An optimization framework for the design of piezoelectric AFM cantilevers

To facilitate further miniaturization of atomic force microscopy (AFM) cantilevers and to eliminate the standard optical beam deflection sensor, integrated piezoelectric actuation and sensing on the chip level is a promising option. This article presents a topology optimization method for dynamic mode AFM cantilevers that maximizes the sensitivity of an integrated piezoelectric sensor under stiffness and resonance frequency constraints. Included in the formulation is a new material model C-SIMP (connectivity and solid isotropic material with penalization) that extends the SIMP model to explicitly include the penalization of unconnected structures. Example cantilever designs demonstrate the potential of the topology optimization method. The results show, firstly, the C-SIMP material model significantly reduces connectivity issues and, secondly, arbitrary cantilever topologies can produce increases in sensor sensitivity or resonance frequency compared to a rectangular topology.