Electrostatic Frequency Tuning Research Articles

Exploring and Identifying Bias-Instability Noise Sources in Mode-Split MEMS Gyroscopes Based on Electrostatic Frequency Tuning

Exploring and Identifying Bias-Instability Noise Sources in Mode-Split MEMS Gyroscopes Based on Electrostatic Frequency Tuning

Electrostatic frequency tuning of flat and curved microplates

Electrostatic frequency tuning of flat and curved microplates

Distinct electrostatic frequency tuning rates for amide I and amide I′ vibrations

Amide I spectroscopy probes the backbone C=O stretch vibrations of peptides and proteins. Amide I spectra are often collected in deuterated water (D2O) since this provides a cleaner background in the amide I frequency range; such data are often referred to as amide I' spectra since deuteration induces changes in the mode structure, including a roughly ∼10 cm-1 redshift. For biological samples, however, deuteration is often not possible. As amide I frequency maps are increasingly applied to quantitative protein structural analysis, this raises the interesting challenge of drawing direct connections between amide I and amide I' data. We here analyze amide I and amide I' peak frequencies for a series of dipeptides and related compounds. Changes in protonation state induce large electrostatic shifts in the peak frequencies, allowing us to amass a sizable library of data points for direct amide I/amide I' comparison. While we find an excellent linear correlation between amide I and amide I' peak frequencies, the deuteration-induced shift is smaller for more red-shifted vibrations, indicating different electrostatic tuning rates in the two solvents. H2O/D2O shifts were negligible for proline-containing dipeptides that lack exchangeable amide hydrogens, indicating that the intrinsic properties of the solvent do not strongly influence the H/D shift. These findings indicate that the distinct tuning rates observed for the two vibrations arise from modifications to the intrinsic properties of the amide bond and provide (at least for solvated dipeptides) a simple, linear "map" for translating between amide I and amide I' frequencies.

A Digital Mode-Matching Control System Based on Feedback Calibration for a MEMS Gyroscope

A digital mode-matching control system based on feedback calibration, where two pilot tones are applied to actuate the sense mode by the robust feedback controller, is presented for a MEMS gyroscope in this paper. A dual-mass decoupled MEMS gyroscope with the integrated electrostatic frequency tuning mechanisms, the quadrature correction electrode, and the feedback electrode is adopted to implement mode-matching control. Compared with the previous mode-matching method of forward excitation calibration, the proposed mode-matching scheme based on feedback calibration has better adaptability to the variation in the frequency of calibration pilot tones and the quality factor of the sense mode. The influences of calibration pilot tone frequency and the amplitude ratio on tuning performance are studied in theory and simulation. The simulation results demonstrate that the tuning error due to the amplitude asymmetry of the sense mode increases with a frequency split between pilot tones and the drive mode and is significantly reduced by the amplitude correction technology of pilot tones. In addition, the influence of key parameters on the stability of the mode-matching system is deduced by using the average analysis method. The MATLAB simulation of the mode-matching control system illustrates that simulation results have a good consistency with theoretical analysis, which verifies the effectiveness of the closed-loop mode-matching control system. The entire mode-matching control system based on a FPGA device is implemented combined with a closed-loop self-excitation drive, closed-loop force feedback control, and quadrature error correction control. Experimental results demonstrate that the mode-matching prototype has a bias instability of 0.63°/h and ARW of 0.0056°/h1/2. Compared with the mode-mismatched MEMS gyroscope, the performances of bias instability and ARW are improved by 3.81 times and 4.20 times, respectively.

Nano-electromechanical Drumhead Resonators from Two-Dimensional Material Bimorphs.

Atomic membranes of monolayer 2D materials represent the ultimate limit in the size of nano-electromechanical systems. However, new properties and new functionalities emerge by looking at the interface between layers in heterostructures of 2D materials. Here, we demonstrate the integration of 2D heterostructures as tunable nano-electromechanical systems, exploring the competition between the mechanics of the ultrathin membrane and the incommensurate van der Waals interface. We fabricate electrically contacted 5 or 6 μm circular drumheads of suspended heterostructure membranes of monolayer graphene on monolayer molybdenum disulfide (MoS2), which we call a 2D bimorph. We characterize the mechanical resonance through electrostatic actuation and laser interferometry detection. The 2D bimorphs have resonance frequencies of 5-20 MHz and quality factors of 50-700, comparable to resonators from monolayer or few-layer 2D materials. The frequencies and eigenmode shapes of the higher harmonics display split degenerate modes, showing that the 2D bimorphs behave as membranes with asymmetric tension. The devices display dynamic ranges of 44 dB, with an additional nonlinearity in the dissipation at small drive. Under electrostatic frequency tuning, devices display a small tuning of ∼20% compared with graphene resonators, which have >100%. In addition, the tuning shows a kink that deviates from the tensioned membrane model for atomic membranes and corresponds with a changing in stress of 14 mN/m. A model that accounts for this tuning behavior is the onset of interlayer slip in the heterostructure, allowing the tension in the membrane to relax. Using density functional theory simulations, we find that the change in stress at the kink is much larger than the predicted energy barrier for interlayer slip of 0.102 mN/m in an incommensurate 2D heterostructure but smaller than the energy barrier for an aligned graphene bilayer of 35 mN/m, suggesting a local pinning effect at ripples or folds in the heterostructure. Finally, we observe an asymmetry in tuning of the full width at half-maximum that does not exist in monolayer resonators. These findings demonstrate a new class of nano-electromechanical systems from 2D heterostructures and unravel the complex interaction of membrane morphology versus interlayer adhesion and slip on the mechanics of incommensurate van der Waals interfaces.

