Electro-thermo-mechanical model for bulk acoustic wave resonators

Abstract

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.

Nonlinear Effects of SiO2 Layers in Bulk Acoustic Wave Resonators

“…The constitutive nonlinear electroacoustic equations for the piezoelectric layer are extensively explained in [5]- [7]. Those equations relate the field magnitudes stress T, strain S, electric field E and electric displacement D to each other using the …”

“…The model will be finally implemented using the strain S and the electrical displacement D as independent variables, and adding the nonlinear voltage sources T c and V c to a conventional distributed Mason model [5], [6]. As done in [2], [7], the piezoelectric layer is discretized into many unit cells of small thickness z, where the strength of the electric field is constant.…”

“…This model was a phenomenological approach to describe the second harmonic (H2) generation and was surpassed by the non-lineal distributed Mason model [5], [6], which was based in the constitutive nonlinear equations. This later model was completed in [7] adding the thermal domain to the constitutive equations. Authors of [2], [4]- [7] outlined the importance of measuring harmonics and intermodulation generation sweeping the frequency of the fundamental/s signal/s.…”

“…This later model was completed in [7] adding the thermal domain to the constitutive equations. Authors of [2], [4]- [7] outlined the importance of measuring harmonics and intermodulation generation sweeping the frequency of the fundamental/s signal/s. The frequency pattern of a given observable must be consistent with the distributed model and it constitutes a fingerprint of the origin of the nonlinearity.…”

“…In addition, different manifestations of nonlinearity, through different experiments, must be also consistent and explained with a unique model. Those works, [4] and [7] using Solidly Mounted Resonators (SMR) and [2], [5], [6] using Thin-Film Bulk Acoustic Wave Resonators (FBAR), concluded that H2 and third order intermodulation (IMD3) was generated in the piezoelectric layer. Accordingly, all models developed were focused on the nonlinearities in the piezo-layer and none of them included the effects other layers could have in the nonlinearities.…”