Enhanced linearity through high-order antisymmetric vibration for MEMS DC power sensor

We present an electric power meter that capitalizes on the interaction of electrothermal strain and mechanical vibration in a micro-electro-mechanical systems (MEMS) beam undergoing the antisymmetric mode of vibration. This is achieved by using a resonant bridge driven with an electrothermal modulation technique. The change in electrical power is monitored through the alteration in the mechanical stiffness of the structure, which is tracked electrostatically. The observed deflection profile of the beam under the influence of electrothermal effects shows that the deflection geometry due to buckling exhibits similar trends as the first symmetric vibrational mode, in contrast to the antisymmetric mode. Therefore, we compare two distinct vibrational modes, converting the compressive thermal stress generated by the input electrical power via Joule heating into a shift in the resonance frequency. By employing antisymmetric vibrational mode, the output of our device is consistently monotonic to the input electrical power, even when the microbeam is experiencing buckling deflections. In addition, the sensing operation based on antisymmetric modes yields only a 1.5% nonlinear error in the response curve, which is ten times lower than that of symmetric modes. The observed deformation shape of the resonator agrees with the results obtained from multi-physics finite simulations. Finally, this approach has the potential to be extended to other frequency-shift-based sensors, allowing for higher linearity.