Differential MEMS Research Articles

Formulation Analysis and Follow-Up Study of Differential MEMS Touch-Mode Sensor Utilizing Capacitive Vacuum Gauge Framework for Low-Pressure Measurements

Differential capacitance diaphragm gauges have become more popular in pressure measurements as they yield superior sensitivity and lesser non-linearity for pressure differential measurements. In addition, differential capacitance diaphragm gauges do not require a high vacuum reference cavity which reduces their manufacturing complexity. Efficient analysis for modelling differential capacitance diaphragm gauges is thus increasingly becoming vital due to their innumerable use cases. The higher sensitivity of circular diaphragm for the same side length in comparison to square diaphragm makes it ideal for sensor design. In this work, a complete formulation for analysis of differential capacitive vacuum gauge with the circular diaphragm in normal and touch mode operation has been presented for the low-pressure range of (1 to 1500 pascals). A comprehensive study of sensor parameters like capacitance, diaphragm deflection, capacitive and mechanical sensitivity has been formulated to aid the choice of sensor characteristics. Computationally complex methods have been used in the past for analysis of circular diaphragms. MATLAB and COMSOL have been used to compute and simulate results.

A Background Test and Calibration Technique of Nonlinear Mismatches in MEMS Oscillating Accelerometers

MEMS accelerometers have benefits of low cost and small volume, however their long-term stability is limited by the fabrication mismatches. This paper proposes a self-test and calibration technique for differential MEMS accelerometers, to reduce the effect of flicker noise in reference voltages due to nonlinear stiffness mismatch in two channels. Through detecting the frequency response induced by the sinusoidal test signal, the oscillating amplitude of the two channels is properly adjusted to meet a theoretically derived noise cancellation condition. A numerical model is established based on practical mechanical parameters of the MEMS structures to simulate the proposed system, and optimize the key design parameters. Finally, a prototype including a MEMS accelerometer chip and an FPGA-based control circuit is implemented to verify the suggested approaches. Compared to that without the proposed technique, the 1-h bias-instability of the SOA is reduced from 6.31 μg to 3.44 μg. At different reference voltages from 1.09 V to 1.33 V, the decrease in instability is between 21.7 % and 45.5 %.

Near-Ultrasonic Transfer Function and SNR of Differential MEMS Microphones Suitable for Photoacoustics

Can ordinary Micro-Electro-Mechanical-Systems (MEMS) microphones be used for near-ultrasonic applications? Manufacturers often provide little information about the signal-to-noise ratio (SNR) in the ultrasound (US) range and, if they do, the data are often determined in a manufacturer-specific manner and are generally not comparable. Here, four different air-based microphones from three different manufacturers are compared with respect to their transfer functions and noise floor. The deconvolution of an exponential sweep and a traditional calculation of the SNR are used. The equipment and methods used are specified, which makes it easy to repeat or expand the investigation. The SNR of MEMS microphones in the near US range is mainly affected by resonance effects. These can be matched for applications with low-level signals and background noise such that the highest possible SNR can be achieved. Two MEMS microphones from Knowles performed best for the frequency range from 20 to 70 kHz; above 70 kHz, an Infineon model delivered the best performance.

Differential resonant MEMS accelerometer: Synchronization characteristics of weakly coupled microbeam sensing elements

This work is devoted to studying the conditions and scenarios for synchronizing oscillations of weakly coupled microbeam elements of a differential resonant MEMS accelerometer operating in the dual-loop self-oscillator mode. The model of a system of two Van der Pol self-oscillators with a nonlinear elastic coupling between moving elements, obtained using the Galerkin method, was studied using the multiscale method. The modes of beats and synchronization of oscillations of two resonators are found analytically and numerically, and the boundary between these modes in the space of system parameters is determined. Along with a local bifurcation analysis of the considered stationary regimes, a global analysis of the evolution and branching of limit cycles in the space of slow variables was also carried out, which made it possible to detect zones of coexistence of stable synchronization and beat regimes with their basins of attraction. The influence of the factor of the designed or technologically determined non-identity of the design of two resonators on the location of the parametric zones of synchronization and beats is studied.

