A Novel Transient PDE Model for Development of Highly Sensitive Microthermal Expansion-Based Angular Motion Sensor

We propose a novel transient partial differential equation (PDE) model for the development of highly sensitive microthermal expansion-based angular motion (μ TEAM) sensors based on the study of time-dependent response. With the efficient prediction of thermal time constant (τ^∗) based on the PDE model, which is >2200 times faster than 3-D CFD simulation (32.67 s versus >20 h) and was validated by the experimental results, the parametric analysis has been conducted for design optimization. The μ TEAM sensors with three pairs of temperature detectors (TDs) were adopted for the systematic study of the PWM frequency (f_PWM) effect on the sensor performance to identify the optimal f_PWM (f_o), which can optimize the sensitivity by >11%. Based on the time-dependent analysis of our PDE model, f_o was verified to be dominated by the thermal response of the sensor. A generalized 'Phase Diagram' regarding the normalized sensitivity (S^∗) was presented, for the first time, as a function of f_PWM and the normalized heater-to-detector distance (D_x/L_x). Accordingly, an optimal region, where S^∗≥0.95, was identified to successfully develop an SF 6-based μ TEAM sensor with a high sensitivity of 1.5631 mV/°/s, which was >3.5 times as large as that of the N2-based sensor (0.4203 mV/°/s). In particular, the SF6-based sensor reveals an excellent normalized sensitivity of 0.0487 mV/°/s/mW compared to the reported thermal angular motion sensors (AMSs); thus, the comprehensive study based on the PDE model enables the significant improvement of sensor sensitivity and would be useful for system-level integration in the future.