In this paper, we derive an exact one-dimensional rule for predicting mass loading effect due to electrodes by analyzing a FBAR structure consisting of a piezoelectric layer and two electrodes in longitudinal resonance. We validate the numerical scheme using aluminum nitride as the piezoelectric material and gold and aluminum for the top and bottom electrodes respectively. Results are compared with three-dimensional finite elements simulations obtained earlier. It is seen that the new rule predicts higher values of the resonant frequency and constitutes an improvement over an elementary rule particularly for electrodes thicknesses greater than 20% of the piezoelectric layer thickness.

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