Gallium nitride MEMS resonators: How residual stress impacts design and performances

Stressed gallium nitride micro-resonators with integrated piezoelectric transducers have been designed, fabricated, and characterized. In resonant beams, it is well known that tensile stress can be used to increase the resonant frequency. Here we additionally calculate the modification of the mode shape functions of out-of-plane flexural modes. We derive an analytical model to predict both the resonant frequency and the piezoelectric actuation factor of our resonators. We show that a good agreement can be obtained and that the actuator must be properly designed to optimize the electromechanical transduction.