory comfort and the durability of the structures in which they are integrated. Several strategies exist such as the introduction into the core of the sandwich of passive materials with viscoelastic properties for example to allow energy dissipation, or the use of electronic circuits for active control strategies. The approach presented in this paper is based in the introduction of vibro-impact zones to generate damping. The local interactions occurring during the impacts allow to dissipate the vibratory energy: it is about nonlinear phenomena which have the advantage to be effective over a wide range of frequencies, and to be few sensitive to environmental conditions such as temperature. A sandwich composite prototype has been designed for the purpose of the study, and small ceramic balls have been inserted in the sandwich core to generate impacts phenomena. Experiments have been performed to evaluate the damping performances obtained depending on the number of balls, on the amplitude on excitation and on the frequency band. Analytical and numerical models of the structure have also been developed to perform parametric studies and evaluate the impact of parameters such as the ball added mass or the positions of the masses for instance : numerical results have been confronted to experimental ones. It has thus been observed that good damping performances could be obtained on a large frequency band.

INTRODUCTION

Vibroimpact systems are nonlinear systems for which oscillations of a small structure as a mass generate collisions with other masses or with a structure or a barrier. Following the impact, exchange of momentum occurs and it leads to energy dissipation. This phenomena has led to the development of passive control device as impact dampers that are used for instance to improve the damping capability of boring tools and suppress chatter vibration [Satoshi, 2000], to control the vibrations of turbomachinery blades [Duffy, 2004], or to suppress wind vibrations on tall buildings [Masri, 1976]. The main advantages of such devices is that their behavior does not depend or temperature, they do not need power requirement and they are quite cheap, so they could be interesting solutions for vibratory control where other solutions fail. Impact dampers can have different configurations, they can consist in single units [Duncan, 2005], multi-units [Iwata, 2016], or granular impacts [Djemal, 2017].

One limitation of the vibroimpact systems for vibration mitigation is that the collision can lead to large contact forces and high noise levels, in particular when collisions occur between metallic elements. The principle of using multiple masses instead than one like in multi-units or granular configurations is to reduce the impact forces and so the impact noise. The association of multiple particles in one chamber has shown good efficiency for vibration suppression but the obtained damping is such a case is due to a combination of impact with other phenomena as shear friction, and so it is difficult to identify the exact effect of impact in the attenuation [Xu, 2005].

The purpose of this work is to investigate analytically and numerically the damping capability of a multi-unit vibroimpact system integrated in a composite structure. The collisions are generated by individual masses inserted in small cylinder where they can move vertically without and friction not contact between them. The question addressed in the research is: " is-it possible to obtain good performances in terms of vibration mitigation with such a device, on a large frequency band and for any environmental conditions ? The paper summarizes the first results obtained on a prototype developed to answer this question.

BACKGROUND

The prototype developed for the study is a sandwich composite composed of two skins as the one presented in Figure 1. The lower and the upper skins present a lot of small holes where ball masses can inserted and move vertically when the two skins are associated together. The master structure is done with aluminium while the masses are in ceramic to improve the impact conditions. The total length of the beam is 300 mm, the thickness is 1 mm, the hole diameter is 1.2 mm and the ball diameter is 1 mm. The structure has been prototyped to evaluate the damping performances, and numerical tools have been developed in a purpose of topology design.

ANALYSIS NUMERICAL INVESTIGATION

The structure is modeled as a beam and a Hertz model is used for the contact between each ball and the structure. The transversal displacement 𝑤 of the beam is written by superposing the normal modes ∅ 𝑘 , (1°)

The equations governing the time behavior of the structure are written as (2°)

Where 𝑚 𝑘 , 𝜉 𝑘 denote the modal mass and damping, 𝑚 𝑚𝑗, 𝑐 𝑚𝑗 are the mass and the damping of each ball placed at 𝑥 𝑚𝑗 . The Hertz stiffness contact between each ball and the master structure is 𝑘 𝑚𝑗 . These equations are solved in the time domain and transferred in the Fourier domain to evaluate the Frequency Response Functions.

EXPERIMENTAL INVESTIGATION

The structure has been excited with an harmonic excitation for different number of balls, from 0 to 90 to observe the influence of this parameter on the damping. Figure 2 presents the frequency response function obtained for the different configurations and the damping factor variates from 0.006 to 0.01 CONCLUSION This work is the beginning of a project to evaluate the performances that could be obtained with a multi-unit configuration of impact dampers. Numerical tools have been developed and will be used to design a new configuration with optimized properties. First experimental results confirm the damping efficiency of the impact strategy, the nonlinear behavior of the structure, and the variations of performances with the level of excitation. Ongoing work aims at improving the model behavior of the contact, understand the different oscillations regimes occurring in the structure, and optimize the repartition of the contact areas.

