Resonant Accelerometer Research Articles

A Seismic-Grade Resonant MEMS Accelerometer

We report on the characterization of a high-resolution micromachined resonant accelerometer fabricated in an SoI-microelectromechanical (MEMS) foundry process. A prototype device demonstrated scale factor of 142.8 Hz/m/s 2 , dynamic range of >140 dB, and noise-limited resolution that is comparable with existing high-resolution macroscale seismometers. Experimental characterisation detailing the benchmarking of the MEMS prototype relative to an existing macroscale seismometer shows that the MEMS device tracks the passive ambient seismic response measured by a macroscale seismometer (Guralp systems CMG-3TD) over a measurement bandwidth extending from near dc (0.02 Hz) up to 100 Hz.

Integrated structure for a resonant micro-gyroscope and accelerometer

This paper presents the study of the mechanical behavior of a microstructure designed to detect acceleration and angular velocity simultaneously. The new resonant micro-sensor proposed, fabricated by the ThELMA© surface-micromachining technique, bases detection of two components of external acceleration (one in-plane component and one out-of plane component) and two components of angular velocity (roll and yaw) on the variation of frequency of several elements set in resonance. The device, despite its small dimensions, provides a differential decoupled detection of four external quantities thanks to the presence of four slender beams resonating in bending and four torsional resonators.

A micromachined differential resonant accelerometer based on robust structural design

This paper describes design, fabrication, and testing of a micromachined differential resonant accelerometer (DRA), which is one of the most common solid proof mass accelerometers; it exploits a correlation between acceleration and shifts in the resonant frequency of oscillating beams loaded axially. The effective and simplified structure of the DRA amplifies the induced inertial force resulting from applied acceleration, while retaining structural stability and robustness. Mathematical and numerical analyses were conducted to optimize the detailed structures of the DRA under appropriate operating conditions. An experimentally measured differential scale factor of 188.5Hz/g showed good agreement with the results of the analysis. Utilizing a silicon-on-insulator wafer provided uniform material properties and thickness of the structural layer, resulting in bias stability of 100μg and a Q factor of 0.37×106.

Simultaneous Formation of Non-coplanar Resonant Beams and Supporting Beams of Bulk Micromachining Resonant Accelerometers by Maskless Anisotropic Wet Etching

The paper presents the design principles and fabrication sequence of a newly developed mechanical structure of bulk micromachining resonant Z axis accelerometers on the same silicon substrate by maskless anisotropic wet etching technique. Four resonant beams are located at the top surface of silicon substrates in order to facilitate the patterning of excited resistors, piezoresistive resistors or electrode plates, whereas the gravity centre of the proof mass lies within the neutral plane of eight supporting beams to minimize the rotating of proof mass under in-plane acceleration. Compared with early reported mechanical structures, the simple structures can eliminate the bending moments caused by in-plane acceleration, as a result, avoid the rotating of the proof mass.

A Differential Resonant Micro Accelerometer for Out-of-plane Measurements

This paper reports the theoretical and experimental characterization of a new z-axis silicon resonant micro accelerometer fabricated by the THELMA© surface micromachining technique, characterized by differential sensing and very small dimensions. The working principle of this device is based on the variation of the electrostatic stiffness of two torsional resonators. This work is a prosecution of the research on resonant accelerometers published in [1,2].

硅微振梁式加速度计的温度检测及闭环控制

To measure the chip-level temperature and to achieve close-loop control for a Micro-ElectroMechanical(MEMS)resonant accelerometer system,this paper investigates non-inertial parts of the system,proposes a method to measure the temperature of the MEMS structure and optimizes the parameters in the close-loop control.Different from the traditional method that using a temperature from a temperature control cover as the conference,this paper proposes design methods of MEMS structures,processing technology and circuits,and achieves the temperature compensation by measuring the MEMS structure temperature directly to improve the temperature measuring accuracy.Furthermore,a diode pre-circuit is applied to detection of the variation of the tiny capacity instead of the transimpedance amplifier and transconductance amplifier,which reduces the requirement for high-performance components from pA to nA magnitudes.Based on the analysis in the time domain,analytical so-lution of diode pre-circuit is proposed to optimize the parameters and to guarantee the linear relationship between input and output.Moreover,a second-order optimal mode is applied to control of the settling time of the post-circuit.Experiment shows that after compensation on temperature,the MEMS resonant accelerometer has the performance of bias stability of 52.0μg,scale factor stability of 16.0×10-6,resolution of 34.9μg.The result indicates that the proposed theories can satisfy the requirements of high-performance MEMS resonant accelerometer systems.

