# Early Measurements of Silicon Axisymmetric MEMS Gyro

Lucas Hudeley, Raphaël Levy, Maxime Duquesnoy, Jérémy Bonhomme, Olivier Le Traon, Alain Bosseboeuf, Marc Faucher, Jérôme Juillard, Benjamin Walter

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Lucas Hudeley, Raphaël Levy, Maxime Duquesnoy, Jérémy Bonhomme, Olivier Le Traon, et al. "Early Measurements of Silicon Axisymmetric MEMS Gyro. 2025 IEEE International Symposium on Inertial Sensors and Systems (INERTIAL), May 2025, Lindau, Germany. pp.1-4, 10.1109/INERTIAL63280.2025.11037183. hal-05166627

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
EARLY MEASUREMENTS OF SILICON
AXISYMMETRIC MEMS GYRO

Lucas Hudeley, Raphaël Levy, Maxime
Duquesnoy, Jérémy Bonhomme, Olivier Le
Traon

Physics, Space, Environment, Instrumentation
Department

ONERA the French Aerospace Lab,
University Paris-Saclay
92320 Châtillon, France
lucas.hudeley@onera.fr

Alain Bosseboeuf
C2N, CNRS, University Paris-Saclay
91120 Palaiseau, France
alain.bosseboeuf@c2n.upsaclay.fr

Marc Faucher
IEMN, UMR CNRS 8520, Univ.
Lille, Villeneuve d'Ascq, France
marc.faucher@univ-lille.fr

Benjamin Walter
Vmicro SAS - Avenue Poincaré Villeneuve
d'Ascq, France
benjamin.walter@vmicro.fr

***Abstract***—This paper presents the first promising results of the new silicon MEMS gyro presented during INERTIAL 2022. This MEMS Coriolis Vibratory Gyroscope (CVG)

) design is based on a link element between the outer frame and the proof mass. We demonstrated high quality factor up to 4e5 for a resonant frequency of 8 kHz. A very good linearity of the scale factor has been demonstrated over a +/- 1000 °/s rate range. The Allan variance have been measured and showed average performance in open loop: 17 °/√h. However, this is expected to give way better result in the near future with close-loop.

***Keywords***—Gyro, Axisymmetric, whole angle, navigation grade, silicon, MEMS

I. INTRODUCTION

Silicon MEMS gyros have shown promising results for the achievement of navigation grade inertial sensors. Axisymmetric designs have notably shown high performances as demonstrated by Thales [1], Safran [2] or Boeing (Disc Resonating Gyro [3]) or in academia (Quad-Mass Gyro [4]). Another approach for gyro design is based on the use of bulk acoustic wave (BAW), example of these are the SD-BAW [5] and the QSG [6]. The axisymmetric design we presented at Inertial 2022 [7], called AXSIGO (AXisymmetric Silicon GyrO) aims at reaching the navigation grade, with a bias repeatability better than 0.1°/h and an ARW < 0.005°/√hr. This performance is excepted thanks to the original patented design based on the compensation of the proof mass momentum via counterweight integrated in the link elements [8].

This paper presents the first characterization of the AXSIGO CVG in open loop architecture but the design is also suitable for close loop and whole angle operation. A first section of the paper depicts the MEMS device and its fabrication. Then, a second section presents both the resonance parameters and the early gyro performance characterization two different devices.

II. MEMS DEVICE

A. *Design*

The first design of the cell and its conception were
presented in [7]. Fig. 1 shows back the simulated modes of
the gyroscope, one orthogonal with the other, which can be
either drive or sense. This structure ensures a perfect
balance of the central mass momentum when vibrating in
the plane, limiting energy losses out of the device

(insulation Q factor larger than 10⁷). Two designs has been
optimized; one axisymmetric (drive and sense at matching
frequency) and one with an imposed 120 Hz frequency split
(Δf). Split frequency sensors will be used for open-loop
operation since the split is directly linked to the sensor
bandwidth (BW) in this architecture (Δf ~ 2.BW).
Axisymmetric sensors will be used for close loop (and
whole angle) operation to reach higher scale factor because
with this type of architecture the bandwidth is given by the
electronic. This paper will only talk about the open-loop
operation.

