Tunability of aluminum nitride acoustic resonators: a phenomenological approach

A phenomenological approach is developed to identify the physical parameters causing the dc-voltage-induced tunability of aluminum nitride (AlN) acoustic resonators, widely used for RF filters. The typical resonance frequency of these resonators varies from 2.038 GHz at -200 V to 2.062 GHz at +200 V. This indicates, based on these RF measurements versus dc bias and the model used, that the AlN stiffness variation versus dc bias is the prominent effect because both resonance and antiresonance experience a similar variation, respectively, 24 MHz and 19 MHz at 400 V. Picosecond ultrasonics were also used to prove independently that the acoustic velocity (and therefore AlN stiffness) is sensitive to dc bias and that the variation induced is comparable to that extracted from the resonance measurements. It turned out that the stiffness relative variation for an electric field of 1 V/μm extracted from picosecond ultrasonics is 54 ppm-μm/V. This is in good agreement with the value extracted from the RF measurements, namely 57.2 ppm-μm/V. The overall tunability of these AlN resonators reaches 1.1%, which is an interesting figure, although probably not high enough for genuine applications.