Electric field sensors (EFSs) are widely used in various fields, particularly in accurately assessing atmospheric electric fields and high-voltage power lines. Precisely detecting electric fields enhances the accuracy of weather forecasting and contributes to the safe operation of power grids. This paper comprehensively reviews the development of micro-electromechanical system (MEMS) resonant EFSs, including theoretical analysis, working principles, and applications. MEMS resonant EFSs have developed into various structures over the past decades. They have been reported to measure electric field strength by detecting changes in the induced charge on the electrodes. Significant advancements include diverse driving and sensing structures, along with improved dynamic range, sensitivity, and resolution. Recently, mode localization has gained attention and has been applied to electric field sensing. This paper reviews the performances and structures of MEMS resonant EFSs over recent decades and highlights recent advances in weakly coupled resonant EFSs, offering comprehensive guidance for researchers.

High-resolution and sensitive MEMS DC electric field sensors offer the possibility for the integration of detection in multiple fields, such as atmospheric electricity, power grids and biomedical sciences. In this work, a mode-localized sensor prototype based on a double-ended tuning fork design (DETF) is presented. The theoretical derivations and lumped model simulations reveal the key performance enhancements regarding the wide measurement range and high resolution of such a coupled resonator structure. A prototype is fabricated using Silicon-On-insulator (SOI) approaches, which is further tested to achieve a sensitivity of $\mathrm{0.016 /(kV/m)}$ , a resolution of $\mathrm{21.3~V/m}$ , a measurement range of $\mathrm{200 kV/m}$ and a bias instability of $\mathrm{0.29~V/m}$ . The metrics are improved compared to the traditional Euler beam designs and the micro-machined counterparts. This shows the capability to meet the demands for electric field sensing in modern atmospheric electricity, power grids and biomedical sciences, with enhanced sensitivity, measurement range and stability. 2024-0154

Coherent control of coupled microelectromechanical resonators within the framework of classical nonlinear dynamics is of relevance in fundamental studies and the development of high-performance sensors. Coherent control can be achieved through the parametric modulation of one of the two coupled resonators. However, microelectromechanical resonators are commonly operated in the nonlinear regime, and a thorough description of key phenomena involving parametric modulation of coupled resonators, such as sideband generation and mode splitting, remains limited in this regime. We use a weakly coupled double-ended tuning fork (DETF) resonator under strong parametric modulation to demonstrate tunable energy transfer and mode interactions governed by classical analogs of well-established quantum phenomena. The method uses a red-sideband parametric signal to manipulate the coupling between two adjacent modes dynamically. This approach is theoretically assessed thanks to a nonlinear reduced-order model that takes into account the modal interactions and virtual coupling induced by the parametric modulation. Furthermore, the proof of concept of the proposed tuning mechanism is validated on a DC electric field sensor with enhanced sensitivity. The nonlinear parametrically driven sensor exhibits two orders of magnitude sensitivity boost while maintaining a broad measurement range. While our investigation focuses on coupled microresonator systems modeled within a classical framework, the observed dynamics and the simulation extend to the advancements of other cognate fields, such as optomechanics and two-level systems.

High-sensitivity and high-resolution electric field sensors have important applications in fields such as atmospheric electricity and industrial electrostatic monitoring, enabling precise detection of weak electric fields. However, existing electric field sensors still face limitations in sensitivity and resolution, making them inadequate for high-precision electric field monitoring in applications such as weather monitoring and high-voltage power transmission lines. This paper presents a method to enhance the performance of Micro electric field mill (MEFM) sensors based on high-order modes and nonlinear effects. The sensitivity expression of the sensor, with amplitude as the output, is derived from the charge induction principle, and the mode shapes are obtained through finite element simulations. The softening effects induced by the nonlinear vibrations of the sensor in the second and third modes are analyzed. The sensitivities of these two modes were tested under various voltage combinations, along with noise and resolution measurements in both the linear and nonlinear regimes. Test results show that within the electric field range of -29.4 kV/m to +29.4 kV/m, the nonlinear region of the second mode exhibits the highest sensitivity [4.77 mV/(kV/m)], noise floor [0.22 V/(m·√Hz)], and resolution [0.46 V/m]. Compared to other modes both in linear and nonlinear regions, these performance metrics exhibit notable improvement. By operating in high-order modes beyond the critical Duffing amplitude, the sensor's performance can be effectively enhanced.

Coherent control of coupled microelectromechanical resonators within the framework of classical nonlinear dynamics is of relevance in fundamental studies and the development of high-performance sensors. Coherent control can be achieved through the parametric modulation of one of the two coupled resonators. However, microelectromechanical resonators are commonly operated in the nonlinear regime and a thorough description of key phenomena involving parametric modulation of coupled resonators, such as sideband generation and mode splitting, remains limited in this regime. Utilising a weakly coupled double-ended tuning fork (DETF) resonator under strong parametric modulation, we demonstrate tunable energy transfer and mode interactions governed by classical analogs of well-established quantum phenomena. This approach is theoretically assessed thanks to a nonlinear reduced order model which takes into account the modal interactions and virtual coupling induced by the parametric modulation. Furthermore, the proof of concept of the proposed tuning mechanism is validated on a DC electric field sensor with enhanced sensitivity. The nonlinear parametrically driven sensor exhibits a significant increment in sensitivity exceeding two orders of magnitude. while simultaneously maintaining a broad measurement range. While our findings remain within the classical regime, the observed dynamics and the simulation extend to the advancements of other cognate fields such as in optomechanics and two-level systems.