A Comprehensive Analysis of MEMS Electrothermal Displacement Sensors

Abstract

For electrothermal microelectromechanical system position sensors, we introduce a novel analytical model that captures the nonuniform distribution of temperature as well as the nonlinear dependence of resistivity on temperature. The proposed model also captures the effects of contoured beam heaters and the nonuniformity of the air gap between the heat-sink and the heaters, which varies with heat-sink position and is differentially transduced into the output voltage. The model accurately predicts the experimentally obtained \(I\) -\(V\) data and the corresponding sensor output. It also explains the considerable improvement achieved 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 uniform electrothermal sensors under two different operating conditions, voltage, and current bias modes. Improved linearity is observed in both cases. The model is also applicable to predict the dynamic response of the sensor. An iterative procedure is developed to solve the additional complexity in voltage mode, which is a nonlinear partial integro-differential equation. Considering different bias modes and heater profiles, we evaluate the sensor bandwidth and linearity using the model and conduct experiments to validate the results. Based on first principles, the proposed model is more transparent than sophisticated software-based approaches and compatible with traditional solvers in MATLAB.