Vacuum-pressure sensing using the 3ω temperature-amplitude response of a suspended microheater

Precise pressure monitoring in rarefied gas environments is essential for process control and system reliability in precision engineering applications. Conventional vacuum gauges, including mechanical deformation-based gauges, ionization gauges, and thermal-conductivity-based Pirani gauges, often require calibration for specific operating conditions or show limited sensitivity in low-pressure ranges. In this study, we propose a suspended microheater-based 3ω sensor designed to suppress substrate heat loss and enhance the contribution of gas-mediated heat transfer to the measured electrothermal response. The low-frequency 3ω response was interpreted using a quasi-steady thermal-resistance framework, in which the inverse temperature amplitude serves as a conductance-like indicator under fixed oscillatory heating. The pressure-dependent gas contribution was described using an effective rarefied-gas thermal-conductivity model with a representative effective length scale. A Pt microheater was fabricated on a SiN x membrane, and 3ω measurements were performed in air over a pressure range of 1.9 × 10 –2 –7.5 × 10 2 Torr and a driving-frequency range of 0.1–10 Hz. As the pressure decreased, both the temperature amplitude and phase delay increased, with the largest pressure sensitivity observed at 0.1 Hz. Comparison between the inverse temperature amplitude and the calculated effective thermal conductivity showed close correspondence in the slip and transition regimes, whereas the low-pressure deviation was consistent with the increasing relative importance of residual, weakly pressure-dependent heat-loss pathways as gas-mediated conduction diminished. These results demonstrate that a suspended 3ω microheater can provide a compact electrothermal platform for vacuum-pressure sensing by directly transducing pressure-dependent changes in rarefied gas heat transfer.