Analysis of Frequency Drift of Silicon MEMS Resonator with Temperature

Abstract

High-quality-factor Micro-Electro-Mechanical System (MEMS) resonators have been widely used in sensors and actuators to obtain great mechanical sensitivity. The frequency drift of resonator with temperature is a problem encountered practically. The paper focuses on the resonator frequency distribution law in the temperature range of—40 to 60 °C. The four-layer models were established to analyze thermal stress caused by temperature due to the mismatch of thermal expansion coefficients. The temperature variation leads to the transformation of stress, which leads to the shift of resonance frequency. The paper analyzes the influence of hard and soft adhesive package on the temperature coefficient of frequency. The resonant accelerometer was employed for the frequency measurements in the paper. In experiments, three types of adhesive dispensing patterns were implemented. The results are consistent with the simulation well. The optimal packaging method achieves −24.1 ppm/°C to −30.2 ppm/°C temperature coefficient of the resonator in the whole temperature range, close to the intrinsic property of silicon (−31 ppm).

Temperature Compensation Method Based on an Improved Firefly Algorithm Optimized Backpropagation Neural Network for Micromachined Silicon Resonant Accelerometers

“…(6) Determine whether the termination iteration condition has been satisfied. If it has been satisfied, save the weights and thresholds and quit training; if update the weights and thresholds of the neural network using the gradient descent method and return to Step (5).…”

“…Due to the influence of the materials and fabrication, the output of the MSRA is prone to drift in a temperature-changing environment. The influence of temperature on the accelerometer is mainly reflected in the following aspects: firstly, the Young’s modulus of the silicon will change with temperature [ 5 ]; secondly, the mismatched thermal expansion coefficient of silicon and the base material will create thermal stress in the resonator; thirdly, the fabricating and packaging process will lead to the generation of residual thermal stress [ 6 , 7 , 8 ]. Temperature drift is one of the key factors limiting further improvements in the accuracy of MSRAs, and it needs to be suppressed [ 9 ].…”

Concepts and Key Technologies of Microelectromechanical Systems Resonators

“…The long-term stability of MEMS resonators is mainly affected by temperature. The spring softening effect by the elastic temperature coefficient (TCE) of silicon can result in a silicon MEMS resonator with a temperature coefficient of frequency (TCF) of approximately −30 ppm/K [87]. Thus, an uncompensated silicon MEMS resonator will have a frequency drift of up to −3750 ppm from −40 • C to 85 • C [88].…”

Feedforward Control Algorithms for MEMS Galvos and Scanners

“…These algorithms depend on knowledge of the resonant frequency and quality factor of the scanner, but this is unlikely to be a limiting factor in performance. Silicon-based resonators have stable resonant frequencies with temperature variation (∼31 ppm/ • C) [21]. Additionally, on-chip thermometers allow for adjusting timings to shifts of the resonant frequency due to temperature changes.…”