Optical Knife-Edge Displacement Measurement With Sub-Picometer Resolution for RF-MEMS

Abstract

The optical knife-edge displacement measurement technique can be used to quantify in-plane vibrations of microstructures at radio frequencies. This paper presents an analytical model and experimental results for this technique that demonstrate precise displacement measurements for electrostatic microelectromechanical resonators 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 can be achieved. The optical knife-edge measurements have a resolution as low as 455 fm/ $\surd$ Hz at 13.6 MHz, and under 1 pm/ $\surd$ Hz up to 1.4 GHz. This paper expands the capabilities of the knife-edge technique by working with all types of in-plane microelectromechanical resonators, improving the resolution by at least a factor of 2, and increasing the frequency range by a factor of 60. [2018-0094]