Theory of bending of Si nanocantilevers induced by molecular adsorption: a modified Stoney formula for the calibration of nanomechanochemical sensors

We investigate the bending of nanometer thick Si cantilevers induced by chemisorption of H atoms and acetylene molecules, using atomistic simulations and continuum theories. We show that the bending curvature of Si nanocantilevers does not follow the classical Stoney formula, but agrees well with a modified Stoney formula that we have derived. Our studies reveal the dominant role of atomic structure and surface stress in governing the bending behavior of nanofilms, and demonstrate that the modified Stoney formula has to be used for the calibration of nanomechanochemical sensors in detecting trace amounts of molecules.