Piezoelectric transduction of flexural modes in pre-stressed microbeam resonators

This paper reports on the optimization of the design of piezoelectric transducer elements integrated on doubly-clamped microbeam resonators utilized as (bio) chemical sensors. We report and emphasize the often forgotten influence of membrane stresses on defining the dimensions and optimal position of the piezoelectric transducer elements. The study takes into account stress induced structural changes and provides models for the equivalent motional parameters of resonators with particular shapes of the transducers matching the flexural modes of vibration. The above is analyzed theoretically using numerical models and is confirmed by impedance measurements and optical measurements of fabricated doubly-clamped beam resonators. We propose various transducer designs and highlight the advantages of using higher order vibration modes by implementing specially designed mode matching transducer elements. It is concluded that the paper describes and highlights the importance of accounting for the membrane stresses to optimize the resonator performance and the low power in electronic feedback of resonating sensing systems.