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This paper presents the analytical modeling, simulation and experimental validation of sensitivity, temperature variation and active controllability of MEMS geometric anti-spring (GAS) devices. Two models, the elasticity model and the thermal drift model, were proposed and analyzed, based on the study of asymmetrical and symmetrical geometric anti-spring structures. With the elasticity model, structural optimization led to analytical frequency-prestress design formula and a dedicated MEMS structure. An independent pre-stress and frequency shift effect is the result of thermal changes, so a thermal drift analytical model was built for the geometric anti-spring device, showing thermal sensitivities of and for the 3-spring and 4-spring devices, respectively. The analytical model was validated by both finite element analyses and experimental measurements. The designed devices (3-springs and 4-springs) were tested afterward in a dedicated setup, for both positive and negative electrostatically induced pre-stresses. Without electrical compensation, the thermal drift of the symmetrical 4-spring GAS device, for temperatures in the range to , is about 2138ppm, and it is reduced to only 8.35ppm when the electrostatic temperature compensation is active. Similarly, the asymmetrical structure has an uncompensated thermal sensitivity of its resonant frequency of 2254ppm in the temperature operation range, and it is reduced to 51.5ppm with electrical compensation within the easily controlled range of the temperature span, from to . As a result, although the benefits of the asymmetrical structure would lead to a higher sensitivity, trade-offs related to thermally-induced drift behavior and controllability also should be taken into consideration in the selection of the structural topology and application environment.

Harmonic displacement of a parallel-plate electrostatic actuator up to 50% of the static pull-in displacement has been achieved despite the non-linear voltage-to-displacement function using a driving voltage with a pre-distorted waveform. The microstructure is fabricated in an epi-poly process and the circuit is implemented in a CMOS process and designed for operation of the MEMS in a frequency range up to 1 kHz. The pre-distorted waveform is synthesized using 16 samples per period with 16 non-uniformly spaced quantization levels, using a ladder with accurately scaled resistors. Harmonic actuation has been demonstrated with 34 dB reduction of second-order distortion compared to systems with sinusoidal actuation. The residual second harmonic content in the harmonic displacement is typically −42 dB.

The meta-stability of the pull-in displacement of an electrostatically operated parallel plate micromechanical structure is used for the capacitive measurement of the mechanical–thermal noise spectrum in a MEMS. Pull-in time depends on force and is not affected by the input-referred noise of the readout circuit. Repeatedly bringing the microstructure to pull-in while measuring the pull-in time followed by FFT enables the measurement of the mechanical noise spectrum with a non-mechanical noise level set primarily by the resolution of the time measurement. The white noise level is found to be in agreement with the theory on damping. The 1/f noise spectrum is found to be independent of ambient gas pressure with a 1/f noise–white noise cross-over frequency at 0.007 Hz for a 1 bar gas pressure and is reproducible for devices fabricated in the same process and the same run.

A careful analysis of the dynamics of the pull-in displacement reveals a metastable transient interval for devices with a Q factor lower than 1.2. The duration of this metastable regime could be up to 20 ms for the structure used in this work, depending on the damping. For typical device dimensions this regime dominates pull-in dynamics. This paper explicitly focuses on the metastable regime. The results of numerical simulations are confirmed with measurement results with the purpose of providing a better understanding of the underlying mechanisms. This may contribute to both improved actuator design and enhanced sensitivity of pressure sensors and accelerometers operating on pull-in time interval measurement. The sensitivity of the pull-in time to external accelerations is 6 ? 10?2 s/ms?2 (~0.6 ms mg?1) for current devices and can be increased by design.