<figure><img src="image_2.png" /><figcaption>Fig. 1: Simulated modal deformation of the gyro modes at 7370 Hz. Electrostatic combs are not represented here.</figcaption></figure>

B. Fabrication

We used 4 inches Silicon on Insulator (SOI) wafers with highly doped device layer. The high doping is used to lower the thermal sensibility of the devices as demonstrated by Jaakkola in [9]. We used deep reactive ion etching (DRIE) to obtain large aspect ratio (20 in our case) which is required to attain large scale factors with capacitive sensing. Then, a Hydrofluoric based etching allows the release of the vibratory parts and the elimination of the sacrificial parts. An example of a fabricated device at the end of process is presented in Fig. 3. As we can see in the picture, the counterweights are not the same size on both direction (u₁ and u₂), this is how frequency split is achieved. These cells are then vacuum-sealed in ceramic packages at less 10⁻⁴ mbar. The packaged device is 16.5 mm x 16.5 mm x 20 mm.

III. CHARACTERIZATION RESULTS

A dedicated PCB has been designed for summing,
amplifying and transforming charges collected on
electrostatic combs in a measurable gyro signal. We also use
a lock-in amplifier form Zurich Instrument (HF2LI) for the
operation and characterization presented in this paper.
<figure><img src="image_3.png" /><figcaption>Fig. 2: Captioned optical microscopy photography of a split frequency gyro cell n° 1</figcaption></figure>

A. Resonator parameters extraction from fast sweep

The theoretical parameters for the best resonator structures are an overall Q factor over 10⁵ (limited by thermoelastic losses) at 7870 Hz. The frequency split between the modes is theoretically null or 120 Hz, and may be adjusted electrostatically in the limit set by the coupling between the modes. For these parameters, the steady state is reached after more than 4 seconds. For a good parameter estimation a classic steady state frequency sweep measurement could easily last more than 5 minutes. During this time, it is difficult to ensure that the parameters has not shifted.

The fast sweep parameter extraction is detailed in [10]. This method consists on measuring the frequency response faster than the steady state and adjust a model to extract the resonant parameters such as the frequencies and quality

factors. An example of such a measurement on the device n°1 (shown in Fig. 2) is represented in Fig. 3. The “drive” (“sense”) curves correspond to the output of the PCB on the drive (sense) direction for instance the sum of the response of all transducers output in u₁ (u₂) direction. Here, the polarization tension on the drive direction (VPD) and on the sense direction (VPS) are asymmetric to electrostatically tune frequencies. Thanks to the tuning, Δf is lowered from 127 Hz to less than 4 Hz.

The sweep realized here is an up and down sweep of the drive excitation over a 12 Hz window containing both gyro mode. No control loop is needed for this method. The sweep is 152 s long and as we can see, the measurement is carried out in transitory state since we observe an oscillation after passing the resonances. On the zoomed part of the figure, we notice the very good agreement between the measured values and the retro simulated model, which confirm the viability of this method.

From this measurement and thanks to the fast sweep extraction method we computed both resonant parameters for this configuration. The first mode is f_1 = 7833.36 Hz with a Qfactor_1 = 36745 and the second mode is at f_2 = 7836.67 Hz with Qfactor_2 = 37281. A leakage problem has been detected on the housing leading to a lower Q factor than previously measured and consequently degraded results. This cell was characterized just after the sealing with a ring-down method and at this time, we measured Qfactor_1 = 156000 and Qfactor_2 = 188000.

A second more promising cell (n°2) has shown even higher quality factor of more than 4.1e5 with a frequency split of 30 Hz with a symmetric polarization. This cell is designed without frequency split however, 30 Hz are measured which show a small imperfection either on the polarization or on the fabrication/integration. The high quality factor leads more toward an operation issue; a degraded fabrication should lower the quality factor. Nonetheless, these high quality factors are promising to reach good performances in open-loop and in future closed-

<figure><img src="image_4.png" /><figcaption>Fig. 3: Fast sweep fit on measurement of the device n° 1 with 3.3 Hz frequency mismatch with a drive polarization of 4.2V and a sense polarization of 6.9V. The excitation is 3 mV on one pair of comb drives.</figcaption></figure>
loop operation.

## B. Gyro characterization

### 1) Sacle-Factor

Now that the resonators are characterized, we measured the scale-factor (SF) on a rate table. We operate the drive mode with a PLL to lock its frequency at resonance and with a PID to fix its amplitude. Then, we measure the free oscillation on the sense direction at the drive frequency for different rate applied. The results for the cell n°1 with symmetric polarization $V_{PD} = V_{PS} = 5$ V and a mean value of the drive excitation $V_d = 1$ mV are presented in Fig. 4. We applied successively 50 °/s, 100 °/s, 300 °/s and 500 °/s. Here, we extract SF = 1.58 µV/(°/s) which is in accordance with the theory that gives 2 µV/(°/s). Since the quality

<figure><img src="image_5.png" /><figcaption>Fig. 5: Scale factor measurment n°1 of a 127 Hz mode missmatch device with a polarization of 5V and an excitation of 1mV over one comb drive.</figcaption></figure>

factor is not high in this configuration, we have a theoretical operating range larger than 10000 °/s.

