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

Starting from Gallium Nitride epitaxially grown on silicon, pre-stressed micro-resonators with integrated piezoelectric transducers have been designed, fabricated, and characterized. In clamped–clamped beams, it is well known that tensile stress can be used to increase the resonant frequency. Here we calculate the mode shape functions of out-of-plane flexural modes in pre-stressed beams and we derive a model to predict both the resonant frequency and the piezoelectric actuation factor. We show that a good agreement between theory and experimental results can be obtained and we derive the optimal design for the electromechanical transduction. Finally, our model predicts an increase of the quality factor due to the tensile stress, which is confirmed by experimental measurements under vacuum. This study demonstrates how to take advantage from the material quality and initial stress resulting of the epitaxial process.