An alternative method for determining the 2nd order nonlinear constants of a piezoelectric film

Nonlinear behaviors of bulk piezoelectric devices have been widely studied. Nonlinear circuit models, such as a nonlinear version of Mason's model, have been developed to model the 2
^nd
harmonic emissions (H2) and intermodulation response (IMD3) of piezoelectric resonators. Such resonators comprise a piezoelectric film sandwiched between two metal electrode films. The layer thicknesses and material properties, including the nonlinear materials properties, are inputs to the nonlinear model. Prior work assumed that the piezoelectric AlN film was the dominant nonlinear source. The values of the nonlinear material parameters for the AlN were chosen so that nonlinear simulations of a resonator comprising the AlN, and measurements of the same were in good agreement. In this work the 2
^nd
order nonlinear parameters of the AlN film are determined using a completely different method — through the small signal S-parameter measurement of a resonator under different dc bias voltage levels. This method is both a cross check as well as a way to refine our choice of 2
^nd
order nonlinear parameter values of the AlN film.