Nonlinear analysis of electrothermal position sensors with contoured heaters

For electrothermal MEMS position sensors, we introduce a novel analytical model capturing the nonuniform distribution of temperature as well as the nonlinear temperature profile of resistivity. The proposed model also includes the effects of contoured beam heaters and the nonuniform proximity of the heatsink, which changes with heatsink position and is differentially transduced into output voltage. The model predicts the experimental I-V data and the sensor output accurately. It also reveals a considerable improvement in the linearity of the sensor response when the beam profiles are appropriately shaped to yield a more uniform temperature distribution. The shaped sensor is compared with conventional electrothermal sensors with uniform beam cross sections under two different conditions, equal bias voltages and equal average temperatures, where improved linearity is achieved in both cases.