Simplified Analytical Damping Constant Model for Design of MEMS Capacitive Accelerometer With Gold Perforated Proof-Mass Structure

This paper describes a simplified analytical model of a damping constant <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> to design a MEMS capacitive accelerometer using the multi-layer metal technology. The proposed model is introduced by combining the theoretical equation with the approximate form factor obtained by the measured data. In order to create the model, we fabricated several types of MEMS capacitive accelerometers with different structure parameters such as the etching hole area, the perforated proof-mass area, and the gap. The calculation results show that by the proposed model, the damping constant <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> was in accord with the measured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> . We also confirmed that the relative error between the measured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> and the damping constant <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> by the proposed model could be improved to one-half of the conventional model. Moreover, the Brownian noise <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${B}_{\text {N}}$ </tex-math></inline-formula> calculated by the proposed model was also consistent with the measured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${B}_{\text {N}}$ </tex-math></inline-formula> . In addition, to confirm the suitability of the proposed model for CMOS-MEMS multi-physics simulation, we performed the simulation of the ring-down characteristics of a gold perforated proof-mass differential MEMS capacitive accelerometer. The simulated results suggested that the ring-down characteristics by the proposed model coincided with those of the measured data. Therefore, we verified that the proposed model would be effective for the analysis and the design of the MEMS capacitive accelerometer with the gold perforated proof-mass.

Differential MEMS capacitance diaphragm vacuum gauge with high sensitivity and wide range

MEMS vacuum gauges have received a great deal of attention in recent years. In this paper, a MEMS capacitance diaphragm vacuum gauge with high sensitivity and wide range is designed for differential pressure measurement. A novel circular silicon diaphragm is used as the pressure-sensing diaphragm of the gauge. The diaphragm has a large radius-to-thickness ratio of 283 and works in touch mode. The design principle of the gauge is introduced in detail, and the finite element software is used for simulation analysis. Based on the techniques of microfabrication, a prototype of the gauge was fabricated, and its performances were investigated using a differential vacuum system. The results show that the MEMS capacitance diaphragm vacuum gauge, having good stability and repeatability, is capable to measure differential pressure from 0 Pa to atmospheric pressure. The capacitance-pressure curve is piecewise linear, with the maximum sensitivity of 26 fF/Pa in the low range and the minimum sensitivity of 0.8 fF/Pa in the high range.

Design and fabrication of a differential pressure MEMS capacitance diaphragm gauge based on heavily boron-doping technique

In this paper, a differential pressure MEMS CDG with a full range of (5–4000) Pa has been developed, and its pressure-sensing diaphragm is manufactured by boron-doping technique. The design principle and manufacturing process of the MEMS CDG were demonstrated in detail. To test the working performance of the CDG, a differential pressure high vacuum pumping system and a precision LCR meter are adopted to obtain the capacitance value of the vacuum gauge varying with pressure. The test results show that the MEMS CDG can work normally in the pressure range of (5–4000) Pa, and the maximum sensitivity is 87.2 fF/Pa. In addition, boron-doped diaphragm can effectively improve the sensitivity of vacuum gauge and further extend its measurement upper limit.

Design and implementation of differential MEMS microphones using the two polysilicon processes for SNR enhancement