Figure 1 :

 1 Figure 1 : Lower skin of the sandwich composite

ACKNOWLEDGEMENTS

This work has been supported by the EIPHI Graduate School (contract "ANR-17-EURE-0002").


Abdenbi Mohand Ousaid

Ismaïl Bouhadda

Gilles Bourbon

Patrice Le Moal

Yassine Haddab

Philippe Lutz

A Mohand-Ousaid

Compact Digital Microrobot Based on Multistable Modules

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. INTRODUCTION

The development of miniaturized products we use every day is growing increasingly during the two last decades. In this regard, there is a clear need for accurate micromanipulation tools. For instance, watch micromechanisms, medical and bio-medical devices, microsystems, optic and electronic devices are products that require efficient and reliable micromanipulation tools for their assembly [START_REF] Régnier | Microrobotics for Micromanipulation[END_REF]. Thanks to the progress in the field of smart materials several microrobotic systems are developed for this purpose. Considering their output displacements, they can be classified into two main categories: microrobots with proportional (continuous) displacements and microrobots with incremental (discrete) displacements.

The first category uses proportional actuation to generate continuous displacements [START_REF] Régnier | Microrobotics for Micromanipulation[END_REF], [START_REF] Rakotondrabe | Quadrilateral modeling and robust control of a nonlinear piezoelectric cantilever[END_REF]. Unlike conventional actuators, smart materials such as piezoelectric materials are particularly privileged for their design since they are suitable and compatible for miniaturization. However, despite their intrinsic high resolution and high dynamics, these materials have some drawbacks. They often exhibit nonlinear and nonstationary behavior. They are also sensitive to environmental conditions such as temperature and humidity [START_REF] Rakotondrabe | Hysteresis and vibration compensation in a nonlinear unimorph piezocantilever[END_REF]. Under these conditions, their design becomes a complex task that requires tiny sensors and bulky instruments for signal processing. 1 are with Université Bourgogne Franche-Comté, FEMTO-ST Institute/CNRS, Besanc ¸on, France. 2 is with Université de Montpellier, LIRMM/CNRS, Montpellier, France.

Multistable module

Multistable module In contrast, the second category namely digital microrobotics uses discrete actuation to generate incremental displacement without closed-loop control (no need for sensors). Inspired by binary paradigm of robotic manipulators [START_REF] Chirikjian | A Binary Paradigm for Robotic Manipulators[END_REF], these robots are based on bistable mechanisms [START_REF] Wu | Design and implementation of a bistable microcantilever actuator for magnetostatic latching relay[END_REF]- [START_REF] Xu | Design of a large-stroke bistable mechanism for the application in constant-force micropositioning stage[END_REF] that generate a displacement between two stable positions (0 and 1). As a consequence, the digital robots guarantee mechanical stability, high accuracy, and the repeatability of their discrete workspace positions in open-loop without energy consumption unlike stick-slip [START_REF] Rakotondrabe | Voltage/Frequency Proportional Control of Stick-Slip Micropositioning Systems[END_REF], inertial [START_REF] Buchi | Inertial drives for micro-and nanorobots: Analytical study[END_REF] or inchworms actuators [START_REF] Chen | Locomotive gait generation for Inchworm like robots using finite state approach[END_REF], [START_REF] Contreras | Dynamics of electrostatic inchworm motors for silicon microrobots[END_REF]. As reported in [START_REF] Chalvet | A microfabricated planar digital microrobot forprecise positioning based on bistable modules[END_REF], this concept is successfully employed to design a digital microrobot suitable for micromanipulation in confined environments such as Scanning Electron Microscope (SEM). Named DiMiBot, it is referred to as the first generation of digital microrobot. It is basically composed of four bistable modules and their elementary displacements are transmitted to the tip of the robot through flexible structures. With this configuration, the robot is able to reach 16 stable positions. Although this microrobot shows great potential, it is subjected to a tradeoff between the stable positions and the dimensions of the mechanism. When several bistables are combined, the size of the robot increases rapidly. Thus, the miniaturization and the calculation of the robot forward and inverse kinematics become complex and non-intuitive.

