Optical Mapping of Surface Vibrations on a Thin-Film Resonator near 2 GHz

An optical scanning interferometer is used to probe the surface vibrations induced when a thin-film resonator (TFR) is excited near its resonance frequency of ~2GHz, in an effort to understand the limitations on the Q of these devices. The interferometer has lateral resolution of 1microns and vertical resolution (perpendicular to the surface) of 0.01angstroms. Maps of both the magnitude and the phase are obtained simultaneously, so that an instantaneous three-dimensional view of the surface can be constructed. A motion picture of the surface vibration can also be constructed from the data to distinguish between standing and traveling waves. Data for typical TFRs near the resonance zero exhibit uniform up and down motion, as expected, with an amplitude of ~1angstroms. For frequencies closer to the resonance pole, a standing wave is superimposed on the uniform motion, in phase with it but having a spatial in-plane periodicity lambda sub x in the range 10-50microns. High resolution scans exhibit an even finer standing-wave structure, in phase with the uniform motion, with several wavelengths in the range 2-5microns. The wave structure is compared with detailed calculations of normal and leaky surface waves in the multi-layered waveguide structure. Good semi-quantitative agreement is observed between data and the numerical simulation.