Optically levitated gyroscopes with a MHz rotating micro-rotor

The optically levitated particles have been driven to rotate at an ultra-high speed of GHz, and the gyroscopic application of these levitated particles to measure angular motion have long been explored. However, this gyroscope has not been proven either theoretically or experimentally. Here, a rotor gyroscope based on optically levitated high-speed rotating particles is proposed. In vacuum, an ellipsoidal vaterite particle with 3.58 $\mu$m average diameter is driven to rotate at MHz, and the optical axis orientation of the particle is measured by the particle rotational signal. The external inputted angular velocity makes the optical axis deviate from the initial position, which changes the frequency and amplitude of the rotational signal. The inputted angular velocity is hence detected by the rotational signal, and the angular rate bias instability of the prototype is measured to be $0.08^o/s$. It is the smallest rotor gyroscope in the world, and the bias instability can be further improved up to $10^{-9o}/h$ theoretically by cooling the motion and increasing the angular moment of the levitated particle. Our work opens a new application paradigm of the levitated optomechanical systems and possibly bring the rotor gyroscope to the quantum realm

Support Loss and Q Factor Enhancement for a Rocking Mass Microgyroscope

A rocking mass gyroscope (RMG) is a kind of vibrating mass gyroscope with high sensitivity, whose driving mode and sensing mode are completely uniform. MEMS RMG devices are a research hotspot now because they have the potential to be used in space applications. Support loss is the dominant energy loss mechanism influencing their high sensitivity. An accurate analytical model of support loss for RMGs is presented to enhance their Q factors. The anchor type and support loss mechanism of an RMG are analyzed. Firstly, the support loads, powers flowing into support structure, and vibration energy of an RMG are all developed. Then the analytical model of support loss for the RMG is developed, and its sensitivities to the main structural parameters are also analyzed. High-Q design guidelines for rocking mass microgyroscopes are deduced. Finally, the analytical model is validated by the experimental data and the data from the existing literature. The thicknesses of the prototypes are reduced from 240 μm to 60 μm, while Q factors increase from less than 150 to more than 800. The derived model is general and applicable to various beam resonators, providing significant insight to the design of high-Q MEMS devices

Effect of Axial Force on the Performance of Micromachined Vibratory Rate Gyroscopes

It is reported in the published literature that the resonant frequency of a silicon micromachined gyroscope decreases linearly with increasing temperature. However, when the axial force is considerable, the resonant frequency might increase as the temperature increases. The axial force is mainly induced by thermal stress due to the mismatch between the thermal expansion coefficients of the structure and substrate. In this paper, two types of micromachined suspended vibratory gyroscopes with slanted beams were proposed to evaluate the effect of the axial force. One type was suspended with a clamped-free (C-F) beam and the other one was suspended with a clamped-clamped (C-C) beam. Their drive modes are the bending of the slanted beam, and their sense modes are the torsion of the slanted beam. The relationships between the resonant frequencies of the two types were developed. The prototypes were packaged by vacuum under 0.1 mbar and an analytical solution for the axial force effect on the resonant frequency was obtained. The temperature dependent performances of the operated mode responses of the micromachined gyroscopes were measured. The experimental values of the temperature coefficients of resonant frequencies (TCF) due to axial force were 101.5 ppm/°C for the drive mode and 21.6 ppm/°C for the sense mode. The axial force has a great influence on the modal frequency of the micromachined gyroscopes suspended with a C-C beam, especially for the flexure mode. The quality factors of the operated modes decreased with increasing temperature, and changed drastically when the micromachined gyroscopes worked at higher temperatures

Analysis and Design of a Polygonal Oblique Beam for the Butterfly Vibratory Gyroscope with Improved Robustness to Fabrication Imperfections

