A MEMS Disk Gyroscope with High Fabrication Precision, High Quality Factor (>810k) and High Overload Characteristic (>15000g)

This paper presents an electromagnetic MEMS disk gyroscope based on fused silica to enhance the accuracy of MEMS gyros under high overload conditions. A laser-induced modified wet etching (LIE) technology was utilized for gyro fabrication and a detailed analysis was conducted on the factors affecting quality factor (Q-value) of the gyro. The LIE process parameters were optimized using a four-factor and three-level orthogonal experiment, and structure compensation were implemented to address machining errors. Impact capability of the resonator and mode characterization as well as Q-value of the gyro revealing that the resonator can withstand high overload up to 15000g, frequency of working mode is 15382.2Hz and 15379.8Hz, respectively, which close to simulated result of 15443Hz exhibited high process precision. The corresponding Q-values of the driving mode and sensing mode are 817k and 819k, respectively, indicating high-performance potential.


Introduction
Gyro is used for measuring angle velocity serves as the core component of an inertial navigation system.Laser gyro, electrostatic gyro, and hemispherical gyros have demonstrated navigation-level performance but facing cost-related challenges.In recent decades, MEMS-based gyros have rapidly developed and emerged as research focus due to the advantages of structure compact, low mass, power conservation, stable batch performance [1][2][3][4], and many research focus on structural optimization and enhance Q-value for a higher performance [5][6][7].
The disk gyro works in frequency matching mode with high performance, and compatibility with planarization MEMS process enables cost-effective mass production.Najafi et al. originally reported on the silicon-based MEMS disk gyroscope in 1998 and subsequently conducted research on Q-value improvement [8,11].The silicon-based MEMS gyro has achieved high Q-values in recent decade by employing novel structural designs [12], mass stiffness decoupling [13,14], topology optimization [15][16][17][18], and other strategies.However, it remains challenging for the silicon-based MEMS gyro to achieve a higher Q-value due to the limitation of thermal elastic damping of silicon material.
Fused silica with low coefficient of thermal expansion is an ideal material for manufacturing high Q-value gyro.Hemispherical gyros based on fused silica exhibit a Q-value exceeding 12 million and have demonstrated potential for navigation-grade performance [7].Boeing proposed a MEMS based disk gyro based on fused silica, aiming to enhance the Q-value by nearly two orders of magnitude compared to silicon-based disk gyro, ultimately improving zero bias instability and angular random walk technical indicators by one order of magnitude [19,20].The MEMS hemispheres gyro based on fused silica through 3D manufacturing process have achieved millions in Q-value and showcased navigation-grade performance [21,22].However, the gyro bases on 3D processing needs to be individually assembled facing the challenge of discrepant performance among individual gyros and cost.The 2D planarization processing, including wet etching [23,24], dry etching [25][26][27], and laser etching [28], with the advantages of mass production enables the MEMS with lower prices.Among them, laser-induced modified wet etching (LIE) technique has been served as an ideal approach for processing high precision fused quartz disk gyros [29].In previous study, a fused silica resonator was fabricated by LIE demonstrated the Q-value exceeding 800,000 [30].This paper developed an electromagnetic-driven fused silica MEMS electromagnetic disk gyro.

Fundamental working principle
The structure illustration of MEMS disk gyro as show in Fig. 1a, comprising a resonator, a substrate, a magnetic core, and double magnetic caps.The resonator was directly bonded to the fused silica substrate, which was fabricated by mechanical grinding that match the size of the magnetic cap.The uniform magnetic field is created by the double Fe-Ni alloy magnetic caps and the Sm-Co magnetic core.The gyro equips with 8 electrodes for vibration exciting and signal detecting and works in n=2 modes (Fig. 1b and Fig. 1c).When a current I is applied to the driving electrodes, neglecting the influence of electrostatic force on the beams, electromagnetic force acting upon the ring has B represent the magnetic field strength, r is the ring radius.The simplified dynamics equation of the gyro can be expressed as Where  is the driving frequency, the motion of the disk gyroscope is Where 12 0 2 12 The induced electromotive force has According to equation (6), the gyro sensitivity is dependent on both the strength of the magnetic field and the Q-value of the resonator.In this research, a Samarium cobalt magnet with high magnetic field strength and fused silica is employed for high Q-value.

