Olivier Français

Marie-Caroline Caroline Jullien

Lionel Rousseau

Patrick Poulichet

et al.. AN ACTIVE CHAOTIC MICROMIXER Serge Desportes

Assia Chouai

Jean-Pierre Lefèvre

Jacques Delaire

Jean Pierre Lefevre

AN ACTIVE CHAOTIC MICROMIXER INTEGRATING THERMAL ACTUATION ASSOCIATING PDMS AND SILICON MICROTECHNOLOGY

Keywords: Active micromixer, PDMS, Microheater, Chaotic effects, Microfluidic

published or not. The documents may come

INTRODUCTION

With the help of microtechnology applied to microfluidics, miniaturized chemical and biological analysis units offer a wide range of opportunities in term of applications and performances [START_REF] Reyes | Micro Total Analysis Systems. 1. Introduction, theory, and technology[END_REF]. Due to the scaling laws, flow behaviour in micro scale is drastically laminar and is associated with very low Reynolds number (<1). The Reynolds number (Re) is the ratio between inertial forces compared to viscous forces in a fluid:

µ VL R e ρ =
with ρ the fluid density, V the mean velocity, L characteristic channel dimension and µ the fluid viscosity.

In consequence, in small channels, the familiar turbulent mixing of macroscopic devices does not occur. In case of two fluids flowing in a channel side by side, a well defined interface appears and only diffusion creates mixing. In microfluidic, diffusion time can be drastically reduce by acting on interface fluids.

Several micromixers have been studied and published so far. Passive ones are based on asymmetric geometric disturbance to induce circular flow between two fluids [START_REF] Song | Microfluidic Systen for Controlling Reaction Networks in Time[END_REF] [3], or for example on the division of the liquids into tiny drops which are collected, after that in each drop, the liquids mix (due to internal friction) [START_REF] Miyake | Micromixer with fast diffusion, Micro Electromechanical Systems Workshop[END_REF]. By comparison, active micromixers present better performance in term of mixing efficiency, time and length of mixing. To achieve mixing, several kinds of actuators exist and mainly stretch liquids. Disturbance in flow can be generated in several manners [START_REF] Volker Hessel | Micromixers-a review on passive and active mixing principles[END_REF] : by ultrasound [START_REF] Yang | Ultrasonic micromixer for microfluidic systems[END_REF], vibration, electrowetting, magneto-hydrodynamic action or external pressure.

Here, an original actuator is presented. It is based on thermal actuation by dilation effects. It offers the capability to integrate the actuator with the channel and keep an actual control on the mixer behaviour. By creating interferences in the liquids interface, chaotic phenomenon occurs and induces exponential growth of the contact interface [7] [8] [9] . This paper will present principle description of the mixer and technology associated. It also presents first results of the mixing efficiency as a function of thermal actuator characteristics.

O. Français, C. Jullien, L.Rousseau, P. Poulichet, S. Desportes, A. Chouai, JP Lefevre, J. Delaire An active chaotic micromixer integrating thermal actuation associating PDMS and Silicon microtec.

STRUCTURE AND WORKING PRINCIPLE

The micromixer is based on a classical microfluidics channel obtained by PDMS moulding and bounded to a silicon or glass wafer [START_REF] Jo | Three-Dimensional Micro-Channel Fabrication in Polydimethylsiloxane (PDMS) Elastomer[END_REF]. It consists of a main channel where two fluids flow side by side. Due to diffusion time, a channel length of several centimeters is needed to obtain a complete diffusion between the two fluids. To reduce this length, a thermal actuator is added to increase the interface of the two fluids by stretching and folding it alternatively. Thus, in order to disturb the interface between the two fluids, an intersection is achieved with a secondary channel perpendicular to the main one. By this way, an oscillating transverse flow can be generated and may modify the position of the liquids interface [START_REF] Niu | Efficient spatio-temporal chaotic mixing in microchannels[END_REF]. Depending on the amplitude and frequency of this transverse flow compared with the one in the main channel, an increase of the contact surface between the two fluids can be obtained. With low transverse flow amplitude, no mixing is obtained. The effective mixing occurs when disturbance shape is sheared by the main flow. Thus, transverse flow may have amplitude greater than the channel width and velocity at least greater than the two fluids. Mixing is achieved by this way in short length similar to channel width and can be dynamically controlled.

