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.

In this work we exploit a multi-scale framework to model the shock-induced failure of polysilicon micro electro-mechanical systems (MEMS), and study the impact of uncertainties at polycrystal length-scale on the results. Because of polysilicon brittleness, MEMS sensors almost instantaneously fail by micro-cracking when subjected to shocks. Since the length of the zone where such micro-cracking is spreading can amount to 5–10% of the characteristic grain size, the morphology of polysilicon films constituting the movable parts of the MEMS is explicitly modeled at the micro-scale within a cohesive approach. Focusing on shocks induced by accidental drops, forecasts of MEMS failure are obtained through a Monte Carlo methodology, wherein statistics of the polycrystalline morphology are accounted for. Outcomes, in terms of failure mode and drop height leading to failure, are shown to correctly represent available experimental evidences relevant to a commercial micro-device.

Monte carlo simulation of micro-cracking in polysilicon MEMS exposed to shocks

A MEMS detection structure is provided with: a substrate having a top surface, on which a first fixed-electrode arrangement is set; a sensing mass, extending in a plane and suspended above the substrate and above the first fixed-electrode arrangement at a separation distance; and connection elastic elements that support the sensing mass so that it is free to rotate out of the plane about an axis of rotation, modifying the separation distance, as a function of a quantity to be detected along an axis orthogonal to the plane. The MEMS detection structure also includes: a coupling mass, suspended above the substrate and connected to the sensing mass via the connection elastic elements; and an anchoring arrangement, which anchors the coupling mass to the substrate with a first point of constraint, set at a distance from the axis of rotation and in a position corresponding to the first fixed-electrode arrangement.

Microelectromechanical z-axis detection structure with low thermal drifts

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 MEMS sensors.

A new micro-machined uniaxial silicon resonant accelerometer characterized by a high sensitivity is presented. The geometrical setting is analytically optimized in order to improve the sensitivity and the linearity of the sensor. The high level of sensitivity is obtained at relatively low quality factors and keeping the dimensions very small, thanks to an innovative and optimized geometrical design of the device. The proposed accelerometer has been fabricated and the first experimental measurements are presented in the paper.

Barbara Simoni

Papers

A Resonant Microaccelerometer With High Sensitivity Operating in an Oscillating Circuit

Monte carlo simulation of micro-cracking in polysilicon MEMS exposed to shocks

Microelectromechanical z-axis detection structure with low thermal drifts

Two-scale simulation of drop-induced failure of polysilicon MEMS sensors.

A high sensitivity uniaxial resonant accelerometer