This study presents the design, fabrication and testing of the capacitive-type MEMS microphone with differential sensing electrodes to improve the sensitivity and signal-to-noise ratio (SNR). The microphone is designed and implemented based on an existing trench-refilled MOSBE process platform with two polysilicon structure layers, one Si3N4 electrical isolation layer and two sacrificial SiO2 layers. The microphone consists of top and bottom diaphragms and backplates. The top diaphragm and bottom backplate form a sensing electrode pair, and the bottom diaphragm and top backplate form the second sensing electrode pair. Moreover, the Si3N4 layer is exploited to partition the structures into three different electrical regions. Thus, the differential sensing MEMS microphone is achieved by using only two polysilicon structure layers. Various auxiliary components such as the central post and the U-shaped springs are also developed to realize the differential microphone. Measurements show that the typical fabricated microphone with a footprint of 800 μm diameter has the single-ended sensitivities of −45.8 and −47.2 dB (ref: 1 V/1 Pa), and the SNR is over 52 dB. Moreover, the ±3 dB bandwidth of the microphone ranges from 50 Hz–22 kHz. In summary, the presented microphone has the differential sensitivity of −40.5 dB (ref: 1 V/1 Pa) and the SNR of over 57.8 dB.

A Novel Differential Optical MEMS Accelerometer Based on Intensity Modulation, Using an Optical Power Splitter

In this paper, a novel highly sensitive differential optical MEMS accelerometer based on intensity modulation is proposed by using dual optical outputs and a two-dimensional (2D) photonic crystal power splitter. A TM-polarized light source, an optical power splitter (OPS) based on 2D photonic crystal (PhC), two typical photodiodes (PDs) and three optical ports build up the optical sensing system of the proposed sensor. The functional characteristics of the proposed device based on simulation results are as follows: Mechanical sensitivity of 0.0750 nm/g, linear measurement range of ±200 g, first mechanical resonance frequency of 17.7 kHz, optical sensitivity of 4.38 %/nm with bandwidth at half maximum (FWHM) of 1 nm (0.13 THz) at optical central wavelength of 1.495 μm (200.7 T Hz). This results in an optical quality factor of 1495 and total sensitivity of 0.3285 %/g. Due to the mentioned functional characteristics, the proposed sensor can be appealing for a wide range of applications, from inertial navigation and automotive to consumer electronics.

A High Resolution Differential Mode-Localized MEMS Accelerometer

A novel differential configuration of a high-resolution mode-localized resonant SOI-MEMS accelerometer is presented in this paper. An effective maximum scale factor of 11/g and a bias-stability of $2.96\mu g$ is demonstrated. A minimum noise floor of $3\mu g/\sqrt {Hz}$ is shown for device operation in an optimum working region. A large bandwidth of 350Hz is reported and methods to electronically tune the working bandwidth are described. These results benchmark mode-localized accelerometers favourably with respect to other high-end low-g commercial MEMS accelerometers.

Design and optimization of fully differential capacitive MEMS accelerometer based on surface micromachining

In this paper, design and simulation of a single-axial, capacitive, fully differential MEMS accelerometer based on surface micromachining with two proof masses is presented. So far, most surface micromachined capacitive accelerometers offered, employed differential interface circuits to measure capacitor variations. However, in the presented structure, the possibility of fully differential design is realized by dividing the proof mass to two electrically isolated parts that are located on a silicon nitride layer. By utilizing two proof masses and altering outputs and stimulation voltage, parasitic capacitor is reduced and the sensitivity is increased. Moreover, some sensor capacitors are embedded inside the proof mass, so that sensitivity could be increased in the limited area and electrode length could be reduced. Furthermore, analytic equations are derived to calculate the sensitivity, as well to optimize the sensor structure. The designed sensor has been simulated and optimized using COMSOL Multiphysics, where the simulation results show the mechanical and capacitive sensitivity of 29.8 nm/g and 15.8 fF/g, respectively. The sensor size is 1 mm × 1 mm that leads to excellent performance, regarding to the defined figure of merit.

Ultimate Limits of Differential Resonant MEMS Sensors Based on Two Coupled Linear Resonators.

In this paper, we investigate how additive noise, e.g., thermomechanical noise, impacts the resolution of mode-localized resonant sensing architectures based on two passively coupled linear resonators. Existing work suggests that the ultimate resolution of these sensors can be improved by decreasing the coupling coefficient of the resonators. The present work gives an analytical proof that this result does not hold, and that the resolution of such sensors is actually independent of the coupling strength. These results are established for different output metrics and operating points, in closed loop and in open loop, and compared to those obtained with other approaches based on actively coupled resonators.

