Tip Motion—Sensor Signal Relation for a Composite SPM/SPL Cantilever

An array of microbeams is a promising approach to increase the throughput of scanning probe microscopes and lithography. This concept requires integrated sensors and actuators which enable individual measurement and control. Thus, existing models for single beams need to be reassessed in view of its applicability for arrays, which involve additional physical interactions and a varying geometry along the beam's length. This paper considers a single composite microbeam, which is excited by a thermal actuator and its displacement is measured by a piezoresistive sensor. We derive a model that incorporates the beam's composite structure, varying geometry along its length, its thermal coupling for actuation, and thermoelastic damping. Subsequently, the influence of the beam's geometry on its eigenmodes and frequencies is analyzed in far and close proximity operation to a surface. We observe parametric excitation phenomena of multiple integers of the fundamental excitation frequency, which originates from the geometrical composition of the beam. Furthermore, we observe that the so far constant assumed factor to convert the sensor signal to the beam's displacement depends on the dissipated power within the actuator, as well as on the dynamic behavior of the system, and thus is not constant.