-→ x 0 -→ y 0 R 0
To overcome this limitation, a multistable module has been investigated in [START_REF] Hussein | Design and fabrication of novel discrete actuators for microrobotic tasks[END_REF]. Compared to a bistable module, it allows switching its moving part between 13 stable positions. Leveraging multistable modules, this paper investigates the second generation of digital microrobots. As illustrated in Fig. 1, the robot comprises two multistable modules and flexible structures. The main advantages of this new microrobot structure are summarized as follows:

-The microrobot can reach a large workspace while having a smaller footprint. In comparison with the previous generation (544 mm 2 /16 stable positions), the new generation has a footprint of 400 mm 2 and can generate 169 stable positions. In other words, the size A mechanical structure of the robot is proposed and its forward and inverse kinematics are calculated. Then, a prototype is fabricated on SOI wafer using a deep reactive ion etching based process (DRIE). Simulations are carried out to validate the forward kinematics model, while experiments are conducted to characterize the robot functional principle and its workspace. Preliminary results show a good agreement between the simulated and the achieved workspace. As expected, the microrobot generates 169 stable positions with a discrete step of 4.125 µm and a resolution of 150 nm. Having these capabilities, this new generation opens a promising perspective for precise micromanipulation applications in confined environments where the working space is becoming smaller and smaller.

II. SECOND GENERATION OF DIGITAL MICOROBOTS

This section focuses on the mechanical design of the second generation of digital microrobots. It describes mainly the proposed architecture, its advantages, and its principle of functioning.

A. Microrobot architecture

The CAD model given in Fig 2 shows how the architecture given in Fig. 1 is implemented. The model reports all the details including the actuators and their connections with the robot tip. Likewise the previous generation, a symmetrical architecture is used, however, it comprises only two multistable modules. Each module is connected to the robot tip through flexible structures that convert their elementary unidirectional displacements to to bidirectional displacements. This new architecture, compact and easy to implement, can reach a larger workspace by combining several stable positions.

B. Multistable module

As can be seen in Fig. 2, the multistable module is the cornerstone of the digital robot architecture. Only two modules are sufficient to generate a large workspace while having a small footprint. The whole module comprises three subsystems that guarantee the switching, the holding, and the guiding of its moving part. Each subsystem consists of flexible structures actuated by two U-shaped actuators. Each actuator can provide respectively a displacement of 200 µm and a force higher than 10 mN, which are largely sufficient to actuate the multistatble and the whole robot. When the actuators are activated in a specific sequence, their combination allows generating 13 stable positions (from 0 to 12) with a step of 10 mm. Reader can refer to [START_REF] Chen | A Tristable Mechanism Configuration Employing Orthogonal Compliant Mechanisms[END_REF] for more detail about the design, the fabrication, and the characterization of multistable modules. He/She can also refer to [START_REF] Contreras | Dynamics of electrostatic inchworm motors for silicon microrobots[END_REF] for the repeatability and the reproducibility characterization of multistable modules.

C. Flexible structures

Figures 1 and2 show how the robot tip and flexible structures are connected. The connection consists of a serial kinematic chain that transmits the module displacements to the robot tip. In this chain, a horizontal link (x-axis) is connected to the multistable moving part through a flexible hinge at one side while the other side is connected to a clamped hinge. Following, a diagonal link connects the middle of the horizontal link and the robot tip through hinges. Such combination results in a parallel kinematic chain that converts the vertical displacements of modules to planar displacements at the robot tip.

D. Flexible hinges dimensioning

Flexible hinges are commonly used to design micronanosystems with high resolution. Thanks to their monolithic structure, they do not involve mechanical backlash and friction between parts that usually affect the accuracy of the system. Here, corner-filleted flexible hinge illustrated in Fig. 3.a (represented by a circle in Fig 1 ) with the same dimensions are particularly used for two reasons: (i) it mimics the behavior of a traditional revolute joint and (ii) provides a large deformation in comparison with simple circular hinge (see Fig. 3.b). Unlike rectangular or ellipse hinges [START_REF] Howell | Compliant Mechanisms[END_REF], they generate an accurate rotation with an approximately fixed center of rotation. However, due to their size, they give rise to two main constraints: (i) when subjected to deformation they produce high stress that may cause irreversible deformation or breakage (ii) their fabrication in particular over-etching could make the robot structure fragile. To prevent these constraints, the optimal dimensions of the hinges have to be determined. As illustrated in Fig. 3.a, three main dimensions are concerned: L the length of the straight beam segment, R the radius of the hinge, and l the minimum engraving width. First of all, by considering the fabrication process limitation, the parameter l is chosen to be 15 µm. This allows minimizing the effect of over-etching that may weaken the robot structure knowing that this phenomenon induces about 2 µm uncertainty. Then, FEA simulations under COMSOL are carried out to find the parameters L and R. Figure 4 reports the mechanical stress curves versus the hinge radius R for different values of L while l is kept fix and equals to 15 µm. For each configuration, the mechanical stress is evaluated for deformation of 120 µm which is the maximum displacement that can be generated by a multistable module.