Design Criteria of Low-Power Oscillators for Consumer-Grade MEMS Resonant Sensors

This paper discusses the constraints in the design of circuits for microelectromechanical systems (MEMS) resonant sensors in consumer applications, presents a novel integrated circuit implementation, and shows that this approach can be competitive with respect to the mostly used capacitive readout. From a circuit design perspective, it is shown how the large equivalent resistance typical of MEMS resonators, their operation close to mechanical nonlinearity, and the effect of feedthrough capacitances on the oscillating loop constrain the power requirements of the driving/readout electronics. As a case study, a resonant accelerometer built in an industrial process is coupled to a suitably designed transimpedance amplifier with a low-power “hard limiter.” The performance shown in terms of linearity across the measurement range (±8 g), minimum measurable acceleration (1 mg with a readout bandwidth of 100 Hz), and power consumption (≈ 100 μW per axis) is comparable to those of state-of-the-art capacitive inertial sensors.

Design and Implementation of a Micromechanical Silicon Resonant Accelerometer

The micromechanical silicon resonant accelerometer has attracted considerable attention in the research and development of high-precision MEMS accelerometers because of its output of quasi-digital signals, high sensitivity, high resolution, wide dynamic range, anti-interference capacity and good stability. Because of the mismatching thermal expansion coefficients of silicon and glass, the micromechanical silicon resonant accelerometer based on the Silicon on Glass (SOG) technique is deeply affected by the temperature during the fabrication, packaging and use processes. The thermal stress caused by temperature changes directly affects the frequency output of the accelerometer. Based on the working principle of the micromechanical resonant accelerometer, a special accelerometer structure that reduces the temperature influence on the accelerometer is designed. The accelerometer can greatly reduce the thermal stress caused by high temperatures in the process of fabrication and packaging. Currently, the closed-loop drive circuit is devised based on a phase-locked loop. The unloaded resonant frequencies of the prototype of the micromechanical silicon resonant accelerometer are approximately 31.4 kHz and 31.5 kHz. The scale factor is 66.24003 Hz/g. The scale factor stability is 14.886 ppm, the scale factor repeatability is 23 ppm, the bias stability is 23 μg, the bias repeatability is 170 μg, and the bias temperature coefficient is 0.0734 Hz/°C.

Temperature Self-Compensation of Micromechanical Silicon Resonant Accelerometer

Temperature is one of the most important factors affecting the accuracy of micromechanical silicon resonant accelerometer (SRA). In order to reduce the temperature sensitivity and improve the sensor performance, a new method of temperature self-compensation for SRA is presented in this paper. Utilizing the differential structure of SRA, the temperature compensation for bias and scale factor can be realized simultaneously in this method. Moreover, because no temperature sensor is needed in this method, the error in temperature measurement due to the temperature gradient between the mechanical sensitive structure and temperature sensor is avoided, and the precision of temperature compensation for SRA can be further improved. The test results obtained on SRA prototype which is developed by MEMS Inertial Technology Research Center show that, by employing the method of temperature self-compensation, the temperature coefficients of bias and scale factor are reduced from 3.1 mg/°C and 778 ppm/°C to 0.05 mg/°C and -9.4 ppm/°C, respectively.