Analysis of Q-value dissipation
The Q-value denotes the ratio of total energy to dissipated energy in each vibration cycle that directly reflecting mechanical amplification and determining the sensitivity and mechanical thermal noise of the resonator.The higher the Q-value the greater sensitivity and the lower mechanical thermal noise of the resonator.The sources of energy loss in resonator includes air damping (1/Qair), thermoelastic loss (1/Qted), support loss (1/Qanchor), surface loss (1/Qsurface), and intrinsic damping loss (1/Qintr) can be concluded as The air damping loss is a consequence of energy transfer from the resonator to surrounding gas molecular, resulting in vibration a decrease in amplitude.Vacuum packaging can effectively reduce air damping loss, which becomes negligible when vacuum level is high enough [31,32], and then other damping losses determine upper limit of Q-value.
Thermoelastic damping originates from the interaction between the solid strain field and temperature field.As the resonator vibrating, structural strain induces a temperature gradient on the resonant ring.The non-equilibrium state of the temperature field inevitably leads to heat conduction (thermal relaxation), with heat flowing from compression to relaxation, resulting in dissipation of mechanical energy in the form of heat [33,34].In this study, Corning 7980 fused silica was utilized for resonator fabrication due to lower thermoelastic damping than silicon.
The intrinsic loss is associated with defects within the resonant material, including internal stress, hydroxyl groups, metal particle impurities and micro bubbles.Internal stress originates from raw materials or processing methods, and its slow release can cause performance instability of the gyro.The fused silica wafer in this research has low stress after precision annealing, while following wet etching and low temperature bonding have little impact on the stress.The hydroxyl groups could affect the lattice structure of fused silica, but no direct study has demonstrated a correlation between hydroxyl group content and resonator Q-value.The presence of micro bubbles within the fused silica induces structural discontinuity, leading to significant intrinsic losses [35,36].The metal particles impurity in the fused silica lattice either as interstitial or substitutional species enhances atom-atom inelastic collisions, resulting in partial conversion of mechanical energy into internal energy and a reduction in resonator Q-value [37,38].The gyro employs Corning 7980 Class type III fused silica allows high purity, minimal micro bubble content, and metal particle content is below 1000 ppb, enabling the resonator has neglectable intrinsic loss.
Surface loss is caused by subsurface damage, such as surface cracks and material defects, as well as surface energy states associated with specific surface area, including surface stress, moisture adsorption, and disruption of surface molecular bonds [39].The impact of surface energy state is linked to the surface area-to-volume ratio of the resonant structure.In high ratios, such as in nano-resonators, surface loss becomes the primary factor limiting Q-value.However, since the gyro in this paper sized in micrometer with low surface area-to-volume ratio, the influence of surface energy state on Q-value can be neglected.Subsurface damage is introduced during mechanical grinding and LIE processing of silica wafers.Surface crack resulting from mechanical grinding and chemical polishing at sub-micrometer level is attribute to both the polish material and technical factors.Extremely high temperature and pressure phases are generated within the fused silica in LIE processing, leading to formation of micro-explosions and cracks [40,41].It is imperative to accurately assess the surface damage resulting from LIE processing, as it may impose limitation on Q-value.
Support loss is the resonator energy transfers to the support anchor in the form of waves and dissipated that is related to structural shape, anchor size and other factors.Generally, gyro with smaller anchor sizes, higher symmetry, and stationary centers of mass during vibration exhibits lower support loss [42,43].However, there is no precise method for support damping evaluation.Relevant studies have reported that reducing the size of the support anchor point [6], increasing the elastic wave isolation layer [44], and using a support beam with a high aspect ratio [45] can reduce the support damping of the resonator.The gyro presented in this paper takes the uniformity of the magnetic field into account, by placing the magnetic core at the center of the resonator, adapted a large anchor area that may contributes the main component of Q-value limitation.

