Semester Project on the balancing of coupled NEMS resonators by the application of voltage on a piezoelectric layer

As understanding the properties of coupled NEMS resonators is essential to their optimal usage, we investigate in this paper the possibility of using the reverse piezoelectric effect to balance the first two coupled eigenmodes of a pair of coupled resonators whose masses are not equal. Indeed, manufacturing NEMS resonators of perfectly identical masses is as of this day still a challenge. The reverse piezoelectricity is used in order to tune the stress along one of the resonators, leading to its respective fundamental eigenfrequency being affected and thus modifying the coupled eigenfrequencies and eigenmodes. The objective of this paper is thus to determine to what extent this approach works and to provide a mathematical model that would predict the required compensating voltage to be applied, given experimentally measurable data such as the coupled eigenfrequencies and the coupled eigenmodes (amplitudes of the resonators at the mode). Simulations are performed to assess the results.