Self-Aligned Single-Electrode Actuation of Tangential and Wineglass Modes using PMN-PT

Transducing wine-glass and tangential modes using piezoelectric film made possible with unique a property of lead magnesium niobate-lead titanate (PMN-PT) film.
Self-Aligned Single-Electrode Actuation of Tangential and Wineglass Modes using PMN-PT
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Piezoelectric MEMS devices are ubiquitous in a broad application space ranging from biological sensing to RF filters used in our cellphones. Utilizing resonant behavior of acoustic waves induced by piezoelectricity enables these applications, especially in sensing domain. Bulk acoustic wave (BAW) and surface acoustic wave (SAW) resonators with various geometries have proven to be useful with robust operation and simple microfabrication techniques.

Within the family of BAW resonators, contour modes are especially attractive for applications where multiple modes or frequencies are required on the same die since resonant frequency of devices are defined by lateral geometry of the resonators. Disk resonators yield interesting mode shapes that are useful in RF filtering, navigation, and bio-sensing applications in particular. Tangential mode resonance, for instance, is an isochoric mode: meaning the total volume of the resonant body does not change during resonance. This purely shear rotation-like mode shape is used in bio-sensing since it produces displacement that is entirely parallel to the fluid flow. This enables high quality factor (Q) resonant modes while immersed in liquid1.  Nonetheless, it has been reported in literature that using piezoelectric transduction to achieve tangential mode was not possible 2–4.

Another mode shape, known as wine-glass mode, is used in rotation sensing (gyroscope)5,6 and RF filtering7,8 applications. Wine-glass resonance mode gets its name from actual wineglass referring to its audible tone when it is struck. 2D projection of the same mode in disk geometry is achieved either via electrostatic7 or piezoelectric actuation8. Piezoelectric actuation results in better performance with more robust microfabrication steps since it does not require small gaps for capacitive coupling. Since the capacitive gaps are not required, the resonant body can operate without vacuum making the operation condition much more relaxed.

Transducing complex mode shapes on disk plates requires electrode shaping due to piezoelectric materials having in-plane coupling coefficients that are isotropic or having the same sign. For instance, inducing the wine glass mode requires split electrodes such that displacement is toward the center on one axis while the displacement on the orthogonal axis is away from the center simultaneously during resonance. Therefore, electrodes are driven with electrical signals with opposite sign (out of phase) to achieve the opposite displacement in the disk plane. One can intuitively think that achieving the same modal shape would be impossible with a single electrode that covers the entire disk surface since all the displacement would be pointing the same way upon electrical drive.

Figure 1: (a) Schematic drawing of a conventional piezoelectric disk with split electrodes that can induce wine-glass mode shape. (b) exaggerated deformation depiction of wine-glass mode shape with displacement quiver plot overlaid. Note that the displacement is away from the center as shown with arrows on one axis while the displacement is toward the center on the other axis.

Figure 1: (a) Schematic drawing of a conventional piezoelectric disk with split electrodes that can induce wine-glass mode shape. (b) exaggerated deformation depiction of wine-glass mode shape with displacement quiver plot overlaid. Note that the displacement is away from the center as shown with arrows on one axis while the displacement is toward the center on the other axis.

In this paper, authors introduce the use of a novel material that exhibits a unique property in this context. A certain crystal orientation of lead magnesium niobate-lead titanate (PMN-PT) has piezoelectric coupling coefficients with opposite signs. This means that the transversely applied electric field causes one axis to move away from the center while the other axis moves toward the center. This property naturally induces the wine-glass mode shape without the need for patterned electrodes. Therefore, a single electrode on PMN-PT can efficiently transduce this mode shape while the electrode acts like a self-aligned mask material that results in no possibility of misalignment.

Figure 2: (a) Schematic drawing of a PMN-PT disk with single gold electrode. (b) Tangential mode shape with displacement vectors quiver plot overlaid. Note that the volume of the disk does not change since all displacement is tangential, not radial. (c) exaggerated deformation depiction of wine-glass mode shape with displacement quiver plot overlaid using PMN-PT and single electrode

Moreover, due to this unique material property, tangential shear forces are generated with a single electrode. Thus, tangential mode resonance is achieved without out-of-plane motion that can enable biological analysis in miniaturized form.

In addition, if the wine-glass mode is used as a rotation sensor (gyroscope), the tangential mode resonance can act like a calibration stage since the rotation rate can be engineered with different input voltage amplitudes to the disk.

In order to verify the mode shapes, authors utilized a commercially available laser Doppler vibrometer (LDV) developed by Polytec to “see” the mode shape for independent verification. In-plane displacement of electrically excited disk resonators is measured using the Doppler shifted scattered light reflected from the disk surface. In order to induce diffused scattering from a smooth gold coated disk surface, pyramid-like photoresist patterns are developed at micron scale.  A grid of scan points is measured and compiled to form animations of the mode shape (operation deflection shapes) using the Polytec scanning vibrometer (PSV) software.

This exciting possibility paves the way for numerous applications in miniaturized sensors and actuators while utilizing robust and simple microfabrication techniques to achieve efficient transduction of tangential and wine-glass mode resonances. 

References

  1. Iqbal, A. et al. Real-time bio-sensing using micro-channel encapsulated thermal-piezoresistive rotational mode disk resonators. in 2012 IEEE Sensors 1–4 (IEEE, 2012). doi:10.1109/ICSENS.2012.6411385
  2. Onoe, M. Contour vibrations of isotropic circular plates. J. Acoust. Soc. Am. (1956). doi:10.1121/1.1908579
  3. Sakr, M. M., El-Shafie, M. K. & Ragai, H. F. Analysis and Modeling of RF-MEMS Disk Resonator. in 2006 International Conference on MEMS, NANO, and Smart Systems 19–22 (IEEE, 2006). doi:10.1109/ICMENS.2006.348208
  4. Pulskamp, J. et al. Electrode-shaping for the excitation and detection of permitted arbitrary modes in arbitrary geometries in piezoelectric resonators. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 1043–1060 (2012).
  5. Cheng, Y., Zhang, W., Tang, J., Sun, D. & Chen, W. A MEMS piezoelectric solid disk gyroscope with improved sensitivity. Microsyst. Technol. 21, 1371–1377 (2015).
  6. Parajuli, M., Sobreviela, G., Pandit, M., Zhang, H. & Seshia, A. A. Sub-Deg-per-Hour Edge-Anchored Bulk Acoustic Wave Micromachined Disk Gyroscope. J. Microelectromechanical Syst. 30, 836–842 (2021).
  7. Abdelmoneum, M., Demirci, M. U. & Nguyen, C. T. C. Stemless wine-glass-mode disk micromechanical resonators. Proc. IEEE Micro Electro Mech. Syst. 698–701 (2003). doi:10.1109/memsys.2003.1189845
  8. Elsayed, M. Y., Cicek, P.-V., Nabki, F. & El-Gamal, M. N. Bulk Mode Disk Resonator With Transverse Piezoelectric Actuation and Electrostatic Tuning. J. Microelectromechanical Syst. 25, 252–261 (2016).

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