Towards Understanding Why the Thin Membrane Transducer Deforms: Surface Stress-Induced Buckling

This study is directed towards a comprehensive exploration on the deformation mechanism of the thin membrane transducer (TMT) caused by surface stress variation. We stress that the biomolecular interaction has changed the magnitude of the surface stress; and when the surface stress exceeds a critical value the TMT will buckle and deform. Based upon Gurtin's theory of surface elasticity and principle of finite deformation, we abstract the TMT as a nanobeam with two clamped ends, and the close-formed governing equation set is derived accordingly. A computer code via the shooting method is developed to solve the presented two-point boundary value problem. In succession, the nanobeam deflection and critical parameters for buckling are quantitatively discussed. This investigation lays the theoretical foundation of TMTs; and it is also beneficial to gain deep insight into characterizing mechanical properties of nanomaterials and engineering nano-devices.