Modeling of Nonlinear Stiffness of Micro-Resonator in Silicon Resonant Accelerometer

Nonlinearities of the resonator in silicon resonant accelerometer (SRA) limit the ultimate short term frequency stability. In SRA, this stability is a measure of the achievable resolution. This paper discusses the nonlinear vibration phenomenon of micro-resonator considering the impact of the entire structure of SRA and builds a model to calculate the micro-resonator nonlinear stiffness K3,eff of the SRA prototype. The dies of SRA were fabricated by Silicon on Insulator (SOI) process. The equivalent model of the micro-resonator is built and the analytical value of the elastic constraint stiffness Ka of micro-resonator is derived as 8.91×104 N/m. It is calculated that K3,eff is equal to 5×1011 N/m3,and as a comparison, the simulation result is 5.026×1011 N/m3. The error between them is 0.52%. The nonlinear vibration experiments show that the maximum error between the theoretical and experimental value of resonance frequency is 2.1%. The prediction for the nonlinear stiffness contributes to further research on nonlinear vibration of the resonant beam. The model in this paper could also provide guidance and reference for optimal design of SRA.

A resonant micro accelerometer based on electrostatic stiffness variation

A new out-of-plane resonant micro-machined accelerometer has been designed, modelled and fabricated. The sensing principle is based on the variation of the electrostatic stiffness of two torsional resonators mechanically coupled with an inertial proof mass. The accelerometer, fabricated by the ThELMA® surface micro-machining process of STMicroelectronics, constitutes a further step of a research focussing on the design of in-plane and out-of-plane resonant micro accelerometers. Preliminary electrostatic measures of the torsional resonators response have been compared with the theoretical predictions.

Research on Surface Mounting Technology of Micromechanical Silicon Resonant Accelerometer

Surface mounting technology is a key process in MEMS packaging. The finite element model of package structures was established in this paper according to the designed micromechanical silicon resonant accelerometer. The effects of package substrate materials, adhesive material characteristics, uneven adhesive thickness, and adhesive defects on the micromechanical silicon resonant accelerometer were analyzed with ANSYS software. Results showed that the package substrate material strongly affected the resonance frequency of the resonator after the application of surface mounting technology. The Young’s modulus and thermal expansion coefficient of adhesives were found to be important factors that affect chip thermal stress and warpage. Uneven adhesive thickness and adhesive defects also affect the resonance frequency of the resonator. DOI: http://dx.doi.org/10.11591/telkomnika.v11i5.2475

Phase noise analysis of micromechanical silicon resonant accelerometer

The phase noise in micromechanical silicon resonant accelerometer (SRA) can perturb its frequency output and determines the minimum detectable change in acceleration (sensor resolution). In order to improve the resolution and optimize the sensor performance, the phase noise of SRA is studied in this paper. Theoretical model of phase noise of SRA is set up, especially the effect of the automatic gain control (AGC) circuit in oscillator to phase noise in low frequency range (1/f3 phase noise and 1/f5 phase noise) is analyzed, and the restriction of resolution performance arising from the 1/f3 phase noise caused by AGC is also illustrated. Phase noise experiments are then performed on a SRA prototype developed in MEMS Inertial Technology Research Center and validate the model. Compared to the previous work, the phase noise model in this paper matches the experiments results more precisely, and could provide guidance and reference for design in MEMS inertial device.

(Invited) Equivalent Circuit Representation of Resonant Accelerometer

The equivalent RLC circuit for the resonant accelerometer isdescribed in detail, which shows that equivalent circuit containstwo variable capacitances and two variable resistances due to theacceleration and amplitude. Using the electromechanical couplingfactor presented here and the mode function of the transversedeflection vibration of the double clamped beam, the equivalent circuit parameters related to the size of the accelerometer and thedrive voltage are derived. In short, the mechanical and electrical parameters of the resonant accelerometer can be calculated andanalyzed accurately by the formulae derived in this paper.