This paper focuses on structural optimization of a Butterfly vibratory gyroscope (BFVG). An oblique suspension beam adopting polygonal cross-section is proposed in order to enhance the sensitivity and robustness. The operation principles of the BFVG are introduced. The suspension beam, which was found to be the key component, is selectively stressed. Varying cross sections of the suspension beam, including parallelogram, pentagon, hexagon, platform of pentagon, L-shaped and convex shapes are compared with each other. In particular, in order to show the advantages of the proposed polygonal cross-section, the convex cross-section is used as a reference. The influence of fabrication imperfections, which includes alignment error, silicon thickness error, etching depth error, upper width error, bottom width error and deep reactive-ion etching (DRIE) verticality error, on the oblique beam’s spindle azimuth angle of the two cross-sections is analyzed. Further, the quadrature error of two cross-sections with a fabrication defect is analyzed. The theoretical arithmetic results suggest that a polygonal cross-section beam is much more stable than a convex cross-section beam in most cases. The robustness of the fabrication imperfection is improved nine-fold and the quadrature error due to fabrication defect is reduced by 70 percent with a polygonal cross-section. It could be a better candidate for BFVG’s oblique beam, which would provide a gyroscope with good robustness and repeatability

Research on a MEMS Microparticles Vacuum Chamber for Optical Levitation with a Built-In Vacuum Gauge

The vacuum chamber is an important part of microparticle optical levitation technology. The traditional vacuum chamber has a large volume and many peripheral components, which cannot meet the requirements of miniaturization and on-chip optical levitation technology. Therefore, this study proposes a novel microparticle vacuum chamber based on the micro-electro-mechanical system (MEMS) process. This MEMS microparticle vacuum chamber adopts a “glass-silicon-glass” three-layer vacuum bonding process, with a volume of only 15 mm × 12 mm × 1.2 mm, including particle chamber, cantilever resonator chamber, and getter chamber, which can encapsulate microparticles in a tiny vacuum environment and realize optical levitation of microparticles. At the same time, the air pressure in the micro vacuum chamber is monitored by the cantilever resonator, which can provide a miniaturized microparticle chamber with a more accurate vacuum environment for microparticle optical levitation. The research of this paper has significance for promoting the development of miniaturized optical levitation technology

A Miniature Optical Force Dual-Axis Accelerometer Based on Laser Diodes and Small Particles Cavities

In recent years, the optical accelerometer based on the optical trapping force effect has gradually attracted the attention of researchers for its high sensitivity and high measurement accuracy. However, due to its large size and the complexity of optical path adjustment, the optical force accelerometers reported are only suitable for the laboratory environment up to now. In this paper, a miniature optical force dual-axis accelerometer based on the miniature optical system and a particles cavity which is prepared by Micro-Electro-Mechanical Systems (MEMS) technology is proposed. The overall system of the miniature optical levitation including the miniature optical system and MEMS particles cavity is a cylindrical structure with a diameter of about 10 mm and a height of 33 mm (Φ 10 mm × 33 mm). Moreover, the size of this accelerometer is 200 mm × 100 mm × 100 mm. Due to the selected light source being a laser diode light source with elliptical distribution, it is sensitive to the external acceleration in both the long axis and the short axis. This accelerometer achieves a measurement range of ±0.17 g–±0.26 g and measurement resolution of 0.49 mg and 1.88 mg. The result shows that the short-term zero-bias stability of the two orthogonal axes of the optical force accelerometer is 4.4 mg and 9.2 mg, respectively. The main conclusion that can be drawn is that this optical force accelerometer could provide an effective solution for measuring acceleration with an optical force effect for compact engineering devices

A 4 mm2 Double Differential Torsional MEMS Accelerometer Based on a Double-Beam Configuration