Electrostatic compensation of structural imperfections in dynamically amplified dual-mass gyroscope

This paper presents a study on dynamics of a dual-mass MEMS vibratory gyroscope in presence of fabrication imperfections and reports a method for precision electrostatic frequency tuning of the operational modes. A number of multi-mass MEMS gyroscopes have emerged in recent years pursuing different goals, such as dynamically balanced structure, increased bandwidth, and dynamic amplification. Along with many perceived advantages of multi-mass devices, several challenges associated with mode-matching in a system with increased number of degrees-of-freedom (DOF) have to be considered. This work shows that it is possible to apply the DC tuning techniques, similar to tuning a conventional single-mass gyroscope, to achieve the precision tuning in a dual-mass sensor, without losing advantages of increased DOF of the system. The presented frequency trimming technique is based on assessing the modes mismatch and cross-coupling between modes by means of fitting the experimental frequency response curves to the analytical solutions of the dual-mass system in presence of imperfections. The tuning algorithm involves two steps. First, the stiffness mismatch along the two axes and the anisoelasticity angles α and β are identified, then the tuning DC voltages for modification of diagonal, off-diagonal, and coupling terms in the stiffness matrix are chosen. The method of electrostatic tuning was validated through the experimental characterization of a dual-mass dynamically amplified gyroscope, where the coupling between the two operational modes was minimized and frequency split was reduced from 26 Hz down to 50 mHz, resulting in 17.5× increase in the gyroscope scale factor and significantly improved noise characteristics. The presented electrostatic compensation method is suitable for both off-line and on-line calibration.

Experimental characterization of graphene by electrostatic resonance frequency tuning

In the last decade, graphene membranes have drawn tremendous attention due to their potential application in Nano-Electro-Mechanical Systems. In this paper, we show that the frequency response curves of graphene resonators are powerful tools for their dynamic characterization and for extracting their equivalent Young's modulus. For this purpose, vibrations of an electrostatically actuated circular graphene membrane are studied both experimentally and numerically. The experiments reveal the dependency of the linear and nonlinear resonance frequency of the nano-resonator on the driving DC and AC voltages. A numerical model is proposed based on the nonlinear membrane theory, and by fitting the numerically calculated change in resonance frequency due to the DC voltage to those of the experimental observations, the Young's modulus is determined. It is shown that by using the obtained equivalent Young's modulus, the numerical model can accurately describe the nonlinear dynamics of the graphene membrane in other sets of measurements.

Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope.

Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes.

A systematic approach for precision electrostatic mode tuning of a MEMS gyroscope

In this paper a systematic approach to precision electrostatic frequency tuning of the operational modes of a MEMS ring vibratory gyroscope is presented. In both rate and rate integrating gyroscopes the frequency split between the two modes of vibration which detect the Coriolis acceleration is one of the principal factors in determining the sensitivity and noise floor of the sensor. In high precision applications in the defence/aerospace sector a frequency split of the order of 10 mHz or less is highly desirable. In the ground-breaking Hemispherical Resonator Gyroscope (HRG) electrostatic tuning has been employed as a tuning mechanism. However, a description of the procedure is not available in the literature. The tuning scheme described here involves assessing mode mistuning by the ratio of the in-phase and quadrature components of the response to an external force that has similar properties to the gyroscopic force resulting from Coriolis action, and choosing the tuning voltages so that independent modification of the elements of the system stiffness matrix can be achieved. Experiments on a commercially available gyroscope with a natural frequency of 14 kHz show that the frequency split can be reduced from 1.5 Hz to 6 mHz. This represents a frequency precision of better than 1 part in a million.

Design and fabrication of a tuning fork shaped voltage controlled resonator for low-voltage applications with additional tuning electrodes

In this work a silicon voltage controlled microelectromechanical tuning fork resonator with electrostatic actuation and separate frequency tuning electrodes is presented. The released device is fabricated using a silicon-on-insulator wafer by a two-step process involving only focused ion beam masking and cryogenic deep reactive ion etching. This process is ideal for rapid prototyping, as the time to turn a design into the final device is only a few hours. The design of the resonator is optimized to accommodate the restrictions of the fabrication process, to maximize the frequency tuning range and to minimize the biasing voltage. Separating tuning and driving electrodes enables the resonance frequency adjustment by over 70 000 ppm (fcenter > 1.5 MHz, quality factor Q ≈ 2000) with a tuning voltage of 29 V in an open loop mode.