Study on Packaging Thermal Stress of Micromechanical Silicon Resonant Accelerometer

Packaging thermal stress is harmful to the performance of the micromechanical silicon resonant accelerometer. In order to decrease the packaging thermal stress, correlations of packaging thermal stress with the material properties, curing temperature and geometrical size of adhesive layers of adhesive materials were discussed. A finite element model of package was developed to analyze the influence of surface mounting technology (SMT） on the micromechanical silicon resonant accelerometer. The simulation results show that the Young’s modulus, thermal expansion coefficient, curing temperature and geometrical sizes of adhesive layers are important influencing factors for packaging thermal stress and the warpage of the chip. The thermal stresses during the process of SMT will cause the resonant frequency shift.

Design and Analysis of Silicon Resonant Accelerometer

In this study, we present an approach for micromechanical resonant accelerometer design, structural optimization and testing method of a kind of resonant accelerometer which is excited by the electrostatic force and detected by the change of capacitance. The structure parameters’ influence on capability parameters are analyzed by MATLAB and the mechanical and model analysis of structure are carried out by ANSYS, also, we optimized the structure parameters. Simulating results validates the design thought.

Microfabrication technology for non-coplanar resonant beams and crab-leg supporting beams of dual-axis bulk micromachined resonant accelerometers

This paper presents the design principles and fabrication techniques for simultaneously forming non-coplanar resonant beams and crab-leg supporting beams of dual-axis bulk micromachined resonant accelerometers by masked-maskless combined anisotropic etching. Four resonant beams are located at the surface of a silicon substrate, whereas the gravity centre of a proof mass lies within the neutral plane of four crab-leg supporting beams on the same substrate. Compared with early reported mechanical structures, the simple structure not only eliminates the bending moments caused by in-plane acceleration, and thereby avoiding the rotation of the proof mass, but also providing sufficiently small rigidity to X and Y axes accelerations, potentially leading to a large sensitivity for measuring the in-plane acceleration.

Analysis of Phase Lock Loop Closed-Loop Drive Circuit for Silicon Micromachined Resonant Accelerometer Based on the Average Method

This paper studies the control theory and the methods of the silicon micromachined resonant accelerometers(SMRAs). According to the structure and movement of the resonant accelerometer, the model of its dynamics and the equations of motion are deduced. The model of the closed-loop control is set up with the phase lock loop (PLL). The principle of PLL is expounded in detail. The requirements for phases and gains of the sinusoidal self-drive-oscillation are met by PLL. The average method is to take the average of slowly changing variables within a cycle to find the solutions of nonlinear equations. Using the average method, it analyzes the PLL’s phase control methods in depth and derives the system stability condition. The simulation results verify the correctness of the stability condition. It provides a guiding theory for the realization of SMRA’s precision control.

The Study of Equivalent Circuit for Vibrating-Beam-Type Resonant Accelerometer

Based on the equivalent simplified model of the vibrating beam, the equivalent RLC circuit of vibrating-beam-type resonant accelerometer is described in detail, which shows that equivalent circuit contains a variable capacitances and a variable resistances due to the acceleration. Using the electromechanical coupling factor presented here and the mode function of the transverse deflection vibration of the double clamped beam, the equivalent parameters of the accelerometer with the size of the beam and comb are derived. These results are the bases of designing the drive /sense circuit of the vibrating-beam-type accelerometer.

Micro-machined resonant out-of-plane accelerometer with a differential structure fabricated by silicon-on-insulator–MEMS technology

A new micro-machined resonant accelerometer with a differential structure enabling the detection of out-of-plane acceleration is described. The microaccelerometer consists of two sensitive structures composed of seismic masses, flexural hinges and double-clamped resonant beams. Owing to thickness differences and neutral axis variations among these three components, in response to an out-of-plane acceleration, the movements of the seismic masses lead to stress build up in flexural hinges, further translated as axial forces applied on resonant beams. In this differential design, under acceleration, one resonant beam is under a tensile stress, whereas the other one is under a compressive stress, producing a differential resonant frequency output. The microaccelerometer was fabricated by a silicon-direct-bonding silicon-on-insulator wafer with MEMS fabrication and a low-stress packaging method was also developed. Based on a closed-loop control circuit for resonant beam excitation and detection, device characterisation was conducted, producing a quality factor of 436 in air and a differential sensitivity of 813 Hz/g.