This paper reports the design and simulation of a 4 mm2 double differential torsional MEMS accelerometer based on a double-beam configuration. Based on the structure of conventional torsional accelerometers, normally composed of one pair of proof masses and one torsional beam, this work explores the double differential configuration: a torsional accelerometer with two pairs of unbalanced proof masses rotating in reverse. Also, the torsional beam is designed as a double-beam structure, which is a symmetrical structure formed by two torsional beams separated by a certain distance. The device area of the novel accelerometer is more than 50 times smaller than that of a traditional double differential torsional MEMS accelerometer. The FEM simulation results demonstrate that the smaller device does not sacrifice other specifications, such as mechanical sensitivity, nonlinearity and temperature robustness. The mechanical sensitivity and nonlinearity of a ±15 g measuring range is 59.4 fF/g and 0.88%, respectively. Compared with traditional single-beam silicon structures, the novel structure can achieve lower maximum principle stress in critical regions and reduce the possibility of failure when high-g acceleration loading is applied along all three axes. The mechanical noise equivalent acceleration is about 0.13 mg / Hz in the theoretical calculations and the offset temperature coefficient is 0.25 mg/ ℃ in the full temperature range of − 40 ℃ to 60 ℃

A New Stress-Released Structure to Improve the Temperature Stability of the Butterfly Vibratory Gyroscope

This paper is devoted to discussing the influence of thermal stress on the performance of the Butterfly Vibratory Gyroscope (BFVG). In many gyroscopes, due to the material properties and the fabrication processes, the deformation caused by residual stress or thermal mechanical stress is of great concern since it directly affects the performance. Here, a new stress-released structure was proposed to reduce the deformation to improve BFVG’s performance considering the symmetry of the electrode and the miniaturization of the structure. Its dimensional parameters relate to the effect of thermal stress release and the stiffness characteristics of the BFVG’s oblique beam. The single parameter analysis method was used to explore the influence of the parameters on the effect of thermal stress release to guide the optimal size of the final design. The effect of thermal stress release in the BFVG at the full range temperature was also tested after the fabrication. The results showed that the influence of thermal stress on the BFVG’s performance effectively reduced

A novel method of quadrature compensation in the butterfly resonator based on modal stiffness analysis

The butterfly gyroscope is simple to manufacture and it is considered as one kind of MEMS gyroscope with high sensitivity due to its unique structure. In reality, fabrication imperfections result in non-ideal geometries in the resonator, which in turn causes the quadrature error. The quadrature error has a great influence on the performance of the sensors in Micro and Nano scale, such as the zero-rate output (ZRO), the detection resolution and the dynamic range. However, the fact that the mechanical parameters of resonators are unknown (due to fabrication variation, fluctuations with temperature and aging) poses serious challenges. This paper presents a simple, yet effective method of quadrature compensation in butterfly resonator by electrostatic tuning. Theoretical calculation of quadrature error in butterfly gyroscope is carried out, establishing the mathematical model of quadrature compensation. Then, the simulation analysis is conducted to further analyze the mechanism of quadrature error and the method of quadrature compensation. Also, 5 butterfly gyroscopes fabricated on the same silicon wafer are selected for the experiment of quadrature compensation and the ZRO of the butterfly gyroscopes improves up to two orders of magnitude with quadrature cancellation, showing the feasibility of the proposed approach to quadrature compensation in the butterfly gyroscope. Finally, the way to decrease the direct current voltage VT required for suppressing the quadrature error is discussed. What is more, the method is not only suitable for the butterfly gyroscope, but also can be applied to other sensors in the Micro and Nanoscale

Biomimetic Superhydrophobic Hollowed-Out Pyramid Surface Based on Self-Assembly

In this paper, we present a periodic hollowed-out pyramid microstructure with excellent superhydrophobicity. In our approach, T-topping pillars and capillary-induced self-assembly methods were combined with the photolithography process to fabricate a hollowed-out pyramid structure. First, a wideband ultraviolet source without a filter was used to fabricate the T-topping pillars during the exposure process; then, the evaporation-induced assembly collapsed the pillars and formed the hollowed-out pyramid structure. Scanning electron microscopy images showed the microstructures of the prepared surface. The contact angle of the surface was 154°. The surface showed excellent high temperature and ultraviolet irradiation tolerance, and the contact angle of the surface barely changed when the temperature dropped. This excellent environmental durability of our superhydrophobic surface has potential applications for self-cleaning and friction drag reduction under water