Bei Peng

Prediction of Gap Asymmetry in Differential Micro Accelerometers

Gap asymmetry in differential capacitors is the primary source of the zero bias output of force-balanced micro accelerometers. It is also used to evaluate the applicability of differential structures in MEMS manufacturing. Therefore, determining the asymmetry level has considerable significance for the design of MEMS devices. This paper proposes an experimental-theoretical method for predicting gap asymmetry in differential sensing capacitors of micro accelerometers. The method involves three processes: first, bi-directional measurement, which can sharply reduce the influence of the feedback circuit on bias output, is proposed. Experiments are then carried out on a centrifuge to obtain the input and output data of an accelerometer. Second, the analytical input-output relationship of the accelerometer with gap asymmetry and circuit error is theoretically derived. Finally, the prediction methodology combines the measurement results and analytical derivation to identify the asymmetric error of 30 accelerometers fabricated by DRIE. Results indicate that the level of asymmetry induced by fabrication uncertainty is about ±5 × 10−2, and that the absolute error is about ±0.2 μm under a 4 μm gap.

Modeling the Microstructure Curvature of Boron-Doped Silicon in Bulk Micromachined Accelerometer

Microstructure curvature, or buckling, is observed in the micromachining of silicon sensors because of the doping of impurities for realizing certain electrical and mechanical processes. This behavior can be a key source of error in inertial sensors. Therefore, identifying the factors that influence the buckling value is important in designing MEMS devices. In this study, the curvature in the proof mass of an accelerometer is modeled as a multilayered solid model. Modeling is performed according to the characteristics of the solid diffusion mechanism in the bulk-dissolved wafer process (BDWP) based on the self-stopped etch technique. Moreover, the proposed multilayered solid model is established as an equivalent composite structure formed by a group of thin layers that are glued together. Each layer has a different Young’s modulus value and each undergoes different volume shrinkage strain owing to boron doping in silicon. Observations of five groups of proof mass blocks of accelerometers suggest that the theoretical model is effective in determining the buckling value of a fabricated structure.

Modified correlation criterion for digital image correlation considering the effect of lighting variations in deformation measurements

The Newton-Raphson (N-R) algorithm based on the sum of squared differences (SSD) function used in the digital image correlation (DIC) may obtain unreliable results in deformation measurements because light source variation is not taken into account. Here, a modified N-R algorithm that includes the effect of light source variations on the measurement results is presented. Instead of involving the mean value and square sum of the gray value of the object, variables were employed in the proposed algorithm. Thus, we refer to it as variables-based sum of squared differences (VSSD) function. VSSD has been validated by comparing the computer generated speckle images, which indicates that it could give rise to more accurate results in calculating deformation than SSD when the surrounding light source changes. In addition, VSSD is compared with the zero-normalized sum of squared differences (ZNSSD) function that is often used to remove the light source variation. The results show that VSSD can achieve the same accuracy within in less time compared to ZNSSD.

Electrostatic compensation method in frequency robustness design of micro accelerometer

Abstract. An electrostatic compensation method is proposed to realize the frequency robustness of a capacitive accelerometer by taking advantage of the electromechanical coupling characteristics, rather than mechanical structure alone. The limitations of microfabrication on structural configuration are overcome by an efficient adjustment of circuit parameters, which have equivalent contributions on the natural frequency as mechanical structures. The results of theoretical analysis and experiments indicate that this design method is practical for different microprocessing conditions, and the robustness of a mechanical structure to error can be achieved by a reasonable electrostatic compensation in electromechanical coupling microdevices. The test results have shown that the frequency deviations in more than 80% of fabricated sensors are less than 1%.

Investigation of the Thermal Drift of MEMS Capacitive Accelerometers Induced by the Overflow of Die Attachment Adhesive

Packaging stress has significant influence on the thermal stability of microelectromechanical system (MEMS) devices, which utilize the die-on-substrate packaging method to connect the chips and the package shell. A certain adhesive, during the packaging process, is deposited on the package shell by hands or machines to shape an intermediate layer for gluing die and substrate. Due to the uncontrollability of deposition amount, the adhesive always flow out to form overflow structure on the side of die chip. The adhesive overflow will change the distribution of thermal stress induced by the changed temperature and further impact the thermal stability of devices, which is characterized by the quantity of thermal drift. This paper investigates the contribution of adhesive overflow to the thermal drift of comb MEMS capacitive accelerometers. The accelerometers with different levels of overflow are modeled by chip-adhesive-substrate models to study the deformation of sensitive component induced by temperature change. The thermal drift is acquired by an analytical method using the structure deformation and the calculation of the differential capacitance. The thermal drift theory for accelerometers with adhesive overflow is verified by a series of experiments. The results indicate that the adhesive overflow can lead to 10% increase of thermal drift compared with accelerometers without adhesive overflow. In addition, this increase can be extended by the asymmetry of supporting beams of accelerometer. Therefore, the overflow phenomenon should be carefully considered in the packaging process for highly accurate MEMS accelerometers.