According to the simulations and the stress limit of the silicon material considered here as ∼0.5 GPa, we selected R = 60 µm and L = 60 µm in order to guarantee a good behavior of the flexible hinges. It is worth to notice that R and L can be increased to decrease the mechanical stress, however, the hinge will become less precise in keeping the position of the rotation center as reported in [START_REF] Lobontiu | Corner filleted flexure hinges[END_REF].

E. Principle of functioning

To reach any position within the workspace, the robot combines vertical displacements of modules and deformations of flexible structures. The displacement sequence starts by converting the targeted position into a binary sequence. This sequence corresponds to the number of elementary steps that both modules have to generate. Each elementary step revolves around several sub-steps that include: moving, opening, and closing of the multistable clamps with or without its moving part. a similar sequence is, then, repeated to generate several successive upward or downward steps. For further details about the combination and the control sequence order that allows generating a displacement step, reader can refer to [START_REF] Hussein | Design and fabrication of novel discrete actuators for microrobotic tasks[END_REF]. Throughout the process, the horizontal rigid links are subjected to the same displacements as moving parts of modules. In return, the horizontal link drives the diagonal link which transmits the deformation to the tip.

multistable L multistable R δ M 2x δ M 2y δ R x δ R y δ T x δ T y δ L x δ L y δ M 1x -→ x 0 -→ y 0 R 0 δ M 1y θ l 2 l 3

III. MICROROBOT'S KINEMATICS

This section deals with the calculation of the robot forward and inverse kinematics models. Unlike the previous generation, the calculation is simpler since the robot has a simple architecture, actuated with only two multistable modules. Furthermore, the following assumptions are considered for practical reasons:

1-Links are rigid (deformations are located within the hinges). 2-Rotations take place at the center of the hinges (perfect joints). 3-Induced rotations are considered small. All these assumptions are due to the robot displacements, which are very small in comparison with the robot structure.

A. Forward kinematics

The forward kinematics model expresses the displacement of the robot tip (δ T x , δ T y ) as a function of multistable states (M 1 and M 2 , which can vary from 0 to 12) and the geometrical parameters of the robot. Based on the kinematics scheme given in Fig. 5, the model is calculated in several steps. We started by expressing the tip displacements according to the displacements of points L and R, noted δ L x , δ L y and δ R x , δ R y , respectively. By taking in consideration the geometrical parameters l 2 and l 3 (see Fig. 5), this relationship can be expressed as (1):

δ T x δ T y = 1 2 1 l 2 l 3 1 -l 2 l 3 l 3 l 2 1 -l 3 l 2 1        δ L x δ L y δ R x δ R y        (1)
Then, we expressed the displacements of points L and R according to the multistable states. Taking into account the horizontal and the vertical distances between two hinges, l 1 Fig. 7. FEA simulation of the robot workspace. Case where each module generates a displacement of 120 µm (M 1 =M 2 =12). and w 1 respectively, which are the same for the left link (see Fig. 6), the relationship can be expressed as:

δ L x δ L y = l 1 2 (cos(θ ) -1) + w 1 sin(θ ) l 1 2 sin(θ ) + w 1 (cos(θ ) -1) (2)
Considering small angles approximation, θ = δ M1y l 1 and displacements of the first module (δ M1 x = 0 and δ M1 y = ×M 1 , where is the module step and M 1 is the state of the first multistable.) the relationship 2 can be written as:

δ L x δ L y = w 1 l 1 × 1 2 × M 1 (3)
The same reasoning is applied to multistable 2 and leads to the following relationship between displacements of point R and displacements of module 2.

δ R x δ R y = -w 1 l 1 × 1 2 × M 2 (4)
Finally, we substituted equations ( 3) and (4) in equation ( 1), which leads to the robot forward kinematics model:

δ T x δ T y = 2 w 1 l 1 + l 2 2l 3 -w 1 l 1 -l 2 2l 3 l 3 w 1 l 2 l 1 + 1 2 l 3 w 1 l 2 l 1 + 1 2 M 1 M 2 (5)
By considering K = 2 ( w 1 l 1 + l 2 2l 3 ) as a common factor, the forward kinematics model can be rewritten as:

δ T x δ T y = K 1 -1 l 3 l 2 l 3 l 2 M 1 M 2 (6)
This model permits to derive the theoretical robot discrete step and the robot workspace size. The first one concerns the distance between two neighboring positions. It corresponds to the tip displacements that result when one module generates a step. By substituting [M 1 M 2 ] T by [1 0] T , the discrete step of the workspace equals r = 2 ( w 1 l 1 + l 2 2l 3 ) (1 + ( l 3 l 2 ) 2 ). The second one concerns the maximum reachable robot workspace. As the robot uses two similar modules, it has the same size along -→ x and -→ y axes and corresponds to (M -1)r, where M is the number of module states.

