In this study, the drift of microelectromechanical system (MEMS) accelerometers stored at room temperature for one year is investigated by both finite-element analysis (FEA) simulation and experiments. In the simulation, a comprehensive FEA model considering the die-attach adhesive viscoelasticity was established to emulate the deformation of the sensor package structure during storage. Then drift models of the scale factor and bias of the accelerometer were built according to the deformed structure. To validate the simulation results, several accelerometers were packaged and their outputs were tested and recorded once per month. The two parameters displayed a continuous drift owing to the release of the packaging stress in the chip. The scale factor drifts were negative and about 2500 ppm for different types of sensors. However, the bias drifts were positive or negative, and their magnitudes were ranging from 12 to 32 mg in storage. Moreover, they reached a steady state after about ten months (< 50 ppm per month for the scale factor) and six months (< 1 mg per month for bias) of room-temperature storage. The results in this article provide meaningful guidance for the application of MEMS accelerometers.

In this work, the drifts of the bias and scale factor induced by the dielectric charging are studied for micro-electro-mechanical system (MEMS) closed-loop accelerometers. At first, the equations of the feedback electrostatic forces, including the built-in voltages resulted from the dielectric charging, are built up for the two capacitors of the accelerometers. Then, the models for the drifts of the bias and scale factor both are established. Based on the models and experimental data, it is found that the drift of the scale factor is always negative because the built-in voltages always decrease the scale factor. However, the drift of the bias can be negative or positive because it is in proportion to the built-in voltages' difference of the two capacitors, which may be negative or positive. The major output error for the small input acceleration is caused by the drift of the bias. However, for the large acceleration, the error induced by the drift of the scale factor is also vital. Finally, the method of choosing the frequency of the ac reference voltage for suppressing the dielectric charging based on the drift of the scale factor is established. The feasibility is verified by the experimental data.

Adhesive polymer is a common and important material used for packaging of microelectronics and microsystem by attaching dies onto packaging shell, and its mechanical property plays a vital role in isolating dies from the thermal stress of substrate. Therefore, it is extremely significant to evaluate the polymer property in a specific packaging process. The molecular dynamics (MD) simulation is conducted in this article to investigate the material properties of the cross-linked epoxy resin formed by epoxy resin component diglycidyl ether bisphenol A (DGEBA) and curing agent 1,6-Diaminohexane. The polymer network with conversion up to 87.5% is successfully generated and simulated by constant pressure-constant temperature ensemble (NPT) and canonical ensemble (NVT) at different temperatures of curing process. Glass transition temperature (T-g) and Young's modulus are extracted and the predicted material properties are in great agreement with the experimental data. The conclusion provides a guideline to design the special curing process for different adhesive requirements.

The drift phenomena of closed-loop capacitive silicon-based micro accelerometers have been hindering their application in the area of precise and rapid industrial positioning, which especially requires a good dynamic performance. Using both theoretical methods and experiments, this paper will systematically investigate the underlying mechanisms of such phenomena. The possible causes of drift, including thermal effects, dynamic response, capacitor charging and dielectric charging, as described in current literature, were evaluated by specific tests. As a result, the first three factors were ruled out as the cause of drift, by both theoretical derivation and experimental observation, and only dielectric charging was identified as the most plausible contributor to the drift. The movement of charges in SiOx on electrodes and glass substrates forms an additional electrostatic field that disturbs the system balance and results in the variation of accelerometer output. The materials analysis and shielding tests carried out demonstrated that the drift phenomena of more than 60% of the tested accelerometers can be explained by the charging effect of dielectric materials, while the remaining sensors require further tests and more complicated models to determine the causes of this drift. The conclusions presented in this paper provide meaningful guidance for improving accelerometer performance in order to meet the demands of high accuracy industrial applications.