Air Damping Analysis in Comb Microaccelerometer

Air damping significantly influences the dynamical characteristics of MEMS accelerometers. Its effects at micro-scale level sharply depend on the structure layouts and size of MEMS devices. The damping phenomenon of comb microaccelerometers is investigated. The air between fixed plate electrodes and movable plate electrodes cannot flow freely and is compressed. The air damping, therefore, exhibits both viscous effects and stiffness effects. The former generates a drag force like that in macromechanical systems, and the damping force is proportional to the velocity of movable electrodes. The latter stiffens the rigidity of structure, and the stiffening level is related to the gap value of capacitors, internal pressure, and temperature. This paper focuses on the dependence of the squeeze film air damping on capacitor gaps. The simulation and experiments indicate that the squeeze film effect is sharply affected by the gap value when the structural dimensions decrease. And the influence of fabrication errors is considered in damping design in comb microaccelerometers.

Effects of dielectric charging on the output voltage of a capacitive accelerometer

Output voltage drifting observed in one typical capacitive microelectromechanical system (MEMS) accelerometer is discussed in this paper. Dielectric charging effect is located as one of the major determinants of this phenomenon through a combination of experimental and theoretical studies. A theoretical model for the electromechanical effects of the dielectric surface charges within the electrode gap is established to analyze the dielectric charge effect on the output voltage. Observations of output voltage drift against time are fitted to this model in order to estimate the possible dielectric layer thickness. Meanwhile, Auger electron spectroscopy is carried out to analyze the electrode surface material composition and confirms a mixture layer of dielectric SiO2 and Si with a thickness about 5 nm, which is very close to the model estimation. In addition, observation of time-varing output drift in the variable bias voltage experiment indicates the movement of dielectric charge can be controlled by the applied electric field.

Dielectric charging induced drift in micro device reliability-a review

Abstract The movement or migration of charges in dielectric materials like silicon oxide, silicon nitride and glass, is recognized as one of the most significant causes of drift instability of MEMS devices which utilize electrostatic capacitive methods for sensing and driving. This paper reviews the current researches on the characteristics of drift phenomenon of three micro capacitive devices, micro switches, micro resonators and micro mirrors. The dielectric charging forms including polarization, ion injection and charge migration are presented in detail to explain the process and mechanism of how the charging effects gives rise to the drift of performance and influence the reliability of micro systems, and then the corresponding solutions to overcome specific drift issues are proposed based on the essential conditions needed to cause dielectric charging.

Sensitivity Jump of Micro Accelerometer Induced by Micro-fabrication Defects of Micro Folded Beams

Abstract The abnormal phenomenon occurring in sensor calibration is an obstacle to product development but a useful guideline to product improvement. The sensitivity jump of micro accelerometers in the calibrating process is recognized as an important abnormal behavior and investigated in this paper. The characteristics of jumping output in the centrifuge test are theoretically and experimentally analyzed and their underlying mechanism is found to be related to the varied stiffness of supporting beam induced by the convex defect on it. The convex defect is normally formed by the lithography deviation and/or etching error and can result in a jumping stiffness of folded microbeams and further influence the sensitivity when a part of the bending beams is stopped from moving by two surfaces contacting. The jumping level depends on the location of convex and has nothing to do with the contacting properties of beam and defects. Then the location of defect is predicted by theoretical model and simulation and verified by the observation of micro structures under microscopy. The results indicate that the tested micro accelerometer has its defect on the beam with a distance of about 290μm from the border of proof mass block.

Modeling the Boron-Doping Silicon Beam by a Multilayer Model

The boron-doping silicon beam commonly used in microdevices exhibits a nonuniform material property along its thickness or width because of the gradient of boron concentration induced by diffusion process. The constant of rigidity, one of the most important parameters of microbeam, needs to be accurately calculated and designed in the development of high precise sensors and actuators. Current design methods, mainly depending on the analytical solutions derived under the assumption of a uniform material property or some commercial software for a varied property, are not adequate and time consuming to calculate the constant of rigidity of boron-doping silicon beam. A multilayer model is proposed in this paper to replace the continuous solid model by dividing the beam into separated layers glued together. The finite element lamination method is utilized to acquire the equivalent Young modulus and moment of inertia of cross section of multilayer model. The equivalent values are calculated from double-layer structures to multilayer ones based on the small deformation theory and the material mechanics theory. The proposed method provides an effective method to design the stiffness or frequency of microdevice and its results are validated by COMSOL simulation.