Low-Temperature Coefficient and Large Range Pressure Sensor Based on Single End Fixed-Support U-Beam Resonator

Temperature variations induce the temperature coefficient effect in microelectromechanical systems (MEMS) resonant pressure sensors, affecting the mechanical properties of vibrating materials and causing frequency drift, which reduces sensor accuracy. To address this, we designed a resonant pressure sensor with a U-shaped beam structure configured in a single-ended fixed form. This design aims to reduce thermal stress on the resonant beam and minimize the impact of temperature on beam stiffness, thereby improving measurement accuracy. Finite element analysis shows that, within a full scale of 120 MPa and a temperature range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$- 45~^{\circ }$ </tex-math></inline-formula>C to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$80~^{\circ }$ </tex-math></inline-formula>C, thermal stress in the main vibrating beam decreases from 75 MPa in the double-end fixed form to 0.938 MPa in the single-end fixed form, and the temperature coefficient reduces from 3.5 to 0.2 Hz/°C. Fabricated using MEMS bulk silicon technology, the sensor undergoes postprocessing with a packaging shell for high-pressure measurement. Experimental data indicate that under gas pressure from 0 to 30 MPa, the sensor sensitivity is 72.4 Hz/MPa, and within the temperature range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$- 45~^{\circ }$ </tex-math></inline-formula>C to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$80~^{\circ }$ </tex-math></inline-formula>C, the temperature coefficient is less than or equal to 0.2 Hz/°C. The reduced temperature coefficient ensures that pressure-frequency curves at different temperatures almost coincide. Using a polynomial fitting algorithm, the measurement error is less than 0.015%. This design significantly reduces thermal stress and temperature sensitivity, offering a more reliable and accurate pressure measurement solution across varying thermal conditions. Thus, the U-shaped beam structure offers a viable solution to the temperature coefficient of frequency (TCF) problem in resonant pressure sensors.