Loss Mechanism and Acoustic Dispersion in FBARs via Vibration Visualization by Femtosecond Pulsed Laser Interferometry

Femtosecond pulsed laser interferometry is developed to visualize and analyze the vibrational mode profiles and dispersion curves of an apodized pentagon-shaped film bulk acoustic resonator (FBAR) above 2.5 GHz. Two distinct kinds of spurious modes are identified, including a tiled-polygon pattern near the series resonance frequency (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub>) and a crossed-stripe pattern near the parallel resonance frequency (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub>), respectively. Near <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub>, the stripes gradually rotate to exactly align with the electrode edges leading to strengthened anchor leakage, which could not be seen in simulations due to its unrealistic boundary conditions and has been previously overlooked. Experimentally derived <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i>-space maps and dispersion curves enable corrections to analytical and simulated models. These analyses suggest the reasons of quality-factor degradation due to strong anchor leakage, where spurious lateral modes propagate across the two electrode edges. A simulated curved edge design is proposed to alleviate such lateral spurious modes. All these findings are not easy to obtain solely from electrical measurements and simulations, as the mode visualization using pulsed laser interferometry provides direct insights into the dynamics of FBARs and guides more effective ways for design optimization.