Differential Capacitive Readout Circuit Using Oversampling Successive Approximation Technique

This paper designs a close loop $\Sigma - \Delta $ readout circuit for differential MEMS accelerometer. A technique named oversampling successive approximation (OSA) is employed to build basic amplifiers and integrators. This technique can largely reduce the gain error and thus low gain amplifier such as single stage amplifier is allowed to be used. As a result, the power consumption and chip area are reduced. However, the OSA-based amplifiers and integrators are vulnerable to the interference caused by charge injection and leakage current from the specific MOSFET switches. This drawback is analyzed in detail and the interference suppressing solutions are given. The OSA-based readout circuit is fabricated in a commercial 0.18 $\mu \text{m}$ BCD process. The measurement results show that the interference is reduced by 20 dB in the circuit with interference suppressing solutions compared with the circuit without interference suppressing solutions. And the noise floor is 24 $\mu \text{g}$ /rtHz. The readout circuit achieves a 0.07% gain error with a low power consumption of 0.5 mW and 9 MHz sampling rate.

A 4 mm² Double Differential Torsional MEMS Accelerometer Based on a Double-Beam Configuration.

This paper reports the design and simulation of a 4 mm2 double differential torsional MEMS accelerometer based on a double-beam configuration. Based on the structure of conventional torsional accelerometers, normally composed of one pair of proof masses and one torsional beam, this work explores the double differential configuration: a torsional accelerometer with two pairs of unbalanced proof masses rotating in reverse. Also, the torsional beam is designed as a double-beam structure, which is a symmetrical structure formed by two torsional beams separated by a certain distance. The device area of the novel accelerometer is more than 50 times smaller than that of a traditional double differential torsional MEMS accelerometer. The FEM simulation results demonstrate that the smaller device does not sacrifice other specifications, such as mechanical sensitivity, nonlinearity and temperature robustness. The mechanical sensitivity and nonlinearity of a ±15 g measuring range is 59.4 fF/g and 0.88%, respectively. Compared with traditional single-beam silicon structures, the novel structure can achieve lower maximum principle stress in critical regions and reduce the possibility of failure when high-g acceleration loading is applied along all three axes. The mechanical noise equivalent acceleration is about in the theoretical calculations and the offset temperature coefficient is 0.25 mg/ in the full temperature range of to .

The Development of the Differential MEMS Vector Hydrophone.

To solve the problem that MEMS vector hydrophones are greatly interfered with by the vibration of the platform and flow noise in applications, this paper describes a differential MEMS vector hydrophone that could simultaneously receive acoustic signals and reject acceleration signals. Theoretical and simulation analyses have been carried out. Lastly, a prototype of the differential MEMS vector hydrophone has been created and tested using a standing wave tube and a vibration platform. The results of the test show that this hydrophone has a high sensitivity, Mv = −185 dB (@ 500 Hz, 0 dB reference 1 V/μPa), which is almost the same as the previous MEMS vector hydrophones, and has a low acceleration sensitivity, Mv = −58 dB (0 dB reference 1 V/g), which has decreased by 17 dB compared with the previous MEMS vector hydrophone. The differential MEMS vector hydrophone basically meets the requirements of acoustic vector detection when it is rigidly fixed to a working platform, which lays the foundation for engineering applications of MEMS vector hydrophones.

A double differential torsional accelerometer with improved temperature robustness

This paper reports the design, realization and characterization of a novel double differential torsional MEMS accelerometer with improved temperature robustness. Based on the structure of conventional torsional accelerometers, normally composed of two unbalanced proof masses and an identical torsional beam, this work explores a torsional accelerometer with two structural optimizations aiming to improve the temperature robustness: a double differential configuration and an on-chip integrated reference capacitor configuration. The double differential configuration realizes the temperature self-calibration by making the two pairs of unbalanced masses have the same sensitivity to temperature but opposite sensitivity to acceleration. And the on-chip integrated reference capacitor realizes the temperature self-calibration by transferring the temperature dependent reference capacitor from ASIC or PCB into the MEMS structure. Totally ten accelerometer prototypes are fabricated with the pre-buried mask wet-etching method and tested. Comparison tests show that, for most of the accelerometers, by taking the double differential configuration and the on-chip integrated reference capacitor configuration, the temperature sensitivity of the scale factor, the bias stability and the output drift of in the full temperature range are greatly improved. The testing results experimentally demonstrate the effectivity of the optimization for improving temperature robustness.

