Co-simulation Framework in COMSOL Multiphysics® for Displacement of a MEMS Cantilever using a Depletion Schottky Transducer
Depletion layer MEMS actuators have been demonstrated in the past in p-n junctions as well as Schottky barrier interfaces to be effective transducers for internal transduction of high Q MEMS resonators without the need for piezoelectric materials or small resonator-electrode gaps. However they remain under-utilized compared to conventional capacitive electrostatic and piezoelectric transducers, and consequently have scant analytical studies in literature. We have devised an analytical model based on equivalent force analysis to derive expressions for the displacement amplitude and transduction efficiency of a Schottky barrier embedded in a micro-cantilever resonator. Here we present an FEM model of this transducer, wherein the electrostatic forces generated in the depletion layer and the displacement amplitude of the cantilever are co-simulated using COMSOL Multiphysics®. We use the Semiconductor Module in COMSOL to simulate the electric field and charge distribution for a defined range of reverse bias voltage. The resultant electrostatic force thus computed is then coupled to the MEMS Module to compute the displacement amplitude at resonance for the cantilever. The figure below shows an illustration of the resonator and transducer modeled in this work. The barrier is essentially assumed to be confined at the top surface of the cantilever which is modeled by assigning the required characteristics of metal layer of schottky diode to the metal contact on top of the cantilever. The FEM simulation results agree well with the analytical model and experimental results reported in literature. The multiphysics simulations therefore provide a possible co-simulation use case for MEMS resonators.