Electromechanical coupling constant extraction of thin-film piezoelectric materials using a bulk acoustic wave resonator

Thin-film piezoelectric materials such as ZnO and AIN have great potential for on-chip devices such as filters, actuators and sensors. The electromechanical coupling constant is an important material parameter which determines the piezoelectric response of these films. This paper presents a technique based on the Butterworth Van-Dyke (BVD) model which, together with a simple one-mask over-moded resonator, can be used to extract the bulk, one-dimensional electromechanical coupling constant K-2 of any piezoelectrically active thin-film. The BVD model is used to explicitly define the series resonance, parallel resonance, and quality factor Q of any given resonating mode. Common methods of defining the series resonance, parallel resonance, and Q are shown to be inaccurate for low coupling, lossy resonators such as the over-moded resonator. Specifically, an electromechanical coupling constant K2 of (2.6 +/- 0.1)% was measured for an (002) c-axis textured AIN film with an x-ray diffraction rocking curve of 7.5 degrees using the BVD based extraction technique.