B. Microrobot workspace

Likewise DiMiBot, the robot generates a 2D discrete workspace. However, the number of achieved positions increases with the use of multistable modules. By considering the multistable discrete step ( =10 µm), the vertical as well as the horizontal distance between two hinges, w 1 = 480 µm and l 1 = 5.9 mm, and the geometrical parameters l 2 = 3.2 mm and l 3 = 2.89 mm, we evaluated the theoretical workspace by using the forward kinematics model given in equation 6. Then, we carried out FEA analysis under COMSOL multi-physics software for numerical evaluation of the workspace. For simplicity, we considered only the flexible structures shown in Fig. 7. Two of the hinges located on the horizontal link are clamped (blue part) while discrete displacements from 0 to 120µm with a step of 10 µm are imposed on the other hinges (red part) to simulate the behavior of the multistable modules. Both results are reported in Fig. 8. As can be seen, the robot can generate 13x13=169 discrete positions arranged inside a square-shaped workspace. On the other hand, Tab. I reports the difference between the FEA analysis and the forward kinematics model. Two metrics are considered: (i) the generated step and (ii) the motion range, i.e, the maximum diagonal straight line that the robot can reach when one multistable is activated from step 0 to step 12 while the other multistable is maintained to a given position. With an error of 0.6% and 0.66%, differences are negligible compared to the resolution of the workspace, thus validating the forward kinematics model.

C. Inverse kinematics

The inverse kinematics model expresses the state of modules according to the robot tip position within the workspace. Unlike DiMiBot or classical digital robots, the robot proposed here has a linear forward kinematics model. Therefore, a simple inversion of the forward kinematics model followed by a round function leads to the inverse kinematics model. In this case, the inverse model can be expressed as:

M 1 M 2 = round(K -1 1 -1 l 3 l 2 l 3 l 2 -1 δ T x δ T y ) (7)
IV. MICROFABRICATION The microrobot is fabricated as a monolithic structure using a single-crystalline silicon-on-insulator (SOI) wafer. As illustrated in Fig. 9, the wafer is composed of four distinct layers: (i) a 100 µm thick silicon layer dedicated to the active area, (ii) a 2 µm thick silicon dioxide insulation layer, (iii) a 380 µm thick handle silicon layer and (iv) a 2 µm thick silicon dioxide layer serves as a hard mask. As the robot uses two modules, its cleanroom fabrication process follows the same process developed for multistable modules. As reported in [START_REF] Hussein | Design and fabrication of novel discrete actuators for microrobotic tasks[END_REF], the fabrication process revolves around five sub-steps:

1-Patterning and dry etching of the wafer backside using reactive ion etching (RIE) process with an opening window of 60 µm (see Fig. (see [START_REF] Hussein | Design and fabrication of novel discrete actuators for microrobotic tasks[END_REF] for more details about the activation procedure), the device is glued on a PCB card, and a wire bonding is performed for electrical connection.

V. EXPERIMENTAL CHARACTERIZATION

This section aims to characterize the fabricated robot. It considers two main aspects: (i) the robot working principle and (ii) the robot workspace.

A. Experimental bench

Figure 11 depicts the experimental bench implemented for this study. It comprises a high-speed camera, an electronic circuit, and the microrobot prototype. During the characterization, the microrobot is placed on an anti-vibration table to guarantee the most favorable experimental conditions. It is also dissociated from the electronic circuit to avoid any vibrations that may be induced by relay switching movements. On the other hand, the PCB is connected to the electronic circuit to supply the robot actuators. Based on an Arduino controller, connectors, and relays, this circuit controls the supply time of the control sequences of the U-shaped actuators. Each relay allows switching on/off the current of an electrothermal actuator stage. Otherwise, the circuit uses buttons to switch control between upward and downward steps. In return, the robot tip moves from a discrete position to another. By repeating the sequence, the robot tip can scan the whole workspace. These displacements are captured, recorded, processed, and visualized through a high-speed camera.

