Two-Dimensional Theoretical Modeling and Experimental Investigations of Micromachined Thermal Expansion-Based Angular Motion Sensor

A two-dimensional (2D) model was developed, for the first time, to describe the characteristics of the micromachined thermal expansion-based angular motion (TEAM) sensor, which has been validated by the experimental results. Scaling analysis on the performance characteristics through the 2D model was conducted to optimize the TEAM sensor’s design in terms of the normalized distances between the microheaters and temperature detectors in $x$ and $y$ directions, the thickness of the thin film, the heater width, the cavity depth, and the heater temperature. Furthermore, the proposed 2D model was normalized by two dimensionless numbers, namely Rayleigh number Ra and Peclet number Pe, with a critical Rayleigh number (Ra $^{\ast }_{\mathrm {c}} =18$ ,000) identified to differentiate linear and nonlinear operation regimes of the TEAM sensor. In particular, our 2D model is much faster than the conventional CFD model by three orders of magnitude (18.91s versus 5.5h), enabling rapid system-level optimization of the critical design parameters. Accordingly, the TEAM sensors with three pairs of platinum thermoresistive temperature sensors were designed and fabricated. The fabricated device demonstrated a normalized sensitivity of $11.8~\mu \text{V}$ /°/s/mW based on the working fluid of air, which was more than three times better than previous thermal angular motion sensors. Thus, with the experimental validation, the proposed 2D model should be a reliable tool to realize the systematical design optimization of TEAM sensors integrated with on-chip microelectronics for future industrial IoT applications. [2020-0355]