Optimization of laser-induced modification
The principle of LIE can be found in reference [30].This process primarily involves inducing cracks and defects in fused silica, thereby creating channels for penetration of etching solution.Ultimately, the structures within the enclosed region of the laser modification track drop from initial fused silica wafer after undergoing etching.Ideally, a low-energy single pulse laser should be utilized to generate perforations and fractures in the wafer, facilitating penetration channels with narrow crack regions for etching solutions.The size of the crack area and the holes diameter have a positive correlation with the single pulse energy, inadequate etching can result in subsurface cracks persistence in the resonator, ultimately leading to high surface loss and limiting the Q-value of the gyro.
The fused silica was subjected to single pulse laser modifications with intensities of 45μj, 60μj, 75μj, and 90μj respectively.When the femtosecond laser is focused within the fused silica, the fused silica was modified due to nonlinear absorption, generating extreme conditions of high pressure (>10TPa) and temperature (>5×10 5 K), ultimately leading to the formation of micro-holes and cracks [46].As depicted in Figure 2a-h, the modified silica exhibits arrays of micro-holes within fused silica towards the direction induced by laser, which may be attributed to a dynamic interplay between self-focusing and self-defocusing effects [47].When single pulse laser energy is insufficient, only small holes can be produced without cracks (Fig. 2a).As single pulse energy increases, the size of small holes expands and cracks form around the hole (Fig. 2b), and an obvious melting zone appears with further energy increase (Fig. 2c-d).Therefore, a single pulse with 60 µj energy is selected for silica modification.The single pulse energy for inducing modification was set to 60μj, with the pulses spaced at intervals of 1μm, 3μm, 5μm and 7μm, respectively.The morphology of the modified sample surface and cross-section is presented in Fig 3 .When the modification interval is 1μm, there is an overlapping hot melt influence area of a single pulse resulting in a loose porous morphology on fused silica with a continuous laser ablation pattern on its surface.At a pulse interval of 3 μm, continuous damage occurs with dense cracks formed between micro-holes.Sparse cracks are observed between micro-holes when the pulse interval is 5 μm.However, the small holes become independent of each other and there is no crack connection between micro-holes when the spacing is increased to 7 μm.During laser processing, micro-holes generated by micro explosions release energy in the form of shock waves to their surrounding areas.Due to the degradation of mechanical properties caused by micro defects in the fused silica, cracks continue to grow under shock waves generated by subsequent micro-holes.When the spacing interval of the hole is short and crack regions overlap, high-density cracks will develop between them.Moreover, the shock wave energy generated by subsequent laser pulse causes pre-existing cracks to grow perpendicular to the laser-induced trajectory, resulting in the formation of high-density defects in a perpendicular direction (Fig. 3a).The shock wave energy of the following laser pulse may not be sufficient to facilitate the growth of pre-exciting cracks when a large interval distance is implemented, resulting in lack of crack penetration between micro-holes (Fig. 3d).The higher the cracks density the more conducive to solution penetration, but higher perpendicular defect may transfer to fabricated resonator and leading to unexceptional surface loss.Therefore, a 3μm interval distance is suitable for resonator fabrication due to the effective entrapment of high-density crack defects between micro-holes and reduced crack density in the perpendicular direction of the laser trajectory.

