Frequency characteristics and thermal compensation of MEMS devices based on geometric anti-spring

Abstract

This paper presents the analytical modeling, simulation and experimental validation of sensitivity, temperature variation and active controllability of MEMS geometric anti-spring (GAS) devices. Two models, the elasticity model and the thermal drift model, were proposed and analyzed, based on the study of asymmetrical and symmetrical geometric anti-spring structures. With the elasticity model, structural optimization led to analytical frequency-prestress design formula and a dedicated MEMS structure. An independent pre-stress and frequency shift effect is the result of thermal changes, so a thermal drift analytical model was built for the geometric anti-spring device, showing thermal sensitivities of 82.5 ppm/°C and 58.4 ppm/°C for the 3-spring and 4-spring devices, respectively. The analytical model was validated by both finite element analyses and experimental measurements. The designed devices (3-springs and 4-springs) were tested afterward in a dedicated setup, for both positive and negative electrostatically induced pre-stresses. Without electrical compensation, the thermal drift of the symmetrical 4-spring GAS device, for temperatures in the range +25°C to +110°C, is about 2138 ppm, and it is reduced to only 8.35 ppm when the electrostatic temperature compensation is active. Similarly, the asymmetrical structure has an uncompensated thermal sensitivity of its resonant frequency of 2254 ppm in the temperature operation range, and it is reduced to 51.5 ppm with electrical compensation within the easily controlled range of the temperature span, from +25°C to +75°C. As a result, although the benefits of the asymmetrical structure would lead to a higher sensitivity, trade-offs related to thermally-induced drift behavior and controllability also should be taken into consideration in the selection of the structural topology and application environment.