Mechanical response of a capacitive microsensor under thermal load

A considerable fraction of commercial sensors are electrostatically actuated. Many sensor diaphragms are operated in different thermal environments that affect their performance. Because the interplay between the thermal and electrostatic loadings is of interest to designers, in this work we investigate such an interplay. We start with the coupled heat conduction equation and the Saint–Venant plate model. We use nondimensional analysis to show that the dissipation and the elastic coupling vary on a slow scale and hence they can be neglected. Consequently, the heat equation is uncoupled from the plate equation. We consider the case in which the temperature at the boundary is kept at a constant value above the ambient temperature. Substituting the resulting temperature distribution into the plate equation yields an equation with an equivalent compressive load and an electrostatic load due to a DC voltage. Then, a reduced-order model is used to investigate the influence of the dual loading on the plate deflection and their interplay.