Recent studies have demonstrated mode localized resonant micro-electro-mechanical systems (MEMS) sensing devices with orders of magnitude improvement in sensitivity. Avoided crossings or eigenvalue veering is the physical mechanism exploited to achieve the enhancement in sensitivity of devices operating either in vacuum or in air. The mode localized MEMS devices are typically designed to be symmetric and use gap-varying electrostatic springs to couple motions of two or more resonators. The role of asymmetry in the design of devices and its influence on sensitivity is not fully understood. Furthermore, gap-varying electrostatic springs suffer from nonlinearities when gap variation between coupling plates becomes large due to mode localization, imposing limitations on the device performance. To address these shortcomings, this contribution has two principal objectives. The first objective is to critically assess the role of asymmetry in the device design and operation. We show, based on energy analysis, that carefully designed asymmetry in devices can lead to even higher sensitivities than reported in the literature. Our second objective is to design and implement linear, tunable, electrostatic springs, using shaped combs, which allow large vibration amplitudes of resonators thereby increasing the signal to noise ratio. We experimentally demonstrate linear electrostatic coupling in a two oscillator device. Our study suggests that a future avenue for progress in the mode localized resonant sensing technology is to combine asymmetric devices with tunable linear coupling designs.

We report novel low-cost and rapid fabrication technologies for the fabrication of movable polymer-based MEMS structures, electrically actuated. Using SU-8 photoresist as structural material, both ordinary and functionalized by conductive fillers (nano-Ag particles and carbon nanotubes), the novel fabrication methods provide simple processes, without the use of any sacrificial layer, for achieving suspended structures (beams and membranes) through either binary or gray-scale photolithography. Experimental validation has demonstrated high yields (over 99% for one of the process flows) in achieving electrostatically actuated microstructures with resonant frequencies in the 0.5–0.8 MHz range, with a stable dynamic behavior tested for a period longer than three months. The technology also confirms that 'doping' SU-8 with conductive fillers can preserve its photo-patterning capabilities, while modifying other physical properties (electrical conductivity). As the patterning of SU-8 films can take place on either rigid or flexible substrates, this low-cost technology promises a wide range of applications.

This paper investigates the enhanced sensitivity to external perturbations through mode localization in a coupled resonant MEMS transducer device. An energy-based framework is developed to analytically study energy localization in the MEMS device by using a novel, electrostatically-induced stiffness perturbation. Specifically, we analyze the mode localization associated with eigenvalue veering phenomenon, resulting from a symmetry-breaking perturbation in a coupled two-resonators MEMS device. The measured mode shape sensitivities are compared with predictions made by both a simplified analytical model and a more detailed Simulink model. The mode shape sensitivity to perturbations is shown to be an order of magnitude higher than that of resonant frequency shifting. The sensitivity can be further increased by decreasing the coupling strength between the two resonators, but with a reduced dynamic range of the external perturbations.

We propose novel feedback control and sensing schemes based on sliding mode control (SMC) for closed-loop micro-accelerometers as alternative digital control architectures to sigma–delta (ΣΔ) approaches. The under-damped micro-device has been designed in Coventorware, fabricated in SOIMUMPs (25 µm thick structural layer) technology and experimentally characterized using a Polytec MSA-500 (micro-system analyzer) equipment. To verify the system architecture robustness, the application of SMC is extended to an over-damped accelerometer model. In either case, the SMC demonstrates the repositioning of the proof mass to null position; however, the over-damped model exhibits shorter transition time (15 ms for 1g acceleration) due to the increased damping. In addition to that, we extend the usage of SMC beyond the classical actuation problem to a novel sensing problem where we demonstrate the extraction of the external acceleration measurement from the switching behavior along the sliding surface. An optimized fixed-point implementation is targeted on a field-programmable gate array (FPGA) using rapid prototyping methodology, where the new proposed method has been compared for reference with a control scheme that employs a ΣΔ modulator. The SMC-based architecture is advantageous in terms of hardware complexity, and the control of the number of degrees of freedom required by an inertial measurement unit can be accommodated on a low-cost FPGA device. SMC offers a sound theoretical framework for the nonlinear control of inertial sensors.

The pull-in voltage of a parallel plate electrostatic transducer is used to determine the amount of over-etching in fabricated devices. A detailed analysis of the capacitor behaviour over the full displacement range yields a model, which is used to describe the relation between over-etching and measured pull-in voltage. SEM photos confirm the over-etching measurement based on pull-in voltage. This information is used to linearize a charge amplifying read-out circuit with an intrinsic nonlinear transfer function. The remaining nonlinearity error of the read-out is less than 1%.