MEMS-IC Co-Design and Experimental Demonstration of a Surface Micromachined CMOS-MEMS Pirani Vacuum Gauge

We present a surface-micromachined Pirani vacuum gauge with integrated on-chip circuitry based on CMOS-MEMS technology. To guide the MEMS design, an analytical model was developed to predict sensor characteristics. The model was validated by FEM simulations and further implemented as an equivalent circuit in an EDA tool, which enables MEMS-IC co-optimization. Co-simulation confirmed that the designed constant-temperature-difference (CTD) circuit maintains the Pirani gauge overheated by 15K with a variation below$\pm 0.02 ~\mathrm{K}$. With optimized MEMS dimensions, the Pirani gauge fabricated by a lithography-free post-CMOS achieves a maximum sensitivity of$1.04 ~\mathrm{V} /$Dec in the$20-30kPa$range, which aligns well with theoretical predictions. Moreover, the gauge heating power increases from 13 to 36mW across$10^{0}-10^{5} ~\text{Pa}$, while long-term sensor signal variations remain below 0.07% at 101kPa and 0.06% at 13Pa with Kalman filtering. The gauge also demonstrates a transient response time of 0.43s. These results confirm that the proposed Pirani vacuum gauge delivers high sensitivity, fast response, and excellent stability, making it a promising candidate for industrial vacuum monitoring.