In this work, the temperature coefficients of capacitive accelerometers operating in closed-loop mode, namely the temperature coefficient of bias (TCB) and temperature coefficient of the scale factor (TCSF), are studied analytically. They are modeled based on the working principle of the sensor and the effects of the thermal deformation on capacitance. The modeling analysis shows that TCB is caused by a rigid displacement of the proof-mass induced by thermal deformation. As such, several methods were proposed to decrease TCB, such as soft die-attaching, middle-located anchors for movable electrodes, and flexible supporting beams. The modeling analysis also shows that variations of the capacitive gap induced by thermal deformation is a critical factor which causes TCSF. However, the temperature dependence of the stiffness of the supporting beam plays no role on TCSF because the inertial force is balanced by the electrostatic force rather than the spring force. Therefore, TCSF can be reduced significantly as long as the thermal deformation is fully suppressed, such as by soft die-attaching and middle-located anchors for fixed electrodes. In addition, the decrease in susceptibility of the electrostatic force to the variation of the gap can also decrease TCSF. Finally, the analysis on TCB and TCSF are both verified by a group of experiments on packaged accelerometers mounted on PCB circuits. (C) 2019 Elsevier B.V. All rights reserved.

Adhesive bonding is one of the most frequently used techniques for die attachment in microelectronics and microsystem packaging. The thermal stress induced by the mismatch of coefficients of thermal expansion(CTE) under temperature change is a key factor to the packaging reliability. An analytical prediction model is proposed to evaluate the interfacial thermal stress of tri-layer packaging with void in adhesive rather than an ideal model which is broadly adopted in current publications. The proposed method focuses on the stresses at the voids and chip edges that always possesses the maximum stress resulting in the delamination and dislocation failure. The prediction results showed a good agreement with numerical simulation and exhibited a more accurate evaluation of interfacial shearing stresses at the edges of void and tri-layer structure than Suhir’s method. The study indicated that the maximum shearing stress occurred at the structure edges of interface of adhesive and smaller CTE material while the maximum stress in interface of adhesive and bigger CTE layer appeared at the edges of voids. The shearing stresses in the areas far from void in void model are almost the same as the model without voids. Both conclusions provided a useful guideline to the design of packaging reliability of micro systems.

The low temperature coefficient and high linearity of the input-output characteristics are both required for high-performance microelectromechanical systems (MEMS) capacitive accelerometers. In this work, a structural designing of a bulk MEMS capacitive accelerometer is developed for both low temperature coefficient and high linearity. Firstly, the contrary effect of the wide-narrow gaps ratio (WNGR) on the temperature coefficient of the scale factor (TCSF) and linearity error is discussed. Secondly, the ability of an improved structure that can avoid the contrary effect is illustrated. The improved structure is proposed in our previous work for reducing the temperature coefficient of bias (TCB) and TCSF. Within the improved structure, both the TCSF and linearity error decrease with increasing WNGR. Then, the precise designing of the improved structure is developed for achieving lower TCB, TCSF, and linearity error. Finally, the precise structural designing is experimentally verified.

The glass polarization effects were introduced in this paper to study the main cause of turn-on drift phenomenon of closed-loop micro-accelerometers. The glass substrate underneath the sensitive silicon structure underwent a polarizing process when the DC bias voltage was applied. The slow polarizing process induced an additional electrostatic field to continually drag the movable mass block from one position to another so that the sensing capacitance was changed, which led to an output drift of micro-accelerometers. This drift was indirectly tested by experiments and could be sharply reduced by a shielding layer deposited on the glass substrate because the extra electrical filed was prohibited from generating extra electrostatic forces on the movable fingers of the mass block. The experimental results indicate the average magnitude of drift decreased about 73%, from 3.69 to 0.99 mV. The conclusions proposed in this paper showed a meaningful guideline to improve the stability of micro-devices based on silicon-on-glass structures.