Development and Characterization of a CMOS-MEMS Accelerometer With Differential LC-Tank Oscillators

This paper presents a CMOS-MEMS accelerometer based on differential LC-tank oscillators. Two LC-tank oscillators composed of differential MEMS capacitors and suspended inductors were designed and fabricated by standard TSMC 0.18 μm CMOS processes and post-CMOS dry etching. The outputs of the differential oscillators are mixed and the output frequency of the mixer is proportional to the capacitance change caused by the external acceleration. The device has been characterized and has a mechanical resonance frequency of 7 kHz, absolute sensitivity of 3.62 MHz/g, relative sensitivity of 1.9×10-3 Δf/f0/g, in-axis nonlinearity of 1.2%FS, bias stability of 2.1 mg, and average noise floor of 0.205-0.219 mg/√Hz in the frequency range of 15-250 Hz.

Design and Characterization of a Fully Differential MEMS Accelerometer Fabricated Using MetalMUMPs Technology

This paper presents a fully differential single-axis accelerometer fabricated using the MetalMUMPs process. The unique structural configuration and common-centriod wiring of the metal electrodes enables a fully differential sensing scheme with robust metal sensing structures. CoventorWare is used in structural and electrical design and simulation of the fully differential accelerometer. The MUMPs foundry fabrication process of the sensor allows for high yield, good process consistency and provides 20 μm structural thickness of the sensing element, which makes the capacitive sensing eligible. In device characterization, surface profile of the fabricated device is measured using a Veeco surface profilometer; and mean and gradient residual stress in the nickel structure are calculated as approximately 94.7 MPa and −5.27 MPa/μm, respectively. Dynamic characterization of the sensor is performed using a vibration shaker with a high-end commercial calibrating accelerometer as reference. The sensitivity of the sensor is measured as 0.52 mV/g prior to off-chip amplification. Temperature dependence of the sensing capacitance is also characterized. A −0.021fF/°C is observed. The findings in the presented work will provide useful information for design of sensors and actuators such as accelerometers, gyroscopes and electrothermal actuators that are to be fabricated using MetalMUMPs technology.

Fully differential current-mode MEMS dual-axis optical inclination sensor

We demonstrate a tilt sensor fabricated in the MultiMEMS SensoNor process. The system uses an array of four photodiodes to determine the position of a bubble fluid pendulum and the tilt angle with respect to gravity. The entire sensing structure was manufactured in the commercial MultiMEMS process so it can be easily reproduced in large quantities. The device was tested across a range of inclinations to verify performance in sensing two axis tilt. Results for tilt measurements from −45° to +45° show correlation to expected values with an R2 value of 0.99595. The resolution of the device is 0.5° at zero degrees of inclination. The outputs of the sensor are mapped to a fit equation to allow calculation of inclination angle. The small size, simple structure, and minimal power consumption make it well-suited for a number of research and industrial applications.

Differential RF MEMS interwoven capacitor immune to residual stress warping

A RF MEMS capacitor with an interwoven structure is designed, fabricated in the PolyMUMPS process and tested in an effort to address fabrication challenges usually faced in MEMS processes. The interwoven structure was found to offer several advantages over the typical MEMS parallel-plate design including eliminating the warping caused by residual stress, eliminating the need for etching holes, suppressing stiction, reducing parasitics and providing differential capability. The quality factor of the proposed capacitor was higher than five throughout a 2-10 GHz range and the resonant frequency was in excess of 20 GHz.