B. Tests, results and discussion

1) Functioning principle: The robot functional principle is dependent upon the multistable states. Its validation requires three experimental verifications. They consist to validate the elementary displacement of the robot as follows: (i) the left module is active, (ii) the right module is active, and (iii) both modules are active. When the left multistable module generates a step, the tip has to move to the right side of the workspace. In contrast, the tip has to move to the left side of the workspace when the right module generates a step. However, the robot tip has to move vertically when both modules generate a step. Figure 12 reports the displacement of the robot with respect to the above-mentioned cases. As expected, the robot tip reaches three different positions. In this figure, the row vector (L, R), which contains the state of the left (L) and the state of the right (R) multistable represents the elementary positions. The origin here corresponds to the couple (0,0) where the state of multistables is equal to 0. When the left module generates a step, the tip moves to the position (1,0) located on the right side of the workspace. In contrast, the robot tip moves to the position (0,1) located on the left side of the workspace when the right module generates a step. The robot tip can also reach the position (1,1) by combining two successive elementary displacements (left module step followed by the right module step or right module step followed by the left module step). It is clear from this analysis that the result shows a good agreement with the expected functioning principle. Based on these elementary displacements, the robot tip can travel through the whole workspace. This will be the scope of the next experiment, aims to characterize the robot workspace.

2) Workspace: After demonstrating the functional principle, we characterized the robot workspace and its features using a series of control sequences. First, a series is applied to make the robot tip traveling through the whole space. Starting from the origin, the robot moves to the next positions located in the same diagonal by activating only the left module, which generates 12 upward steps. Then, the only right module generates one upward step to reach the next diagonal. The left module generates again and 12 downward steps to travel along this diagonal. Before repeating the whole cycle, the right module generates again an upward step. The path described by this cycle is illustrated in Fig. 13 (see dashed blue path). Figue 13 reports also the reachable workspace. Each position of this workspace corresponds to a given combination of the robot module states. According to the result, it is trivial that there is a satisfying agreement between the experimental and the simulation data. The robot succeeds to cover 169 discrete positions with a step of 4.125 µm. Second, the same series is applied seven times to characterize the repeatability of the robot. The set of rules given in [START_REF] Jcgm | International vocabulary of metrology: basic and general concepts and associated terms (VIM)[END_REF] are respected to ensure the most favorable conditions: same operator, same measurement system (highspeed camera), same operating conditions, same location, and same device for all measurements. For each series, the tip is tracked by a high-speed camera. The resulted data are recorded and then processed to extract the tip displacements.

All the obtained displacements are reported in Fig. 13. As shown in the zoom (see Fig. 13), the measurements are scattered over a circle with a diameter of 300 nm. This means that the proposed robot can reach a discrete position with a resolution of 150 nm. Table . II reports the difference between the experimental characterization and the numerical simulation. The difference is calculated for both the generated step and the robot motion range. Unlike the previous comparison, a slight difference (about 4.7%) can be observed between the experiment and the numerical simulation. This difference is mainly due to the over-etching phenomenon that affects the robot structure and its geometrical parameters. For instance, Fig. 14 illustrates the effect of this phenomenon in particular when it comes to fabricate the robot hinges (instead of having a hinge with a width of 15 µm, we obtained a hinge with a width of 13.31 µm). Overcoming this phenomenon is challenging, but it would improve the robot resolution and accuracy.

VI. DISCUSSION

It is clear from the result that the multistable modules open promising perspectives to the design of a new generation of microrobots. It is of particular importance as the number of stable positions and the step resolution can be changed. Indeed, the number of stable positions with the same step can be increased by adding teeth to the multistable moving part and redesigning the guiding beams. On the other hand, the multistable step can vary by modifying the distance between two successive teeth. As can be seen in Fig. 15, the relative distance between two successive teeth fixes the step resolution of the multistable. In our case, this distance is about 10 µm, which corresponds to the multistable step resolution. Changing this relative distance allows varying the multistable step. From theoretical point of view, a large range of steps can be reached however, the fabrication process limits the minimum step that can be reached because of the etching phenomenon.

VII. CONCLUSION

This paper presents the design of a new digital microrobot. Unlike the previous generation, it uses two multistable modules and flexible structures. The new microrobot can generate several stable positions while having a small footprint. Starting from the robot sketch the forward kinematics model of the robot is derived under small rotation approximation. Then, the robot workspace features are analyzed theoretically and validated through FEA analysis. The result leads to a workspace composed of 169 positions with a numerical step of 4.318 µm. A prototype is fabricated using a cleanroom process. Then, a series of experiments are conducted to characterize the robot functional principle and its workspace. Preliminary results show a good agreement and confirm theoretical and FEA analysis expectations. The functional principle is demonstrated by generating elementary displacement while the workspace is validated by generating 169 stable positions with a step of 4.125 µm and a resolution of 150 nm.

