Electro-thermo-mechanical model for bulk acoustic wave resonators

We present the electro-thermo-mechanical constitutive relations, expanded up to the third order, for a BAW resonator. The relations obtained are implemented into a circuit model, which is validated with extensive linear and nonlinear measurements. The mathematical analysis, along with the modeling, allows us to identify the dominant terms, which are the material temperature derivatives and two intrinsic nonlinear terms, and explain, for the first time, all observable effects in a BAW resonator by use of a unified physical description. Moreover, the terms that are responsible for the second-harmonic generation and the frequency shift with dc voltage are shown to be the same.