This paper reports an acceleration sensing method based on two weakly coupled resonators (WCRs) using the phenomenon of mode localization. When acceleration acts on the proof masses, differential electrostatic stiffness perturbations will be applied to the WCRs, leading to mode localization, and thus, mode shape changes. Therefore, acceleration can be sensed by measuring the amplitude ratio shift. The proposed mode localization with the differential perturbation method leads to a sensitivity enhancement of a factor of 2 than the common single perturbation method. The theoretical model of the sensitivity, bandwidth, and linearity of the accelerometer is established and verified. The measured relative shift in amplitude ratio ( $\sim 312162$ ppm/g) is 302 times higher than the shift in resonance frequency ( $\sim 1035$ ppm/g) within the measurement range of ±1 g. The measured resolution based on the amplitude ratio is 0.619 mg and the nonlinearity is $\sim 3.5$ % in the open-loop measurement operation. [2015-0247]

An Acceleration Sensing Method Based on the Mode Localization of Weakly Coupled Resonators

A new micromachined uniaxial silicon resonant accelerometer characterized by a high sensitivity and very small dimensions is presented. The device's working principle is based on the frequency variations of two resonating beams coupled to a proof mass. Under an external acceleration, the movement of the proof mass causes an axial load on the beams, generating opposite stiffness variations, which, in turn, result in a differential separation of their resonance frequencies. A high level of sensitivity is obtained, owing to an innovative and optimized geometrical design of the device that guarantees a great amplification of the axial loads. The acceleration measure is obtained, owing to a properly designed oscillating circuit. In agreement with the theoretical prediction, the experimental results show a sensitivity of 455 Hz/ ( g being the gravity acceleration) with a resonant frequency of about 58 kHz and a good linearity in the range of interest.

A Resonant Microaccelerometer With High Sensitivity Operating in an Oscillating Circuit

An analysis of the dynamic characteristics of pull-in for parallel-plate and torsional electrostatic actuators is presented. Traditionally, the analysis for pull-in has been done using quasi-static assumptions. However, it was recently shown experimentally that a step input can cause a decrease in the voltage required for pull-in to occur. We propose an energy-based solution for the step voltage required for pull-in that predicts the experimentally observed decrease in the pull-in voltage. We then use similar energy techniques to explore pull-in due to an actuation signal that is modulated depending on the sign of the velocity of the plate (i.e., modulated at the instantaneous mechanical resonant frequency). For this type of actuation signal, significant reductions in the pull-in voltage can theoretically be achieved without changing the stiffness of the structure. This analysis is significant to both parallel-plate and torsional electrostatic microelectromechanical systems (MEMS) switching structures where a reduced operating voltage without sacrificing stiffness is desired, as well as electrostatic MEMS oscillators where pull-in due to dynamic effects needs to be avoided.

Dynamic pull-in of parallel plate and torsional electrostatic MEMS actuators.

We report a new silicon Microelectromechanical systems (MEMS) accelerometer based on differential frequency modulation (FM) with experimentally demonstrated thermal compensation over a dynamic temperature environment and $\mu g$ -level Allan deviation of bias. The sensor architecture is based on resonant frequency tracking in a vacuum packaged silicon-on-insulator (SOI) tuning fork oscillator. To address drift over temperature, the MEMS sensor die incorporates two identical tuning forks with opposing axes of sensitivity. Demodulation of the differential FM output from the two simultaneously operated oscillators eliminates common mode errors and provides an FM output with continuous thermal compensation. The first SOI prototype with quality factor of 350000 was built and characterized over a temperature range between 30 °C and 75 °C. Temperature characterization of the FM accelerometer showed less than a 0.5% scale-factor change throughout a temperature range from 30 °C to 75 °C, without any external compensation. This is enabled by an inherently differential frequency output, which cancels common-mode influences, such as those due to temperature. Allan deviation of the differential FM accelerometer revealed a bias instability of $6\,\, \mu \text{g}$ at 20 s, along with an elimination of any temperature drift due to increases in averaging time. After comparing the measured bias instability with the designed linear range of 20 g, the sensor demonstrates a wide dynamic range of 130 dB. A second design iteration of the FM accelerometer, vacuum-sealed with getter material, was created to maximize $Q$ -factor, and thereby frequency resolution. A $Q$ -factor of 2.4 million was experimentally demonstrated, with a time constant of >20 min.

