Optical Knife-Edge Displacement Measurement with Sub-Picometer Resolution for RF-MEMS
Vikrant J. Gokhale, Jason J. Gorman
Optical knife-edge measurements can be used to quantify in-plane displacements of microstructures vibrating at high frequencies. This work presents an analytical model and experimental results for optical knife-edge measurements that demonstrate precise displacement measurements for electrostatic MEMS resonators with a narrow actuation gap. The model is experimentally validated using silicon RF-MEMS resonators with predominantly in-plane motion at frequencies ranging from 13 MHz to 895 MHz. It is also shown that high-resolution spatial mapping of displacement mode shapes for fundamental and higher-order vibration modes is possible. Mode shape mapping reveals the true dynamics of fabricated devices, and can be used to improve device performance. The optical knife-edge measurements have a resolution as low as 455 fm/√Hz at 13.6 MHz, and under 1 pm/√Hz up to 1.4 GHz. This work expands the scope of the knife-edge technique to work with any type of MEMS resonator, improves the resolution by at least a factor of 2, and increases the demonstrated frequency range by a factor of 60.