To activate the transverse flow, an original thermal actuator has been integrated in the chip. On each side of the transverse channel, a circular microcavity is placed and associated to a heating resistance. Thus, heating the fluid will generate a volume expansion in the cavity and induce a fluid displacement in the transverse channel. By controlling the frequency and voltage value applied on the heating resistance, the oscillating transverse flow is generated. At microscales, thermal diffusion is a fast process, leading to a quasi simultaneous response of the system with respect to the actuation. In fact, with silicon substrate, a cut frequency of about 10Hz had been obtained for a thermal cavity surface of around 3.1mm² for 100µm thick. Compare to macroscale, this cut frequency value is very interesting. This thermal actuator is obtained by deposition of a conductor on the substrate. It is in contact with the cavity filled by a liquid and connected to the microfluidic channel. Two thermal cavities are needed (each side) and activated one after the other (Fig. 1). Thermal properties of the heated fluid will modify the mixer behaviour. Here, two cases have been considered. The first one supposed that a temperature above the boiling point is reached. To achieve the mixing, the cavity temperature was always above the boiling point with an oscillating value. Thus, the transverse flow was generated by a bubble volume variation. This case has been used with water, by heating this liquid above 100°C, a gas bubble was created and caused transverse flow across the main channel. This principle gave very large transverse flow due to bubble volumetric expansion coefficient. But, it was difficult to control. In figure 2, bubbles located in transverse channel are visible. One bubble is growing by activating the heating resistance; the other is collapsing due to passive cooling across the device.

Figure 2 : Photography of bubbles expansion and collapsing with water

The second one supposed that cavity temperature was always under boiling point. In this case, no bubble was generated, but only fluid volumetric dilation activated the transverse flow. A mixture of 70% of Glycerol with 30% of DI water has been used. The advantage is a very robust control of the amplitude generated, and here, associated to fluorescein in order to label one of the two liquids, characterisation of the mixing was simplest due to low value of the diffusion coefficient (fig. 3).

O. Français, C. Jullien, L.Rousseau, P. Poulichet, S. Desportes, A. Chouai, JP Lefevre, J. Delaire An active chaotic micromixer integrating thermal actuation associating PDMS and Silicon microtec.

The fluid volumetric dilation ol V ∆ in heating cavity is then concentrated in the channel associated. By applying the volume expansion value in the channel, the average length transverse flow x can be estimated:

x h h h d T V ol )². . ( 4 . . . 4 =         ∆ = ∆ π α
With α the fluid dilation coefficient, T ∆ the temperature increase, d the cavity diameter, h thickness of all microfluidic parts. The channel section is considered square.

A value of 0,425*10 -3 for α has been estimated (mixture between glycerol and water value), h is equal to 100µm and d is 2mm. By this way, the average length

x is connected to T ∆ with the relation :

) ( . 13 µm T x ∆ =
In case of laminar flow, the transverse flow length will be the double of x . Thus, a 10 °C temperature increase will generate a transverse flow of around 260µm of maximum amplitude. This value is similar to measurement achieved but is slightly over-estimated due to temperature gradient in heating cavity. Numerical simulation are to be made to precise modeling.

FABRICATION PROCESS AND ASSOCIATED ELECTRONICS

The thermal micromixer is composed of two parts. The electrical part is made on silicon by metal deposition and the micro fluidic part is made in PDMS [START_REF] Jo | Three-Dimensional Micro-Channel Fabrication in Polydimethylsiloxane (PDMS) Elastomer[END_REF]. By a classical method, the two parts are sealed together to avoid any leak.

First Silicon wafers were placed at 1050°c during 40 minutes on a steam furnace to obtain an oxide layer (SiO 2 ) of 0.4 µm thickness. This layer was used as an insulator for electrical parts. The wafers were then placed on RF magnetron sputtering and covered by 100 nm of chromium and 500 nm of gold. Chromium layer was used to allow a good adhesion on the substrate. A classical photolithography process was done to pattern the design of the heating resistances. The gold layer and chromium layer were etched successively by wet etching to obtain the heating resistance.