As we can see, this cell has a high bias caused by the coupling between both modes (equivalent to > 3000 °/s) which is classic in MEMS without corrections. It can be caused by a non-symmetric excitation, a misalignment between the direction of vibration and the direction of vibration and/or the fabrication imperfections. We expect to lower this coupling with active correction in the near future. Another issue is the high noise on the measurement leading to high uncertainty on the measurement. This will cause a large offset value in the Allan variance. The high coupling between modes probably causes this noise. A part of the drive noise, composed of electronic control noise (PLL + PID) and the intrinsic drive noise ends on the sense axis. We hope to reduce the noise by reducing the coupling.

Another example of measurement, this time with different rotation direction and on the n°2 sensor is presented in Fig. 5. We applied successively positive and negative rates to verify the linearity even when changing direction. This time we imposed a 5 V symmetric polarization and a 5 mV excitation. We have a larger scale-factor than the n°1 because the drive displacement is higher SF = 12 µV/(°/s). The linearity is still very high (R² = 0.99999) over the larger range of rate +/- 1000 °/s. Unfortunately, this cell also have a high coupling that needs to be corrected to improve the performance in noise and scale-factor.

<figure><img src="image_6.png" /><figcaption>Fig. 4: Scale factor measurment of n°2 cell with a 28 Hz mode missmatch device with a polarization of 5 V and an excitation of 5 mV over one comb drive.</figcaption></figure>

### 2) Allan variance

We then proceeded to Allan deviation measurement on the sensor even if we already know that the noise is high on this cell. The Allan variance measurement is shown in Fig. 6. This measurement is carried out on sensor n°1 with a 39 Hz frequency split in open loop, the drive polarization is $V_{PD} = 6.5$ V and $V_{PS} = 9$V. We imposed an excitation $V_d = 10$ mV leading to a scale factor of 17 µV/(°/s). At this time, quality factors of both modes were about 6800 because of the leakage in the vacuum housing. The measured ARW is 17 °/√h, which is high but coherent with these degraded conditions. Indeed, theoretically, by taking nonlinear limits and electronic saturation to maximize the drive motion and polarization of this gyro cell, at low pressure (less than 10⁻³ mbar), we obtain an optimal scale factor of 75 µV/(°/s). In open-loop, the noise is dominated by the electronic noise, therefore with this optimal scale factor we compute an ARW of 1 °/√h. We can further extrapolate this value in closed-loop with matched modes (same frequency), we would then achieve an ARW of 0.01 °/√h which is promising for high performances MEMS gyro. The bias instability (BI) is probably cause by the leakage that cause an early rise of the Allan deviation. At this point, its value should not be taken into account.

<figure><img src="image_7.png" /><figcaption>Fig. 6: Allan variance of the device n° 1 over 300 s for a 6.5 V drive polarisation, a 9V sense polarisation and an exciation of 10 mV (equivalent to a pilote displacement of 0.1 µm).</figcaption></figure>
CONCLUSION

We demonstrated in this paper that the idea presented
during INERTIAL 2022 [7] not only is working but also
gives promising results for achieving high gyro performance
at low cost and footprint. These cell have proven their
capability to reach high quality factor, larger than 4e5 at
about 8 kHz. We also shown the gyro sensor operation over
a large range of rate (+/- 1000 °/s) while keeping a very
good linearity. For now, the noise performances are low (17
°/√h) but the use of correction and better operating loop
should solve this issue. The sensors still need some
improvement to reduce the noise and coupling between
modes. To achieve this, we want to further study the
electrostatic tuning. We already are capable of modifying
the frequency and we are developing a way to actively act
on the coupling between modes. With these
implementations and the use of advanced control loop we
hope to reach better performance and reach navigation grade
with our MEMS CVG.

ACKNOWLEDGMENTS

This work is part of an ANR PROJECT N° ANR621-ASTR-
0017-01, authors would like to thanks the French Armed
forces Ministry for partially supporting this work.

This work was partially supported by the French RENATECH
network. This work used equipements funded by the CPER
Hauts de France project IMITECH, CPER WAVETECH@hdf,
and equipex NANOFUTUR 21-ESRE-0012

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