AVS 60th International Symposium and Exhibition
    MEMS and NEMS Tuesday Sessions
       Session MN-TuP

Paper MN-TuP4
Finite Element Model Verification of High Frequency Piezoelectric Contour-Mode MEMS Resonators Using Laser Vibrometry

Tuesday, October 29, 2013, 6:00 pm, Room Hall B

Session: MEMS and NEMS Poster Session
Presenter: K.R. Qalandar, University of California, Santa Barbara
Authors: K.R. Qalandar, University of California, Santa Barbara
B.A. Gibson, University of California, Santa Barbara
L.A. Shaw, University of California, Santa Barbara
S.Y. Chiu, University of California, Santa Barbara
A. Tazzoli, Carnegie Mellon University
J. Segovia, Carnegie Mellon University
M. Rinaldi, Northeastern University
G. Piazza, Carnegie Mellon University
K.L. Turner, University of California, Santa Barbara
Correspondent: Click to Email

This paper reports the first FEA model verification of AlN contour-mode resonators (CMRs) using laser Doppler vibrometry (LDV) at frequencies above 1GHz. Full 3D models of UHF resonators are able to determine electrical and mechanical responses, including AF response, admittance curves, and full 3D mode shapes. The modal analysis here differs from previous works [1-3] by making direct quantitative comparisons between measured and simulated responses.

The 1GHz lateral-field CMRs consist of a thin film of AlN patterned with interdigitated metal electrodes on top and a floating electrode on bottom. An AC signal to the electrodes excites the contour-extensional mode through the equivalent d31 piezoelectric coefficient of the AlN [4,5]. The devices are characterized by mechanical and electrical measurements. A Polytec UHF120 LDV captures phase and out-of-plane displacement data, with ±1.4pm resolution down to a noise floor of 4pm (Fig. 1). Spatial scans across the surface generate 3D mode shapes (Fig. 2). By performing frequency sweeps and fitting data to the equations of motion, we extract mechanical parameters such as the linear and nonlinear stiffness and damping coefficients. Electrical measurements further validate simulation results; through the electromechanical coupling coefficient the mechanical measurements can also be confirmed.

The 3D FEA models are developed in COMSOL and used to determine both mechanical and electrical responses. We compare simulated frequency response, out-of-plane displacement, and Q with experimental data to verify the models (Table 1). Fig. 2 shows the 3D mode shape, and the out-of-plane displacement profile of individual fingers is shown in Fig. 3. The maximum seen in experiments is 119.5pm, which agrees well with the simulated value of 117pm. To compare mechanical response, the wavelength λ in the lateral direction is studied. Simulations show a 3.2um and 7.9um wavelength at resonance. Experimentally, a 4um and an 8um wavelength appear. The multiple wavelengths at resonance are the result of a mismatch in acoustic velocity between AlN and Al and their existence in the simulation serves as further validation. Simplified five-finger device simulations show good fit with experimental admittance (Fig. 4). Full 33-finger device simulations, currently in progress, will improve this fit.

The experimental data gives further insight into the operation of the devices and is essential to the verification the 3D FEA models. With confirmed accuracy, these models can be used for predictive modeling of GHz-range CMRs. This allows optimization of geometric parameters such as electrode spacing and anchor performance.