Multi-coefficient eigenmode operation—breaking through 10°/h open-loop bias instability in wideband aluminum nitride piezoelectric BAW gyroscopes

In this paper,a modification to the eigenmode operation of resonant gyroscopes is introduced.The multi-coefficient eigenmode operation can improve cross-mode isolation due to electrode misalignments and imperfections,which is one of the causes of residual quadrature errors in conventional eigenmode operations.A 1400µm annulus aluminum nitride(AlN)on a silicon bulk acoustic wave(BAW)resonator with gyroscopic in-plane bending modes at 2.98 MHz achieves a nearly 60 dB cross-mode isolation when operated as a gyroscope using a multi-coefficient eigenmode architecture.The as-born frequency mismatches in multiple devices are compensated by physical laser trimming.The demonstrated AlN piezoelectric BAW gyroscope shows a large open-loop bandwidth of 150 Hz and a high scale factor of 9.5 nA/°/s on a test board with a vacuum chamber.The measured angle random walk is 0.145°/√h,and the bias instability is 8.6°/h,showing significant improvement compared to the previous eigenmode AlN BAW gyroscope.The results from this paper prove that with multi-coefficient eigenmode operations,piezoelectric AlN BAW gyroscopes can achieve a noise performance comparable to that of their capacitive counterpart while having the unique advantage of a large open-loop bandwidth and not requiring large DC polarization voltages.

Resonant pitch and roll silicon gyroscopes with sub-micron-gap slanted electrodes:Breaking the barrier toward high-performance monolithic inertial measurement units

This paper presents the design,fabrication,and characterization of a novel high quality factor(Q)resonant pitch/roll gyroscope implemented in a 40μm(100)silicon-on-insulator(SOI)substrate without using the deep reactive-ion etching(DRIE)process.The featured silicon gyroscope has a mode-matched operating frequency of 200 kHz and is the first out-of-plane pitch/roll gyroscope with electrostatic quadrature tuning capability to fully compensate for fabrication non-idealities and variation in SOI thickness.The quadrature tuning is enabled by slanted electrodes with sub-micron capacitive gaps along the(111)plane created by an anisotropic wet etching.The quadrature cancellation enables a 20-fold improvement in the scale factor for a typical fabricated device.Noise measurement of quadrature-cancelled mode-matched devices shows an angle random walk(ARW)of 0.63°√h^(−1) and a bias instability of 37.7°h^(−1),partially limited by the noise of the interface electronics.The elimination of silicon DRIE in the anisotropically wet-etched gyroscope improves the gyroscope robustness against the process variation and reduces the fabrication costs.The use of a slanted electrode for quadrature tuning demonstrates an effective path to reach high-performance in future pitch and roll gyroscope designs for the implementation of single-chip high-precision inertial measurement units(IMUs).

Substrate-decoupled,bulk-acoustic wave gyroscopes:Design and evaluation of next-generation environmentally robust devices

This paper reports on a new type of high-frequency mode-matched gyroscope with significantly reduced dependencies on environmental stimuli such as temperature,vibration,and shock.A novel stress-isolation system is used to effectively decouple an axis-symmetric bulk-acoustic wave(BAW)vibratory gyro from its substrate,minimizing the effect that external sources of error have on the offset and scale factor of the device.Substrate-decoupled(SD)BAW gyros with a resonance frequency of 4.3 MHz and Q values near 60000 were implemented using the high aspect ratio poly and single-crystal silicon(HARPSS)process to achieve ultra-narrow capacitive gaps.Wafer-level packaged sensors were interfaced with a customized application-specific integrated circuit(ASIC)to achieve low variations in the offset across temperature(±26°s^(−1) from−40 to 85℃),supreme random-vibration immunity(0.012°s^(−1) gRMS−1)and excellent shock rejection.With a scale factor of 800μV(°s^(−1))^(−1),the SD-BAW gyro system attains a large full-scale range(±1250°s^(−1))with a non-linearity of less than 0.07%.A measured angle-random walk(ARW)of 0.39°/√h and a bias instability of 10.5°h^(−1) are dominated by the thermal and flicker noise of the integrated circuit(IC),respectively.Additional measurements using external electronics show bias-instability values as low as 3.5°h−1,which are limited by feed-through signals coupled from the drive loop to the sense channel,which can be further reduced through proper re-routing of the gyroscope pin-out configuration.

Eigenmode operation of piezoelectric resonant gyroscopes

The theory of eigenmode operation of Coriolis vibratory gyroscopes and its implementation on a thin-film piezoelectric gyroscope is presented.It is shown analytically that the modal alignment of resonant gyroscopes can be achieved by applying a rotation transformation to the actuation and sensing directions regardless of the transduction mechanism.This technique is especially suitable for mode matching of piezoelectric gyroscopes,obviating the need for narrow capacitive gaps or DC polarization voltages.It can also be applied for mode matching of devices that require sophisticated electrode arrangements for modal alignment,such as electrostatic pitch and roll gyroscopes with slanted electrodes utilized for out-of-plane quadrature cancellation.Gyroscopic operation of a 3.15MHz AlN-on-Si annulus resonator that utilizes a pair of high-Q degenerate in-plane vibration modes is demonstrated.Modal alignment of the piezoelectric gyroscope is accomplished through virtual alignment of the excitation and readout electrodes to the natural direction of vibration mode shapes in the presence of fabrication nonidealities.Controlled displacement feedback of the gyroscope drive signal is implemented to achieve frequency matching of the two gyroscopic modes.The piezoelectric gyroscope shows a mode-matched operation bandwidth of~250Hz,which is one of the largest open-loop bandwidth values reported for a mode-matched MEMS gyroscope,a small motional resistance of~1300Ω owing to efficient piezoelectric transduction,and a scale factor of 1.57nA/°/s for operation at atmospheric pressure,which greatly relaxes packaging requirements.Eigenmode operation results in an~35dB reduction in the quadrature error at the resonance frequency.The measured angle random walk of the device is 0.86°/√h with a bias instability of 125°/h limited by the excess noise of the discrete electronics.

Low motional impedance distributed Lame mode resonators for high frequency timing applications

This paper presents a novel high-Q silicon distributed Lamémode resonator(DLR)for VHF timing reference applications.The DLR employs the nature of shear wave propagation to enable a cascade of small square Lamémodes in beam or frame configurations with increased transduction area.Combined with high efficiency nano-gap capacitive transduction,it enables low motional impedances while scaling the frequency to VHF range.The DLR designs are robust against common process variations and demonstrate high manufacturability across different silicon substrates and process specifications.Fabricated DLRs in beam and frame configurations demonstrate high performance scalability with high Q-factors ranging from 50 to 250 k,motional impedances<1 kΩ,and high-temperature frequency turnover points>90°C in the VHF range,and are fabricated using a wafer-level-packaged HARPSS process.Packaged devices show excellent robustness against temperature cycling,device thinning,and aging effects,which makes them a great candidate for stable high frequency references in size-sensitive and power-sensitive 5 G and other IoT applications.