Future work will focus on the force characterization of the microrobot and the path planning. It would also concern the application of the robot for micromanipulation inside a confined environment.

VIII. ACKNOWLEDGMENT

This work has been supported by the EIPHI Graduate school (contract "ANR-17-EURE-0002") and the Labex AC-TION project (contract ANR-11-LABX-01-01). It has been partly supported by the French RENATECH network and its FEMTO-ST technological facility. This work has been also partially supported by the Bourgogne Franche-Comté region project COMPACT.

Fig. 1 .

 1 Fig. 1. Sketch architecture of the second generation of digital microrobot.

Fig. 2 .

 2 Fig. 2. CAD model of the digital microrobot.

Fig. 3 .

 3 Fig. 3. Flexible hinges. a) corner-filleted flexible hinge, b) circular flexible hinge.

Fig. 4 .

 4 Fig. 4. Mechanical stress versus hinge radius and straight beam segment length.

Fig. 5 .

 5 Fig. 5. Simplified microrobot kinematics.

1 Fig. 6 .

 16 Fig. 6. Horizontal and vertical distances between hinges.

Fig. 8 .

 8 Fig. 8. Theoretical versus simulated microrobot workspace.

Fig. 9 .

 9 Fig. 9. Clean room fabrication process.

  9.a). 2-Patterning and dry etching of the wafer front side with an opening window of 20 µm (see Fig.9.b). 3-Dry etching of the handle layer (backside layer) using the DRIE process (see Fig.9.c). 4-Release useless parts by diving the wafer into a hydrofluoric acid (HF 49%) and transversely etching the buried silicon dioxide located between the device and handle openings using HF solution. (see Fig.9.d). 5-Deposition of gold layer of 200 nm thick through a shadow mask (see Fig.9.e). Achieving all these sub-steps leads to the prototype shown in Fig. 10. After activating the two multistable modules

Fig. 10 .

 10 Fig. 10. Fabricated prototype.

Fig. 11 .

 11 Fig. 11. Experimental Bench.

Fig. 12 .

 12 Fig. 12. Elementary displacements of the microrobot tip.

Fig. 13 .

 13 Fig. 13. Experimental characterization of the microrobot workspace.

Fig. 14 .

 14 Fig. 14. Effect of over-etching on the geometrical parameters of the hinges.

Fig. 15 .

 15 Fig. 15. Multistable teeth mechanism.

TABLE II COMPARISON

 II BETWEEN FEA SIMULATION AND EXPERIMENTATION

		generated step resolution motion range
	COMSOL (FEA) 4.318 (µm)	-	51.816 (µm)
	Experimentation	4.125 (µm)	150 nm	49,5 (µm)
	Error	4.7%	-	4.7%


A Didier

J Millo

B Maréchal

C Rocher

C Lacroûte

M Ouisse

E Rubiola

Y Kersalé

Compact Ultra-Stable Laser

We present an ultra-stable laser based on a compact Fabry-Perot cavity with a thermal noise limit expected at 2 ⇥ 10 15 in trems of fractional frequency stability. The 25 mm long cavity is housed in a cubic vacuum chamber with a volume of about 2.2 L. The measured phase noise is 3 dBrad 2 /Hz at 1 Hz with a simple optical set-up at 1542 nm.

I. INTRODUCTION

High finesse Fabry-Perot cavities are widely used as frequency reference to stabilize lasers sources. The improvement of these cavity stabilized lasers are of prime importance for optical frequency standards [START_REF] Ludlow | Optical atomic clocks[END_REF]. Consequently, many laboratories are developping technics to reduce the thermal noise of cavities that is now in the 10 17 decade but require complex systems such as cryocoolers [START_REF] Kessler | A sub-40-mHz-linewidth laser based on a silicon single-crystal optical cavity[END_REF], [START_REF] Häfner | 8 ⇥ 10 17 fractional laser frequency instability with a long room-temperature cavity[END_REF] and many active controls such as residual amplitude modulation, doopler effect, power stabilisation [START_REF] Zhang | Reduction of residual amplitude modulation to 1 ⇥ 10 6 for frequency modulation and laser stabilization[END_REF].