In this work, an analytical model for adhesive die-attaching under thermal loads is proposed. The second-order beam theory is employed to model the die and substrate, so the shearing deformations can be evaluated more accurately comparing to models based on the Timoshenko beam theory and interface compliance. Then, governing equations are solved by Fourier series with the elastic foundation for the adhesive layer. As such, numerical calculations for eigenvalues are avoided, and explicit closed-form solutions are obtained. Based on the analytical model, effects of material properties and dimensions on the thermal deformation in the die are discussed. In the die, the longitudinal expansion and transverse warpage induced by thermal deformation both decrease with decreasing Young's modulus of adhesive. The longitudinal expansion decreases with increasing die thickness. However, the transverse warpage increases with increasing die thickness.

Capacitive micro accelerometer, as one of promising micro devices, utilizes the parallel-plate capacitor arrays to covert input acceleration into differential capacitance, so its characteristics highly depend on an accurate capacitance evaluation. The traditional capacitance formula used in macro-scale systems design could not meet the requirement of micro-scale field because the fringe effects of capacitors have great contribution to the total measured capacitance under a few millimeters of separation distance. In this paper, the theoretical equation of capacitance with fringe effects is utilized to design the sensitivity and nonlinearity of a capacitive micro accelerometer. The proposed analytical method provides a quantitative evaluation of sensing capacitance of micro accelerometers. Experimental results indicate that the theoretical design with fringe effects has a better agreement with experiments than ideal parallel-plate capacitor principle.

The output of one typical capacitive microelectromechanical system (MEMS) accelerometer under square wave bias voltage is discussed. Output drift of the accelerometers should be suppressed to improve the device performance. Theoretical analysis indicates that square wave bias voltage can be applied instead of the DC bias voltage to mitigate the dielectric charging-induced output drift. Theoretical models of the sensing structure under square wave bias voltage indicate that both square wave and DC bias voltage can generate the same electrostatic force among the sensing structure. Therefore, the system equilibrium can be maintained with square wave bias voltage when the same input acceleration is applied. Configuration and the frequency of the square wave bias voltage are analyzed to maintain the system equilibrium and device function. Experimental results show that although the magnitude of the output voltage is slightly decreased, output drift can be significantly suppressed when the square wave voltage is applied. (C) 2017 Society of Photo-Optical Instrumentation Engineers (SPIE)

Polymer-based materials are commonly used as an adhesion layer for bonding die chip and substrate in micro-system packaging. Their properties exhibit significant impact on the stability and reliability of micro-devices. The viscoelasticity, one of most important attributes of adhesive materials, is investigated for the first time in this paper to evaluate the long-term drift of micro-accelerometers. The accelerometer was modeled by a finite element (FE) method to emulate the structure deformation and stress development induced by change of adhesive property. Furthermore, the viscoelastic property of the adhesive was obtained by a series of stress–relaxation experiments using dynamic mechanical analysis (DMA). The DMA curve was imported into the FE model to predict the drift of micro-accelerometers over time and temperature. The prediction results verified by experiments showed that the accelerometer experienced output drift due to the development of packaging stress induced by both the thermal mismatch and viscoelastic behaviors of the adhesive. The accelerometers stored at room temperature displayed a continuous drift of zero offset and sensitivity because of the material viscoelasticity. Moreover, the drift level of accelerometers experiencing high temperature load was relatively higher than those of lower temperature in the same period.

For the scale factor thermal drift(SFTD)of capacitive microaccelerometers,its semi-analytical model is established based on the detection principle and thermal deformation results of microaccelerometers. Then ,the main factors affecting SFTD are analyzed. The results show that SFTD is composed of two parts. The first part, which is mainly determined by the temperature coefficient of elastic modulus of silicon,can be reduced by heavy-doping. The second part caused by the thermal deformation has relationship with the elastic modulus of adhesives for packaging,finger width,the ratio between wide gap and narrow gap,and the location of the anchor for the fixed comb fingers. The first part and second part are positive and negative respectively,so they compensate each other. Based on the MEMS bulk silicon micromachining,experimental samples of microaccelerometers are fabricated. The testing results of SFTD verify the theoretical analysis results of SFTD.

