Quantifying local mechanical work at the nanoscale in optically driven piezoelectric membranes

Abstract

Quantifying mechanical work generation in active micro- and nanoscale systems requires measuring both displacement and force under controlled loading conditions, yet most approaches probe these quantities separately. Here, we present an atomic force microscopy (AFM)-based method to determine nanometer-scale displacement, local force response, and mechanical work in optically actuated piezoelectric photodiode membranes. Suspended membranes with diameters from 1 to 8 mm were driven by modulated optical excitation and probed using AFM cantilevers with different spring constants to impose controlled mechanical loads. By alternating between constant-force and constant-height operation modes, displacement and force amplitudes were independently extracted, and the local mechanical work was calculated from their product. The optomechanical response depends strongly on membrane size and probe loading. Radial measurements reveal non-uniform deformation, including off-center displacement maxima in smaller devices and a radial sign change in large membranes. The results further indicate that probe–membrane coupling plays an important role when the cantilever stiffness becomes comparable to the effective membrane stiffness. This approach provides a practical framework for evaluating load-dependent mechanical work in active materials and for optimizing micro- and nanoscale actuators and energy-converting devices.