The impetus of writing this paper is to propose an efficient detection mechanism to scan the surface profile of a micro-sample using cantilever-based atomic force microscopy (AFM), operating in non-contact mode. In order to implement this scheme, the principal parametric resonance characteristics of the resonator are employed, benefiting from the bifurcation-based sensing mechanism. It is assumed that the microcantilever is made from a hyperelastic material, providing large deformation under small excitation amplitude. A nonlinear strain energy function is proposed to capture the elastic energy stored in the flexible component of the device. The tip–sample interaction is modeled based on the van der Waals non-contact force. The nonlinear equation governing the AFM’s dynamics is established using the extended Hamilton’s principle, obeying the Euler–Bernoulli beam theory. As a result, the vibration behavior of the system is introduced by a nonlinear equation having a time-dependent boundary condition. To capture the steady-state numerical response of the system, a developed Galerkin method is utilized to discretize the partial differential equation to a set of nonlinear ordinary differential equations (ODE) that are solved by the combination of shooting and arc-length continuation method. The output reveals that while the resonator is set to be operating near twice the fundamental natural frequency, the response amplitude undergoes a significant drop to the trivial stable branch as the sample’s profile experiences depression in the order of the picometer. According to the performed sensitivity analysis, the proposed working principle based on principal parametric resonance is recommended to design AFMs with ultra-high detection resolution for surface profile scanning.

An alternative packaging method, termed built-in packaging, is proposed for single terminal devices, and demonstrated with an actuator application. Built-in packaging removes the requirements of wire bonding, chip carrier, PCB, probe station, interconnection elements, and even wires to drive single terminal devices. Reducing these needs simplifies operation and eliminates possible noise sources. A micro resonator device is fabricated and built-in packaged for demonstration with electrostatic actuation and optical measurement. Identical actuation performances are achieved with the most conventional packaging method, wire bonding. The proposed method offers a compact and cheap packaging for industrial and academic applications.

This study demonstrates the realization of localized in-plane optomechanical microcavities embedded within an electrostatic MEMS architecture. The system consists of a curved, clamped-clamped microbeam, fabricated on a silicon-on-insulator (SOI) wafer. A green laser emitted from a Laser Doppler Vibrometer (LDV), is directed perpendicularly onto the device under a vacuum pressure of 7 mTorr, with the beam aligned to fill the gap between the movable microbeam and its adjacent side fixed mirror. This configuration forms localized cavity optomechanical resonators that enable the generation of optomechanical soliton frequency combs through phonon lasing without electrical excitation. The optomechanical resonators' dynamics are examined through experiments and numerical simulations. First, the experimental findings unveil that in electrostatic MEMS structures, the two reflective electrodes positioned to form a capacitive gap can inadvertently form localized cavities. These cavities significantly affect optical readouts, as the photodetected signal encodes contributions from both Doppler-shifted electromagnetic waves and light scattered from the intracavity optical field. This dual contributions can distort mechanical response interpretation unless appropriately filtered. Second, experiments show that optical pumping at various positions along the microbeam induces periodic pulse trains with distinct free spectral ranges (FSRs), each corresponding to different mechanical modes. Our results present the generation of solitary optical wavepackets using in-plane localized Fabry-Pérot microcavities formed within a MEMS device. The results suggest a path toward chip-scale, soliton frequency combs generators featuring frequency spacing on the order of kilohertz, without relying on integrated fiber optics.