High-sensitivity MEMS magnetoresistive (MR) sensors have attracted ever-increasing attention due to their ability to detect weak magnetic fields, but the resolution is severely limited by the $1/f$ noise. This paper reports a MEMS MR sensor that can effectively suppress the $1/f$ noise by modulating the magnetic field signal to the higher frequency region utilizing magnetic tunnel junction vertical motion modulation based on the MEMS piezoelectric cantilever resonator. The magnetic sensitivity can be increased to 2283.3%/mT with a high magnetic gain of 39.3 by integrating the structure-optimized fixed magnetic flux concentrators. The signal-to-noise ratio of the MEMS MR sensor can be improved by three orders of magnitude and the 160 pT/√Hz resolution can be reached. These results make the MEMS MR sensor based on the MTJ motion modulation a competitive candidate in the pico-Tesla magnetic detection.

A mode-localized ΔE-effect magnetic sensor model is established theoretically and numerically. Based on the designed weakly coupled resonators with multi-layer film structure, it is investigated how the ΔE-effect of the magnetostrictive film under the external magnetic field causes the stiffness perturbation of the coupled resonators to induce the mode localization effect. Using the amplitude ratio (AR) as the output in the mode-localized ΔE-effect magnetic sensor can improve the relative sensitivity by three orders of magnitude compared with the traditional frequency output, which has been verified by simulations based on the finite element method (FEM). In addition, the effects of material properties and geometric dimensions on sensor performance parameters, such as sensitivity, linear range, and static operating point are also analyzed and studied in detail, providing the theoretical basis for the design and optimization of the mode-localized ΔE-effect magnetic sensor in different application scenarios. By reasonably optimizing the key parameters of the weekly coupled resonators, a mode-localized ΔE-effect magnetic sensor with the sensitivity of 18 AR/mT and a linear range of 0.8 mT can be achieved.

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 study presents a novel dual phase-locked loop two-dimensional synchronized motion modulation (TDSMM-DPLL) system designed to enhance the low-frequency detection capability of magnetoresistive (MR) sensors by effectively mitigating 1/f noise. The TDSMM-DPLL system integrates a comb-driven resonator and a piezoelectric cantilever beam resonator, achieving synchronized magnetic field modulation through a DPLL circuit that adjusts the resonant frequency of the comb-driven resonator to twice that of the cantilever beam resonator. Theoretical analysis and finite element simulations demonstrate a modulation efficiency of 38.98%, which is significantly higher than that of traditional one-dimensional modulation methods. Experimental validation confirms the system’s effectiveness, showing a 3.13-fold reduction in frequency Allan variance, decreasing from 217.32 ppb to 69.46 ppb, indicating substantial noise suppression. These results highlight the TDSMM-DPLL system’s potential to improve the performance of MR sensors in low-frequency applications, making it a promising solution for high-precision magnetic field detection.

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

Magnetoresistive (MR) sensors have emerged as promising candidates for miniaturized, high-performance magnetic sensing applications. However, their performance in low-frequency magnetic field detection is severely limited by intrinsic 1/f noise. To address this challenge, magnetic flux modulation technology that utilizes magnetic flux concentrators (MFCs) and micro-electro-mechanical systems resonators has been proposed to suppress the 1/f noise. In this study, a mechanical synchronous motion modulation (MSMM) architecture is introduced, which integrates MFC motion modulation (MFCMM) with MR element longitudinal motion modulation (MRLMM). The proposed MSMM architecture achieves mechanical synchronization of dual MEMS resonators through microlever couplings and chevron-type (V-shaped) actuators, eliminating the need for complex synchronous phase-locked loop circuits. Theoretical analysis and finite element method simulations were conducted to comparatively evaluate the modulation efficiencies of MSMM, MFCMM, and MRLMM. The results demonstrate that MSMM significantly improves magnetic field modulation efficiency, thereby enhancing the low-frequency detectivity of MR sensors. The designed MSMM actuator has been successfully fabricated, exhibiting a resonant frequency above 10 kHz (the typical corner frequency of the 1/f noise spectrum) and enabling frequency tuning through applied bias voltage. These findings demonstrate the effectiveness of the MSMM technique and highlight its potential for improving the low-frequency magnetic detection performance of MR sensors.