Design and fabrication of a tuning fork shaped voltage controlled resonator with additional tuning electrodes for low-voltage applications

In this work a silicon voltage-controlled microelectromechanical tuning-fork resonator with electrostatic actuation and separate frequency tuning electrodes is presented. The released device is fabricated using a silicon-on-insulator (SOI) wafer by a 2-step process involving only Focused Ion Beam (FIB) masking and Cryogenic Deep Reactive Ion etching (DRIE). This process is ideal for rapid prototyping, as the time to turn a design into the final device is only a few hours. The design of the resonator is optimized to accommodate the restrictions of the fabrication process, to maximize the frequency tunability and to minimize the biasing voltage. Separating tuning and driving electrodes enables the resonance frequency adjustment by over 10000 ppm (fcentral>1.5MHz, quality factor Q≈2000) with a tuning voltage of 12 V.

A low-cost rate-grade nickel microgyroscope

This paper presents a low-cost microgyroscope with a resolution in the rate-grade at atmospheric pressure, which is fabricated using a CMOS-compatible nickel electroforming process. Angular rate resolution of the gyroscope is increased by matching the resonance frequencies of the drive and sense modes close to each other using symmetric suspensions and electrostatic frequency tuning; whereas, undesired mechanical coupling between the two modes during matched mode operation is reduced by the fully decoupled gyro flexures. Reduced mechanical coupling results in a stable zero-rate output bias, i.e., providing excellent bias stability. The fabricated gyroscope has 18 μm-thick nickel structural layer with 2.5 μm capacitive gaps providing an aspect ratio above 7, which results in sensor capacitances about 0.5 pF. The resonance frequencies of the fabricated gyroscope are measured to be 4.09 kHz for the drive-mode and 4.33 kHz for the sense-mode, which are then matched by a tuning voltage less than 12 V dc. The gyroscope is hybrid connected to a CMOS capacitive interface circuit, and the hybrid system operation is controlled by external electronics, constructing an angular rate sensor. The gyroscope is oscillated along the drive-mode to vibration amplitude above 10 μm. The rate sensor demonstrates a noise-equivalent rate of 0.095 (°/s)/Hz 1/2 and short-term bias stability better than 0.1 °/s. The nominal scale factor of the sensor is 17.7 mV/(°/s) in a measurement range of ±100 °/s, with a full-scale nonlinearity of only 0.12%. The measurement bandwidth of the gyroscope is currently set to 30 Hz, while it can be extended beyond 100 Hz depending on the application requirements. The quality factor of the sense-mode improves by an order of magnitude at vacuum, which yields an estimated noise-equivalent rate better than 0.05 (°/s)/Hz 1/2 in a narrowed response bandwidth of 10 Hz.

VHF Single Crystal Silicon Capacitive Elliptic Bulk-Mode Disk Resonators—Part II: Implementation and Characterization

This work, the second of two parts, reports on the implementation and characterization of high-quality factor (Q) side-supported single crystal silicon (SCS) disk resonators. The resonators are fabricated on SOI substrates using a HARPSS-based fabrication process and are 3 to 18 /spl mu/m thick. They consist of a single crystal silicon resonant disk structure and trench-refilled polysilicon drive and sense electrodes. The fabricated resonators have self-aligned, ultra-narrow capacitive gaps in the order of 100 nm. Quality factors of up to 46 000 in 100 mTorr vacuum and 26000 at atmospheric pressure are exhibited by 18 /spl mu/m thick SCS disk resonators of 30 /spl mu/m in diameter, operating in their elliptical bulk-mode at /spl sim/150 MHz. Motional resistance as low as 43.3 k/spl Omega/ was measured for an 18-/spl mu/m-thick resonator with 160 nm capacitive gaps at 149.3 MHz. The measured electrostatic frequency tuning of a 3-/spl mu/m-thick device with 120 nm capacitive gaps shows a tuning slope of -2.6 ppm/V. The temperature coefficient of frequency for this resonator is also measured to be -26 ppm//spl deg/C in the temperature range from 20 to 150/spl deg/C. The measurement results coincide with the electromechanical modeling presented in Part I.

A micromachined vibrating rate gyroscope with independent beams for the drive and detection modes

We investigated the mechanical coupling between the drive and detection modes of micromachined vibrating rate gyroscopes, and designed and fabricated a gyroscope with a new structure to reduce the coupling. The coupling of the oscillator was measured using a new measurement system with a two-dimensional laser displacement meter. The oscillations were found to have an elliptical motion due to the coupling. When the frequency mismatch was reduced by means of electrostatic frequency tuning with a DC bias voltage, the coupling increased. The new structure, which has independent beams for the drive and detection modes, exhibited weaker coupling; and the resolution was 0.07°/s at a band width of 10 Hz.