Optimization of wet etching
A four-factor, three-level orthogonal experiment was conducted to investigate the influence of solution concentration (5%, 10%, 15%), etching temperature (20°C, 45°C, 70°C), ultrasonic power (0 W, 100 W, 200 W) and etching time (10 min, 20 min, 30 min) against the etching rate of both the side wall and the surface.The 10 mm ×10 mm fused silica samples with a thickness of 0.5 mm were processed under different etching parameters.The micrometer and step profiler (Bruker DektakXT) were used to measure the etch depth and roughness respectively.
The relationship between ultrasonic power and etching time against etching rate is depicted in Fig. 4 at the same concentration (15%) and temperature (55°C).It can be observed that ultrasonic vibration has small effects on etching rate and can be approximated save as uniform etching.The results of the step meter test indicate that wet etching does not alter the surface roughness.It is noticeable that the laser-modified side wall has a higher etching rate compared to the surface (approximately 1.5 times).This can be attributed to the wave-shaped morphology of the side wall surface, which possesses a higher specific surface area and consequently enhances the wet etching rate.etching rate versus temperature and solution concentration The etching process was analyzed by using 10%HF at 25° for different durations, as shown in Fig. 6.In the initial stage of etching, the etchant penetrates into the fused silica through micro-holes and cracks, it can be observed that the holes and cracks undergo expansion, gradually etching into the material creating a micro-channel (0-7min).The etch rate within the fused silica is lower than near the surface area due to the decrease in concentration of the etchant as it penetrate, resulting in a slight sidewall tilt angle of approximately 2°.In the next stage of the etching process, etching is performed in the direction perpendicular to the laser-induced trajectory, and the final sidewall slope is approximately 89°, fully demonstrating the potential of the LIE process for processing high aspect ratio microstructures.

Figure. 6
The side wall morphology versus etching time In addition to etchant concentration and temperature, the duration of etching is influenced by the thickness of the sample and the geometry of the processing structure.High aspect ratio structures require more time to remove from the wafer.In this research, the 0.5mm thickness resonator requires 13 minutes for complete etching under the conditions of 10% etching etchant concentration, 70° temperature and 200W ultrasonic power.The precise etching width of 11µm was evaluated by previous orthogonal experiment and qualified by an etching experiment, as shown in Fig. 7.

Figure. 7
The structural deviation caused by wet etching

mechanical properties measurement
The mechanical properties of a 2mm×10mm×0.5mmsample fabricated by the LIE process carried out at various etching times (10% HF, 40°C,100W), including 0,5, 10, 15, 20 and 25 minutes duration , and were subjected to tensile tests (Fig. 8).The tensile strength of the sample is nearly 45MPa when the etch time exceeds 10 minutes.The etching widths of the side and surface, as evaluated from previous orthogonal experiment after a duration of 10 minutes, were measured to be 4 µm and 1.5 µm respectively.It is suggested that the width of the laser-induced crack in a single laser pulse energy of 60µj is approximately 4 µm, which coincides with the measurement results showed in Fig. 3h.The compensation for etching deviation is 11µm, which exceeds the range of cracks introduced by laser (4 µm), allows the gyro to achieve high precision fabrication and a high Q-value that is independent of surface damping loss.

impact measurement
More than 40 resonators were subjected to impact measurements in the vertical plane direction, as illustrated in Fig. 9a.The impact magnitude increases steadily from 2000g at 0.5ms.No damage resulted from three impacts below 12000g, but some parts sustained damage after three impacts of 15000g.Figure 9b shows the spectrum line of the impact at 12000g.The pulse duration was restricted to 0.1ms due to limitation imposed by the experimental equipment.The COMSOL simulation results indicate the point of maximum stress during impact is located at the intersection of the anchor points on the edge, which is supported by experimental dates shows in Fig9c-e.

Mode characteristics of the electromagnetic disk gyro
The assembled gyro as show in Fig. 10a, the modes characteristics are depicted in

Q-value measurement
A gyro with a circuit was placed in the high vacuum chamber (with a background limit vacuum pressure lower than 1×10 -3 Pa), and high purity nitrogen (99.999%) was introduced into the chamber through a flowmeter (seven star D07) to adjust the chamber pressure.The Q-values of the gyro were measured by utilizing ring down time.As illustrated in Fig. 11, the driving mode and sensing model exhibit nearly identical quality factors at the same pressure due to their exceptional symmetry.The driving mode and sensing mode demonstrate Q-values of 819k and 817k, respectively, highlighting the potential of fused silica in high-precision planarized gyros.The deviation in Q-values within the range of 1Pa-5Pa can be attributed to intermittent measurements from both the ionization vacuum gauge and resistance vacuum gauge, both of which have high levels of uncertainty.As depicted in Fig. 11b and c, the sensing mode demonstrates a Q-value of 817k at 1.5×10 -3 Pa but the value experiences a significantly decrease to 606k at 0.95 Pa.Therefore, it is imperative to maintain a vacuum pressure below 0.1Pa within the package to ensure optimal gyro performance.

