Unified model for Bulk Acoustic Wave resonators' nonlinear effects

Rocas, Eduard; Collado, C.; Booth, James C.; Iborra, E.; Aigner, Robert

doi:10.1109/ultsym.2009.5441686

Cited by 17 publications

(6 citation statements)

References 10 publications

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“…If the beat period of the input tones is large compared with the thermal time constant, then the temperature of the resonator fluctuates at the beat frequency and follows the instantaneous power dissipation; hence, large IMD3 is generated through the temperature dependence of the material constants, exceeding the intrinsic nonlinear IMD3 response of the AlN. This topic is also discussed in detail by Collado and coworkers [10]. This type of nonlinear response due to parametric mixing is well known among other disciplines such as in the power amplifier community.…”

Section: Determination Of Model Coefficientsmentioning

confidence: 98%

A general nonlinear Mason model and its application to piezoelectric resonators

Shim

Feld

2011

Int J RF and Microwave Comp Aid Eng

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The one-dimensional electroacoustic behavior of a uniform piezoelectric plate may be modeled by electrical equivalent circuits such as Mason or KLM models. Such models yield mathematically exact solutions to the governing equations, i.e., a set of constitutive equations and the differential equations of electrostatics and mechanics. In this article, we present an extension of the Mason equivalent circuit to the case of arbitrary nonlinear constitutive equations by the use of telegrapher's equations in a mathematically exact way. The resulting model consists of the original Mason circuit, distributed nonlinear voltage sources along its acoustic arm, and a nonlinear voltage source at the electrical terminal. We also show the proof that the circuit meets all the governing equations, and comparison of simulated results and harmonic measurements of FBAR devices. V C 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE 21:486-495, 2011.

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Section: Determination Of Model Coefficientsmentioning

confidence: 98%

A general nonlinear Mason model and its application to piezoelectric resonators

Shim

Feld

2011

Int J RF and Microwave Comp Aid Eng

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“…A main concern in BAW resonators is about the second order nonlinearities which are usually characterized by second harmonic H2 generation [2], [4]- [7], [10] A. Narrowband Second Harmonic Measurements Fig. 5 shows the measured second harmonic with a DUT input power of 21 dBm.…”

Section: Nonlinear Measurementsmentioning

confidence: 99%

Nonlinear Effects of SiO₂ Layers in Bulk Acoustic Wave Resonators

Collado

Mateu

Garcia-Pastor

et al. 2018

IEEE Trans. Microwave Theory Techn.

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“…But, there is no agreement on which physical parameter(s) are responsible for this response. For example, Collado developed a physical model based on the stress dependence of the bulk modulus [1,2]. Ueda developed a model based on strain and electric field dependence of the displacement vector [3,4], and Feld developed a physical model based on a strain dependent piezoelectric constant [5].…”

Section: Nonlinearity; Second Harmonic; Intermodulation Distortion; Pmentioning

confidence: 99%

“…As in [5] we have chosen to use the stresscharge form of the constitutive equations which relate T (stress) and D (free charge density, or electric displacement field) to linear and higher orders of S (strain) and E (electric field) (1,2). c E , e, and ε S are the bulk modulus, piezoelectric constant, and dielectric constant respectively.…”

Section: Extension Of Lippmann's Constitutive Equationsmentioning

confidence: 99%

Determination of the nonlinear physical constants in a piezoelectric AlN film

Feld

Shim

2010

2010 IEEE International Ultrasonics Symposium

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Recent models vary widely as to the mechanism in the piezoelectric AlN film that gives rise to the measured 2 nd and 3 rd order nonlinear behavior in BAW resonators. As an example one model suggests that a strain dependence of the bulk modulus in a piezoelectric AlN film is responsible for both the 2nd and 3rd order response of BAW and FBAR resonators [Collado]. We call this model the "bulk-bulk" model since the bulk modulus depends on the strain in each order respectively. We find that this "bulk-bulk" model is not capable of modeling our measured second harmonic (H2), and intermodulation distortion (IMD3) data simultaneously. When the 2nd order coefficient is chosen to match the measured 2nd harmonic response, it generates an IMD3 response through a process of remixing at a frequency 2F 1 -F 0 which is larger than our measured data by ~45 dBs when two +24 dBm tones are applied. It appears the authors did not fully incorporate their chosen non-linearity into their model. As a result the "bulk-bulk" non-linear model of the AlN film must be abandoned in favor of a new model --a "general" nonlinear Mason model, in which a complete set of 2nd and 3rd order nonlinear mechanisms can be evaluated to see which are consistent with the data. Such a model is described in this work and in a companion paper. Using this model we show that a strain dependent piezoelectric coefficient must be employed to model the H2 behavior without modeling an IMD3 response that is much larger than what is measured. To fit the IMD3 data a 3rd order strain dependent bulk modulus must also be incorporated. The resulting model is a "piezo-bulk" model for suggesting that the piezo coefficient and the bulk modulus have a 2nd and 3rd order dependence on strain, respectively. We also show that another recent model [Ueda] is not suitable for evaluating the underlying nonlinear physics because it violates conservation of energy and does not allow for remixing.

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Unified model for Bulk Acoustic Wave resonators' nonlinear effects

Cited by 17 publications

References 10 publications

A general nonlinear Mason model and its application to piezoelectric resonators

A general nonlinear Mason model and its application to piezoelectric resonators

Nonlinear Effects of SiO₂ Layers in Bulk Acoustic Wave Resonators

Determination of the nonlinear physical constants in a piezoelectric AlN film

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Unified model for Bulk Acoustic Wave resonators' nonlinear effects

Cited by 17 publications

References 10 publications

A general nonlinear Mason model and its application to piezoelectric resonators

A general nonlinear Mason model and its application to piezoelectric resonators

Nonlinear Effects of SiO2 Layers in Bulk Acoustic Wave Resonators

Determination of the nonlinear physical constants in a piezoelectric AlN film

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Nonlinear Effects of SiO₂ Layers in Bulk Acoustic Wave Resonators