Regimes in the axisymmetric stiction of thin elastic plates

Abstract

This work considers the adhesion of a thin, prestressed elastic plate to the bottom of a microcavity – a scenario that can be found frequently in thin-film devices from pressure sensors to microfluidics. This adhesion phenomenon is also referred to as stiction in the field of nano/microelectromechanical systems (N/MEMS); the geometry we consider is axisymmetric (thereby we term this problem axisymmetric stiction). Motivated by the extreme thinness of increasingly exploited nanofilms such as 2D materials in functional devices, various limiting regimes of the axisymmetric stiction problem that arise due to the interplay of the bending, stretching, and pretension effects are discussed. Specifically, key dimensionless physical parameters in this problem are discussed and the range of these parameters for the classification of different regimes is outlined. This classification allows for analytical/asymptotic solutions for the critical adhesion conditions and the adhesion length in different regimes, many of which are not yet available in the literature. These analytical results are verified numerically and also compared with experiments based on 3-500 nm thick 2D materials. As such, this work provides a complete overview of the physically relevant regimes associated with axisymmetric stiction, establishing a regime diagram that can be directed used for the evaluation of the structural reliability of rapidly emerging thin plate devices.