Electrical equivalent circuit for air and liquid characterization of a multilayer micromembrane with piezoelectric actuation and read-out capabilities

International audienceDuring the last decade, piezoelectric-based microresonators have shown a great interest in the micro electromechanical systems (MEMS) field, especially for biosensing applications. Micromembranes have revealed a particular potential for biological experiments [1]. In order to optimize their design, the analytical modeling of their dynamic behavior is of critical importance. We report the elaboration of an analytical model for the case of a micromembrane with piezoelectric actuation and detection vibrating either in air or in a viscous fluid. The model, based on an equivalent electrical circuit, enables the computation of specific characteristics like mass sensitivity, resonance frequency and minimum detectable mass. The model was established for a five-layer stack membrane with a circular lead zirconate titanate 46/54 PbZrxTi1-xO3 (PZT) active cell (Fig 1). The method was based on the separation of the membrane's electromechanical behaviour into three parts. First, a purely mechanical transfer function, linking the force exerted on the membrane by the piezoelectric layer to the relative displacement of the membrane, was determined[2]. Then, the actuation coupling coefficient was determined by relating the applied voltage and moment applied to the membrane [3]. Finally, the sense electromechanical coupling coefficient is found linking the deflection of the membrane and the resulting charge creation at output electrode. The global admittance, resulting from the merging of the three previous parameters corresponds to an equivalent electrical circuit modeling the vibrations of the piezoelectric membrane in air. We also realised the implementation of the model for the case of vibration in a viscous fluid by adding two extra equivalent electrical components modelling the effects of the surrounding fluid (a.k.a fluidic resistance and inductance) respectively corresponding to the damping and added mass induced by the fluid. The final equivalent electrical circuit allows the determination of theoretical values for the membranes' characteristics as biosensors. The fabrication process has been described in details elsewhere [4] and a top view of a membrane's chip is shown on fig 2. The dynamic behaviours of fabricated membranes, with a 100 µm global radius and piezoelectric cell radius of 30, 50 and 70 µm, have been extracted experimentally. The curves for real and imaginative part of the complex admittance were obtained with a HP4294A impedance analyzer. The comparison between experimental and theoretical behaviour is reported for the three types of membranes and good agreement between the theoretical experimental curves is observed for the case of vibrations in air (Fig 3). In the case of operation in fluid, good accordance in amplitude is observed even though a constant shift in frequency (8%) between theoretical and experimental values still remains as shown on fig 4. Work is now under progress to compare the theoretical and the experimental mass sensitivity and minimum detectable mass of the membranes in real biological assays