An online test structure for the thermal expansion coefficient of surface micromachined polysilicon beams by a pull-in approach

Abstract

An online test structure for measuring the thermal expansion coefficient (TEC) of surface micromachined polysilicon beams is presented by using clamped–clamped beams. In this structure, the polysilicon beam is heated by applying direct current voltage between two anchors, causing it to expand. The thermal expansion of the beam is restricted due to the clamped–clamped boundary, while the pull-in voltage is measured by applying the other varying voltage between the beams and substrate. Based on the electrothermal properties of the test structure and the pull-in approach, an analytical model and an extracting method for the TEC are developed. Validation of the analytical model has been confirmed by FEM simulation and experiments. In the experiments, current–voltage measurements are only required, and all measurements can be carried out in free air. Measured average value of the TEC is (2.49 ± 0.03) × 10−6 K−1 with temperature ranging from 300 to 350 K.