Figure 4: Cut view of the process microchip

For the microfluidic part, polydimethysiloxane (PDMS) was used. This product offers a large number of possibilities for achieving a prototype. First a mould had to be done. It was realised by using Deep Reactive Ion Etching (DRIE) technique. The DRIE technique [START_REF] Yu | 3-D microarrays biochip for DNA amplification in polydimethylsiloxane (PDMS) elastomer[END_REF] allows etching silicon with high aspect ratio and gives vertical side walls with better aspect than polymer technique. Concerning PDMS [START_REF] Fujii | PDMS-based microfluidic devices for biomedical applications[END_REF], it is composed of two products: base and reticulant. They were mixed together in proportion of 10:1 v/v. Before pouring PDMS on the mould, all the surface of the mould was treated with dimethysilixone vapour deposition during 30 minutes to make easier peeling off. The PDMS was poured in the mould and cured during two hours at 70 °C.

Then, all the PDMS micro-fluidics parts were delicately peeled off and sealed on the silicon wafer with hot resistance. To insulate the heating resistances from the liquid, a thin layer of PDMS is spin coated (fig. 4). This wafer with PDMS was cured in an oven at 70°C during 2 hours . To perform a permanent bonding between silicon wafer with heating resistances and PDMS microfluidics, activation by a plasma cleaner (O 2 gas ) was done on both PDMS surfaces during 30 seconds at a pressure of 300 mtorr. Plasma-treated samples were immediately bonded together with activated surfaces facing each other and then baked in an oven at 70 °C for 30 minutes (Fig. 5).

An homemade electronic circuit is used for generating the voltages applied on the two heating chambers. This circuit enables to choose frequency, duty cycle and voltage. These parameters are adjusted in order O. Français, C. Jullien, L.Rousseau, P. Poulichet, S. Desportes, A. Chouai, JP Lefevre, J. Delaire An active chaotic micromixer integrating thermal actuation associating PDMS and Silicon microtec.

to find the best conditions leading to the best mixing. Therefore, the power applied on the chamber can be controlled. The two heating resistances are in fact used in an opposite mode. An adjustable delay has been added to eventually use dissymmetric voltage. The frequency can be varied from 0.1 Hz to 100 Hz and the duty cycle is adjusted from 0.01 to 0.99. The heating resistor value is about 88 Ω. Thus, with a 30 V source and a duty cycle of 0.5, an electrical power of 6 W can be reached.

MEASUREMENT AND FIRST RESULTS

The performance of the mixing depends on the liquids velocity, length of transverse disturbances and frequency associated. Presently, the use of thermal actuators induces a limitation in frequency response because of substrate thermal resistivity. Consequently, two kinds of substrates have been used : one is a glass wafer which leads to a low frequency response (around 1Hz) but enables back side characterization, the other one is a silicon substrate which leads to a better frequency response (close to 10Hz).

Once the linear dependence of temperature versus injected electrical power had been validated [START_REF]Study of a thermally controlled Micro-cavity for Bio-MEMS applications based on PDMS technology[END_REF], a design was developed to obtain the thermally activated micromixer. All channels have a section of 100 µm*100 µm. Length of the main channel and transverse channel was 4 mm. The two thermal cavities were circulars with a diameter of 2 mm and 100 µm thick. The heating resistance value was 88Ω.

In order to characterize the micromixer, specific liquid with low diffusion value has been used. So Glycerol in 70% concentration associated with 30% DI water (fluorescein is added for the second fluid) has been injected in the device (Fig. 3). The fluid flow was constant and fixed at 10 µl/hr in the main channel corresponding to an average velocity of 0.28 mm/sec. The shape voltage applied on each resistance was square with a duty cycle of 0.5. Heating resistance were activated in opposite way. Study was done for a frequency from 1 Hz to 7 Hz with a voltage value varied from 0V to 30V corresponding to a total power varying from 0 to 5.1 W.

