Due to the working principle of MEMS resonant accelerometers, their thermally induced frequency drift is an inevitable practical issue for their extensive application. This paper is focused on reducing the thermally induced packaging effects on the frequency drift. A leadless ceramic chip carrier package with a stress-buffering layer was proposed for a MEMS resonant accelerometer, and the influences of packaging structure parameters on the frequency drift were investigated through finite element simulations and verified experimentally. Because of the thermal mismatch between dissimilar materials, the thermo-mechanical stress within the resonant beam leads to a change in the effective stiffness and causes the frequency drift to decrease linearly with increasing temperature. Furthermore, our investigations reveal that increasing the stress-buffering layer thickness and reducing the solder layer thickness can significantly minimize the thermo-mechanical stress within the resonant beam. As the neutral plane approaches the horizontal symmetry plane of the resonant beam when optimizing the packaging structure, the effects of the compressive and tensile stresses on the effective stiffness of the resonant beam will cancel each other out, which can dramatically reduce the frequency drift. These findings provide guidelines for packaging design through which to improve the temperature stability of MEMS resonant accelerometers.

Accurate predictions of elastic properties under varying doping concentrations and temperatures are critical for designing reliable silicon-based micro-/nano-electro-mechanical systems (MEMS/NEMS). Empirical potentials typically lack accuracy for elastic predictions, whereas density functional theory (DFT) calculations are precise but computationally expensive. In this study, we developed a highly accurate and efficient machine learning-based Deep Potential (DP) model to predict the elastic constants of phosphorus-doped silicon (Si_64−xP_x, x = 0, 1, 2, 3, 4) within a temperature range of 0–500 K. The DP model was rigorously validated against benchmark DFT results. At 0 K, the elastic constants predicted by our DP model exhibited excellent agreement with experimental data, achieving a mean absolute percentage error (MAPE) of only 2.88%. We investigated the effects of doping on elastic constants in single-crystal silicon and determined their second-order temperature coefficients. The calculations demonstrated distinct doping-induced variations, showing pronounced decreases in C₁₁ and C₄₄ and a moderate increase in C₁₂. Finite-element analyses using the fitted temperature coefficients indicated improved thermal stability of silicon resonators through phosphorus doping. Our study explores the integration of machine learning-based atomic-scale simulations with MEMS/NEMS design, providing practical guidance for optimal dopant selection to enhance silicon resonator thermal stability.

This paper presents a comprehensive optimization of an outer frame anchor disk resonator gyroscope (DRG) with enhanced resistance to vibration and shock, achieved by increasing the resonant frequency of the tub and translation modes. Furthermore, the wineglass mode retains a high quality factor, enhancing sensitivity and reducing the angle random walk (ARW). The performance of the proposed DRG is analyzed using dynamic equations, and its structural parameters are optimized through finite element analysis (FEA). The prototype device was fabricated using a two-mask silicon-on-insulator (SOI) process on (100) single-crystal silicon (SCS), which is better suited for complementary metal-oxide–semiconductor (CMOS) integration compared to (111) SCS. Experimental results show an ARW of $0.63°/\sqrt{\mathrm{h}}$ and a bias instability (BI) of $7.7°/\mathrm{h}$, with no significant performance degradation observed under vibrational environments, indicating potential for tactical-grade performance.

This work presents a high-performance piezoelectric MEMS yaw gyroscope fabricated on a single-crystal silicon platform, which achieves a quality factor of 75 k—the highest reported to date among silicon-based piezoelectric gyroscopes. The device employs a wide annular resonator that operates at 132 kHz in the in-plane wineglass mode. To maximize transduction efficiency, we develop an analytical model that relates output charge to the area-integrated in-plane stress under modal deformation, and we use this model to guide parametric optimization of the annular width. The resulting geometry simultaneously enhances the mechanical quality factor and the piezoelectric coupling. A back-etching fabrication process is used to eliminate front-side release holes, thereby preserving structural continuity and suppressing thermoelastic damping. In open-loop rate mode operation with a native frequency split of 28 Hz, the gyroscope demonstrates an angle random walk of 0.34°/√h and a bias instability of 8.19°/h. These performance metrics are comparable to those of state-of-the-art lead zirconate titanate (PZT)-based annular gyroscopes, while the use of lead-free aluminum nitride as the transduction material ensures compliance with RoHS environmental regulations.

We studied the temperature effects on the resonant frequency of nano piezoelectric mechanical resonators based on Hf $_{0.5}$ Zr $_{0.5}$ O $_{2}$ thin films. Two square-shaped resonators of 30 $\mu $ m and 50 $\mu $ m in length were fabricated and tested, having a resonant frequency of 225.8 kHz and 98.5 kHz, respectively. The temperature coefficient of frequency (TCF) of the devices was characterized in the range from $-$ 20 $^{\circ}$ C to 147 $^{\circ}$ C. Both devices exhibited a positive TCF around 83.6 ppm/ $^{\circ}$ C to 105 ppm/ $^{\circ}$ C in the range from 30 $^{\circ}$ C to 147 $^{\circ}$ C, which may result from the combined effect of thermal expansion mismatch between the materials and the temperature coefficient of Young’s modulus of the HZO material. Moreover, the 50 $\mu $ m device shows a negative TCF around $-$ 110 ppm/ $^{\circ}$ C to $-$ 99.9 ppm/ $^{\circ}$ C within the range from $-$ 20 $^{\circ}$ C to 30 $^{\circ}$ C, which may be due to stress relaxation during the heating process. These results underscore the significance of HZO material in nanoscale piezoelectric resonator applications and lay the foundation for our future work aimed at developing nanoscale piezoelectric devices based on HZO.2024-0040