Optical mapping of surface vibrations on a thin-film resonator near 2 GHz

An optical scanning interferometer is used to examine the mode structure of a solidly-mounted thin-film resonator (TFR) when it is excited electrically in the neighborhood of its resonant frequency. Scans across the surface with <1 μm lateral resolution and 0.3 pm (0.003 Angstrom) vertical resolution reveal a rich spectrum of modes. At the mechanical resonance a uniform up-and-down motion is observed, while at slightly higher frequencies near the pole frequency the mode pattern breaks up into standing waves with wavelengths ranging from 10-100 μm. A second set of standing waves with discrete wavelengths in the range 2-5 μm and with random orientation is observed over a broader frequency range. Semi-quantitative agreement is found between the data and the dispersion curves calculated with a transfer matrix technique for the multilayer waveguide structure of the TFR