Figure 6 : Transverse flow amplitude evolution with applied voltage for a main fluids flow of 10µl/hr

First measurements have been achieved in order to validate the actuator principle. Depending on the frequency and voltage values, amplitude of the transverse disturbances was modified. For a fixed frequency, this amplitude increases quadratically with the applied voltage (fig. 6). Furthermore, mixing occurred for disturbance amplitude greater than the channel size. Figure 6 shows the evolution of the transversal displacement as a function of the applied voltage, for a given frequency (3Hz). The pattern at crossing is also shown for different couple (displacement, applied voltage). The evolution is not linear, however, as expected, the trend is an increase of the displacement versus an increase of the applied voltage. Note that this plot has to be handle with care. Indeed, the frequency plays a key role on the transversal displacement, i.e. the interface can be stretched and folded several time at crossing, this is an explanation for a non linear increase of the displacement as a function of applied voltage, even at a given frequency. Consequently, different couples (frequency, applied voltage) may lead to identical displacements. This will be further represented on figure 7.

The principle of the mixer has been validated, the efficiency of mixing was quantitatively measured using classical image treatment. At the exit of the crossing, when the main flow has been perturbed by the transversal oscillating flow, images were recorded and further processed. For each image, the histogram of concentration distribution was calculated.

O. Français, C. Jullien, L.Rousseau, P. Poulichet, S. Desportes, A. Chouai, JP Lefevre, J. Delaire An active chaotic micromixer integrating thermal actuation associating PDMS and Silicon microtec. In a configuration in which there was no transverse oscillating flow, this histogram had a twopeaks shape, one peak corresponds to a high concentration of the dye, while for a full mixing of the two liquids, this histogram tends to a Gaussian. The root mean square of the distribution is a measure of mixing efficiency. Indeed, for poor mixing, the root mean square is larger than for a good mixing situation. In order to characterize the efficiency of the mixer as a function of both control parameters (frequency, electrical power), the reverse of root mean square is evaluated with transversal displacement (Fig. 7).

From figure 7, the relationship between mixing efficiency as a function of transversal displacement is represented for different forcing frequencies. The general trend, as expected, is an increase of mixing efficiency with respect to an increase of transversal displacement. Under the experimental conditions, i.e. a flow velocity of 0.28 mm/sec, the maximal mixing efficiency is achieved for a frequency of 3 Hz. The fact that for a given transversal displacement the mixing efficiency is not a constant underlines the strong influence of the frequency. Indeed, the flow velocity and the forcing frequency are intrinsically connected, this may lead to a single or several stretching and folding of the two liquids interface inside the crossing, i.e. even if the displacement reaches a given value the interface can undergo several times the displacement.

The microfluidic device will be next used in quantitative detection of cations dedicated to potassium by fluorometric method.

CONCLUSION

In this paper, an active micromixer is depicted. Based on a chaotic like mixer, it used an integrated heating resistance to be activated. The thermal dilation obtained generates the transverse flow necessary to obtain the stretching and folding of the main flow.

Concerning manufacture, the microchip is realised using classical MEMS technology associated to PDMS moulding. By this way, the thermal actuator has been integrated with all microfluidic.

O. Français, C. Jullien, L.Rousseau, P. Poulichet, S. Desportes, A. Chouai, JP Lefevre, J. Delaire An active chaotic micromixer integrating thermal actuation associating PDMS and Silicon microtec.

The phenomenon used to activate the micromixer has been described and shown to be dependant of fluid thermal properties. Two cases have been considered concerning the obtaining of the transverse with the thermal actuator. The first is based on boiling of the liquid and, thus, on bubbles expansion or collapse. The second used only liquid dilation with temperature without boiling. Experiments have validated the two principles.

To characterize the mixer, image treatment is used by calculating the histogram of concentration distribution. From first measurement, a good mixing region is shown related to actuator characteristics.

Figure 1 :

 1 Figure 1 : Principle of the micromixer

Figure 3 :

 3 Figure 3 : Photography of transverse flow with glycerol

Figure 5 :

 5 Figure 5 : Micro-chip with microfluidic and electronic connection

Figure 7 :

 7 Figure 7 : Mixing efficiency as a function of transversal displacement for different forcing frequencies.


Archit Giridhar

Fabrice Verjus

Frédéric Marty

Alain Bosseboeuf

Tarik Bourouina

Electrostatically- Driven Resonator

ELECTROSTATICALLY-DRIVEN RESONATOR ON SOI WITH IMPROVED TEMPERATURE STABILITY

published or not. The documents may come

INTRODUCTION

The reference oscillator is among the most difficult to realize, since its stability specifications are quite demanding. The resonators for digital communication are currently built with the quartz crystal. The high quality factors and high temperature stability of such components make them more reliable in application. However quartz resonators have limited integration level and therefore their use in circuits and systems is still expensive.