Conclusion
This article presents a fused silica electromagnetic MEMS disk gyro that has been fabricated using the LIE process, and analyzed the various factors that affect its Q-value.The LIE process has been optimized to ensure complete elimination of laser-induced cracks.The gyro with high process precision through structure compensation, resulting in resonance frequencies of 15382.2Hz and 15376.8Hz for the driving and sensing modes, respectively, which close to the simulated result of 15443Hz.The impact experiments have demonstrated that the gyro's overload capacity exceeds 15000g, rendering it suitable for high overload application.The gyro exhibits exceptional symmetry with high Q-value exceeding 810,000, demonstrating tremendous potential for practical applications.

Figure. 1
Figure. 1 (a) Structural illustration of electromagnetic MEMS disk gyroscope, (b) driving mode, (c) sensing mode.The gyro equips with 8 electrodes for vibration exciting and signal detecting and works in n=2 modes (Fig.1band Fig.1c).When a current I is applied to the driving electrodes, neglecting the influence of electrostatic force on the beams, electromagnetic force acting upon the ring has

Figure. 2
Figure.2 (a) surface morphology, 45µj, (b) surface morphology, 60µj, (c) surface morphology, 75µj, (d) surface morphology, 90µj, (e) inside morphology, 45µj, (f) inside morphology, 60µj, (g) inside morphology, 75µj, (h) inside morphology, 90µjThe single pulse energy for inducing modification was set to 60μj, with the pulses spaced at intervals of 1μm, 3μm, 5μm and 7μm, respectively.The morphology of the modified sample surface and cross-section is presented in Fig 3.When the modification interval is 1μm, there is an overlapping hot melt influence area of a single pulse resulting in a loose porous morphology

Figure. 4
Figure.4 (a) surface etching rate, µm/min (b) side wall etching rate, µm/min Under the same time (15min) and ultrasonic power (50W), the relationship between the etching reaction temperature, solution concentration and the etching rate of the sample surface and side is shown in Fig.5.The etching rate is highly dependent on the concentration of solution and temperature.Increasing the concentration of solution and the etching temperature can significantly increase the etching rate.

Figure. 5
Figure. 5 (a) surface etching rate versus temperature and solution concentration (b) side walletching rate versus temperature and solution concentration The etching process was analyzed by using 10%HF at 25° for different durations, as shown in Fig.6.In the initial stage of etching, the etchant penetrates into the fused silica through micro-holes and cracks, it can be observed that the holes and cracks undergo expansion, gradually etching into the material creating a micro-channel (0-7min).The etch rate within the fused silica is lower than near the surface area due to the decrease in concentration of the etchant as it penetrate, resulting in a slight sidewall tilt angle of approximately 2°.In the next stage of the etching process, etching is performed in the direction perpendicular to the laser-induced trajectory, and the final sidewall slope is approximately 89°, fully demonstrating the potential of the LIE process for processing high aspect ratio microstructures.

Fig. 10b .
The resonance frequencies of the driving mode and the sensing modes are 15382.2Hz and 15376.8Hz, respectively.These results are consistent with the simulation result of 15443Hz.The vibrating movement of the sensing mode was measured by exciting the driving mode, as depicted in Fig.10c.The observed small amplitude of the sensing mode indicates CSMNT-2023 Journal of Physics: Conference Series 2740 (2024) 012062 IOP Publishing doi:10.1088/1742-6596/2740/1/01206210 that the gyro with a high degree of symmetry in terms of stiffness and damping.

Figure. 11
Figure.11 (a) The relationship between pressure and ring down time; (b) ring down time of the sensing mode in 1.5×10 -3 Pa (c) ring down time of the sensing mode in 0.95 Pa