为了使微加速度计满足线性度指标,准确计算微加速度计的非线性误差是非常必要的.在考虑边缘和寄生电容的前提下,提出了计算微加速度计的非线性误差的方法.首先根据表芯结构的电容分布特点建立了其等效电路模型,并推导了微加速度计的输出电压与检测电容和寄生电容之间的关系式,其中检测电容包含了边缘电容;其次,基于有限元法,分别提出了计算微加速度计的寄生电容和检测电容的方法;最后建立了微加速度计的输出电压与输入加速度之间的关系式,并基于三次多项式拟合,推导出微加速度计的非线性误差的计算公式.通过对比分析非线性误差的理论计算结果与实验测量结果,提出的方法的正确性得到了验证.

Dimension uncertainty inevitably occurs in almost every fabrication of micro structure due to its small size and uniformity of material.The dimension error,however,will result in the asymmetry of the sensi-tive structure.The unsymmetrical structure will change the distribution of the thermal stress when the micro sensors are subjected to changed temperature and further impact the thermal stability of devices which is charac-terized by the quantity of thermal drift.This study investigates the effects of fabrication error on the thermal drift of a comb capacitive micro accelerometer fabricated by deep reactive ion etching(DRIE)process.The accel-erometers with supporting folded beams width error ranging from the ideal layout design to the actual fabricated dimension are modeled to simulate the deformation of sensitive component induced by temperature change.The thermal drifts are acquired by the calculation of the differential capacitance of the deformed structure.In order to reduce the thermal drift induced by the fabrication error,the design dimension of the beam width is enlarged under the premise of constant sensitivity of the accelerometer.The calculated results indicate that the support-ing beam fabrication error will significantly affect the thermal drift of the capacitive micro accelerometers and an increased design dimension of the beam width can improve the symmetry of the sensor,and then reduce the thermal drift.

An analytical study and a compensation structure for temperature drifts of bias and scale factor of a bulk silicon MEMS capacitive accelerometer are presented. The analytical model for the temperature drift of bias (TDB) and temperature drift of scale factor (TDSF) is established based on the analysis results of thermal deformation and stiffness temperature dependence. The model shows that TDB is only caused by thermal deformation, while TDSF consists of two parts caused by stiffness temperature dependence and thermal deformation, respectively. The two parts are positive and negative, respectively, but the second part has greater absolute value. First part of TDSF can be reduced by high doping. TDB and second part of TDSF can be both reduced by soft adhesive die attaching or increasing substrate thickness. In silicon structure, TDB can be reduced by middle-locating anchors for moving electrodes in sensitive direction or decreasing the stiffness asymmetry of springs, while second part of TDSF can be reduced by middle-locating anchors for fixed electrodes in sensitive direction. By middle-locating anchors both for moving electrodes and fixed electrodes, a temperature compensation structure is designed to reduce TDB and second part of TDSF. Consequently, TDSF is reduced by making the two parts of TDSF cancel each other. Experimental results show that TDB is suppressed from 1.85 mg/degrees C to 0.52 mg/degrees C, while TDSF from -162.7 ppm/degrees C to -50.8 ppm/degrees C. (C) 2016 Elsevier B.V. All rights reserved.

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.

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.

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.

In order to obtain a more accurate physical model for a micro accelerometer, the influence of the structural buckling deformation caused by boron doping on the performance of the sensor was studied in this paper. The sensitivity of the accelerometer with different doping states was investigated combined with analytical calculation, finite element simulation and experimental method. The analytic expression of sensitivity of the accelerometer with different doping states was obtained. Both the theoretical and experimental results indicate that the sensitivity of the accelerometer with boron doping is about 5 mV/g less than that of the accelerometer without boron doping, and the sensitivity varies by about 2 mV/g when the boron diffusion depth changed from 90μm to 120μm. The sensitivity of the accelerometer will decrease when considering the buckling deformation caused by boron doping, and the sensitivity increases with the increasing diffusion depth.