On the other hand, the demonstrated MEMS resonators are theoretically sufficient to satisfy the shortterm stability needs of reference oscillators, but their aging stability and their temperature stability still remains a challenge. It has been shown that the long-term aging rate of these resonators is equivalent to commercial quartz crystal resonators. Also, unlike quartz resonators, no initial aging or stabilization and no measurable hysteresis are found [START_REF] Kim; Candler | Frequency stability of waferscale encapsulated MEMS resonators[END_REF]. Indeed, the temperature excursion for an uncompensated clamped-clamped beam polysilicon micro mechanical resonator is more than 15 times higher than that of the worst AT-cut quartz crystal. Though MEMS resonators satisfy the requirements of ICcompatible tanks for use in the low phase noise oscillators and highly selective filters of communications systems [2] yet they fall short of the marks required by oscillators with respect to temperature stability. In order to achieve more stable MEMS resonators, the design technique challenges between the thermal dependence of geometrically tailored stresses and temperature variations of Young's modulus and density [START_REF] Nguyen | Mechanically Temperature-Compensated Flexural-Mode Micromechanical Resonators[END_REF]. Further demonstrates that it is possible to reduce the temperature coefficient of the resonance frequencies by selfcompensation, without any additional power consumption.

WORKING PRINCIPLE

This operation principle of the self-compensated resonator was described in a report from N'Guyen's group and demonstrated experimentally on surface micro machined polysilicon resonators.

The self-compensation of the resonance frequency method is based on reducing the effect of material properties thermal variation by the stress induced in a compensating structure. The compensating structure is designed so that it will expand faster with increasing temperature, generating a net mechanical tensile stress in the resonator beam. This tensile stress serves to increase the beam's resonance frequency and thus oppose frequency decrease caused by Young's modulus temperature dependence, resulting in a smaller (and even nil) overall frequency excursion over a given temperature range.

RESONATOR ARCHITECTURE

The flexural mode resonator beam is attached to the wings containing the comb fingers with the help of the wing support on either side (Fig. 3.1). The resonator beam is connected to a horizontal truss beam at the top end and the bottom end is anchored to the substrate. The truss beam is fixed to the compensating beams on either side of the horizontal truss beam. The other ends of the compensating beam are anchored similar to that of the resonator beam. To insure that only the resonator beam vibrated when excitation signals are applied, the outer support beams are made much wider than the resonator beam, making them rigid against lateral motions. The comb drive (not shown in Fig. 3.1) employed for the electrostatic actuation of the resonator is placed in between the compensating beam and the wing with the movable fingers.

Archit Giridhar 1,2 In addition to reduced temperature sensitivity, this design also features a support on the substrate that effectively reduces energy radiation into the substrate during resonance vibration [START_REF] Melamud | Effects of stress on the temperature coefficient of frequency in double clamped resonators[END_REF]. Although one end of the resonator beam is rigidly anchored to the substrate, the other end is held flexible by the supporting system resulting in an end condition that is more decoupled from the substrate than a rigidly anchored end condition. This end condition, together with the use of a lateral vibration mode, effectively reduces anchor losses to the substrate, providing higher resonator Q than conventional clampedclamped beam resonator.

SIMULATION

A simple structure of the proposed design was simulated using ANSYS © commercial software. The structure taken for simulation is shown in (fig. 3.1). The simulated results give information about the rank of modes of the useful resonance, frequencies and effect of thermal variation. The simulated structure has the following characteristics given in table 1.

Density (kg/m3) 2330

Young's modulus (N/m2) 1.61e11

Temperature coefficient of the Young's modulus (ppm/°C) -7.406

Thermal expansion coefficient (ppm/°C) 2.4

Structure thickness t (µm) 20 Resonator beam length L (µm) 560

Resonator width w (µm) 2

Compensating width (perforated) W (µm) 40 Compensating Length ratio L1/L2 530/560 540/560 550/560

Table.1: Dimensions and material properties

where L 1 is the length of the compensating beams and L 2 is the length of the resonating beam.

