A theoretical and experimental comparison of 3-3 and 3-1 mode piezoelectric microelectromechanical systems (MEMS)

Two piezoelectric transducer modes applied in microelectromechanical systems are (i) the 3-1 mode with parallel electrodes perpendicular to a vertical polarization vector, and (ii) the 3-3 mode which uses interdigitated (IDT) electrodes to realize an in-plane polarization vector. This study compares the two configurations by deriving a Norton equivalent representation of each approach - including expressions for output charge and device capacitance. The model is verified using a microfabricated device comprised of multiple epitaxial silicon beams with sol-gel deposited lead zirconate titanate at the surface. The beams have identical dimensions and are attached to a common moving element at their tips. The only difference between beams is electrode configuration - enabling a direct comparison. Capacitance and charge measurements verify the presented theory with high accuracy. The Norton equivalent representation is general and enables comparison of any figure of merit, including electromechanical coupling coefficient and signal-to-noise ratio. With respect to coupling coefficient, the experimentally validated theory in this work suggests that 3-3 mode IDT-electrode configurations offer the potential for modest improvements compared against 3-1 mode devices (less than 2×), and the only geometrical parameter affecting this ratio is the fill factor of the IDT electrode.