Key Takeaways & Executive Findings
- •• A distributed static model based on the deflection equation improves prediction accuracy of static mechanical quantities in MEMS cantilever beams for microwave power detection chips. • The pull-in voltage increases with the gap but decreases with the length, with a relative error of only 6.5% compared to simulation, outperforming other models. • Measured return loss varies between −66.46 and −10.56 dB over 8−12 GHz, showing a V-shaped trend; measured sensitivity of 66.5 fF/W closely matches theoretical 69.3 fF/W (5.6% error). • The distributed model provides superior accuracy and physical realism, offering important reference for microwave power detection chip design.
Abstract
To improve the theoretical prediction accuracy of static mechanical quantities in MEMS cantilever beams for microwave power detection chips, a distributed static model is proposed based on the deflection equation. An analytical framework is established through the precise characterization of cantilever beam bending. The framework can accurately extract key electromechanical parameters, and the correlation between these parameters and geometric changes is systematically studied. Results show that the pull-in voltage increases with the gap but decreases with the length. The predicted pull-in voltage indicates a relative error of only 6.5% between the distributed static model and the simulation, which is significantly lower than that of the other two models. The overload power and sensitivity are also analyzed to facilitate performance trade-offs in chip design. The measured return loss varies between −66.46 and −10.56 dB over the 8−12 GHz frequency band, exhibiting a characteristic V-shaped trend. Moreover, the measured sensitivity of 66.5 fF/W closely matches the theoretical value of 69.3 fF/W, showing a relative error of 5.6%. These findings confirm that the distributed model outperforms the other two in terms of both accuracy and physical realism, thereby providing important reference for the design of microwave power detection chips.
1. Introduction
With the rapid development and widespread adoption of the fifth-generation of communication (5G), internet of things (IoT), and radar sensing technology, the operating frequency band of microwave power sensors continues to extend into higher-frequency millimeter-wave regions, while the signal modulation formats are growing increasingly complicated. These developments pose unprecedented challenges to the performance of microwave power detection chips. Detection sensitivity is a key performance metric, and its requirements are becoming increasingly stringent. The cantilever beam structure, one of the most fundamental configurations in micro-electro-mechanical-systems (MEMS), has attracted significant attention due to its high sensitivity.
In 2005, Fernandez et al. firstly proposed a capacitive MEMS microwave power monitoring chip based on a fixed-fixed beam structure, which detected microwave power by measuring the capacitance change induced by beam displacement. However, no detailed analysis was conducted on the influencing factors of the pull-in voltage. In 2008, Lin et al. developed a new analytical model based on the Rayleigh−Ritz method to determine the pull-in voltage of electrostatically actuated microbeams. They introduced three dimensionless parameters related to the square of voltage to account for the contributions of stretching stress gradient, nonlinear stiffening, bending, and residual stress. In 2014, Shoaib et al. conducted an in-depth investigation of the pull-in effect in electrostatically actuated MEMS devices. Several professional simulation software packages were used to establish...
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Ruifeng Li, Debo Wang (2025). A distributed static model of capacitive MEMS microwave power detection chip. SinoTechIntel Verified Research. https://doi.org/10.1088/1674-4926/25100007
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Frequently Asked Questions
What is the main contribution of this paper?
The paper proposes a distributed static model for capacitive MEMS microwave power detection chips, which improves the accuracy of predicting static mechanical quantities such as pull-in voltage and sensitivity, outperforming existing models.
How does the pull-in voltage vary with geometric parameters?
The pull-in voltage increases with the gap between the cantilever and the substrate but decreases with the length of the cantilever beam.
What are the measured performance metrics of the chip?
The measured return loss varies between −66.46 and −10.56 dB over the 8−12 GHz frequency band, and the sensitivity is 66.5 fF/W, closely matching the theoretical value of 69.3 fF/W.
How does the distributed model compare to other models?
The distributed model shows a relative error of only 6.5% for pull-in voltage prediction, significantly lower than other models, and provides better physical realism.
What is the significance of this work for chip design?
The model enables accurate prediction of key parameters, facilitating performance trade-offs in the design of microwave power detection chips, particularly for high-frequency applications.
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