The simulation focused on the resonant frequency and then to optimise for the temperature stability. We can observe the lateral in-plane displacement of the resonating structure, with a slight out-of-plane flexural displacement of the compensation structure (second resonance mode). Modes 3, 4 and 5 correspond to twisting modes but were strongly rejected into the considered frequency range. The simulated result of 33.6 kHz resonance frequency was achieved with a 30 fingers equivalent geometry. The mechanically stressed zones can be observed with an energy analysis. An important stress exists at the lower resonating beam anchor and on the comb-drives support. However, the compensation structure anchor was low-stressed.

FABRICATION

SOI Technology

The SOI technology consists of a two-mask process. The first one was used to pattern gold electrodes. The second one defines the geometry of the resonator mechanical structure, which was obtained by deep etching of silicon using DRIE with photo resist as a mask material. Finally the release of the structures was performed using hydrofluoric acid (HF). SOI technology provides electrical isolation between the bodies of individual SCS resonators which can be used for instance in an array implementation (for filter synthesis for instance). In general, it enables sub-micron precision fabrication of stiff SCS resonators with height to width ratio > 10 for better electro-mechanical coupling and higher frequency operation.

Fig. 5.1 The top view of the fabricated structure (resonator)

The SEM picture of the fabricated resonator corresponds to the structure considered for the simulation. The release etch holes were taken into consideration for the laying out the structure during fabrication of the resonator (fig. 5.1).

COMPENSATION STRUCTURE RELEASE HOLES METAL PADS COMB-DRIVE WINGS RESONATING BEAM

Archit Giridhar 1,2 , Fabrice Verjus 1 , Frédéric Marty 2 , Alain Bosseboeuf 3 , Tarik Bourouina 2 Electrostatically -driven Resonator on SOI with Improved Temperature Stability

EXPERIMENTAL RESULTS

The experimental data shows that the resonator was quite stable to a large thermal variation for a range of 25°C to 80°C. Measurements were performed by an optical vibrometer using the knife edge method [5], in order to have access to in-plane vibrations. Measurements were performed in vacuum (7x10 -2 mbar) in order to emphasize the quality factor. The results were plotted by simultaneously mapping the vibration [START_REF] Sylvain Petitgrand | Simultaneous mapping of out-of-plane and in-plane vibrations of MEMS with (sub)nanometer resolution[END_REF]. The measured resonant frequency was 6320 Hz at room temperature (25°C). When the temperature was varied up to 80°C the resonant frequency shifted to 6330 Hz. This slight change by 10 Hz in the resonant frequency was equivalent to 29 ppm/°C, which was in the same order of magnitude of the simulation results on non-optimised structures.

A study on the experimental results has been proposed to analyse the deviation in the theoretical simulation and experimental results. Measurements are now underway on devices having different truss and compensating beam dimensions and also different overall dimensions of the resonator. As already seen in the design and simulation sections, the ratio of the length of the compensating beam and the resonating beam were expected to have an impact on the temperature coefficient of the resonance frequency.

POST PROCESS SIMULATION

In order to analyse the results of the experiment, i.e. measurements made on the fabricated resonator the post process simulation of the structure was done. During this simulation all parameters were considered including the release etch holes. The structure identified in the simulation was similar to the structure fabricated. This simulation was done to study the deviations in the experimental results in contrast with the previously simulated results. By this simulation procedure, the idea of achieving the resonator with improved temperature stability at the required frequency (32.786 KHz) is enhanced.

The various parameters were considered for the post process simulation. The dimensions of the structure (fabricated resonator) observed with the interferometer were defined for simulation along with the etch holes imposed on the resonator for the release of the structures. The effect of variation in resonant frequency with temperature variation from (-40 to 80) i.e. Mechanical simulations between -40°C to 80°C

The first level of post process simulation concentrates more on the study to analyse the difference in the resonance frequency from 33.6 KHz to 6.3 KHz. at 25°C. Later, the second level of simulation was to relate the experimental results and the simulated results based on the real dimensions of the fabricated structure obtained from the SEM pictures. Finally, third level of simulation focused on the stability on resonant frequency with a variation in temperature.