Moreover these highly stable lasers are also used to synchronize optical frequency combs for ultra-low phase noise microwave signal generation [START_REF] Fortier | Generation of ultrastable microwaves via optical frequency division[END_REF], [START_REF] Didier | Ultra-low phase noise all-optical microwave generation setup based on commercial devices[END_REF]. High precision spectroscopy is also a field of interest. Such applications do not need state-of-the-art stabilized lasers, but the compactness and the simplicity is an important critera [START_REF] Davila-Rodriguez | A compact, thermal noise limited reference cavity for ultra-low noise microwave generation[END_REF]. For such purpose, we are developping a laser based on a 25 mm long cavity with a very compact vacuum chamber and an optical set-up reduced to the quintessential components.

II. ULTRA-STABLE CAVITY

Two high finesse mirrors made of fused silica substrats and cristalyne coatings are optically contacted to a spacer in ULE glass. The high mechanical quality factor of materials used for the mirrors leads to a reduced thermal noise of 1.8 ⇥ 10 33 / f L 0 2 Hz 1 . The length of the spacer made of ULE glass L 0 = 25 mm is a compromise between the level of thermal noise and the compactness.

The geometry of the spacer has been optimized using finite element modeling tools to reduce coefficients of sensitivity to vibration to a few 10 12 /(m.s 2 ) in order to avoid the use of an active vibration isolation system. The cavity is maintened by three points in the middle plan (perpendicular to the optical axis) and protected by two thermal shields (see Fig. 1). A first one in stainless steel for the high thermal capacitance is also used to support the cavity. Around it, a second shield in copper to reduce gradiant is temperature controlled. The quasi-cubic vacuum chamber (136⇥132⇥128 mm 3 ) is placed on an active vibration isolation table that can be used to apply modulation in order to estimate the vibration sensitivity of the cavity.

III. OPTICAL SETUP

The optical set-up is based on pigtailed components with polarisation maintening fiber for compactness. The laser source is a compact extented cavity laser diode at 1542 nm showing a phase noise of 6.3 ⇥ 10 7 /f 3 rad 2 /Hz from few Hertz to tenth of kilohertz (grey curve on Fig. 2). An optical coupler is used to pick-up the beam for comparison with an other optical reference. The phase modulator for the Pound-Drever-Hall detection is connected just before the output collimator. A freespace part is mandatory to match the mode of the fiber with the mode of the cavity with two lenses. Two mirrors are used to align the beam onto the optical axis of the cavity, and a beam spliter cube sends the reflexion of the cavity to the photodiode for the frequency detuning detection. All these free-space components are mounted on cage systems compatible with half inch optical elements and directly attached to the vacuum chamber.

IV. RESULTS

The phase noise and the frequency stability are measured by comparison with another cavity stabilized laser. This laser has been caracterized using a cryogenic saphire oscillator (with optical frequency division technics) [START_REF] Didier | Ultra-low phase noise all-optical microwave generation setup based on commercial devices[END_REF]. Its frequency stability is better than that of the compact cavity stabilized laser under test.

We measure a phase noise of 3 dBrad 2 /Hz at 1 Hz with a slope in f 2 (see Fig. 2). We can see the influence of the active vibration isolation platform between ⇠ 4 Hz and ⇠ 60 Hz whereas the noise at 1 Hz is not impacted. The fractional frequency stability measured is at 7.5⇥10 15 at 1 s. This result is consistent with the fractional frequency stability computed from the phase noise measured at 1 Hz (5 ⇥ 10 15 ).

The phase noise measured at 1 Hz is 13 dB higher than the thermal noise of the cavity. It is important to point out the 978-1-5386-2916-1/$31.00 ©2017 IEEE Fig. 2. Phase noise power spectral density of the free runing laser, the laser locked to the cavity with the vibration isolation table on and off. simplicity of the optical set-up. For example, due to the cage system lenses, waveplates and the photodiode can not be tilted to avoid back reflexions. Furthermore there is no free-space isolator to prevent this problem.

V. CONCLUSION

We have developed a compact ultra-stable laser with a simple optical set-up that is compatible with a phase noise of 3 dBrad 2 /Hz at 1 Hz. The last improvements, and a complete characterization of the cavity and perturbations impacting the frequency stability will be presented at the conference.

Fig. 1 .

 1 Fig. 1. 25 mm long cavity on the left. The cavity mounted in its support with three contact points on the right.

ACKNOWLEDGMENT

The authors would like to thank the national network for time and frequency Labex FIRST-TF, the Region Franche-Comté and the PIA for funding. The authors also thank A. Bakir, E. Dordor and P. Abbé for electronical and mechanical support.