A two-port electrothermal model for suspended MEMS device structures with multiple inputs

Abstract

Advances in micromachining have led to the development of microelectromechanical systems (MEMS) devices with suspended structures used in a variety of sensors. Of note for this work are sensor types where two elements exist on the suspended membrane, including examples like air flow and differential pressure detectors, gas detection, and differential scanning calorimetry sensors. Intuitively one would argue that some thermal loss exists between the two elements. However, surprisingly little is documented about this electrothermal interaction. The work presented here addresses this shortcoming by defining a new parameter set, a matrix of thermal coupling coefficients. They are used within our novel two-port electrothermal model based on the heat flow equation adapted as a linear system of equations. However, the model is only effective with knowledge of these coefficients. We introduce an approach to extract the coefficients using finite-element method (FEM)-based multiphysics simulation tools and revisit and extend our previous method of non-ideal power coupling, this time to extract the coefficient matrix from measured data. Both specialist simulation tools and device manufacturing are very expensive. However, they are the only choices in the absence of an analytic model. A major contribution of this work is the derivation of a model to predict the coefficients by analytic means from the device dimensions and material properties. The research contribution and paper culminate in a comparison of analytic, simulated, and experimentally extracted values of two different devices to verify and demonstrate the effectiveness of the proposed models. The values compare well and show that the best results achieved are approximately 90 % and 70 % thermal linkage respectively for vacuum and atmospheric pressure conditions.