Modeling Graphene–Polymer Heterostructure MEMS Membranes with the Föppl–von Kármán Equations

Ultra-thin graphene-based membranes have shown significant promise for high-performance nano-electro-mechanical (NEMS) devices. The key challenge in the modeling of such membranes is that they often operate in deflection regimes where the assumptions or approximations of "pure bending" or "pure stretching" are not satisfied. We present a model of graphene-polymer heterostructure (GPH) NEMS membranes based on Föppl-von Kármán (FvK) equations which take into account both bending and stretching forces. The experimental GPH membrane shape obtained through atomic force microscopy topography mapping is compared to the inflation shapes predicted by FvK-based finite element method simulation, and they show excellent agreement with each other. When the GPH membranes are deflected under pressure in a capacitive pressure sensor configuration, the effectiveness of this model is further exemplified through accurately predicting the capacitance change of deflecting GPH membrane devices at varying pressures. This model serves as a powerful new tool in the design and development of graphene-based NEMS devices, being able to predict the performance of graphene NEMS devices or to aid in the design of device geometries to match required performances.