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In this paper, we proposed an efficient and high-precision process for fabricating large-area microlens arrays using thermal reflow combined with ICP etching. When the temperature rises above the glass transition temperature, the polymer cylinder will reflow into a smooth hemisphere due to the surface tension effect. The dimensional differences generated after reflow can be corrected using etching selectivity in the following ICP etching process, which transfers the microstructure on the photoresist to the substrate. The volume variation before and after reflow, as well as the effect of etching selectivity using process parameters, such as RF power and gas flow, were explored. Due to the surface tension effect and the simultaneous molding of all microlens units, machining a 3.84 × 3.84 mm2 silicon microlens array required only 3 min of reflow and 15 min of ICP etching with an extremely low average surface roughness Sa of 1.2 nm.

In this paper, we analyze the residual stress of different components of the crystal structures of electronic device materials following exposure to elevated temperatures using a combination of experimental tests and finite element simulations. X-ray diffraction (XRD) and LXRD micro-area residual stress analyzer were employed to determine the residual strain and stress of the CBGA sample encapsulation cover and solder joints. Subsequently, the experimental data were utilized to verify the accuracy of the simulation. The discrepancy between experimental measurements and simulation outcomes of the residual stress following reflow soldering of CBGA-assembled micro-solder joints is below 14%. The analysis also included thermal warping deformation of the CBGA encapsulation cover and how the residual stress was influenced by the diameter, spacing, and height of the solder joints. The study reveals that the residual stress following reflow soldering of BGA solder joints is non-uniformly distributed within the array. Within a single solder joint, residual stress gradually increases in distribution from its middle to the point where it make contact with the PCB and chip, with the highest level of residual stress observed where the solder joint contacts the chip. The variation in material parameters, such as the coefficient of thermal expansion, is the primary cause of thermal warping deformation on the surface of CBGA encapsulation covers. Three primary factors significantly impact the residual stress on BGA solder joints: solder joint diameter, spacing, and height. The maximum value is inversely proportional to the height of the solder joints and the residual stress. Conversely, the diameter and spacing of the joints are positively proportional to the highest value. When the diameter of the solder joint is increased from 0.55 mm to 0.75 mm, the maximum residual stress in the BGA solder joint increases from 37.243 MPa to 36.835 MPa. Conversely, increasing the height of the solder joint from 0.36 mm to 0.44 mm reduces the stress from 39.776 MPa to 36.835 MPa.

A method for measuring vibration characteristics of MEMS (Micro Electro Mechanical System) is presented. This method aims to simulate a real environment where MEMS operates. At first, the method of applying high and low temperature in a vacuum environment is studied. And the excitation method applying to movable microstructures of MEMS in this environment is found. Based on the above environmental conditions, the vibration characteristics of MEMS movable microstructure are measured by micro-laser vibration measurement. The base excitation method is used to measure the vibration characteristics of MEMS movable microstructures outside the plane. ANSYS 14.0 was used for finite element simulation to verify this method. The electrostatic excitation method is used to measure the inside of the plane. The stroboscopic method is used to verify the electrostatic excitation by fitting the displacement signal of the movable microstructure and the excitation output signal. The results show that the out-of-plane first-order frequency is 11.926 kHz, and the error is 0.30% compared with the experimental results. The amplitude is 44.218 nm, and the error is 0.59%. The in-plane first-order frequency is 5715.7Hz, which achieves the requirement of design precision. Both the numerical simulation and the stroboscopic method verify the excitation method well. The effect of temperature on the natural frequency of the structure is negatively correlated. And as the temperature drops, the motion of the structure becomes increasingly violent. The findings of this study provide important guidance for maintenance, reliable operation and optimal design of MEMS.

During long-term use, MEMS accelerometers will experience degradation, such as bias and scale factor changes. Bias of MEMS capacitive accelerometers usually comes from the mismatch of parasitic capacitance and sensitive capacitance. This paper focuses on the mismatch of sensitive capacitance and analyzes the mechanism of long-term degradation of MEMS accelerometers. Firstly, the effect of sensitive capacitance mismatch on the performance of a MEMS accelerometer was investigated. Secondly, a method of measuring the mismatch of sensitive capacitance was proposed, and the validation experiment shows that the accuracy of this measurement can be less than 1.10×10−5 of the sensitive capacitance. For the samples in this experiment, the measurement error of this method can be less than 0.36 fF. Finally, a high-temperature acceleration experiment was performed. The mismatch of the sensitive capacitance during the experiment was monitored based on the proposed method, and the experimental results are analyzed. The experimental result demonstrates that the mismatch of sensitive capacitance varies linearly with time. The change rates of sensitive capacitance mismatch for the two samples are 2.95×10−7 C0/h and 2.66×10−7 C0/h in the high-temperature acceleration experiment at 145 °C, respectively. The change in sensitive capacitance mismatch seems small, but it is not to be ignored during long-term use. The rate of change is similar for the same batch of samples. This could imply that the adverse effects due to the mismatch of sensitive capacitance changes can be reduced by compensating for this variation.