Effect of release etch holes

In the first level of the post process simulation a few etch holes were introduced in the structure (fig. 7.1.1). The release etch holes were consideration to evaluate the effect on the structure i.e. the variation in the resonant frequency and the temperature stability of the structure.

Fig. 7.1.1: A view of the simulated structure

The simulations have shown that the required flexural resonant mode (Fig. 7.1.2) was achieved typically at a frequency of 8335 Hz. This mode was at the first rank, whose frequency was far from higher order modes: more than 3700 Hz frequency difference with the second mode. This shows that the effect of the etch holes reduced the stiffness of the structure resulting in the lowering of the resonant frequency. The curves shown in (Graph. 7.1.1) summarize the simulation results for the temperature dependence of the first flexural resonance frequency. The relative variation of frequency versus temperature has either a positive or negative slope depending on the value of the beam length ratio L1/L2. One can also see that the minimum slope was obtained for the ratio L1/L2 = 540/560 (=0.964), corresponding to a theoretical frequency temperature coefficient of -1.6 ppm/°C for this optimised structure. Other values for the frequency temperature coefficients of non-optimised structures were -10.9 ppm/°C for L1/L2 = 530/560 (=0.946) and 8.2 ppm/°C for L1/L2 = 550/560 (=0.982).

Etch Holes

Archit Giridhar 1,2

Deviation Analysis

The second level of simulation was done on the structure approximately identical to that of the fabricated structure (fig. 7.2.1).

Fig. 7.2.1: The view of the simulated structure with holes

Simulations show that mode of resonance close to the required flexural resonant mode (Fig. 7.2.2) was achieved typically at a frequency of 12590Hz at 25°. This mode was at the first rank, whose frequency was far from higher order modes: more than a few kHz in difference with the second mode. The resonance occurs with a slight indent in the y-axis, which was observed during simulation. The results shown in (Fig. 7.2.2) summarize the simulation results for the temperature dependence of the first flexural resonance frequency. The relative variation of frequency versus temperature has either a positive or negative slope depending on the value of beam length. With respect to the previous structure there was a slight optimisation in the dimension of the structure. Though there was a very small change in the dimension, there was

Archit Giridhar 1,2 , Fabrice Verjus 1 , Frédéric Marty 2 , Alain Bosseboeuf 3 , Tarik Bourouina 2 Electrostatically -driven Resonator on SOI with Improved Temperature Stability a significant effect on the temperature stability. The simulations have shown that the required flexural resonant mode (Fig. 7.3.1) was achieved typically at a frequency of 12707 Hz. This mode was at the first rank, whose frequency was far from higher order modes: more than a few kHz in difference with the second mode. There was no relative variation of frequency versus temperature.

One can also see that with the temperature stability was obtained for the ratio L1/L2 = 540/560 (=0.964),

CONCLUSION

Fig. 3 .

 3 Fig. 3.1: A 3D view of the resonator

Fig. 7 1 :

 71 Fig. 7.1.2: The simulation results on the structure

Fig. 7

 7 Fig. 7.2.2: The simulated results to show the temperature stability of the structure 7.3. Temperature StabilityThe third level of simulation focused to achieve temperature stability closer in dimension to the fabricated structure. An optimisation process overlapped with the post process simulation was felt in the results of the simulation. This leads to the optimisation of the structure for the required resonant frequency with improved temperature stability.

Fig. 7. 3 . 1 :

 31 Fig. 7.3.1: The simulated results to show the temperature stability of the structure.

  , Fabrice Verjus 1 , Frédéric Marty 2 , Alain Bosseboeuf 3 , Tarik Bourouina 2 Electrostatically -driven Resonator on SOI with Improved Temperature Stability

  , Fabrice Verjus 1 , Frédéric Marty 2 , Alain Bosseboeuf 3 , Tarik Bourouina 2 Electrostatically -driven Resonator on SOI with Improved Temperature Stability

  This work has shown preliminary results on SOI electrostatically driven MEMS resonators with improved temperature stability. ANSYS simulations have shown that a frequency temperature coefficient in the order 1 ppm/°C is attainable based on the assumption of precision of 10 microns in structure length. First experimental results have shown a measured coefficient of 29.3 ppm/°C on non-optimised structures. Characterization of optimised structures is underway. Prospective work is the study of the impact of crystal orientation in the temperature behavior.

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