High Quality Factor Resonant MEMS Accelerometer With Continuous Thermal Compensation

This paper describes the development of aluminum nitride (AlN) resonant accelerometers that can be integrated directly over foundry CMOS circuitry. Acceleration is measured by a change in resonant frequency of AlN double-ended tuning-fork (DETF) resonators. The DETF resonators and an attached proof mass are composed of a 1-mum-thick piezoelectric AlN layer. Utilizing piezoelectric coupling for the resonator drive and sense, DETFs at 890 kHz have been realized with quality factors (Q) of 5090 and a maximum power handling of 1 muW. The linear drive of the piezoelectric coupling reduces upconversion of 1/f amplifier noise into 1/f 3 phase noise close to the oscillator carrier. This results in lower oscillator phase noise, -96 dBc/Hz at 100-Hz offset from the carrier, and improved sensor resolution when the DETF resonators are oscillated by the readout electronics. Attached to a 110-ng proof mass, the accelerometer microsystem has a measured sensitivity of 3.4 Hz/G and a resolution of 0.9 mG/radicHz from 10 to 200 Hz, where the accelerometer bandwidth is limited by the measurement setup. Theoretical calculations predict an upper limit on the accelerometer bandwidth of 1.4 kHz.

Post-CMOS Compatible Aluminum Nitride Resonant MEMS Accelerometers.

A micromechanical structure for a MEMS structure is provided with: a substrate; a single inertial mass having a main extension in a plane and arranged suspended above the substrate; and a frame element, elastically coupled to the inertial mass by coupling elastic elements and to anchorages, which are fixed with respect to the substrate by anchorage elastic elements. The coupling elastic elements and the anchorage elastic elements are configured so as to enable a first inertial movement of the inertial mass in response to a first external acceleration acting in a direction lying in the plane and also a second inertial movement of the inertial mass in response to a second external acceleration acting in a direction transverse to the plane.

Microelectromechanical three-axis capacitive accelerometer

A new biaxial silicon resonant accelerometer characterized by a high sensitivity and a low cross-axis sensitivity is presented in this paper. The device allows for the simultaneous measure of acceleration acting along two different axes using two couples of resonating slender beams linked to two couples of flexible beams and to a proof mass. The conceptual scheme used for the biaxial resonant accelerometer is similar to the one applied for the uniaxial resonant accelerometer reported in [1]–[3]. Experimental results demonstrate a differential sensitivity of 201 Hz/g around a resonance frequency of 84 kHz.

A new biaxial silicon resonant micro accelerometer

In this paper, an industrially-oriented two-scale approach is provided to model the drop-induced brittle failure of polysilicon MEMS sensors. The two length-scales here investigated are the package (macroscopic) and the sensor (mesoscopic) ones. Issues related to the polysilicon morphology at the micro-scale are disregarded; an upscaled homogenized constitutive law, able to describe the brittle cracking of silicon, is instead adopted at the meso-scale. The two-scale approach is validated against full three-scale Monte-Carlo simulations, which allow for stochastic effects linked to the microstructural properties of polysilicon. Focusing on inertial MEMS sensors exposed to drops, it is shown that the offered approach matches well the experimentally observed failure mechanisms.

https://www.mdpi.com/1424-8220/11/5/4972/pdf

Two-Scale Simulation of Drop-Induced Failure of Polysilicon

A microelectromechanical detection structure for a MEMS resonant biaxial accelerometer is provided with: an inertial mass, anchored to a substrate by elastic elements to be suspended above the substrate. The elastic elements enabling inertial movements of the inertial mass along a first axis of detection and a second axis of detection that belong to a plane of main extension of said inertial mass, in response to respective linear external accelerations. At least one first resonant element and one second resonant element have a respective longitudinal extension, respectively along the first axis of detection and the second axis of detection, and are mechanically coupled to the inertial mass through a respective one of the elastic elements to undergo a respective axial stress when the inertial mass moves respectively along the first axis of detection and the second axis of detection.

MEMS biaxial resonant accelerometer

A microelectromechanical device has a mobile mass that undergoes a movement, in particular a spurious movement, in a first direction in response to an external event; the device moreover has a stopper structure configured so as to stop said spurious movement. In particular, a stopper element is fixedly coupled to the mobile mass and is configured so as to abut against a stopper mass in response to the spurious movement, thereby stopping it. In detail, the stopper element is arranged on the opposite side of the stopper mass with respect to a direction of the spurious movement, protrudes from the space occupied by the mobile mass and extends in the space occupied by the stopper mass, in the first direction.

Barbara Simoni

Papers

Microelectromechanical three-axis capacitive accelerometer

A new biaxial silicon resonant micro accelerometer

Two-Scale Simulation of Drop-Induced Failure of Polysilicon

MEMS biaxial resonant accelerometer

Planar microelectromechanical device having a stopper structure for out-of-plane movements