Vacuum packaging is used extensively in MEMS sensors for improving performance. However, the vacuum in the MEMS chamber gradually degenerates over time, which adversely affects the long-term performance of the MEMS sensor. A mathematical model for vacuum degradation is presented in this article for evaluating the degradation of vacuum packaged MEMS sensors, and a temperature-accelerated test of MEMS gyroscope with different vacuums is performed. A mathematical degradation model is developed to fit the parameters of the degradation of Q-factor over time at three different temperatures. The results indicate that the outgassing rate at 85 °C is the highest, which is 0.0531 cm2/s; the outgassing rate at 105 °C is the lowest, which is 0.0109 cm2/s; and the outgassing rate at 125 °C is in the middle, which is 0.0373 cm2/s. Due to the different mechanisms by which gas was released, the rate of degradation did not follow this rule. It will also be possible to predict the long-term reliability of vacuum packaged MEMS sensors at room temperature based on this model.

For linear accelerometers, calibration with a precision centrifuge is a key technology, and the input acceleration imposed on the accelerometer should be accurately obtained in the calibration. However, there are often errors in the installation of sample that make the calibration inaccurate. To solve installation errors and obtain the input acceleration in the calibration of the accelerometer, a calibration method based on the rotation principle using a double turntable centrifuge is proposed in this work. The key operation is that the sub-turntable is rotated to make the input axis of the accelerometer perpendicular to the direction of the centripetal acceleration vector. Models of installation errors of angle and radius were built. Based on these models, the static radius and input acceleration can be obtained accurately, and the calibration of the scale factor, nonlinearity and asymmetry can be implemented. Using this method, measurements of the MEMS accelerometer with a range of ±30 g were carried out. The results show that the discrepancy of performance obtained from different installation positions was smaller than 100 ppm after calibrating the input acceleration. Moreover, the results using this method were consistent with those using the back-calculation method. These results demonstrate that the effectiveness of our proposed method was confirmed. This method can measure the static radius directly eliminating the installation errors of angle and radius, and it simplifies the accelerometer calibration procedure.

In a MEMS capacitive accelerometer, there is an offset due to mechanical and electrical factors, and the offset would deteriorate the performance of the accelerometer. Reducing the offset from mechanism would benefit the improvement in performance. Yet, the compositions of the offset are complex and mix together, so it is difficult to decompose the offset to provide guidance for the reduction. In this work, a decomposition method of offset in a MEMS capacitive accelerometer was proposed. The compositions of the offset were first analyzed quantitatively, and methods of measuring key parameters were developed. Based on our proposed decomposition method, the experiment of offset decomposition with a closed-loop MEMS capacitive accelerometer was carried out. The results showed that the offset successfully decomposed, and the major source was from the fabricated gap mismatch in the MEMS sensor. This work provides a new way for analyzing the offset in a MEMS capacitive accelerometer, and it is helpful for purposefully taking steps to reduce the offset and improve accelerometer performance.

For the MEMS capacitive accelerometer, parasitic capacitance is a serious problem. Its mismatch will deteriorate the performance of accelerometer. Obtaining the mismatch of the parasitic capacitance precisely is helpful for improving the performance of bias and scale. Currently, the method of measuring the mismatch is limited in the direct measuring using the instrument. This traditional method has low accuracy for it would lead in extra parasitic capacitive and have other problems. This paper presents a novel method based on the mechanism of a closed-loop accelerometer. The strongly linear relationship between the output of electric force and the square of pre-load voltage is obtained through theoretical derivation and validated by experiment. Based on this relationship, the mismatch of parasitic capacitance can be obtained precisely through regulating electrostatic stiffness without other equipment. The results can be applied in the design of decreasing the mismatch and electrical adjusting for eliminating the influence of the mismatch.